Training machine learning models for digital oral care applications using flow matching

Abstract

A system and method are disclosed for training generative models to predict transformations between initial and final configurations of 3D oral care representations. The system comprises one or more processors and non-transitory computer-readable storage containing instructions that, when executed, cause the processors to receive a first distribution of data samples representing initial 3D oral care configurations and corresponding ground truth samples in final configurations. A second distribution is generated from the ground truth samples. Using flow matching, the system iteratively trains one or more generative models to learn mappings between the initial and final distributions. For each sample, an estimated vector field is generated to define transformations that iteratively convert the initial configuration into the final configuration. These vector fields are aggregated into a representation used to define and output trained generative models capable of predicting such transformations.

Description

TRAINING MACHINE LEARNING MODELS FOR DIGITAL ORAL CARE APPLICATIONS USING FLOW MATCHINGRelated Documents

[0001] The entire disclosure of PCT Application No. PCT / IB2022 / 057373 is incorporated herein by reference. The entire disclosures of each of PCT Applications with Publication Nos. WO2022123402A1, WO2021245480A1, W02020026117A1, WO2023 / 242757, WO2023 / 242765, WO2023 / 242776, W02023 / 100078, WO2024 / 127302, WO2023 / 242767, WO2023 / 242771, WO2023 / 242774, WO2023 / 242763, WO2023 / 242768, WO2023 / 242761, and WO2024 / 127302 are incorporated herein by reference. The entire disclosure of each of the following Provisional U.S. Patent Applications is incorporated herein by reference: 63 / 609581; 63 / 588028; and 63 / 609938.Technical Field

[0002] This disclosure relates to configmations and training of machine learning models based on neural networks (e.g., flow-based models) to improve the accuracy and data precision of 2D or 3D representations of 3D oral care representations.Summary

[0003] This disclosure is directed to systems and / or methods for generating and / or modifying 3D oral care representations. The system includes one or more computer processors and non-transitory computer-readable storage communicatively coupled with the processors. The storage has instructions stored thereon that, when executed by the processors, cause the processors to perform several functions.

[0004] The present disclosure includes techniques for training and using one or more flow-based machine learning models for the generation of 3D oral care representations (as described herein). The flow-based models (e.g., continuous normalizing flows, denoising diffusion probabilistic models, or the like) may be trained using flow matching. The flow-based models may be trained to generate and / or optimize 3D oral care representations (e.g., 3D printing supports, oral care appliances which customize the force applied to teeth, treatment plans, etc.). In some instances, the flow-based models may be trained to perform style transfer between 3D oral care representations.

[0005] Firstly, the system can receive a first distribution of data samples defining one or more 3D oral care representations in initial configmations and one or more corresponding ground truth 3D oral care representations in respective final configurations. The system can generate a second distribution which can include samples from the ground truth 3D oral care representations. Using flow matching, the system can iteratively train one or more first generative models to predict mappings between the first distribution and the second distribution. This training may involve generating an estimated vectorfield for each data sample in the first distribution, which defines transformations that, when iteratively applied, transform the data sample from the first distribution into a respective final configuration. The estimated vector fields can be combined into an aggregate representation, which is used to define and output the trained first generative models.

[0006] In some embodiments, the system generates the estimated vector field by providing representations of the patient’s dentition to one or more trained second neural networks, which generate the estimated vector fields. These second neural networks may include an encoder-decoder structure. Alternatively, the system may use ordinary differential equation solvers to generate the vector fields based on representations of the patient’s dentition.

[0007] The trained first generative models can be configured to generate various outputs, including tooth restoration designs, layered tooth restoration designs, transforms for orthodontic setups, fixture model components, appliance components, and transforms describing local coordinate systems for the patient's teeth. The patient's dentition includes 3D representations, and the trained first generative models can generate mesh element labels for the mesh elements of the patient's 3D dentition. These labels can be used to segment and perform cleanup operations on the 3D representations of the patient's dentition.

[0008] The first generative models may include normalizing flow-based models, denoising diffusion-based models, and cascade-based machine learning models. The system can also receive oral care arguments, which influence the output of partially trained generative models during iterative training. These oral care arguments specify customizations, and the trained generative models use them to generate output customized for the patient’s dentition.

[0009] Further aspects of the present disclosure relate to systems or methods for generating oral care appliances that incorporate interproximal reduction (IPR) as part of an orthodontic treatment plan. The disclosed method leverages digital modeling and automated processes to enhance the precision and efficiency of orthodontic appliance design. In one embodiment, the method includes receiving one or more three-dimensional (3D) representations of a patient’s dentition, which comprises a plurality of teeth. Based on this digital input, a first orthodontic setup is automatically generated. The method further includes generating one or more arch lengths and determining one or more oral care metrics, such as the Bolton index or arch length discrepancy. These metrics are used to calculate a total amount of IPR to be applied to the dentition. The method may also incorporate oral care arguments, including procedure parameters and constraints, to refine the orthodontic setup. Tooth packing may be performed prior to arch length generation to optimize spatial alignment. In some embodiments, machine learning modules are employed to generate transforms that reposition teeth into clinically desirable poses. The method may further include applying IPR to specific teeth, modifying their shapes accordingly, and outputting updated 3D representations. Subsequent orthodontic setups may be automatically generated in iterative stages — second and third setups — based on prior configurations and modified dentition. These setups may include additional transformsand undergo further tooth packing to ensure treatment readiness. Finally, the method culminates in the fabrication of the orthodontic appliance, which may be produced using 3D printing technology. This end-to-end digital workflow enables a streamlined and customizable approach to orthodontic treatment planning and appliance manufacturing.

[0010] Still further aspects of the present disclosure relate to systems or methods for generating a three-dimensional (3D) design of an oral care appliance that includes one or more pontic secmement apparatuses. The method comprises receiving a 3D representation of an oral care appliance and generating, via one or more machine learning modules, pontic securement apparatuses that are integrated into the appliance design. These apparatuses are positioned relative to the appliance using generated transforms, and the resulting design may be modified through operations such as Boolean functions to incorporate the apparatuses effectively. The system may also receive 3D representations of a patient’s dentition, which inform the generation of the oral care appliance. In some embodiments, the 3D representation of the appliance is itself generated by the system. The output may include a modified 3D model that integrates the pontic securement apparatuses, which can be fabricated using 3D printing technologies. Additional steps may include the application and curing of a flowable curable material or the attachment of physical apparatuses from a predefined library. Additionally, the system may generate and incorporate tooth shapes from a library of digital tooth representations to complete the appliance design.Brief Description of Drawings

[0011] FIG. 1 shows a method of training a cascade of machine learning (ML) models.

[0012] FIG. 2 shows a method of training one or more ML models to generate 3D printing supports.

[0013] FIG. 3 shows a method of using a fully trained ML model to generate 3D printing supports.

[0014] FIG. 4 shows a method of using a fully trained denoising diffusion ML model to generate (or modify) 3D oral care representations.

[0015] FIG. 5 shows a method of training a denoising diffusion ML model to generate 3D oral care representations.

[0016] FIG. 6 shows a method of using a fully trained denoising diffusion ML model to generate 3D oral care representations.

[0017] FIG. 7 shows the forward and / or reverse passes of a denoising diffusion ML model for generating 3D oral care representations.

[0018] FIG. 8 shows a method of training a continuous normalizing flow-based ML model to generate (or modify) 3D oral care representations.

[0019] FIG. 9 shows a method of using a fully trained continuous normalizing flow-based ML model to generate (or modify) 3D oral care representations.

[0020] FIG. 10 shows a method of using a fully trained transformer-based ML model to generate (or modify) 3D oral care representations.

[0021] FIG. 11 shows a method of using a fully trained autoencoder-based ML model to generate (or modify) 3D oral care representations.

[0022] FIG. 12 shows a method of generating an FEA map based on two or more examples of ground truth data (or based on generated data).

[0023] FIG. 13 shows a method of generating an FEA map based on ground truth data (or based on generated data).

[0024] FIG. 14 shows an example method of computing loss between 3D representations of oral care data.

[0025] FIG. 15 shows an example method of computing loss which is enhanced through the use of finite element analysis (FEA).

[0026] FIG. 16 shows a computing system that can be used to train ML models.

[0027] FIG. 17A shows an example of an aligner tray that includes pontic secmement apparatuses.

[0028] FIG. 17B shows an example of an aligner tray that includes pontic secmement apparatuses.

[0029] FIG. 18A shows an example of an aligner tray that includes pontic secmement apparatuses.

[0030] FIG. 18B shows a digital fixture model includes pontic securement apparatuses.

[0031] FIG. 19 shows a method of generating orthodontic setups which include interproximal reduction (IPR).Detailed Description

[0032] The techniques of this disclosure may train deep learning methods for the generation or optimization of 3D data structures which pertain to digital oral care (e.g., 3D oral care representations, as described herein). The techniques may generate 3D representations of oral care data, or other 3D oral care representations, which are optimized to withstand or to apply one or more forces (e.g., the force of gravity acting on a physical workpiece during 3D printing, or the force applied by an appliance on the patient’s dentition, etc.). The techniques can generate 3D oral care representations which are suitable for clinical treatment of the patient and / or which are configured (or optimized) for fabrication (e.g., fabrication using a 3D printer).

[0033] In some implementations, a force applied by a first 3D representation of oral care data (e.g., an oral care appliance or appliance component) may be estimated by computing an overlap between the first representation and a second 3D representation of oral care data (e.g., the patient’s dentition, hardware, or an appliance, etc.). For example, when estimating the force applied by an oral care appliance on the patient’s dentition, the oral care appliance may first be registered with the dentition (e.g., using a transform to place the appliance into a pose that the appliance would assume during treatment, or an approximation of that pose, etc.). Computing an overlap of two or more 3Drepresentations of oral care data may include computing the volume of overlapping 3D representations of oral care data, a cross-sectional area of overlapping 3D representations of oral care data, a penetration depth of overlapping 3D representations of oral care data, and / or a penetration vector between two or more 3D representations of oral care data. For example, a relatively large overlap volume, or a large penetration depth may be associated with a relatively large force magnitude. Conversely, a relatively small overlap volume, or a relatively small overlap volume may be associated with a relatively small force magnitude. The X, Y, or Z coordinates of the overlap may be used to estimate the location of the application of a force. In some implementations, the direction of a force may be computed, at least in part, using one or more normal vectors. For example, a first normal vector may be computed as the average normal vector of the portion of the surface of a first 3D representation of oral care data (e.g., oral care appliance, etc.) that intersects a second 3D representation of oral care data. A second normal vector may be computed as the average normal vector of the portion of the surface of the second 3D representation of oral care data (e.g., the patient’s dentition, etc.) that intersects the first 3D representation of oral care data. In some implementations, an average vector may be computed between the first and second normal vectors. The direction of the force may be estimated by be parallel to the average vector, and pointing from the first 3D representation of oral care data to the second representation of oral care data. Other methods of computing the direction of a force are also possible (e.g., computing the vector associated with a lengthwise axis of an overlapping or intersecting volume, etc.).

[0034] The one or more estimated forces may be provided to a finite element analysis (FEA) module 208, which may compute one or more physical conditions experienced by the second 3D representation of oral care data as a result of interactions with the first 3D representation of oral care data. Physical conditions may include stresses (e.g., internal force per unit area or force per unit volume, etc.), strains (e.g., deformation or change in structure or shape of the object as a result of the stress, etc.), tensions, displacements (e.g., displacements of portions of a 3D representation, etc.), electrical potentials, temperature distributions (e.g., thermal analysis), pressure distributions (e.g., fluid mechanics analysis), or other interactions which are experienced by the second 3D representation of oral care data (e.g., the patient’s dentition, a digital workpiece, etc.). Reconstruction autoencoders may be used to generate latent representations of FEA maps. The latent representations of FEA maps may be used in loss calculation, and the resulting loss(es) may be used to train the generative ML models described herein. The latent representations of FEA maps may be provided as inputs to the generative ML models, to instruct the models regarding the initial state or configuration of the patient’s dentition and / or to instruct the ML models regarding interactions between an appliance and the dentition (e.g., force applied by appliance on dentition, or force appliance by a first appliance component on a second appliance component, etc.).

[0035] In order to reduce the data footprint, conventional techniques in this area have relied upon certain types of dimensionality reduction (e.g., principle component analysis (PCA), or independentcomponent analysis (ICA), etc.). These approaches prevent reconstruction of the original input data after the dimensionality reduction has been performed. This can create a number a different issue which may ultimately undermine the accuracy of the systems that implement conventional techniques. For example, conventional techniques lack a means of validating the correctness of the reduced dimensionality form of the input data. The conventional techniques do not provide opportunities to improve the accuracy of the underlying system. For example, the results of the dimensional reduction using conventional techniques cannot be used to train accurate downstream generative ML models, because the data which are used to train those models cannot be known to be correct.

[0036] Techniques of this disclosure may reconstruct latent representations of FEA maps (e.g. using decoder 1116, or other decoders described herein) into reconstructed FEA maps. Reconstruction error may be computed to measure how closely the reconstructed FEA maps match the original input FEA maps. When the reconstruction error is measured to be small, then the latent representation of the FEA map is shown to be an information-rich and / or reduced dimensionality representation. Such representations are especially suited to be provided to the generative ML models described herein, because the ML models can more easily encode the distribution of smaller-footprint data than larger- footprint data. Furthermore, the ML models can make more accurate inferences and / or can generate output which is more accurate when the input data are more easily encoded by the generative ML models described herein.

[0037] An encoder 210 (or other encoders described herein) may impart a consistent structure to one or more generated FEA map latent representations. This consistent structure lends itself to encoding by downstream generative ML models, promoting downstream generative ML models to generate more accurate results. Stated another way, the consistent structure can promote the generative ML models to more accurately encode the distribution of the input data during model training, more-accurate inferences to be generated. In some implementations, before 3D representations of oral care data are provided to encoder 210 (or other encoders described herein), the 3D representations of oral care data may first be reorganized so that the 3D representations of oral care data have known, standardized or reference connectivity. Stated another way, a new 3D representation may be generated which has the same shape of the original 3D representation, however, the structure of mesh elements is modified to be consistent with the structure of one or more reference 3D representations of oral care data (e.g., a 3D mesh of a reference tooth, one or more teeth of a reference arch, a reference appliance, a reference fixture model, a 3D trimline, etc.). The structure of a 3D mesh can include the count of mesh elements, the set of mesh elements, and / or the relationships between mesh elements. In some examples a first 3D mesh of a molar (or another tooth, or a fixture model, etc.) may include anatomical features, such as fossae, cusp tips, facial surface, groves, lingual surface, mesial surface, distal surface, roots, or the like. A corresponding reference 3D mesh may contain largely those same anatomical features. The first 3D mesh may be remeshed to have largely the same vertices as the reference 3D mesh within corresponding anatomical features of the two meshes. The edges in the remeshed first 3D mesh may largely mirrorthe structure of edges in corresponding portions of the reference 3D mesh (e.g., in terms of edge alignment, and / or in terms of which vertex is connected with vertex). The faces present within given portions of the first 3D mesh may be rearranged to largely mirror the sizes, shapes, and / or orientations of the faces in corresponding portions of the reference 3D mesh. Modifying the structure of a 3D representation of oral care data to have a structure that is consistent with the structure of a corresponding reference will improve the consistency of downstream processing. Downstream modules (e.g., generative modules, or FEA modules, etc.) will generate outputs which have a consistent structure when the inputs have a consistent structure. This consistent structure in generated outputs lends itself to encoding into latent form by encoders. Stated another way, an encoder can be more accurately trained to encode input data into latent representations, when those samples of input data have a consistent structure. When the samples of input data contain a consistent structure, the signal contained those data samples is stronger and / or is more easily encoded by an encoder during model training.

[0038] In some implementations, the 3D representations with known connectivity may be provided to an FEA module, which may generate one or more FEA maps which, in turn, have improved structural consistency as a result of the known connectivity. This improved structural consistency lends itself to a more-accurate encoding of an FEA map into a latent representation. In some examples, an FEA map may be integrated with a 3D representation (e.g., voxels, a 3D mesh, a 3D point cloud, etc.) of oral care data. Stress or strain values (or other measurements) may be included within the 3D representation (e.g., stress or strain values may be included with the mesh element feature vectors which are associated with the mesh elements). This FEA-enhanced 3D representation may be provided to an encoder, which may generate one or more latent representations of the FEA-enhanced 3D representation. The latent representations may be provided to downstream generative models for further refinement and / or improvement of the 3D representation.

[0039] The example method 100 may train an ML model to generate one or more 3D oral care representations using a cascade of generative modules, wherein the output of a first generative module may be provided to the input of one or more of the subsequent generative modules (e.g., a count of modules which is designated by n). Each module in the cascade may generate one or more 3D oral care representations (e.g., designated by integers 1, 2, 3, ... n). According to various examples, a generative module may be trained to generate one or more 3D representations of oral care data (e.g., digital fixture models, oral care appliances, tooth restoration designs, or 3D trimlines, etc.), to perform orthodontic setups prediction, to predict coordinate systems, to predict mesh element labels (e.g., for segmentation or mesh cleanup), or to generate other 3D oral care representations described herein. The generative modules may generate output which is optimized to fulfill one or more treatment needs of the patient. Digital representations for 3D representations of oral care data may be provided to a 3D printer, and / or rendered into physical form.

[0040] According to particular implementations, FEA may be performed on the inputs or outputs associated with the generative modules. For example, a generated 3D representation of an oral careappliance (e.g., an aligner tray) can be combined with a 3D representation of the patient’s dentition to determine the forces that the appliance applies to the dentition. The one or more estimated forces may be provided to an FEA module, which may generate one or more FEA maps that describe the strain or stress (among other measurements) that the dentition experiences as a result of interaction with the aligner tray. In other examples, FEA may generate FEA maps that describe the strain or stress (among other measurements) that a 3D printed part is expected to experience during the 3D printing process. Such FEA maps may estimate the ability of 3D printing support structures to support a physical workpiece during 3D printing. FEA maps may be encoded into latent representations by encoder neural networks, and / or the latent representations of the FEA maps may be provided as inputs to downstream generative modules. The latent representations of FEA maps may provide those downstream generative modules with information about the initial state of a 3D representation of oral care data (e.g., a 3D representation of an oral care appliance, or of a digital fixture model, etc.) to a generative module which is trained to improve or modify those input data. For example, when regions of high stress or high strain (among other measurements) are detected within a digital representation of an oral care appliance (e.g., among other 3D representations of oral care data), a downstream generative ML module may respond by modifying the shape and / or structure of that appliance to reduce stress or strain (among other measurements) on the appliance. Alternatively, the downstream generative modules may design the appliance to increase the stress or strain on certain portions of the appliance, for the purpose of doing work on the patient’s dentition. An FEA map may evaluate whether a network of 3D printing support structures is sufficient to withstand one or more applied forces (e.g., gravity, or forces applied by the 3D printing resin, etc.). A network of 3D printing support structures can include one or more columns, one or more branches, or one or more contact points, among other structural elements. FEA maps may include information pertaining to one or more aspects of stress within an object, aspects of strain within an object, aspects of one or more forces applied to an object, or aspects of one or more moments applied to an object, among other measurements.

[0041] Method 100 may compute losses after execution of one or more modules in the cascade of generative modules. For example, after the execution of the 1thgenerative module, a 1thgenerated 3D oral care representation may be provided to a loss calculation module. A corresponding 1thground truth 3D oral care representation may also be provided to the loss calculation module. The resulting loss may be used to train, at least in part, the 1thgenerative module. In this manner, the output of a generative module may be compared to the corresponding ground truth data, and the computed loss may be used to train, at least in part, the generative module. One or more of the generated 3D oral care representations may be used in various oral care applications (e.g., restoration design generation, oral care appliance generation, etc.). According to various implementations of this disclosure, the loss may compare the shapes and / or structures of generated data structures with corresponding ground truth data structures. In some implementations, the loss may compare one or more predicted labels to one or morecorresponding ground truth labels. Ground truth labels, or other ground truth data may include accurate, verified data used to train and evaluate an ML model.

[0042] Method 100 may use interconnected generative modules 118a-118n to generate 3D oral care representations, based at least in part on inputs such as 3D oral care representations 102 (e.g., patient’s 3D dentition). The cascaded ML model described in example method 100 may be particularly well-suited when a stage n of generative processing depends on one or more inputs from prior processing modules (e.g., stage “n-1”). Stated another way, a first generated output may influence a second generated output, which may then influence a third generated output, and so on, until a (n-2)thgenerated output influences a terminal (n-l)thgenerated output.

[0043] For example, generative module 118a may generate interproximal webbing (or another fixture model component) to an initial fixture model (e.g., which includes 3D meshes of the patient’s teeth, gums and / or a base), which may then be provided to generative module 118b. Generative module 118b may apply interproximal webbing to the interproximal spaces between two or more pairs of teeth. There may be one or more subsequent generative modules which further improve the fixture model that was generated (or modified) by prior stages of the cascade. The cascade of generative modules may culminate in generative module 118n, which may generate a 3D trimline which is customized for use with the fixture model that was generated by the prior generative modules in the cascade.

[0044] Generative modules 118a-118n (or other intervening generative modules) may contain any number of ML models, including diffusion models (e.g., as shown in method 600, etc.), transformerbased models (e.g., as shown in method 1000), multi-layer perceptron (MLP)-based models, or autoencoder-based models, among others. Generative modules 118a- 118n can be configured to contain different combinations of ML models, or generative modules 118a-118n can alternatively contain substantially similar collections of ML models. In some implementations, generative modules 118a- 118n may contain ML classifiers, such as support vector machines (SVM), Gaussian process models, or Logistic regression models, which may output classifications of their respective inputs. In some implementations, generative modules 118a-118n may make targeted recommendations for treatment based upon analysis of the one or more 3D oral care representations 102. For example, the recommendations for patient treatment may be influenced by pre-treatment 3D meshes or 2D images (or other representations) of the patient’s dentition which are included in one or more 3D oral care representations 102. For example, when a chipped tooth or a malformed tooth is detected by a generative module 118a-118n, the techniques of this disclosure may determine that a dental restoration appliance (e.g., the FILTEK Matrix, etc.) is indicated for use. In a further example, when a fixture model is provided to a generative module in the cascade (e.g., any of modules 118a-118n), that generative module may determine that the fixture model warrants modification by the generation of one or more fixture model components (e.g., the generation of blockout on one or more portions of the fixture model, to resolve undercuts).

[0045] Techniques of this disclose (e.g., implementations using diffusion models) more accurately generate predicted smiles over existing techniques. For instance, experiments using conventional techniques resulted in a loss value (which indicates an error rate between predicted outcomes and ground truth data) of 0.009. Implementations of the present disclosure were trained on substantially similar data, and resulted in a loss value of 0.002, which is a 450% improvement in accuracy over conventional techniques.

[0046] Referring again to FIG. 1, oral care arguments 136, and / or 3D oral care representations 102 may be provided to generative module 118a. Oral care arguments 136 may enable generative models of this disclosure to generate output which is customized for the patient’s dentition, or which is customized to the treatment instructions (or prescription) provided by clinicians. Stated another way, oral care arguments 136 may describe one or more treatment needs of the patient (e.g., the desire to correct malocclusions, the desire to have a more aesthetic dentition, etc.). 3D oral care representations 102 may include pre-modification (or initial) data which are to be modified. 3D oral care representations 102 may include 2D or 3D representations of the patient's dentition. Generative module 118a may output generated output “1” (or output from the first model in the arrangement), which may be provided to one or more of the subsequent generative modules, for example, generative module 118b. Generative module 118b may output generated data 120b, which may be provided to the next generative module in the cascade, and so on. The outputs may be passed from generative module to generative module, up to the last generative module, here represented by example generative module 118n. Generative module 118n may output generated data 120n. Generative module 118a may be trained, at least in part, through the calculation (112a) of one or more loss values. The loss calculation may compare data 120a to the corresponding ground truth data 106a. Generative module 118b may be trained, at least in part, through the calculation (112b) of one or more loss values. The loss calculation may compare data 120b to the corresponding ground truth data 106b. Loss calculation may proceed for further modules, by comparing predicted outputs to the corresponding ground truth data 104. The final generative module in a particular arrangement, such as the example generative module 118n depicted in FIG. 1, may be trained, at least in part, through the calculation (112n) of one or more loss values. The loss calculation may compare generated data 120n to the corresponding ground truth data 106n. Shapes, structures, labels (e.g., determinations that treatment is warranted for the patient, mesh element labels, etc.), or other aspects of predictions may be compared to their corresponding ground truth data as a part of a loss calculation. Generative module 118a may output one or more generated 3D oral care representations 130a (e.g., a 3D mesh describing the outer surface of a generated tooth restoration design, etc.). Generative module 118b may output one or more generated 3D oral care representations 130b (e.g., a 3D mesh describing the boundary between enamel and dentin for a generated tooth restoration design, etc.). Generative module 118n may output one or more generated 3D oral care representations 130n (e.g., the inner-most shell of a generated tooth restoration design, etc.). In some implementations, generated data 120a, 120b, or 120n can include one or more generated (or modified)3D oral care representations. In some implementations, the generated outputs can undergo latent encoding (e.g., using encoders, etc.) before the generated outputs are provided to the next generative modules in the cascade. Oral care arguments 136 may include data that describes patient treatment goals (e.g., including numerical thresholds for one or more oral care metrics, discrete values, or freeform text), or other examples described herein. Generated data 120a, 120b, or 120n may correspond to generated 3D oral care representations 130a, 130b, or 130n, respectively.

[0047] Oral care arguments may include oral care parameters, preferences, oral care metrics, and other values (e.g., real values, natural language text, enumerations, vectors, images, 3D representations, etc.) which are intended to influence the output of the generative techniques of this disclosure.

[0048] Oral care parameters are intended as instructions and / or specifications which describe the shape, structure, or other intended aspects of a 3D oral care representation which is to be generated using techniques of this disclosure. Oral care parameters may include orthodontic procedure parameters (OPP), restoration design parameters (RDP), to name a few examples. Oral care parameters may define one or more intended aspects of a 3D oral care representation which is to be generated using techniques of this disclosure, and may be provided to an ML model to promote that ML model to generate output which may be used in the generation of oral care appliances that are suitable for the treatment of a patient. Non-limiting examples of orthodontic procedure parameters include: Teeth To Move: {AnteriorsOnly, AnteriorsAndBicuspids, FullArch}, Spacing: {CloseAllSpaces,LeaveSpecificSpaces}, Resolve Lower Crowding by IPR - Posterior Right: {Primarily, AsNeeded, None}, or Resolve Lower Crowding by IPR - Posterior Left: {Primarily, AsNeeded, None}, among others. Doctor preferences may pertain to a clinician’s past treatment practices, whereas oral care parameters may pertain to the treatment of a particular patient.

[0049] Restoration Design Parameters (RDP) may, in some implementations, specify at least one value which defines at least one aspect of planned dental restoration treatment for the patient (e.g., specifying desired target attributes of a tooth which is to undergo treatment with a dental restoration appliance). Doctor Restoration Design Preferences (DRDP) may, in some implementations, specify at least one typical value for an RDP, which may, in some instances, be derived from past cases which have been treated by one or more oral care practitioners.

[0050] Restoration design parameters (RDP) may be used to encode aspects of smile design guidelines, such as parameters which pertain to the intended dimensions of a restored tooth. Nonlimiting examples of restoration design parameters include Tooth width at base (mesial to distal distance) in millimeters (or other clinically appropriate measurements), Overall tooth shape {rectangular or ovoid, squared edges or rounded edges, etc. }, Amount of tooth display when the lips are at rest in millimeters (or other clinically appropriate measurements), Tooth morphology - shape style guide {triangular, oval and rectangular, etc.}, Tooth morphology - Mamelon grooves {mamelon styleOl, mamelon_style02, mamelon_style03, etc.}, Tooth morphology - perikymata [perikymata styleOl, periky mata_style02, perikymata_style03, etc.], among others.

[0051] Other types of oral care arguments include doctor preferences (DP), restoration design preferences (RDP), or other types of preferences (e.g., preferences which pertain to the designs or specifications of fixture models or oral care appliances). Doctor preferences, restoration design preferences, or other types of preferences may define the typical treatment choices or practices of a particular service provider, whether it be specific to a hospital, clinic or other dental institutions / locations, the institution’s dental care providers (e.g., clinicians, dentists, dental assistants, and the like), and combinations thereof. Restoration design preferences are subjective to a particular clinician, and so differ from restoration design parameters. In some implementations, DP, RDP, or other preferences may be computed by unsupervised means, such as clustering, which may determine the typical values that a clinician uses in patient treatment.

[0052] Oral care arguments may include oral care metrics. Oral care metrics may include orthodontic metrics (which may measure physical relationships between two or more teeth), restoration design metrics (which may measure physical relationships between two or more teeth, or may quantify physical aspects of particular tooth), or other types of metrics (which may measure aspects of an existing or generated 3D representation of oral care data).

[0053] Orthodontic metrics may be used to quantify the physical arrangement of an arch of teeth for the purpose of orthodontic treatment or for other oral care treatments (e.g., fixture model generation or appliance component generation). These orthodontic metrics can measure how badly maloccluded the arch is, or conversely the metrics can measure how correctly arranged the teeth are. In some implementations, one or more orthodontic metrics may be taken from this section and incorporated into a loss computation, to quantify patterns of errors or deficiencies which may appear in predicted outputs. Within-arch orthodontic metrics include:Alignment - A 3D tooth orientation vector may be calculated using the tooth's mesial-distal axis.Canine Overbite - A distance may be computed between the upper canine and the lower canine on a given side, and / or between the upper pre-molar and the corresponding lower pre-molar.Leveling - The difference in height between two or more neighboring teeth.Midline - May compute the position of the midline for the upper incisors and / or the lower incisors, and then may compute the distance between them.Oveijet - The upper and lower central incisors may be compared along the y-axis. The difference along the y-axis may be used as the oveijet score.Many other orthodontic metrics are also possible.

[0054] The following restoration design metrics (RDM) may be measured and used in the generation of crowns, dental restoration appliances, veneers (veneers are a type of dental restoration appliance), or the like, with the objective of making the resulting teeth natural looking. Symmetry is generally a preferred facet. Shade and translucency may pertain, in particular, to the generation of crowns, though some implementations of dental restoration appliances may also consider thisinformation (e.g., when a succession of dental restoration appliances is used to form nested veneers with at least one inner structure). Examples of inter-tooth RDM include:1) Bilateral Symmetry and / or Ratios: A measure of the symmetry between one or more teeth and one or more other teeth on opposite sides of the dental. For example, for a pair of corresponding teeth, a measure of the width of each tooth.2) Proportions of Adjacent Teeth: Measure the width proportions of adjacent teeth as measured as a projection along an arch onto a plane (e.g., a plane that is situated in front of the patient's face). The ideal proportions for use in the final restoration design can be, for example, the so-called golden proportions.3) Arch Discrepancies: A measure of any size discrepancies between the upper arch and lower arch, for example, pertaining to the widths of the teeth, for the purpose of dental restoration.4) Midline: A measure of the midline of the maxillary incisors, relative to the midline of the mandibular incisors. Techniques of this disclosure may measure the midline of the maxillary incisors, relative to the midline of the nose (if data about nose location is available).5) Proximal Contacts: A measure of the size (area, volume, circumference, etc.) of the proximal contact between adjacent teeth. In the ideal circumstance, the teeth touch along the mesial / distal surfaces and the gums fill in gingivally to where the teeth touch.6) Embrasure: In some implementations, techniques of this disclosure may measure the size (area, volume, circumference, etc.) of an embrasure, the gap between teeth at either of the gingival or incisal edge. Examples of Intra-tooth RDM are enumerated below, continuing with the numbering of other RDM listed above.7) Length and / or Width: A measure of the length of a tooth relative to the width of that tooth. This metric may reveal, for example, that a patient has long central incisors. Width and length are defined as: a) width - mesial to distal distance; b) length - gingival to incisal distance; c) other dimensions of tooth body - the portions of tooth between the gingival region and the incisal edge.8) Tooth Morphology: A measure of the primary anatomy of the tooth shape, such as line angles, buccal contours, and / or incisal angles and / or embrasures. The frequency and / or dimensions may be measured.9) Shade and / or Translucency: A measure of tooth shade and / or translucency. Tooth shade is often described by the VITA classical shade guide or VITA Toothguide 3D-MASTER. Tooth translucency is described by transmittance or a contrast ratio. Tooth shade and translucency may be evaluated (or measured) based on one or more of the following kinds of data pertaining to teeth: the incisal edge, incisal third, body and gingival third. The enamel layer translucency is general higher than the dentin or cementum layer. Shade and translucency may, in some implementations, be measured on a per-voxel(local) basis. Shade and translucency may, in some implementations, be measured on a per-area basis, such as an incisal area, tooth body area, etc . Tooth body may pertain to the portions of the tooth between the gingival region and the incisal edge.10) Height of Contour: A measure of the contour of a tooth. When viewed from the proximal view, all teeth have a specific contour or shape, moving from the gingival aspect to the incisal. This is referred to as the facial contour of the tooth.

[0055] 3D printers may benefit from having one or more paths between each pixel in a first layer and the build platform. Examples of such 3D printers include those based on Fused Deposition Modeling (FDM, or filament printing), Stereolithography (SLA, or vat polymerization), and / or Inverse Vat Polymerization (resin printing). These supports may be used to ensure the integrity of the printed workpiece (e.g., a physical workpiece based on the digital design of one or more 3D oral care representations). The term ’’digital workpiece” can describe a 3D representation of the part that is to be printed. The term “physical workpiece” describes the corresponding physical 3D part has been printed (or is being printed) by a 3D printer based on the digital 3D design. Every pixel (e.g., a 3D printing voxel) in any given layer should be connected either to a pixel in the same layer or in the previous layer (e.g., the layer that underlies the current layer, or the layer that was previously built-up by the 3D printer). Resin printing and / or filament printing may share some structural parameters in common, and may each have some structural parameters which are specialized to the respective 3D printing method. Stated another way, in some instances, there may be different structural parameters for resin printing than there are for filament printing. In general, FDM printing may rely on gravity to lay down a bead of filament or slurry on the physical workpiece, and the physical workpiece typically provides at least partial support to the new bead of filament (such that various rules apply). Otherwise, auxiliary supports may be needed. 3D printing supports may include trunks or columns (e.g., lengths of resin or filament material which are built-up by the printer), and / or branches (e.g., bifurcations of trunks), contact points (e.g., regions or cross-sectional areas where trunks meet, or where a trunk meets the physical workpiece). Trunks or columns may be hollow to optimize the weight of the 3D printed physical workpiece (e.g., part that is being 3D printed). The thickness of a trunk or column may be optimized to achieve a balance between strength, weight, and / or cost.

[0056] Resin printing is largely agnostic to the effects of gravity due to the liquid resin providing support through neutral buoyancy of the cured resin within the liquid resin. Therefore, new pixels in the incident layer may be supported by cured material in the previous layer. According to particular implementations, new pixels in the incident layer may be connected to other pixels in the incident layer which are supported either directly or indirectly by cured material that is connected to the build plate.

[0057] Techniques of this disclosure (e.g., diffusion-based or normalizing flow-based methods, etc.) may be trained to generate digital 3D designs for 3D printing support structures. In the context of 3D printing, adequate support can be defined in different ways. The path taken from any given pixel inthe incident layer to the build plate through cured material in the physical workpiece can be quite complicated. Furthermore, there are structural considerations for the extant physical workpiece, including auxiliary supports, at any given moment of the printing process. Inverse vat printers exert tension on the physical workpiece, between the build plate and the window at the bottom of the vat, as the physical workpiece is drawn away after each iteration of light exposure. Tensions may be exerted due to weak bonding of the incident layer to the window film. Tensions may also be exerted due to fluid dynamic drag of the viscous resin flowing into the gap after the weak bond is broken. Normal vat printers (e.g., stereolithography printers) may exert shear stress on the physical workpiece as the wiper blade sweeps across the top surface of the resin to level the resin surface. Shear forces occur due to the blade itself contacting the cured incident layer of the physical workpiece, as well as due to fluid dynamic drag as viscous resin is swept along the top surface of the resin in the vat. It should be appreciated by one of ordinary skill in that art that resin "piles up" ahead of the wiper, like a wave, causing shear forces within the resin near the surface as the excess is pushed along. This moving resin, in turn, exerts lateral forces on the top of the physical workpiece which may amount to slight shearing of the physical workpiece, since the coupling force is the lateral reaction force of the build plate in the opposite direction.

[0058] To solve the problems described above, flow-based ML models (e.g., a Diffusion Model, or a continuous normalized flow-based model) can be trained to automatically generate a minimal support structure which may prevent deformation of the 3D printed physical workpiece beyond a given threshold during the printing process. Such ML models may, in some implementations, optimize the 3D shape and / or structure of the 3D printed part. In some implementations, the ML models may optimize the topologies of 3D representations of oral care data. Topology refers to aspects of a 2D or 3D object which are invariant under continuous deformations. Under this definition, for example, a 3D representation of oral care data may initially have a first shape, and / or a first topology. Then, the 3D representation may undergo a continuous deformation, after the completion of which the 3D representation may have a second shape, by the same topology. Although the shape, size, or volume of the 3D representation may have changed, the topology (e.g., the structure, connectivity, or geodesic relationships between two or more portions of the 3D representation) is unchanged by the continuous deformation. Techniques of this disclosure may be used for topology optimization (TO), and / or for shape optimization (SO) of 3D representations of oral care data. Topology or Shape Optimization (TSO) is inclusive of either or both optimizations.

[0059] The example method 200 of FIG. 2 describes the training of one or more ML models for the generation of digital designs for one or more 3D printing digital workpieces and / or digital designs for one or more 3D printing support structures. The digital 3D printing support structures may be generated so that the physical 3D printing support structures which are printed by a 3D printer support the physical workpiece during the 3D printing process. The physical 3D printing supports may minimize deflection of the physical workpiece during printing. Input data 202 (e.g., 3D representationsof patient’s pre-treatment dentition, appliance components, fixture models, or other 3D oral care representations, etc.), and / or oral care arguments 136 may be provided as inputs to generative modules 218a-218n. In some implementations, oral care guide objects 308 may be provided as inputs to generative modules 218a-218n. In some implementations, generative modules 218a-218nmay generate respective 3D representations of oral care data 220a-220n. For example, generative module 218b may generate 3D representation of oral care data 220b, which may included in one or more 3D representations of oral care data 230b and processed as described elsewhere in this disclosure. 3D representations of oral care data may include 3D meshes, 3D point clouds, or voxelized representations of oral care data (e.g., 3D meshes describing fixture models, appliance components, tooth restoration designs, etc.). Generated representations 220a-220n may be compared to respective ground truth data 206a-206n as a part of calculating loss (212a-212n). For example, generated representation 220b may be compared to ground truth data 206b as a part of calculating loss (212b). The computed loss may be used to train, at least in part, generative modules 218a-218n. Ground truth data 204 may include ground truth representations of 3D printing supports. Ground truth data 204 may also include ground truth representations of digital workpieces. Generated representations 220a-220n may be provided to further automated processing modules, using respective outputs 230a-230n. In some implementations, one or more of generated representations 320a-320n may be provided to finite element analysis (FEA) module 208, which may generate one or more FEA maps. The one or more FEA maps may be provided to encoder 210, which may encode one or more FEA maps into one or more latent representations. The one or more latent representations may be provided to one or more subsequent generative modules in a cascade of generative modules 318a-318n.

[0060] The example method 300 of FIG. 3 describes the operational use of the one or more fully trained ML models which were trained using method 200. In some implementations, fully trained generative modules 318a-318n may generate respective 3D representations of oral care data 320a-320n. Generated representations 320a-320n may be provided to further automated processing modules, using respective outputs 330a-330n. For example, fully trained generative module 318b may generate one or more 3D printing support structures 320b, which may be included in one or more 3D representations of oral care data 330b and processed as described elsewhere in this disclosure.

[0061] In some instances, the applied loads which are to be applied to a 3D printing digital workpiece are known, or may be estimated. Boundary conditions may be specified and subsequently provided to the denoising ML model 410 as a part of optional oral care arguments 136 (e.g., using crossattention or self-attention, to enable the denoising ML model to pay attention to boundary conditions or other oral care arguments 136). The physical forces acting on various parts of the digital workpiece may be determined using Finite Element Analysis (FEA), the 3D geometry of the digital workpiece, and / or one or more applied loads (e.g., linear forces and / or rotational moments). FEA may provide ground truth data for use in training a generative ML model (e.g., method 600) or other types of TSO for generative design. For example, a fully trained diffusion ML model (or another fully trained TSO) maybe used to generate the shape and / or structure of one or more 3D printing supports. The 3D printing supports may support a physical workpiece while the physical workpiece is being printed. An FEA module 208 may generate one or more FEA maps. An FEA map may include one or more of a strain map, a stress map, a force vector map, or the like. An FEA map may describe the deformation of a digital workpiece and / or associated 3D printing supports. In some instances, an FEA map may include a vector or a matrix of data values. In some instances, an FEA map may include values which are associated with mesh elements within a 3D representation. For example, a mesh element feature vector which is associated with a mesh element of a 3D representation may be assigned one or more values which are generated by FEA (e.g., the mesh element feature vector may include stress, strain, force vector, or other information which is generated by FEA). Stated another way, in some implementations, mesh element feature vectors may be enhanced with the outputs of FEA module 208, to provide the generative ML models of this disclosure with improved information about the inputs to those generative ML models. For example, a cascaded ML model may be provided with stress, strain, and / or force estimates that describe the interaction of an initially configmed oral care appliance (e.g., an orthodontic aligner tray, a palatal expander, transverse appliance, Herbst appliance, brackets with archwire, etc.) and the patient’s dentition. In some implementations, an FEA map may describe the interactions between a first appliance component and a second appliance component (e.g., or the interactions between two or more other 3D representations of oral care data). The cascaded ML model may then generate one or more improved appliance designs which optimize the forces applied by the appliance to the patient’s dentition (or to optimize the stress or strain applied on the dentition by the appliance), in accordance with treatment instructions included in oral care aiguments 136. In other words, the cascaded ML model may modify an orthodontic appliance which is provided in an initial configmation (e.g., initial shape and / or structure), and output a modified orthodontic appliance which is optimized to achieve the patient’s desired clinical outcome.

[0062] According to various implementations, any of methods 100, 200, 400, 500, 800, 900, 1000 or 1100 (or other example methods) may be used for 3D printing supports generation. One or more FEA maps may be provided as input data to the generative modules described in any of those methods. In fact, using method 600 (or other example methods described herein), the total geometry, including the digital workpiece and / or the support structures, may be analyzed together to predict deformations which may occur in the physical workpiece (e.g., deformations which may occm during 3D printing when 3D printing supports provide inadequate support). Techniques of this disclosure may generate digital 3D printing support designs which minimize or eliminate deformation. Examples of digital workpieces include 3D representations of oral care data (e.g., 3D printing support structures, appliances, fixture models, restoration designs for teeth, etc.). Digital support structures may be modified as part of TSO.

[0063] As can be appreciated by someone skilled in the art of 3D printing, one reason for adding temporary support structures to the physical workpiece is to ensure the connectedness of every physicalaspect of the 3D printed object and to ensure the structural integrity of the entire assembly during the printing process. Additionally, the supports should be designed in such a way as to prevent significant deformation of the physical workpiece, at least to the extent that neighboring layers in the 3D print are aligned to within a given tolerance within the XY plane and / or distance between layers along the Z axis (e.g., in either the XZ or YZ planes). One or more tolerance values may be included in oral care arguments 136, which may be provided to a generative ML module (e.g., such as those found in method 600 or other examples of generative methods described herein). The one or more tolerance values may pertain to neighboring layer alignment, among other possible measures of accuracy, such as spatial distortion of features within the XY plane or layer adhesion strength in the 3D print. One or more design parameters may be included in oral care arguments 136, which may be provided to a generative ML module (e.g., such as those found in method 600 or other examples of generative methods described herein) to provide improved generated output. The improved generated output may lead to improved accuracy of the 3D printed workpiece by ensuring adequate structural rigidity of the entire printed assembly. Examples of design parameters include, for example, values that specify minimal or sufficient support structure volume, minimal or sufficient number of support structures, minimal or sufficient support cross-sectional area at each contact point (which may correlate to ease of 3D printing support break-away), minimal or maximal consolidation of nearby supports into branches or trunks, minimal or sufficient wall thickness of hollowed-out support columns, trunks, or branches, etc. In some instances, design parameters can include a minimum or maximum count of bifiircations which may take place when a branch or trunk bifurcates. Such design parameters may be provided to a generative module 218a or 218b (among others) at training time, to enable those generative modules to learn the distribution of possible design parameters values. The fully trained generative modules 318a or 318b (among others) can then generate output which is customized to those design parameters, when those design parameters are provided as inputs to the fully trained model.

[0064] Note that it is most often the case that one seeks to optimize the printing process by keeping both print time and material usage to a minimum while providing adequate support to the physical workpiece, thereby ensuring reliable and accurate results. It is possible to minimize supports to such an extreme that the printing process fails due to broken supports under the strain of moving machine parts and fluids. These can be very costly mistakes on large print jobs that run for many hours and use costly materials. Techniques of this disclosure (e.g., method 600, etc.) may generate digital designs for 3D printing supports which have sufficient strength to avoid such failures. In some implementations, mechanical modeling may be performed (e.g., by FEA module 208) to validate a 3D design in a digital 3D environment before sending the 3D design to a physical 3D printer. The results of the mechanical modeling may be provided to a generative module 318n, which may generate one or more refined or improved 3D printing support structures 320n. The refined or improved structures may be included as part of the output data 33 On.

[0065] In some implementations, ML models may be trained to validate the correctness (or suitability for patient treatment) of 3D oral care representations (e.g., the validation of 3D printing supports). For example, a representation generation ML model (e.g., an encoder, or a spectral encoding module, etc.) may generate one or more latent representations (or spectral representations, etc.) of the 3D oral care representation which is to be validated. The one or more latent representations (or spectral representations) may be provided to a validation ML model (e.g., a convolutional neural network, support vector machine, logistic regression model, etc.). The validation ML model may output one or more indications regarding whether the inputs are suitable for use in patient treatment. In some implementations, the validation ML model may classify the inputs are suitable, or unsuitable for patient use (among other categories). The generated outputs may be compared to corresponding ground truth objects, to compute one or more loss values. The one or more loss values may be used to train, at least in part, the validation ML model (or the representation generation ML model). In some implementations, an ML model may be trained to validate the digital design of 3D printing supports, and used to determine the suitability of the design for use in 3D printing and / or patient treatment. For example, the validation ML model may predict whether the digital design of the 3D printing supports has sufficient strength to withstand the 3D printing process.

[0066] A flow-based model for TSO (e.g., a diffusion model) may be trained using flow matching, among other methods. A Markov chain of progressively noisier 3D representations of digital workpiece data (e.g., which may include dental arch models, fixture models, dentures, orthodontic appliances, dental restorations, etc.) may be generated as part of the forward pass 702, and used to train, at least in part, the flow-based model (e.g., using method 500). In some examples, however, the training data might include one or more oral care guide objects 308. Examples of guide objects 308 may include one or more 3D representations of less complex digital workpieces, such as a geometric primitive (e.g., sphere, cube, cylinder, prism, etc.) and a single support structure, such as a cone based on the build platform and its vertex in contact with the digital workpiece. These examples of guide objects 308 may be varied to generate other training data including cones of varying heights, base diameters, vertex penetration depths (diameters of intersection at the height of truncation), axis slope angles, etc. Furthermore, a variety of different digital workpiece orientations, contact points, and / or base positions may be generated by ML models described herein. In some implementations, the ML models may generate a plurality of support structures, including branches which include permutations of the elements described above. The 3D printing supports may exert a system of forces (e.g., one or more forces) on the digital workpiece (e.g., a system that is more complex than a single cantilever beam, etc.). Training data which are used to train the ML models may, in some instances, include incomplete portions of a digital workpiece and / or associated support structme(s), representing the extant half-space of the printed assembly above or below a given 2D plane. The 2D plane may correspond to a moment in time during the 3D printing process (e.g., including the geometry that has already been printed while omitting geometry that has not yet been printed). Generative ML models described herein may betrained to augment, modify or complete such incomplete digital workpieces. The fully trained ML models may be used in deployment to complete one or more incomplete 3D representations of oral care data which are included in input data 102, input data 202, instant patient case data 416, or the like.

[0067] In some implementations, the forward pass 702 may combine (518) random noise with the digital workpiece (e.g., a 3D representation of oral care data, such as a fixture model) which is being diffused. According to some noise introduction techniques, “islands”, or disconnected portions of the geometry of the digital workpiece may be formed which violate the connectedness mle for support structures. Instead of producing a large percentage of solutions that violate these rules and subsequently rejecting the structures, a denoising ML model (e.g., based on a U-Net) may be trained to uphold the connectedness rule. An example of such training is described in method 500, which may train a UNet to predict noise tensors, based on a Markov chain of increasingly noisy training data examples. Training the ML model in this way advantageously ensures that the generated (or predicted) output does not violate the connectedness rule and improves the overall accuracy of the system. In some implementations, oral care arguments 136 (e.g., including design parameters, etc.) may be assigned any of a plurality of random values, and those oral care arguments 136 may be used to generate digital designs for 3D printing supports (or other 3D oral care representations). For example, these randomly assigned values of oral care arguments 136 may be provided to a generative module (e.g., such as those described in method 600, among other example methods described herein), and used to generate a plurality of differently designed 3D oral care representations. The resulting 3D oral care representations may be evaluated using optimization algorithms such as genetic algorithms, simulated annealing, or ant colony optimization (among others). For example, each of the randomly generated 3D oral care representations may be evaluated by one or more objective (or fitness functions), which may estimate the suitability (or fitness) of the 3D oral care representation for use in patient treatment. The plurality of 3D oral care representations which are determined to be of higher fitness are retained in a population of such 3D oral care representations. 3D oral care representations which are determined to be of lesser fitness are removed or overwritten by copies of the more fit 3D oral care representations. The method may then iterate by varying aspects of the remaining 3D oral care representations in the population (e.g., by randomly varying one or more design parameters, or other oral care arguments 136).

[0068] The complexity of 3D printed supports may be further increased by introducing slopes, bends, branches, hollows, non-linear tapers, polygonal or irregular cross-sections, etc. Designs may be evaluated via FEA to generate physical fields, such as strain energy density and von Mises stress. The outputs of such analyses (e.g., which may include information about forces, loads, or moments, etc.) may be provided as inputs to ML models of this disclosure, to provide additional information of the structures and / or physical capabilities of 3D representations which are included in inputs such as patient dentitions, digital fixture models, appliances, etc. In some implementations, oral care arguments 136 may include boundary conditions (e.g., of the build plate or vat window, or of the resin surface), or volume fraction (e.g., describing the presence or absence of 3D printing material). Physical fields mayindicate the relative importances of one or more portions of a digital design of a 3D representation that is to be 3D printed (e.g., 3D printing supports, or the digital workpiece that is to be 3D printed). Stated another way, when there is no stress on the 3D printing supports, then the 3D printing supports are not serving to resist deformation of the digital workpiece by the applied loads. 3D printing supports are necessary when there is stress present on the 3D printing supports. The presence of any unloaded voxels (or volumes of material) may be penalized by optimization algorithms of this disclosure. For example, loss calculation may include FEA of a 3D digital design for 3D printing supports. That FEA may identify one or more portions of those 3D printing supports which are unloaded or are otherwise not serving the intended purpose of supporting the digital workpiece. The loss calculation may penalize the presence of such unloaded voxels. Such loss calculation may be performed during the training of ML models of this disclosure (e.g., method 500, etc.). FEA may also be used in the loss calculation for the training of ML models to generate other 3D representations of oral care data, as described herein. As a result, ML models of this disclosure may generate 3D printing supports which include only the most vital material which is needed to resist deformation of the digital workpiece within prescribed deformation limits. For example, the example method 500 may include FEA when the loss is computed (526), so that the reverse pass 704 of the fully trained denoising diffusion model (e.g., as described in method 600) may generate 3D printed supports which are optimized to balance strength and optimal use of 3D printing resin.

[0069] In some instances, data which are used to train ML models of this disclosure may include data which iteratively produces an FEA simulation of the physical fields, and / or then removes voxels of material (elements) that carry insufficient amounts of stress (or which have strain energies that are below a certain threshold). Such optimization may be performed until only the most vital material needed to resist deformation of the digital workpiece remains. For example, a digital workpiece which includes an orthodontic appliance may be positioned in 3D space proximal to a build plate and offset by a given distance (in a manner sufficient to allow for later removal of supports after the 3D printing process completes). A bounding box may be defined for a given stage of 3D printing that has one face based on the build plate and its opposing face based on the incident surface of the 3D printer at a given moment in time. This incident surface of the 3D printer may include a plane that defines a half-space, wherein lies the extant material already cured by the printer. The opposite half-space encloses geometries that have not yet been rendered; they do not yet exist in physical space. The bounding box of the extant material may enclose geometries which include both the digital workpiece and the array of temporary 3D printing support structures. At a maximum, the boundary conditions for the FEA used in generative design (GD) are defined by the bounding box. Opposing faces of the bounding box may also be used for applied loads, which are transmitted from one face, through the digital workpiece and support structures, to one or more points or geometries on the opposing face. Examples of the opposing face include an extruder nozzle or wiper blade. According to particular implementations, the digital workpiece may be treated as part of the boundary conditions during this step. This may allow, forexample, the system to advantageously analyze the forces on the digital workpiece during the FEA while preventing the digital workpiece from being modified as part of the iterative step during GD.

[0070] This approach to GD may further include initially filling-in the entire volume between the physical workpiece and the bounding box with support material. As loads are applied to the build plate on one side of the bounding box and the extruder nozzle or wiper blade on the opposite side (and optionally to the physical workpiece as a result of gravity and / or fluid dynamic drag or other physical forces), loads may be transmitted through the digital workpiece and / or the support volume, and a physical field may be defined based, at least in part, on strain energy density, and / or von Mises stress. In a subsequent step of the same iteration of GD, support material residing in voxels which have stress (or strain) values that are below a given threshold may be removed (given a reduced or zero volume fraction or density). The process may then repeated by running FEA on the remaining support material and subsequently removing superfluous voxels of 3D printing support material. Superfluous voxels may be removed until a given distribution of strain energy density (or von Mises stress) is measured in the remaining 3D printing supports structure (e.g., measured using FEA, etc.). In some implementations, there is an advantage to using a relatively low threshold initially and progressively increasing the threshold in subsequent iterations. This approach to iteratively increasing thresholds may enable techniques of this disclosure to generate a variety of 3D printing support structures. A plurality of optional designs from earlier iterations may be refined after one or more iterations. Aspects of 3D support structures which provide little or no support to the digital workpiece may be iteratively removed through the course of optimization. It should also be understood that islands of support material are unlikely to form during this iterative process, because without a path between loads and boundaries, there may be no stress (or strain) in the voxels of material which are included in an island. Islands may therefore be removed like any other unneeded material by the functioning of the method.

[0071] The 3D geometry data that is produced using the above process of GD can be used as ground truth data provided as input during the forward pass 702 of training a Diffusion Model (e.g. in method 500), or in the training of other generative methods described herein. Such ground truth data has been validated digitally by FEA. Further validation of the design could be performed via physical testing after 3D printing is completed. As described above, a wide variety of permutations of training data may be generated. The training data may include a variety of digital workpieces, singular or plural supports, varied support geometries and / or positions, and / or various applied loads. However, for any given permutation, the resultant 3D design is deterministic (e.g., the design will always produce the same or at least a substantially similar result for a given set of inputs). A 3D design may include aspects of the shape, and / or topology of a 3D representation of oral care data. According to various implementations, techniques of this disclosure may produce a variety of valid 3D designs which result from slightly different conditions in the GD process. Minute variations in any of one or more oral care argument 136 (e.g., design parameters) may result in different 3D designs after multiple iterations of FEA and subsequent selective removal of aspects of a 3D printing support structure. In someimplementations, noise may be introduced into one or more model inputs. For example, inputs may be perturbed, such as applied loads, the position or scale of the digital workpiece, the position of the extmder or wiper blade, the density of the support voxels, or the like. Thus, techniques disclosed herein advantageously generate a variety of solutions for the 3D design of the support structures associated with a given set of inputs, not merely one deterministic solution. In some instances, a plurality of 3D designs may be substantially similar. In other instances, the 3D designs may differ considerably. In every instance, however, the 3D designs may be considered valid, since the 3D designs have verified by FEA as being optimal for the given set of inputs.

[0072] It should be appreciated that FEA is often highly computationally intensive as a function of model resolution, and therefore in some instances, optimal performance may be achieved by performing FEA on a subset of data samples in a production process (e.g., where computational resources are limited, or time is limited, etc.). This is particularly true for applications involving mass customization, where every 3D print job is unique, and high production throughput is required. ML models of this disclosure (e.g., 100, 200, 1000, 400, 500, 800, 900, 1000 or 1100, etc.) enable this mass customization by dramatically reducing computational loads and reduces the time to generate digital designs for 3D representations of oral care data which are to be 3D printed (e.g., by optimizing the digital designs of 3D printing support structures).

[0073] According to particular implementations, computation can be front-loaded into the training phase of deep learning. ML models may be trained on data which include a wide variety of patient cases. Some patient cases may be considered optimal due to GD and / or inherent FEA verification. Some patient cases may be considered sub-optimal, and therefore may be penalized by loss calculation during model training (e.g., using the outputs of FEA). In some implementations, a diffusion model may be trained (e.g. using method 500) using a large number of increasingly "noisy" data samples (e.g., patient dentition data, etc.). In some instances, data samples may be varied in one or more respects, which is defined herein as “varietization.” For instance, varietization can include using stochastic methods to generate variations in the data samples. Through this process of varietization, a training dataset may be expanded with a significant quantity of additional variations.

[0074] For instance, Convolutional neural networks may be trained to map between 3D representations of the patient’s dentition, and 3D representations of one or more appliances, or other 3D representations of oral care data. Convolutional neural networks may include numerical models (e.g., including compositions of one or more basis functions) which are capable of interpolating between a plurality of data inputs and a plurality of data outputs . Patient dentition data from a plurality of historical patient cases may be used to train the convolutional neural networks. The patient dentition may be provided to the input of the neural network. The neural network may generate output data. The generated output data may be compared to corresponding ground truth data, and loss may be computed. The loss may be used to train, at least in part, the neural network.

[0075] The fully trained neural network may be used in a production environment to make predictive inferences for use in digital oral care. In some implementations, the fully trained neural network may function in a generative manner, using statistical methods, and / or compositions of basis functions (e.g., as encoded by network weights and / or activation functions) to generate one or more outputs which are customized to the patient’s dentition data which is provided as input data. When the neural network is presented with inputs that are substantially similar in value to inputs that were used during training, then the one or more generated outputs may approximate the ground truth values used in training. The neural networks may be trained to learn the distribution of the input dataset, enabling the neural networks to generate correct predictive outputs even when the exact configuration of input data does not correspond to the data examples found within the training dataset. When fully trained, the outputs of the neural networks comport logically with the patterns seen in the training data. The time and / or computational resources required to generate these predictive inferences (e.g., using the fully trained neural networks) may be much less than the time and / or computational resources required to evaluate a fully FEA. In some implementations, FEA may nonetheless be used in the generation of ground truth data (e.g., when predicting the performance of 3D printing support structures).

[0076] Techniques of this disclosure (e.g., denoising diffusion ML model 410) may be trained to generate 3D oral care representations, such as fixture models or fixture model components (e.g., 3D trimlines) as described here. Other examples of 3D oral care representations which may be generated include 3D printing supports for use in generating physical 3D models of oral care appliances, or the like. The techniques include denoising diffusion models (e.g., methods 500 or 600), or continuous normalizing flows models (e.g., method 800 or 900). The generative models may, in some implementations, be trained using Flow Matching. The techniques also include transformer-based methods for generating or modifying 3D oral care representations, such as shown in method 1000.

[0077] The example method 400 shown in FIG. 4 describes the use of fully trained denoising diffusion ML model 410.

[0078] Input data 424 may include one or more 3D Oral care representations, such as representations of patient dentition (e.g., tooth restoration designs, etc.), appliance components, mesh element labels (e.g., for 3D mesh segmentation or mesh cleanup), or other 3D oral care representations described herein. Input data 424 may be provided to denoising ML model 410, which may output data 420 (which may include generated data).

[0079] In some implementations, input data 424 may include one or more 3D oral care representations which are to be modified. Input data 424 may include aspects which are customized to the data from a partial patient case (e.g., customized to the patient's dentition). Input data 424 may include a 3D oral care representation in an initial state (e.g., dentition in a pre-treatment state, or an appliance component which is in an incomplete state, or the like). Denoising ML model 410 may modify the input data 424, and output data 420 (which may include modified data).

[0080] Latent encoding modules 414, 412, 418, or 428 may encode their respective inputs into respective latent representations, which may be provided to one or more internal modules of denoising ML model 410.

[0081] In some implementations, one or more guide objects. Guide objects 308 may be drawn from a library of example data structures which are stored in the computing environment, and / or may include default data structures which correspond to the initial state of generated outputs. Guide objects 308 may include data structures which are generic, as opposed to input data 424 which may include aspects which are customized to one or more particular patients. Guide objects 308 can include, for example, a framework lattice of vertices and / or edges which is to be used to deform one or more 3D meshes, a 3D mesh of a generic tooth shell (e.g., for use in a layered 3D restoration design), or other examples described herein.

[0082] In some implementations, oral care arguments 136 may be provided to the input of the denoising ML model 410 (e.g., to the input of a U-Net or other encoder-decoder structure which has been trained to perform denoising). In some implementations, oral care argument 136 may be encoded into one or more latent representations by latent encoding module 412, and then the resulting one or more latent representations may be provided to one or more internal modules of denoising ML model 410. In some implementations, the one or more latent representations may be concatenated with one or more latent representations which are found within denoising diffusion ML model 410. For example, the one or more latent representations may be concatenated with the latent vector (or embedding vector) which lies between the encoder and decoder portions of a UNet which appears in denoising ML model 410 (e.g., concatenated with the embedding vector which lies inside a U-Net which has been trained to predict data structures that describe noise).

[0083] Among the oral care arguments 136 disclosed herein are oral care metrics (which may quantify aspects or dimensions of an individual tooth, or quantify physical relationships between two or more teeth), oral care parameters, restoration design parameters, or other values which are configmed to influence or customize intended aspects of a 3D oral care representation which is generated according to techniques described herein. Oral care arguments 136 may include real values, categorical values, natural language text, or other data types described herein. In some implementations, oral care arguments 136 may be defined which are used for topology optimization, or to optimize the 3D shape and / or structure of a 3D representation of oral care data. For example, the aspects of connected components (e.g., count of connected components, area or volume of connected components, etc.) within a 3D representation of oral care data may be computed, and may be provided to the denoising ML model 410, enabling the denoising ML model 410 to optimize the generated design. For instance, the generated design (e.g., support structures for a 3D printing model, etc.) may be optimized to minimize or eliminate disconnected or “floating” material within the 3D representation that is generated. The benefit of eliminating such floating material is that floating material may complicate the 3D printing process (floating material may not have sufficient support to enable fabrication by a 3Dprinting machine). Additional examples of oral care arguments 136 include values which quantify aspects of the compliance (e.g., relative rigidity) of a 3D representation of oral care data that is to be 3D printed. Compliance may estimate the translational compliance, or the rotational compliance (among others) of a 3D representation which is to be 3D printed. Compliance may estimate whether a 3D support (or other structure) within the 3D representation is strong enough to hold a 3D printed tooth, appliance, or other 3D representation of oral care data (e.g., digital 3D representations which are to be 3D printed as physical objects for use in patient treatment).

[0084] In some implementations, a 3D trimline (e.g., described by one or more splines, one or more 3D meshes, or one or more 3D polylines, one or more transforms, one or more Euler angles, one or more quaternions, etc.) may be generated (e.g., using a diffusion model or CNF model that was trained using flow matching). The 3D trimline may describe a path that is to be following by a knife, laser, or spinning cutting tool that is used to separate a thermoformed aligner tray (e.g., a plastic tray that is thermoformed onto a 3D printed fixture model) from a physical fixture model (as defined herein). Techniques of this disclosure can generate a trimline that accounts for the custom geometry of the patient’s dentition (e.g., guiding the cutting instrument around any maloccluded teeth which may be present in the dentition, etc.). The trimline can be used to control the poses of one or more cutting instruments. In some implementations, oral care guide objects 308 may include an initial set of values that quantify the angle of approach between a cutting tool and the fixture model at each of a series of 3D points along the 3D trimline. An angle of approach (or other angles described herein) may be described by Euler angles, transforms, quaternions, or the like. This initial set of values may be modified or optimized by the generative ML models described herein. For example, the initial set of values may be provided to the denoising ML model 410, and may enable the denoising ML model 410 to generate an optimized set of values (e.g., optimized set of angles for each of a series of time points). The optimized set of values may be used to describe a 3D trimline which is optimized for manufacturability. Stated another way, the denoising ML model may denoise a series of quantified approach angles, in a manner which customizes the series of quantified approach angles (e.g., which may include translations, and / or rotational angles that correspond to tool movement) to the dentition of a patient case. In some implementations, a guide object 308 data structure of incremental steps may be provided to denoising diffusion ML model 410, which may then modify that guide object 308 to be customized the patient’s dentition data which is included in input data 424. In some implementations, ground truth data 104 may include one or more ground truth sets of approach angles which may be compared with a corresponding generated set of approach angles, for the purpose of computing loss. In some implementations, ground truth data 104 may include one or more ground truth trimlines which may be compared with a corresponding generated trimline, for the purpose of computing loss.

[0085] One or more oral care constraints may be included in oral care arguments 136. Oral care constraints include constraints on the angle of approach (or other angles described herein including an allowable range of angles of approach) of a cutting tool relative to the tangent (or plane) of a 3D surfacethat is being cut. For example, oral care constraints may be provided to a generative ML model, instructing the model to generate a trimline which ensures that the cutting tooth never cuts the aligner tray at an angle outside of a threshold angle from the perpendicular. Stated another way, the cutting tool is to be as near to 90 degrees relative to the surface of the aligner tray (and / or relative to the fixture model under the aligner tray) as possible. The angle of approach may describe the angle between a cutting tooth and a surface of a fixture model or a thermoformed aligner tray (e.g., the pre-trimmed tray, etc.). When the generative ML model is being trained, loss may be computed that discredits or otherwise questions the accuracy of generated designs which vary too far from established oral care constraints. For example, when a partially trained generative ML model outputs a 3D design (e.g., for a trimline) which is outside of the tolerances described in oral care constraints, then the resulting loss may be computed to be high. This high loss value may be used to train, at least in part, the ML model, and deter the ML model from generating similarly out-of-tolerance output in future executions of the ML model. In this manner, an ML model (e.g., an ML model for generated trimline designs) can be trained to generate trimlines which are formed according to one or more oral care constraints. Oral care constraints can include an angle of approach (or a range of allowable angles) that describe the angle by which a cutting instrument (or tool) approaches a digital fixture model. The digital fixture model can be 3D printed, resulting in a physical fixture model. An aligner tray can be thermoformed onto the physical fixture model, and the excess plastic material of the aligner tray can be removed using a cutting instrument. Oral care constraints can specify a range of acceptable angles of approach, to make sure the cutting instrument does not cut the tray in a manner that results in sharp edges, among other considerations. Other examples of oral care constraints may include aspects of excess material that is to be removed. Oral care constraints may include information pertaining to the rigidity of the aligner tray (e.g., pertaining to the rigidity of the plastic of the aligner tray).

[0086] Stated another way, denoising ML model 410 may be trained to generate (or modify) a 3D trimline that defines a cutting path that is manufacturable by the cutting tool that removes the aligner tray from the fixture model. A cutting tool may operate optimally when the cutting tool approaches the fixture model from an approximately 90-degree (normal) angle. Such oral care arguments 136 may enable a 3D trimline to be generated which assures that the cutting tool follows a manufacturable path (a plausible path). A manufacturable path means that the cutting tool is able to access all points along the trimline, and is not blocked by adjacent teeth, other aspects of the patient’s dentition, hardware, etc.

[0087] Techniques of this disclosure (e.g., cascade-based ML models, or flow-based models trained by flow matching) may be trained to place one or more first oral care meshes relative to one or more second oral care meshes. For example, the methods may place two or more teeth relative to each other, such as for setups prediction. In other examples, the methods may place oral care meshes (e.g., hardware meshes, or appliance component meshes, etc.) relative to one or more teeth. Oral care meshes may include 3D representations of oral care data described herein, such as teeth, gums, appliance components, hardware, or the like.

[0088] Representation learning may train a first module to encode an embedded representation of a 3D oral care representation (e.g., converting a mesh or point cloud into a latent representation using an autoencoder, or using a U-Net, encoder, transformer, block of convolution & pooling layers or the like). That latent representation may comprise a reduced dimensionality form and / or information-rich version of the inputted 3D oral care representation. In some implementations, the generation of a representation may be aided by the calculation of a mesh element feature vector for one or more mesh elements (e.g., each mesh element). In some implementations, a representation may be computed for an oral care mesh.

[0089] One or more of such latent representations may be provided to a second ML module, which may perform a generative task, such as transform prediction or 3D point cloud generation. Such a transform may comprise an affine transformation matrix, translation vector or quaternion or the like. The second ML model may include generative neural networks, such as multilayer perceptions (MLP), Kolmogorov-Arnold Networks (KAN), transformer encoders, transformer decoders, encoders (e.g., trained as a part of variational autoencoders, KAN-based networks, etc.), support vector machines, logistic regression models or the like. In some implementations, the second ML model may include flow-based ML models, or cascade-based ML models. According to various implementations, neural networks of this disclosure may include aspects which specify how inputs are used to generate outputs at a respective layer. The neural network aspects can include weights, which connect nodes, and / or activation functions (e.g., which determine the passage of data through associated nodes, or whether the nodes activate), among other examples. Either a first or a second ML module may include one or more Kolmogorov-Arnold Networks (KAN), each of which may include one or more trained activation functions.

[0090] Systems of this disclosure may be trained using past cohort patient case data. The past patient data may include at least: one or more ground truth transforms and one or more 3D oral care representations (such as tooth meshes, or other elements of patient dentition). In the instance where a U-Net (among other neural networks) is trained to generate the representations of tooth meshes, the mesh convolution and / or mesh pooling techniques described herein enjoy invariance to rotations / translations / scaling of those tooth meshes.

[0091] A denoising diffusion model (e.g., shown in FIG. 4) may include a forward pass 702 over the input data 424 (e.g., a 3D point cloud of a tooth, a transform, or another 3D oral care representation described herein) which may generate a Markov chain 706 of steps which may introduce successively more noise (e.g., 2D or 3D Gaussian noise, etc.) to the input data 424. The type of noise that is introduced may vary depending on the data type of the particular 3D oral care representation for which noise is being introduced (e.g., 3D mesh, transform, set of mesh element labels, etc.). For example, a 3D mesh that describes an oral care appliance component may include vertices, edges and / or faces. In implementations where vertices, edges and / or faces are used, the positions of the vertices may be further perturbed with each successive noising step, which may change the positions of the vertices in space,and consequently change the positions and / or orientations of the associated faces and edges. In other examples, when the 3D oral care representation is a transform (e.g., a transformation matrix or quaternion for transforming teeth or appliance components), that transform for which noise is introduced by making a succession of small random perturbations to the values contained within the transform. In further examples, when the 3D oral care representation is a set of mesh element labels (e.g., for use in mesh segmentation or mesh cleanup), each perturbation step may alter the label associated with one or more mesh elements. In some implementations, maximum and / or minimum limits may be configured to control the distributions of perturbations. For example, in some implementations, the width, height, length or another dimension of a 3D representation of oral care data may be measured, and the max and / or min perturbation limits may be configmed relative to that dimension (e.g., the maximum perturbation may be set to be no more than 0.1% of the width of a tooth mesh or an oral care appliance). Table 1 describes further examples of the methods by which noise may be introduced to 3D oral care representations as a part of the forward pass 702 in training a denoising diffusion model. w%, x%, y%, or z% in Table 1 could be configmed as inputs or learned from a dataset (e.g., as a part of model training). For example, when computing loss during training, when loss is too high, the values of w%, x%, y%, or z% may adjusted and the forward pass 702 may be rerun. In Table 1, jitter refers to the addition of small random values to one or more values described by the rows of Table 1. For example, when mesh elements me jittered, the X, Y or Z coordinates of a mesh element may be modified using small perturbations. Jitter may, in some implementations, refer to small random perturbations to the data structure that describes a 3D oral care representation. In other examples, jitter may refer to random perturbations of the values of mesh element labels. In still other examples may refer to random perturbation of the values in transforms (e.g., inside transformation matrices), such as the transforms that describe tooth coordinate systems, or the transforms that describe tooth poses in setups.Table 1

[0092] The forward pass 702 may generate training data, which may be used to train, at least in part, denoising ML model 410. The Markov chain may generate a set of successively noisier training data examples. Input oral care arguments (or attributes) 136 may influence the functioning of the denoising diffusion model 410, causing the denoising diffusion model 410 to generate output to the specification of the clinician (e.g., enabling the customization of the output that is generated by the denoising diffusion model 410). The output may be customized to the treatment needs of the patient (e.g., treatment needs can include the need to resolve clinical and / or aesthetic problems with the patient’s dental anatomy, etc.). Oral care arguments 136 may include oral care parameters, oral care metrics, or other values which describe, at least in part, aspects of an intended 3D oral care representation or oral care appliance which is to be generated. In some implementations, such as with stable diffusion, an optional latent encoding module 414 may encode input data 424 (e.g., 3D oral care representations, etc.) into latent form. A latent encoding module may be trained to encode data into a reduced dimensionality latent form. For example, the encoder portion of a reconstruction autoencoder can encode a tooth mesh (possibly containing thousands of vertices, edges, and faces), into a vector of numbers with a lower order of dimensionality than the original representation. Examples of data which may be encoded include a transform (e.g., a tooth transform, etc.), a point cloud or mesh describing a tooth (e.g., the exterior contours of a tooth crown’s enamel, the interior boundary between the enamel and dentin, or the interior boundary between the dentin and the pulp, etc.), a set of mesh element labels, or the like. Such data may be encoded into a latent vector or latent capsule. Likewise, an optional latent encoding module 412 may, in some implementations, encode one or more oral care arguments 136 into latent form.

[0093] The Markov chain 706 may generate a succession of increasingly noisy versions of the input data 424. The Markov chain may be used to train, at least in part, a denoising ML module 410 (e.g., which may operate in deployment as a part of the reverse pass 704). The denoising ML module 410 may also be trained, at least in part, by one or more losses which are computed (526) by comparing noise tensor 516 (e.g., or another data stmcture containing noise) with predicted noise data structure 524. In some implementations, a denoising ML module 410 can be included in a generative module 118a-118n of method 100. In such implementations, losses may be generated by loss calculation modules 112a-112n, or the like, each of which computes loss after a step in a cascade of generative modules. The denoising ML module 410 which is trained for use in reverse pass 704 of a diffusion process, may include one or more neural networks (e.g., U-Net, VAE, 3D SWIN transformer, pyramid encoder-decoder, or the like) and may be trained to de-noise an initially noisy representation 602. (e.g., starting with a completely randomized version of the input data structure, and iteratively de-nosing that data structure until the data structure takes on aspects of a generated output that are suitable for use in the generation of an oral care appliance or other digital oral care of a patient). The reverse pass 704 may be used a fully trained denoising ML model 410. For example, the reverse pass 704 may start with a point cloud (or other raw data structure - such as a transforms or mesh element labels) that has aGaussian distribution, and over successive applications of the reverse pass denoising ML model 410 gradually shape that point cloud (or other data structure) into a suitable example of the target 3D oral care representation (e.g., an outer tooth crown design, or an inner structure of a tooth, which is suitable for use in creating a dental restoration appliance, or a restorative appliance such as a crown or bridge). In some implementations, a loss function (e.g., cross-entropy or MSE, chamfer distance, earth mover’s distance, among others) may be computed to quantify the differences between a generated 3D oral care representation and a corresponding ground truth (or reference) 3D oral care representation, for example, as in loss calculation modules 112a-l 12n, the loss is computed (526) in method 500.

[0094] In some implementations, loss may be computed (526) and used to train, at least in part, the denoising ML model 410. In some implementations, such as when an orthodontic setup or a tooth restoration design (e.g., a layered tooth restoration design) is generated, oral care metrics may be computed on the generated 3D oral care representation 420. The oral care metrics may be used, at least in part, to assess the quality or fitness for use of the generated 3D oral care representation 420 (e.g., to measure whether the generated 3D oral care representation meets the specification of the oral care arguments 136, and / or is ready for use in generating an oral care appliance). For example, when an ML model is trained for restoration design generation, an oral care parameter (e.g., the restoration design parameter, such as “Tooth width at base - mesial to distal distance”) may specify that the generated tooth crown should have a width at the base of X millimeters. The oral care metric “Length and / or Width” (e.g., which may measure the length of a tooth relative to the width of that tooth) may be measured on the generated tooth crown to determine whether the ML model generated a tooth crown which satisfies the specification of the “Tooth width at base” oral care argument. In some implementations, a difference between the expected and actual outputs may be computed, and that difference may be considered as a part of a loss calculation, which is then used in training the ML model.

[0095] Stated another way, in some instances, the forward pass 702 of the denoising diffusion model 410 may generate a training dataset of increasingly noisy examples of the input data 424, oral care guide objects 308, instant patient case data 416, or oral care arguments 136. Noise may be introduced to disfigure the input data (e.g., an image, a 3D point cloud, a transform, or latent representations of one or more of these inputs, etc.) and those noisy examples may be used, at least in part, to train a denoising diffusion machine learning model 410 to reverse of this noise-introducing process (e.g., in model deployment). The reverse pass 704 may be trained to reconstruct the pristine input data by removing the noise from a noisy example of that input data. This reverse pass 704 may generate a new output data based upon a data structure of an initially random configmation. In other words, the reverse pass 704 output a modified version of an initial data structure which is provided to the input of the reverse pass 704. Stated yet another way, after the denoising ML model 410 (which may include a U-Net, etc.) is trained, the denoising ML model 410 is capable to generate new 3D oral care representations by passing a noisy data example (e.g., a randomly generated noisy example)through the denoising diffusion process (e.g., through the reverse process 704). Furthermore, the trained denoising ML model 410 is capable to modify an initial 3D oral care representation which is provided to the input of the reverse pass 704, and output a resulting 3D oral care representation which is suitable for use in generating an oral care appliance which is customized to the treatment needs of the patient.

[0096] In some implementations, the denoising ML model 410 of the reverse pass 704 may modify an existing 3D oral care representation (e.g., modify a pre-restoration tooth design, etc.). For instance, the existing 3D oral care representation (e.g., an example of optional instant patient case data 416) can be provided to the input of the reverse pass 704, and then undergo a succession of denoising steps by the denoising ML model 410, until modifications are complete (e.g., as measured by oral care metrics, loss functions, or a threshold number of iterations has expired, etc.). Optional instant patient case data 416 may include data pertaining to the dentition of a patient. The instant patient case data may, in some implementations, be introduced so that the outputs of the denoising diffusion ML model 410 are customized to the dentition of the patient. In some implementations, the instant patient case data 416 may be provided to latent encoding module 418, which may generate one or more latent representations (or embedded forms). In some implementations, the instant patient case data 416 may be provided to the denoising diffusionML model 410. In other implementations, the instant patient case data 416 may include an appliance component or a fixture model component which requires modification. In still other implementations, the instant patient case data 416 may include other 3D oral care representations which are to be modified.

[0097] In some implementations, a data structure that undergoes iterative denoising by the denoising ML model 410 may be initialized, at least in part, according to a stochastic process. For example, the data structure can be initialized by introducing random noise, normally distributed noise, or other random configmations. The data structure may be initialized by aspects of the instant patient case data 416, or by a combination of two or more of these data. The instant patient case data 416 may include 3D oral care representations described herein, including tooth transforms (e.g., maloccluded transforms for one or more teeth during setups prediction), tooth meshes with transforms already applied, tooth meshes without transforms applied, one or more 3D representations of pre -restoration tooth designs, pre-segmentation dental arch mesh(es), pre-cleanup dental arch mesh(es), one or more mesh element labels (e.g., for segmentation or mesh cleanup), one or more segmented teeth for use in coordinate system prediction, one or more coordinate systems (e.g., each of which may be described by a transform), one or more 3D representations of appliance components (e.g., parting surfaces, etc.), one or more fixture model components (e.g., digital pontic teeth or interproximal webbing, etc.), or the like.

[0098] The denoising diffusion ML model 410 may be trained to generate one or more generated 3D oral care representations 420 (e.g., as described herein) for clinical or aesthetic treatment of the patient. In some implementations, output 420 may include one or more modified 3D oral carerepresentations. Generated (or modified) 3D oral care representation 420 may be generated as output by the reverse pass 704 of the denoising ML model 410.

[0099] A generated 3D oral care representation 420 (e.g., a denoised representation) may be generated over one or more iterations of denoising by the denoising diffusion ML model 410. Generated 3D oral care representations 420 may include setups transforms for one or more teeth, transforms for the placement of one or more appliance components (e.g., for the generation of a dental restoration appliance), one or more 3D representations of post-restoration tooth designs, one or more generated (or modified) appliance components (e.g., a parting surface or gingival ribbon for use in generating a dental restoration appliance), one or more generated (or modified) fixture model components (e.g., one or more trimlines, etc.), post-segmentation dental arch mesh(es), post-cleanup dental arch mesh(es), one or more mesh element labels for use in segmentation or mesh cleanup, one or more object masks (e.g., masks to be applied to mesh elements) for use in segmentation or mesh cleanup, one or more coordinate axes for one or more predicted coordinate systems, one or more archforms, or other of the 3D oral care representations described herein.

[0100] Referring to FIG. 5, the encoder-decoder structure 522 may generate a predicted data structure describing noise (e.g., a predicted noise tensor 524, etc.). Loss may be computed (526) between the predicted noise tensor 524 and the noise tensor 516. Among the other losses described herein, the loss may compute the mean squared error difference between the noise tensor 516 and the predicted noise tensor 524. The computed loss may be used to update (528) the weights of the encoderdecoder structure 522 (e.g., a UNet), until training is done (520). In some implementations, the computed loss may be used to update (528) one or more configurable activation functions included within encoder-decoder structure 522 (or other ML models described herein), until training is done (520). In some implementations, training may proceed (510) until loss drops below a threshold value, or until a target count of epochs have been completed.

[0101] Encoder-decoder stmcture 522 may include a UNet. For simplicity, a UNet is used interchangeably with encoder-decoder structure 522, but it should be understood tfiat the UNet may be replaced with other encoder-decoder structures 522. In some implementations, a predicted 3D oral care representation may be generated by a partially trained UNet, and be used to compute loss. For example, the partially trained UNet may be used to denoise input data, which may result in one or more predicted 3D oral care representations. Loss may be computed by comparing a predicted output (e.g., the output of UNet, etc.) to a corresponding ground truth 3D oral care representation.

[0102] In some implementations, non-latent representation inputs to the methods of this disclosure may be provided to encoder 508, to encode those inputs into latent representation forms (e.g., latent representation 512). Training of the encoder-decoder structure 522 may proceed for any number of iterations. In some implementation, training may be complete (520) after the outputs achieve a threshold accuracy, or other threshold statistics are met. Latent representation 512 may be combined (518) with noise (e.g., noise tensor 516), and the resulting latent representation may be provided toencoder-decoder structure 522. The noise 516 may be generated by the computing (514) of Gaussian noise, or another type of noise. Oral care arguments 136 may specify the nature of noise to be computed (514). Encoder-decoder structure 522 may generate one or more predicted noise tensors 524. Alternatively, when the inputs to encoder-decoder structure 522 are not latent representations, encoderdecoder 522 may generate other forms of noise (e.g., by adding jitter to the coordinates of mesh elements, by adding jitter to transforms, by modifying mesh element labels, etc.).

[0103] Loss may be computed (526) which quantifies the difference between the generated noise data (e.g., generated or predicted noise tensor 524) and the corresponding ground tmth or reference noise data (e.g., noise tensor 516). ML models of this disclosure (e.g., encoder-decoder structure 522, etc.) may be trained, at least in part, by the computed loss. For example, the loss may be used to update the weights (e.g., via backpropagation) of one or more UNets which are included in encoder-decoder structure 522. Training proceeds until done (520).

[0104] The fully trained generative modules (e.g., the fully trained versions of partially trained generative modules 118a-118n) may include one or more denoising ML models, or other ML models described herein. Referring to FIG. 6, method 600 describes the operational use of the fully trained generative modules, for example, in a time-constrained setting (e.g., while the patient waits in the treatment chair). According to various implementations, various input data may be provided to the fully trained denoising diffusion ML model of FIG. 6, including 1) patient's 2D or 3D dentition data (e.g., included in input data 424), 2) the (optional) latent representation 502 generated by the prior stage of a cascade, 3) oral care arguments 136, 4) one or more guide objects 308 for the stage n of the cascade (e.g., the current stage of the cascade), 5) one or more other types of oral care guide object, 6) noisy representation 602 (e.g., a noisy 3D representation), or other examples described herein. Inputs which have not yet been encoded into latent representations may be provided to one or more encoders 508 to encode those inputs into one or more latent representations 612. The denoising ML model may iterate (610) for M iterations, until a target accuracy is achieved, or until the outputs are otherwise deemed to be clinically or aesthetically suitable. For example, the outputs (e.g., predicted orthodontic setups, predicted mesh element labels, predicted tooth restoration designs, etc.) may be combined with 2D or 3D representations of the patient’s current anatomy, to generate one or more predicted smiles. The one or more predicted smiles may be used to evaluate the clinical and / or aesthetic value of the output data 420. In some implementations, noise may be added (626) to the output of encoder 508. This noise may provide the encoder-decoder 614 with an improved initial configuration for the iterative denoising process.

[0105] In some implementations, a latent representation 612, a latent representation 502 generated by the prior stage of a cascade, and / or a noisy representation 602 (e.g., a noisy 3D point cloud or other noisy 3D representation) may be provided to fully trained encoder-decoder structure 614 (e.g., a UNet), which may generate predicted noise tensor 616. In some implementations, latent style representation 628 may be provided to encoder-decoder structure 614, to enable encoder-decoder structure 614 togenerate outputs which include one or more aspects of the style information which is contained within latent style representation 628. Predicted noise tensor 616 may be removed (620) (e.g., by subtraction between matrices or tensors, etc.) from the latent representation 612 (e.g., a latent vector or latent embedding, etc.).

[0106] The oral care guide objects 308 may provide the method 600 with an initial or default configmation for one or more 3D oral care representations which are to be generated (or modified). For example, guide objects 308 may include one or more layered tooth shells, which may undergo shape modification and / or style transfer by encoder-decoder structure 614.

[0107] In some implementations, data which is in non-latent form may be provided to encoderdecoder 614, which may output versions of the input data into which noise has been added. For example, noise may be added to mesh elements, noise may be added to transforms, or noise may be added to other data structures (e.g., data structures that describe 3D oral care representations described herein). When non-latent data are denoised by encoder-decoder structure 614, the resulting one or more denoised data structures may be directly generated as output data 420.

[0108] A stopping criterion may be evaluated, for example, the method 600 may determine whether M interactions have transpired (610). Alternatively, other stopping criteria described herein may be used (e.g., a target metric is achieved, such as a target accuracy or a target oral care metric value is achieved). When done, the denoised latent representation may be provided to decoder 622, which may reconstruct the denoised latent representation into one or more 3D oral care representations (e.g., layered tooth restoration designs, predicted smiles, predicted orthodontic setups, predicted mesh element labels, or other 3D oral care representations described herein). The resulting generated output data 420 (e.g., a generated layered tooth restoration design, or other 3D oral care representation) may be generated for use in clinical treatment of the patient (e.g., generating dental restoration appliances, etc.).

[0109] When the input data includes 3D mesh data (or other 3D representations, such as 3D point clouds, 3D surfaces, etc.), mesh element feature vectors may be computed (e.g., a mesh element feature vector may be computed for each 3D point, 3D vertex, 3D edge, 3D voxel, or 3D face of a 3D representation). The mesh elements and corresponding mesh element feature vectors of the 3D input data may be provided to the neural networks of this disclosure (e.g., encoders 508, or encoder-decoder structures 522 or 614, among others), to improve the ability of those neural networks to encode the distribution of the 3D input data (e.g., enable the neural networks to better encode the shapes and / or structures of those 3D representations). The structure of a 3D representation may include aspects of the 3D representation such as: 1) which mesh elements are adjacent to each other; 2) which mesh elements are connected to each other; 3) which mesh elements are within a threshold Euclidean distance of each other; and / or 4) which mesh elements are within a particular count of connections of each other (or within a particular geodesic distance of each other), to name a few examples.

[0110] Referring again to FIG. 7, an example method 700 shows the forward pass 702 which is used in the training of a denoising diffusion ML model 410, and / or the reverse pass 704 which uses a fully trained denoising diffusion ML model 410. The forward pass 702 may generate a Markov chain 706 of increasingly noisy examples of the input data over a series of training timesteps t, or training iterations.

[0111] Generative machine learning models, such as normalizing flows or denoising diffusion probabilistic models, may be trained to generate or to modify 3D oral care representations (e.g., including 3D representations of oral care data, mesh element labels, transforms which are applied to 3D representations of oral care data, transforms that describe tooth coordinate systems, or other examples described herein). Techniques of this disclosure may train machine learning models (e.g., denoising diffusion probabilistic models, or other flow-based models) to generate 3D oral care representations. Flow matching is a method for training flow-based models, such as continuous normalizing flow-based models, denoising diffusion probabilistic models, denoising score matching models, or the like. Flow matching may be used to train machine learning models to generate or modify 3D oral care representations (e.g., normalizing flow-based modules, point flow networks, etc.). Point flow networks (e.g., point flow networks trained using flow matching, etc.) can be used for point cloud generation (e.g., to generate 3D representations of oral care data), scene flow estimation, or point cloud upsampling (e.g., to increase the level of detail in 3D representations of oral care data - such as tooth meshes). A point flow network may be trained to generate a 3D representation of oral care data, such as one or more 3D tooth restoration designs. In some examples, the ML models described herein may be trained to generate a 3D tooth restoration design which include geometrical features which have customized shapes and / or structures. Any of the following can be customized in the generated 3D restoration design, according to particular implementations: size or shape of cusp tips, the shape of incisal edges, or the presence or shape of tooth textures, among others. Tooth textures can include: mamelon grooves, vertical striations or perkimata, among others. In some implementations, a point flow network may generate a tooth restoration design which is upsampled relative the input tooth mesh(es). Examples of input tooth meshes include tooth meshes which are included in 3D oral care representations 102, or which are included in oral care guide objects 308. This upsampling can enable the generated tooth restoration design to include detailed tooth textures. Such a point flow network could be trained on a dataset that includes pre-modification teeth, and / or corresponding ground truth examples of upsampled post-modification teeth which include one or more tooth textures.Techniques of this disclosure (e.g., flow matching, etc.) may train a flow-based machine learning model which maps a first (simplified) distribution pO into approximations of one or more additional (more complex) distributions, which are designated qO ... qn, where the one or more additional distributions are approximated using one or more data samples selected from the one or more additional distributions. In some implementations, a flowbased machine learning model which maps a first (simplified) distribution pO into an approximation of a second (more complex) distribution q, where the second distribution is approximated using one ormore samples selected from the second distribution. In some implementations, the flow-based models of this disclosure may be invertible, meaning that a model may be trained in an initial configuration, subsequently be inverted, and then be used in deployment in an inverted configuration. Stated another way, data A may be provided as inputs to the ML model during training, and / or the ML model may generate the corresponding data B during training. After the completion of training, the ML model may, in some implementations, be reconfigured to support inverted operation. For instance, in inverted operation, the ML model may be provided B to generate A instead of A to generate B, as trained. For example, a vector field Vtwhich implements a flow £2 may be trained in a first configuration, and then be inverted and used in deployment in a second configuration. The more data samples 802 that are available for training, the more accurately the second distribution may be approximated. The flow £2 may include one or more diffeomorphic maps. A generative model for generating (or modifying) 3D oral care representations may include one or more of a flow £2, a vector field Vtor an inverted version of vector field Vt.

[0112] In some implementations, one or more invertible mappings (e.g., a cascade or succession of interconnected modules of invertible mappings, etc.) may be generated using flow matching. In some implementations, the one or more invertible mappings may include one or more vector fields. In some instances, a vector field may implement a diffeomorphic flow or diffeomorphic mapping. A vector field may, in some implementations, be inverted using a ODE solver, according to techniques known to one skilled in the art. In some implementations, the inverse of a vector field may be approximated using numerical methods.

[0113] The example method 800 of FIG. 8 may use flow matching to train an ML model (e.g., a continuous normalizing flow, or a diffusion model, etc.). One or more data samples 802 of 3D oral care representations (e.g., 3D representations of oral care data, transforms, mesh elements labels, or others disclosed herein) may, in some implementations, provided to a mesh element feature module. When data sample 802 contains one or more 3D representations, the mesh element feature module may generate (804) one or more mesh element feature vectors for the mesh elements of each 3D representation (e.g., a point cloud, 3D mesh, etc.). The data sample 802 may then be provided to encoder 806, which may generate one or more latent representations. The one or more latent representations may be provided to concatenation module 822. Oral care arguments 136 may be encoded (820) into one or more latent representations and then be provided to concatenation module 822. One or more oral care guide objects 308 may be encoded (818) into one or more latent representations and then be provided to concatenation module 822. In some implementations, one or more latent representations 502 which were generated by a prior stage of a cascaded ML model may be provided to concatenation module 822. Concatenation module 822 may concatenate, merge, sum, or otherwise combine one or more latent representations.

[0114] The flow matching technique may train a flow-based ML model by first computing individual conditional flows for each of a plurality of data samples 802 which are selected from atraining dataset, and then regressing a marginal predictive model by combining the conditional flows into an aggregated marginal flow. A flow may, in some implementations, include an aggregate vector field Vt. In some implementations, an aggregate vector field Vtmay include one or more multidimensional matrices of transformations (e.g., directional vectors, rotational vectors, etc.). In some implementations, an aggregate vector field Vtmay be described by one or more neural networks (e.g., encoder-decoder structures described herein, among others).

[0115] According to particular implementations, a vector field vt810 may be used to transform or modify a data sample (e.g., data corresponding to a 3D oral care representation, such as a latent representation of a 3D oral care representation), to implement the mapping from the first distribution to the second distribution (alternately, from a first distribution to the one or more additional distributions described above). The variable p is a time-variable function (e.g., which may change with the passage of time), called a probability density path. The path associated with a data sample may be described, at least in part, by a vector field vt810. The path travelled through a vector field vt810 may, in some implementations, include a flow Q. The flow Q at time t=0 is simply the original latent representation W 808, also denoted as W. In some implementations, W may be encoded in latent form, such as latent representation W 808. A latent representation may include one or more vectors of real values, categorical values, binary values, or the like. Latent representation W 808 may undergo modification by one or more vector fields vt810. Table 2 describes non-limiting examples of how vector fields vt810 or Vtmay be used to modify latent representation W 808, data sample 802, oral care guide object 308, or other data described herein. In some implementations, vector field vt810 or aggregate vector field Vtmay be applied iteratively to the input data to transform the input data from an initially simple or default configuration (e.g., a Gaussian distribution of mesh elements, etc.) to a more complex configmation. The resulting configmation of data describes one or more 3D oral care representations which me customized for use in patient treatment. In some implementations, vector field vt810 or aggregate vector field Vtmay be described by one or more neural networks.

[0116] One or more input data streams may be combined or concatenated by concatenation module 822. Concatenation module 822 may output one or more latent representations W 808, which are also denoted as W. The rate of change of the flow Q may, in some implementations, be described by an ordinary differential equation. Stated another way, each vector field vt810 determines how a data value within each data sample 802 is to "flow" at each parametric time t, between times t=0 and t=l. Techniques of this disclosure (e.g., the example method 800 of FIG. 8) may be used to train a machine learning model (e.g., neural networks - such as encoder-decoder structures) to generate a vector field vt810 which may be used to modify a data sample, and / or transform that data sample into a modified version of the data sample which has properties which are customized for use in oral care treatment (e.g., customized to the dentition of the patient). Examples of encoder-decoder structures include autoencoders, transformers, U-Nets, vision transformers (ViT), among others. Ordinary differential equation (ODE) solver 812 may generate ODE output 814. ODE output 814 may be used to updatevector field vt810. One or more vector fields vt810 may be regressed (or combined) to generate aggregated vector field Vt. In some implementations, aggregated vector field Vtmay used to flow (or modify) one or more data values (or latent vector dimensions) of latent representation W 808. In some implementations, method 800 may iterate. Stated another way, for the t=l iteration, the resulting modified latent representation may be provided to ODE Solver 812. ODE Solver 812 may output an updated ODE output 814. The updated ODE output 814 may be used to update (816) aggregated vector field Vt. In this manner, method 800 may, in some implementations, iterate until done. In some implementations, the stopping criterion may be specified by a maximum count of iterations specified in oral care arguments 136. Oral care arguments 136 may include tolerance values, step size values, or othervalues which may influence the operation of ODE Solver 812. In some implementations, method 800 may iterate until error drops below one or more threshold values (e.g., threshold values specified by oral care aiguments 136). In some implementations, error may be computed by applying aggregated vector field Vt(e.g., or an inverted version of aggregated vector field Vt) to latent representation W 808, and then using decoder 908 to reconstruct latent representation W into reconstructed 3D oral care representation 910. The resulting reconstructed 3D oral care representation 910 may be compared to the corresponding ground data. The corresponding ground truth data may be included within data sample 802 (e.g., which may include one or more 3D oral care representations). The error can be computed using loss calculation methods disclosed herein (e.g., reconstruction loss, etc.). In some implementations, reconstruction error may be computed and compared against one or more corresponding thresholds. As a result of the comparison, the stopping criterion may, in some implementations, be evaluated.

[0117] A fully trained continuous normalizing flow (CNF) <|>t 904 may be used after model deployment. CNF <|>t 904 may, in some implementations, use an inverted version of aggregated vector field Vtto modify input data. Latent representation x| / 0902 that has a simple distribution may be provided to CNF <|>t 904. The latent representation x| / 0902 may contain data which is drawn from a normal distribution, a random distribution, or another initial distribution. In some implementations, latent representation x| / 0902 may contain one or more latent representations of one or more 3D oral care representations. Such 3D oral care representations may be in an initial configmations, and are to be modified. Fully trained CNF <|>t 904 may output latent representation x| / t906, which may include a transformed or modified version of the latent representation x| / 0902 and / or of the data which are generated by concatenation module 822. Latent representation x| / t906 may contain one or more data values, which collectively are drawn from a more complicated distribution (a distribution which is more complex than the distribution from which latent representation x| / 0902 is drawn). Stated another way, the data values contained within latent representation x| / t906 may, in some implementations, contain a more information-rich signal than the data values in latent representation x| / 0902. Latent representation X| / t 906 may be provided to decoder 908, which may reconstruct the latent representation x| / t906 into one or more reconstructed 3D oral care representations 910. Examples of reconstructed 3D oral carerepresentations 910 include: 1) mesh elements of 3D representations; 2) mesh element labels for use in segmentation or mesh cleanup; 3) transforms for use in setups generation or the placement of hardware or appliance components relative to dentition; 4) 3D representations for use in the generation of fixture models, appliance components, or tooth restoration designs, or other 3D representations of oral care data; 5) oral care guide objects 308; 6) archforms; 7) tooth coordinate systems; or other 3D oral care representations described herein.

[0118] Encoder 806 and / or decoder 908 may, in some implementations, be trained as parts of a reconstruction autoencoder (e.g., a variational autoencoder that uses optional continuous normalizing flows, etc.). In some implementations, CNF <|>t 904 may apply aggregated vector field Vtto the input data (e.g., latent representation x| / 0902, and / or to the output of concatenation module 822). Oral care arguments 136 may be encoded (820) into one or more latent representations of oral care arguments, and then be provided to concatenation module 822. Oral care arguments 136 may provide values that guide the operation of CNF <|>t 904, such as one or more oral care metrics that define intended aspects of reconstructed 3D oral care representation 910, etc. Examples of such oral care metrics include Alignment, or Midline, among others described herein. In some implementations, one or more oral care guide objects 308 may undergo latent encoding (818), and then be provided to concatenation module 822. The one or more oral care guide objects 308 may include standard or default designs of 3D oral care representations (e.g., one or more tooth shells that have average shapes, etc.). The one or more oral care guide objects 308 may provide starting configurations for one or more 3D oral care representations which are to be generated (e.g., reconstructed 3D oral care representation 910, etc.). In some implementations, the CNF <|>t 904 may modify and / or flow the oral care guide objects 308 until the guide objects 308 is modified according to the specification of one or more oral care arguments 136. In some implementations, CNF fy 904 may be applied to its inputs iteratively, and thereby make successive modifications to those inputs.

[0119] In some implementations, the continuous normalizing flows-based ML models of this disclosure may be integrated into a cascade-based ML model (e.g., as described in the example method 100 of FIG. 1). When latent representation 502 from a prior stage of a cascaded ML model are available, those latent representation 502 may be provided to concatenation module 822. CNF fy 904 may operate, at least in part, based upon the latent representation 502. For example, oral care arguments 136 may specify that the CNF fy 904 is to generate a tooth shell for an upper right cuspid, where the tooth shell describes the boundary between the enamel and dentin. A guide object 308 (e.g., one or more tooth shells, etc.) may be provided to CNF fy 904 (e.g., a 3D mesh that is generated by averaging many examples of comparable 3D meshes drawn from a dataset of cohort patient case data, etc.). Latent representation 502 may be provided from a prior stage of a cascaded ML mode. Latent representation 502 may include the 3D mesh of the exterior of a tooth crown of the patient. CNF fy 904 may modify (or flow) oral care guide object 308 so that oral care guide object 308 takes on the shape and / or structure of a tooth shell that corresponds to the boundary between enamel and dentin. Further tooth shells (e.g.,corresponding to the boundary between dentin and pulp, etc.) may be generated, through the execution of further cascaded stages. The example method 900 show in FIG. 9 describes a possible ML model (among others described herein) which may be included within a generative module 118a-118n. CNF <|>t 904 may apply one or more vector fields Vtto the inputs, to modify those inputs. Table 2 describes how vt810 or Vtmay, in some implementations, be applied to assorted examples of 3D oral care representation. Combinations of the techniques described in Table 2 are also possible. In some implementations, oral care arguments 136 may include minimum or maximum modification thresholds (e.g., which may describe the magnitude of change to be applied to one or more data values, etc.), directional vectors, scaling factors, or other values which may influence the modifications that are described in Table 2.Table 2

[0120] The one or more samples from the second distribution q may characterize the entire flow between the two distributions. Alternately, the one or more samples from the additional distributions q0...qn may characterize the entire flow between the two distributions. Stated another way, a probability density path may be computed which is associated with each of the one or more samples from the second distribution q. The resulting one or more probability density paths for individual data samples (e.g., as described by vector fields vt810) may be aggregated, to generate an aggregate path.

[0121] A vector field vt810 or aggregate vector field Vtmay, in some implementations, describe incremental modifications which may be applied to a 3D oral care representation (or a latent representation of a 3D oral care representation) at each of a series of parametrized timesteps. In some implementations, a 3D oral care representation may be encoded into a latent representation (e.g., a latentvector of multiple elements). The vector field may describe modifications which may be applied to the dimensional elements of that latent representation vector. A vector field may, in some implementations, be implemented by a neural network (e.g., encoder-decoder structures such as transformers, autoencoders, U-Nets, etc.). In some implementations, a vector field may vary at each parameterized step between time t=0 and t=l. In some implementations, a vector field may vary with time. In other implementations, a vector field may be fixed and not vary with time (e.g., such as some instances where optimal transport is used to generate the vector field). For example, in some implementations, a vector field may be applied to an instant data sample (e.g., a latent vector that represents a 3D oral care representation such as a tooth restoration design, or a set of mesh element labels, etc.), where the modification applied by the vector field to the instant data sample at time t=n is different than the modification applied by the vector field to a substantially similar instant data sample at time t=n+l.

[0122] Flow matching may enable training of ML models which yields a reduced training time and an improved accuracy relative to prior techniques for training normalizing flows or denoising diffusion models. Flow matching may compute a flow (e.g., as described, at least in part, by one or more vector fields vt810 - such as parameterized vector fields which may vary with time) associated with one or more data samples 802 in a plurality of training data samples, and then aggregate the flows for the one or more data samples 802 into one or more aggregate flows (which may include one or more aggregate vector fields Vt). In some implementations, the techniques may use the vector fields vt810 associated with the one or more flows to generate one or more aggregate representations. For example, an aggregate representation may be generated by combining two or more vector fields in a manner that reveals the average distribution of the two or more vector fields. Techniques described herein may use the one or more aggregate representations to generate 3D oral care representations which are suitable for use in generating oral care appliances. Generative models (e.g., normalizing flows or diffusion models) which are used to generate or modify 3D oral care representations, examples of which are described herein, may be trained using flow matching. For example, flow matching may train normalizing flows (or diffusion) models to generate (or modify) orthodontic setups (e.g., which may comprise teeth and / or the transforms applied to those teeth), tooth restoration designs (e.g., which may be used in the generation of dental restoration appliances), oral care appliance component designs (e.g., for orthodontic or dental restorative treatment), mesh element labels (e.g., for segmentation or mesh cleanup), or other 3D oral care representations.

[0123] An ML model may be trained which describes a flow from a first distribution of oral care data to one or more second distributions of oral care data. In some implementations, oral care data in an initial configuration or state may be provided to a flow-based model (e.g., a neural network that describes a continuous normalizing flow). The flow-based model may generate a modified version of the provided oral care data. In some implementations, data which are distributed normally, uniformly, or randomly may be provided to the flow-based model. For example, the flow-based model may subsequently generate one or more 3D oral care representations. In some implementations, a pre-restoration tooth mesh (or other aspect of patient dentition) may be provided to a flow-based ML model, which may modify the mesh elements of the tooth mesh iteratively, until the 3D tooth mesh assumes a final shape that is suitable for restoration treatment of the patient (e.g., for use as a crown, a bridge, etc.) In some implementations, the 3D tooth mesh may be used in generating a tooth restoration appliance such as the FILTEK Matrix, etc. Stated another way, an aggregate representation or aggregate vector field Vtmay be iteratively applied to a latent representation of 3D oral care representation (e.g., including a tooth mesh, etc.), such as may be included in latent representation 902. The CNF cjrt 904 may, in some implementations, be iteratively applied until the tooth mesh takes on a final configuration or shape. The resulting latent representation 906 may be reconstructed using decoder 908. The reconstructed tooth mesh may be compared to a corresponding ground truth tooth mesh as a part of loss calculation. In some implementations, the resulting loss may be used to train, at least in part, a neural network which embodies the flow-based model (e.g., an encoder-decoder structure, etc.).

[0124] In some implementations, the flow-based model may generate one or more predicted smiles that include 2D representations (e.g., pixel-based images, etc.) or 3D representations (e.g., 3D meshes, etc.). For example, a 3D representation of the patient’s post-treatment dentition may be provided to the flow-based model as a part of data sample 802. In some implementations, 3D representations of this disclosure, such as 3D representations of the post-treatment dentition, may be projected into 2D form using optimized camera parameters (e.g., using ray tracing, etc.). The camera parameters may be generated using a genetic algorithm, or other optimization algorithm. The patient’s pre-treatment 2D photograph may likewise be provided to the flow-based model as a part of data sample 802. An image mask that corresponds to the area of the patient’s dentition in the pre-treatment photo may likewise be provided to the flow-based model as a part of data sample 802. Any of these inputs may be encoded into latent representations by representation generation modules (e.g., encoder 806, etc.). The flowbased model may generate one or more predicted smiles that combine the patient’s pre-treatment photo (or pre-treatment 3D representation, etc.) with the patient’s predicted post-treatment dentition (e.g., 2D or 3D dentition). The resulting predicted smile may be compared to corresponding ground truth posttreatment smile data as a part of loss calculation (e.g., using Huber loss, LI loss, L2 loss, etc.). The resulting loss may be used to train, at least in part, the flow-based model (e.g., diffusion model or normalizing flow, etc.). In some implementations, a vector field may be trained to modify the pixel values of a 2D image (e.g., for a predicted smile, etc.). Such a vector field can be used as a part of a continuous normalizing flow-based ML model to generate predicted smiles.

[0125] In some implementations the one or more second distributions may be estimated by first computing the individual flow associated with each of a plurality of data samples (e.g., samples of oral care data, such as pre-restoration tooth meshes, sets of mesh element labels for segmentation or mesh cleanup, fixture models, or transforms for use in orthodontic setup generation, or other 3D oral care representations described herein). An individual flow may be defined using one or more vector fields (e.g., time-varying vector fields - such as may be implemented by neural networks described herein),and may modify a 3D oral care representation, causing that 3D oral care representation to transition from a first configuration (or state) into one or more second configurations (or states). For example, a 3D representation of the patient’s dentition may be provided to a flow-based ML model (e.g., which may include one or more neural networks). The dentition may include 3D meshes for one or more tooth crowns, and / or the gums. The flow-based ML model may modify the dentition to generate one or more fixture model components, using the learned flow. Examples of fixture model components include bite ramps, gingival trim lines, or others described herein.

[0126] Oral care arguments 136 may be provided to ML models described herein to guide those ML models in the generation of 3D oral care representations which are customized to the treatment of the patient. For example, oral care metrics may be provided to define, at least in part, aspects of the target tooth shapes (e.g., for dental restoration design generation), or taiget tooth poses (e.g., for orthodontic setups). In further examples, oral care arguments 136 may include dimensional measurements that define target dimensions of fixture model components (e.g., the amount of interproximal webbing to apply between teeth, etc.), or of dental restoration appliance components (e.g., the thickness of a gingival trim surface, etc.). In some examples, oral care argument 136 may include clustering parameters (e.g., count of expected teeth) or other segmentation parameters. Segmentation parameters may inform the operation of a diffusion-based segmentation method (e.g., which predicts mesh element labels for one or more mesh elements of the patient’s pre-segmentation dentition, etc.). Segmentation parameters can include volume (or area) thresholds, curvature thresholds, smoothness parameters, geodesic distances (e.g., distance between two or more mesh elements through the connectivity of the 3D representation), or normal vector deviation thresholds. Diffusion-based segmentation methods can segment 3D meshes, voxelized 3D representations, or other 3D representations described herein.

[0127] One or more oral care arguments 136 may be provided to a flow-based model (e.g., by appending one or more values to an input vector that is provided to a neural network which defines the flow-based model). Oral care arguments 136 may describe one or more intended aspects of a 3D oral care representation which is generated (or modified) by the techniques of this disclosure. In turn, oral care arguments 136 may influence a model which is trained using flow matching to generate output which is customized to the treatment needs of the patient. For example, the oral care arguments 136 specify one or more aspects of one or more 3D oral care representations which are to be generated by the model (e.g., a model which is trained using flow matching). In some examples, oral care arguments 136 may specify aspects of one or more fixture model components which are to be generated from the patient’s dentition meshes. The one or more generated 3D oral care representations may subsequently be used in the generation of one or more oral care appliances (e.g., aligner trays, restorations, dental restoration appliances, or others disclosed herein). Examples of oral care arguments 136 include oral care metrics (as described herein), orthodontic procedure parameters (as described herein), dental restoration parameters (as described herein), doctor preferences (as described herein), dental restorationpreferences (as described herein), or other values which describe intended attributes of 3D oral care representations or oral care appliances which are generated according to techniques of this disclosure (e.g., methods 100, 200, 1000, 600 or 900, among others ). Oral care arguments 136 may, in some instances, describe aspects of the dimensions, appearance, or medical functionality of an oral care appliance, and may be used to customize the oral care appliance to the treatment needs of the patient. For example, an oral care metric (e.g., the dental restoration metric “Embrasure”, etc.) may be provided to a setups prediction model, which specifies that a generated orthodontic setup is to have a gap between two specified teeth (at either of the gingival or incisal edges) which is of a specified number of millimeters. In other examples, an oral care metric (e.g., Shade and / or Translucency) may be provided to techniques of this disclosure (e.g., methods 100, 200, 1000, 600 or 900, among others) which specifies that a generated tooth restoration design (e.g., a layered restoration design) is to have a specified translucency (e.g., which can be implemented using a combination of layers within a tooth restoration design, where different layers have particular translucencies and shades). Oral care arguments 136 may specify how many layers of tooth shells are to be included in a layered tooth restoration design.

[0128] Examples, of oral care appliances include clear tray aligners (CTA), indirect bonding trays or digital bonding trays (DBT), dental crowns, bridges, partials, dentures, orthodontic brackets (e.g., which may have a custom generated shape, or an automated placement on the teeth), retainers, palatal expanders (e.g., for treating crossbite), mouth guards for treatment of sleep apnea or the grinding of teeth during sleep, custom arch wires, dental restoration appliances (e.g., FILTEK Matrix, etc.), or the like. An archwire may conform to the alveolar or dental arch, and / or may apply force to orthodontic hardware which is attached to the teeth during orthodontic treatment. In some implementations, a flowbased model which has been trained using flow matching (e.g., using method 800) may generate transforms for the placement of 3D representations of oral care data (e.g., tooth meshes, oral care appliances, oral care appliance components, oral care hardware, etc.). Oral care hardware may include lingual brackets, labial brackets, buttons, hooks, temporary anchorage devices (TADS), etc.

[0129] Some implementations of the diffusion models of this disclosure may generate 3D representations of oral care data by denoising volumetric radiance fields. A 3D volumetric radiance field may include a volumetric space contains one or more voxels (e.g., possibly hundreds, thousands or millions, though greater counts are possible). A denoising ML model may be trained to denoise an initially randomly configured volumetric radiance field space, and over one or more iterations of the denoising reverse pass 704, to rearrange and / or relabel the voxels within that radiance field so that the voxels come to describe one or more 3D representations of oral care data (e.g., a trimline, a tooth restoration design, or other examples described herein).

[0130] In some implementations, a 3D oral care representation (e.g., an aspect of the patient’s dentition, such as a pre-treatment tooth, etc.) in an initial state may be provided to a flow-based model. The flow-based model may apply CNF <[>t 904 to modify the 3D oral care representation, and output areconstructed 3D oral care representation 910 in a final or post-treatment state (e.g., a tooth restoration design which describes the post-restoration state of a tooth, etc.).

[0131] In some implementations, an oral care guide object 308 may be provided as input to a flowbased model. One or more aspects of the patient’s dentition (e.g., the teeth and / or gums) may be provided to the flow -based model. The flow-based model may use apply CNF <|>t 904 to modify the oral care guide object 308, and output a 3D oral care representation in a final or post-treatment state. For example, a guide object tooth shell (e.g., which describes the boundary between two or more regions of a tooth) may be provided to CNF <|>t 904. The flow-based model may modify the guide object 308 to be compatible with the provided patient dentition. Stated another way, the flow-based model may modify the oral care guide object 308 to modify the guide object to be customized to the patient’s dentition. For example, a generic guide object tooth shell may undergo modification of size, shape, and / or pose so that the shell does a good job approximating a tooth shell which is interior to a 3D mesh of a tooth crown. This example of a flow-based method may generate one or more tooth shells, which collectively comprise a layered tooth restoration design.

[0132] Examples of oral care guide objects include 1) lattice of edges and / or vertices which describe a deformation of a 3D mesh; 2) 3D representation of a generic tooth restoration design (or tooth shell) which is drawn from a library of such 3D representations and / or is to be modified to be compatible with the patient’s dentition; 3) 3D representation of a generic oral care appliance, appliance component, hardware element, or fixture model component which is drawn from a library of such 3D representations; 4) a set of default mesh element labels which may be used as the starting configmation for mesh segmentation or mesh cleanup; or 5) other generic versions of 3D oral care representations which are to be modified by generative techniques of this disclosure, or the like.Transformer-based model

[0133] In some implementations, the generative transformer-based ML model of method 1000 may be trained on a dataset of 3D oral care representations. In some implementations, the 3D oral care representations of the training dataset may include fixture model component data. Method 1000 may be trained to generate (or modify) digital fixture model components (examples of which are described herein) or digital fixture models. Oral care arguments 136 may be provided to generative transformer module 1018, or other modules of method 1000. Oral care arguments 136 may enable generative models of this disclosure to generate output which is customized for the patient’s dentition, or which is customized to the treatment instructions (or prescription) provided by clinicians. For example, oral care arguments 136 may enable customization of the generated (or modified) fixture models. For example, a generative transformer module 1018 may be trained to generate (or modify) a 3D oral care representation, such as a fixture model component (e.g., a digital trim line, or others digital representations described herein). In some examples, training dataset of cohort patient case data contains patient dentition data, which may be included in 3D input data 424.

[0134] Oral care arguments 136 may influence the output of generative models of this disclosure. In some implementations, the generative models may be trained iteratively. The training of one or more generative models may include generating one or more partially trained generative models based at least in part on output generated by one or more previous iterations of training of the one or more generative models.

[0135] The patient case data (which is included in input data 424) may be provided to ML models of this disclosure in order to generate one or more orthodontic setups. For each intermediate stage, and / or the final setup, a digital fixture model can be generated. One or more digital fixture model components may be generated by generative transformer module 1018. For example, generative transformer module 1018 may generate a digital gingival trimline, which defines a cutting path. The digital trimline may be used to guide a cutting tool, which may be used to remove a thermoformed aligner tray from the physical 3D version of the fixture model. The physical fixture model may be 3D printed by providing the digital fixture model to a 3D printer. In some implementations, one or more instant patient data 416 (e.g., or other 3D oral care representations) to be modified may be provided to one or more components of method 1000. The one or more instant patient data 416 (e.g., or other 3D oral care representations) may be provided to encoder 508, which may output one or more latent representations. The one or more latent representations may be provided to generative transformer module 1018. Generative transformer module 1018 may modify the one or more 3D oral care representations (e.g., an incomplete fixture model which requires the addition of a bite ramp, or other fixture model component, etc.).

[0136] The patient case data (which is included in input data 424) may also include ground truth (or reference) data. For example, a ground truth trim line, or a ground truth patient dentition that has an attached bite ramp. Loss may be computed by quantifying the difference between the generated 3D oral care representation! 024 (e.g., a representation which has been reconstructed by decoder 1020) and the corresponding ground truth data. Optional mesh element features for the patient case data (which is included in input data 424) using a mesh element feature module 1004.

[0137] The patient case data (which is included in input data 424) may be provided to a hierarchical neural network feature extraction module (HNNFEM) 1006, which may generate a latent representation 1012 of the case data 424. Such a latent representation 1012 may contain global, intermediate, or local neural network features. In some implementations, spectral encoding module 1026 may encode the patient case data (which is included in input data 424) into vector of spectral frequencies 1014. One or more of representations 1010 may include latent representation 1012 and / or vector of spectral frequencies 1014. In some implementations, encoder 508 can perform latent encoding on the vector of spectral frequencies 1014. The one or more representations 1010 may be provided to latent representation modification module (LRMM) 1016. LRMM 1016 may modify the one or more representations 1010, according to the specification of one or more oral care arguments 136. An example of such modification is to cause one or more bite ramps to form on the lingual surfaces of one or moreteeth in the digital fixture model, to ease the release of the thermoformed aligner tray from the physical fixture model. Generally, the oral care arguments 136 may cause generative transformer module 1018 to modify the patient’s dentition in a fashion which is intended to bring about a desired shape and / or structure to the generated (or modified) 3D oral care representation 1024.

[0138] In some implementations, the output of LRMM 1016 may be provided to generative transformer module 1018, which may output one or more modified latent representations. The one or more modified latent representations may be reconstructed by decoder 1020. Decoder 1020 may output one or more generated (or modified) 3D oral care representations 1024. In some implementation, one or more latent representations 1028 may be provided to one or more subsequent stages of a cascaded ML model.

[0139] The example method 1100 shown in FIG. 11 depicts the use of a fully trained generative module which includes an autoencoder for layered restoration design generation. In some implementations, input data 424 or latent representation 502 generated by a prior stage of a cascade may be provided to the encoder-decoder structure of FIG. 11. Oral care arguments 136 may be encoded (1130) into one or more latent representations 1126 of oral care arguments. Input data 424 may include patient dentition data or other 3D oral care representations, etc.). The inputs may be encoded by fully trained encoder 1110, the resulting latent representation 1114 may, in some implementations, be combined with the latent representations 1126 of oral care arguments, and / or then be reconstmcted by fully trained decoder 1116. In some implementations, the resulting reconstructed representation 1118 (e.g., a generated 3D printing support structure, etc.) may be provided to the generated output 1024 (e.g., layered tooth restoration design, 3D printing support structure(s), fixture mode, appliance component, or other 3D oral care representation, etc.). In some implementations, the resulting reconstructed representation 1118 may be encoded (1120) into one or more latent representations 1028, to be provided to the next stage of a cascade. Selector module 1106 may be configured to multiplex or reroute one or more input data streams to the output, according to the specification of oral care arguments 136.

[0140] The generated latent representation may be reconstructed using decoder 1020 into a 3D oral care representation which is suitable for use in oral care appliance generation. For example, the generated latent representation may be reconstructed using decoder 1020 into one or more generated (or modified) digital pontic teeth. Either or both of the generated (or modified) digital pontic teeth may be compared to corresponding ground truth or reference digital pontic teeth, to compute one or more loss values. Losses include LI, L2, cross-entropy or other losses described herein. Such loss (or losses) may be used to train (e.g., using backpropagation), at least in part, one or more of HNNFEM 1006, generative transformer module 1018, or decoder 1020.

[0141] ML models of this disclosure may be trained, at least in part, using loss functions which quantify the difference between predicted values, and corresponding ground truth values. Examples include LI loss, L2 loss, mean squared error (MSE) loss, cross entropy loss, softmax loss, multiplenegatives ranking loss, MSE margin loss, KL-divergence loss, reconstruction loss, Huber loss, Hinge loss, Categorical hinge loss, cosine similarity, Poisson loss, Logcosh loss, mean squared logarithmic error loss (MSLE), Earth mover’s distance, chamfer distance, or the like. Cross entropy may, in some implementations, be used to quantify the difference between two or more distributions. MSE loss calculation may involve the calculation of an average squared distance between two (or more) sets, vectors or datasets. A KL-Divergence loss may be used, at least in part, to train one or more of the neural networks of the present disclosure, such as a mesh reconstruction autoencoder, with the advantage of imparting Gaussian behavior to the optimization space.

[0142] Reconstruction error may quantify the accuracy with which the original input data may be reconstructed by techniques of this disclosure. Systems of this disclosure may compute reconstruction error as a combination of LI loss and MSE loss, as shown in the following line of pseudocode: reconstruction error = 0.5*Ll (all_points_target,all_points_predicted) + 0.5*MSE (all_points_target,all_points_predicted). All points target may include a point cloud corresponding to a ground truth tooth restoration design (or a ground truth example of some other 3D oral care representation). All_points_predicted may include a point cloud corresponding to a generated example of a tooth restoration design (or a generated example of some other kind of 3D oral care representation).

[0143] Reconstruction loss may quantify the difference between one or more reconstructed 3D representations which is generated by ML models of this disclosure, and one or more corresponding ground truth 3D representations. In some implementations, reconstruction loss may compute one or more aspects of reconstruction error. Systems of this disclosure may compute reconstruction loss as a combination of LI loss and MSE loss, as shown in the following line of pseudocode: reconstruction loss = 0.5*Ll(all_points_target,all_points_predicted) + 0.5*MSE(all_points_target,all_points_predicted). In the above example, all_points_taiget is a 3D representation (e.g., a 3D mesh or point cloud) corresponding to ground truth data (e.g., a ground truth tooth restoration design, or a ground truth example of some other 3D oral care representation). In the above example, all_points_predicted is a 3D representation (e.g., a 3D mesh or point cloud) corresponding to generated or predicted data (e.g., a generated tooth restoration design, or a generated example of some other kind of 3D oral care representation). Other implementations of reconstruction loss may additionally (or alternatively) involve L2 loss, mean absolute error (MAE) loss or Huber loss terms.

[0144] Ground truth labels, or other ground truth data may include accurate, verified data used to train and evaluate an ML model.

[0145] In some implementations, a discriminator may be used to train, at least in part, one or more of these modules (e.g., generative transformer module 1018).

[0146] In some implementations, one or more oral care guide objects (e.g., a guide object bite block which is to be modified, which is drawn from a library of guide object parts, etc.) may be providedto method 1000. The one or more oral care guide objects 308 may undergo latent encoding using encoder 508, and then be provided to generative transformer module 1018.

[0147] In some implementations, latent representation 502 may be provided to generative transformer module 1018. Latent representation 502 may contain information from a prior stage of a cascaded ML module (e.g., as described by method 100). For example, when the method 1000 is used to generate a layered tooth restoration design, the latent representation 502 may contain one or more latent representations of the stage n-1 concentric tooth shell.

[0148] In some implementations, an ML model for TSO can be applied to Generative Design (GD) of custom orthodontic appliances, custom fixture models, tooth restoration designs (e.g., for use in crowns or dental restoration appliances), or the like. ML models of this disclosure may be trained for GD include example methods 100, 500, or 800 (among others). In particular, the example methods may be used to generate custom digital designs for these 3D representations of oral care data. The methods may generate designs which have been optimized for 3D printing (e.g., through the inclusion of optimally generated 3D printing support structures, etc.).

[0149] Some techniques of this disclosure may optimize the designs of 3D printing support structures (e.g., temporary support structures used during the printing process). Those techniques may optimize for minimum deflection of the 3D printing material. Some techniques of this disclosure may optimize other aspects of 3D printed objects, for example, the shapes and / or stmctures of the objects after 3D printing is completed, and / or during clinical use. For example, oral care appliances may be generated which apply predefined loads, and / or exhibit desired deflections of the material during use. For example, techniques of this disclosure may generate designs for oral care appliances which exert custom forces on the patient’s dentition during treatment (e.g., orthodontic aligner trays, retainers, palatal expanders, or the like). The techniques may customize which one or more 3D locations within the patient’s dentition are acted upon by customized force vectors.

[0150] Orthodontic appliances may store eneigy, and / or do work on the patient’s teeth by moving the teeth in prescribed directions. This means that various parts of the appliance may apply forces in predefined directions over predefined distances. In some implementations, each force may be described by one or more vectors. Each moment may be described by a pair of vectors forming a couple. The distances or angles over which these forces act correspond to deflections of one or more of the materials which are included in the orthodontic appliance. Collectively, these forces and moments comprise a system of physical loads on the orthodontic appliance. The shape and / or structure of the appliance may be customized so that the appliance is manufacturable and / or has sufficient structural strength during clinical use. For example, the appliance may be designed so as not to occupy the same space as one or more teeth. Furthermore, the appliance thickness can be designed to be within one or more thresholds, and / or to be within a defined offset from the tooth surfaces. Applied loads may be describes, at least in part, by one or more contact points on the tooth surfaces.

[0151] A 3D representation of oral care data (e.g., one or more 3D meshes of an appliance, or one or more 3D meshes of 3D printing supports) or other digital workpieces. A digital workpiece may be provided to a module which performs FEA. The FEA module may generate one or more FEA maps which describe forces, moments, strains, or stresses (among other characteristics of a mechanical system) of the digital workpiece. According to various examples, an FEA module may generate stress maps, strain maps, deflection maps, or the like. Such a map may include voxels. Each voxel may have one or more associated values which are associated with forces or moments (e.g. stress, strain, or deflection magnitudes and / or directions). In some implementations, a patient’s 3D dentition, and / or a 3D representation of an appliance may be provided to an FEA module, and the FEA module may quantify forces and / or moments which the appliance applies to the patient’s dentition.

[0152] In some implementations, ML models of this disclosure (e.g., methods 100, 200, 1000, 400, 500, or 800, etc.) may generate predictions one or more loads to be applied to one or more teeth, such that the applied loads cause the desired tooth movements (e.g., tooth movements which are warranted to move the teeth into predicted final setup poses). In some examples, a predicted load may include the locations, directions and / or magnitudes of one or more forces or moments which are applied to the dentition by an appliance (e.g., an aligner tray, etc.). Each stage of a treatment plan may include a pose (e.g., target position and / or orientation) of each tooth for an iteration of treatment. Affine transforms may move the teeth from the teeth’s current poses to the teeth’s target poses. A 3D Affine transform may include a translation and / or a rotation. The translation may correspond to a force. The rotation may correspond to a moment. Considering reaction forces from the tooth's root and periodontal ligament (PDL), a force and / or a moment can be applied to the crown to cause forces to be transmitted to the root. The forces transmitted to the root may cause bone remodeling due to stresses on the PDL (e.g., via an inflammatory response that drives activity in certain types of white blood cells, e.g., osteoclasts and osteoblasts).

[0153] In some implementations, one or more FEA maps may be provided to an ML module which has been trained for 3D oral care representation generation (e.g., generating 3D printing support structures, or oral care appliances). In some implementations, the one or more FEA maps may be provided to an encoder 508, which may encode the maps into one or more latent representations (e.g., latent FEA maps). The latent FEA maps may be provided to the ML module which has been trained to generate 3D oral care representations. Stated another way, an FEA map (or a latent representation of an FEA map) may be provided to generative ML modules described herein (e.g., methods 100, 200, 1000, 400, 500, or 800, etc.), to customize the outputs which are generated by those modules. This customization may enable generated digital workpieces to be customized to the treatment needs of the patient. For example, the techniques may customize forces which are to be applied by an appliance to the patient’s dentition, or the techniques may customize the design of 3D printing supports such that the 3D printing supports prevent significant deflection (e.g., deflection beyond a threshold number of microns, etc.) of the physical workpiece during 3D printing.

[0154] This makes appliance design a suitable application for automated design generation techniques of this disclosure, because appliance generation can include TSO. Automated appliance generation and / or the automated generation of temporary support structures are both examples of TSO. The automated design generation techniques of this disclosure may generate appliance designs which precisely specify where 3D printing material (e.g., resin, etc.) is to be deposited by a 3D printing nozzle, to customize appliance deflections. The appliance deflections may be customized to point along prescribed vectors, and / or to be associated with prescribed magnitudes of force. The locations of forces, magnitudes of forces, and / or desired directions of forces may be provided as inputs to the ML models of this disclosure.

[0155] In some implementations, one or more dimensional thresholds may be provided to an ML model with has been trained for the generation of 3D oral care representations, such as oral care appliances. Examples of oral care appliances include dental restoration appliances, clear tray aligners (CTA), retainers, or mouth guards. An oral care appliance may include one or more inner surfaces which are shaped, at least in part, based upon the clinical surfaces of the patient’s dentition. The outer surface of such an appliance may, in some instances, include portions which are uniformly offset from the inner surface by a thickness that corresponds a one or more dimensional thresholds. A dimensional threshold may be configmed to generate an appliance which is comfortable, and / or aesthetically acceptable for the patient (e.g. Q millimeters).

[0156] In some instances, a doctor’s instructions may include the specification of one or more fixed teeth in the course of orthodontic treatment. Stated another way, a treatment plan may specify one or more teeth to remain fixed in their respective mal poses throughout the course of orthodontic treatment. For example, a treatment plan may specify that the molars are to remain fixed during orthodontic treatment using aligners. An aligner may use the fixed teeth as anchors, and / or push against the fixed teeth, so as to resolve crowding, improve aesthetics, or to improve masticatory function of the anterior teeth (among other examples). When one or more teeth are designated to be “fixed” (e.g., when molars are designed to remain in their mal poses), the thickness of an oral care appliance may be customized to suit the treatment needs of the patient. For example, more material may be concentrated around the molars, thereby adding structural rigidity to the oral care appliance (e.g., an orthodontic aligner, etc.), preventing relative movement between the molars, and / or providing anchorage (or reaction forces) to neighboring teeth that need to move according to treatment goals. A deflection threshold may specific a maximum or minimum deflection of one or more aspects of an oral care appliance. When a deflection limit is set to zero millimeters (or nearly zero millimeters), then the generative ML models described herein may generate an appliance geometry wherein the appliance experiences little or substantially no deflection in the segment of the appliance corresponding to the deflection limit of zero (although de minimis deflection may still occur according to particular implementations). The generated appliance design may include relatively thicker portions, portions which are thick enough to resist significant deformation in the vicinity of one or more fixed teeth. Forexample, the appliance may approach the limit associated with one or more dimensional thresholds (e.g., a thickness of W millimeters), because for real materials any force greater than zero may result in a greater than zero deflection. It is therefore preferable to establish an acceptable deflection threshold (or deflection limit, or tolerance), that is greater than zero to allow for some degree of topology optimization, e.g., 0.05 millimeters. In this case, the thickness of the appliance surrounding the molars might be reduced to a minimally sufficient S millimeters (e.g. 1.5 millimeters, among other values) in some areas. In some instances, the appliance may include thin spots or holes where no material is needed to resist deformation. For example, the appliance in these areas might resemble an open truss structure or porous bone.

[0157] For the segments of the dental arch in which teeth are prescribed to move, such as in the anterior region of the dental arch, the one or more loads may be specified (e.g., as a part of a treatment plan, or clinician’s instructions). The one or more loads may be specified to achieve the orthodontic treatment goals for one or more teeth. The orthodontic treatment goals may include one or more intended movements. Such movements are the result of forces and / or moments which are exerted by the appliance on the teeth. One or more physical forces (e.g., including direction, magnitude, and / or location) may be provided as inputs to the generative ML models described herein.

[0158] An advantage particular to this disclosure is to provide prescribed deflection limits for one or more regions of the appliance to the generative ML models of this disclosure (e.g., denoising diffusion ML models, etc.). The result is a more accurate treatment plan, which renders the generative ML models more capable of handling such constraints than conventional techniques. An appliance may perform work (e.g. work equals force times displacement) on teeth in order to move the teeth. In this way, the deflection of the appliance material may be optimized. Stated another way, the appliance may be generated so that certain amounts of both force may be applied to corresponding portions of the appliance, resulting in corresponding deflections. The generative ML models of this disclosure may generate an appliance which has a geometric structure that allows for the deflection in one or more particular areas of interest within the appliance (e.g., as defined by the treatment plan). In some implementations, dimensional thresholds may be provided to the generative ML models described herein. The target poses of the teeth may be provided to the ML models. The ML models may predict one or more forces (or moments) which may be applied to the teeth to carry out orthodontic treatment.

[0159] An FEA map may describe one or more the physical properties (stresses, strains, forces, etc.) of one or more materials which form a 3D representation of oral care data. For example, a digital layered tooth restoration design may include regions which correspond to two or more different materials in the physical article (e.g., a physical crown or veneer which includes two or more composite materials, etc.).

[0160] One or more forces may be applied to a digital 3D representation of an appliance (or other 3D representation of oral care data), and FEA may generate one or more FEA maps which quantify the resulting stress or stain (among other properties) on the patient's dentition. Such FEA maps may beprovided to ML models described herein, enabling those ML models to optimize the designs of generated outputs (e.g., optimize generated tooth restoration designs, appliance components, fixture model components, etc.). In some implementations, such as the example method 100 of FIG. 1, one or more ground truth FEA maps may be included in ground tmth data 106a-106n (included within ground truth data 104). The ground truth data may be compared to corresponding generated data 120a-120n, as a part of loss calculations (112a-112n). The resulting losses may be used to train, at least in part, one of more generative modules 118a-118n.

[0161] In some implementations, an oral care appliance may be combined with one or more aspects of the patient’s dentition, and then the combined 3D representations may be provided to an FEA module for analysis. For example, a 3D representation of an aligner tray may be combined with a 3D representation of teeth which the aligner tray is designed to move, or upon which to exert force. The combined 3D representations may be provided to an FEA module, which may quantify aspects of the force (or strain, or stress, etc.) applied by the aligner tray to the patient’s dentition. Such an FEA analysis may be performed on ground truth data, and / or then the resulting one or more FEA maps may be provided to an encoder. The encoder may generate one or more latent representations of the one or more FEA maps of ground truth data. Similarly, an FEA analysis may be performed on generated data, and / or then the resulting one or more FEA maps may be provided to an encoder. The encoder may generate one or more latent representations of the one or more FEA maps of generated data.

[0162] Loss may be computed (112a-112n) between the one or more latent representations of FEA maps of ground truth data 106a-106n, and the one or more latent representations of the one or more FEA maps which are generated through the analysis of generated data 120a-120n. The resulting loss may be used to train, at least in part, one or more of generative modules 118a-118n to generate aligner tray designs (or other 3D representations of oral care data). The modules may generate aligner tray designs which exert customized forces on one or more teeth of the patient’s dentition, and / or cause the dentition to experience strain or stress which is within tolerance of one or more thresholds included within oral care arguments 136. For example, customized forces may be generated to move the patient’s teeth into poses which are indicated by a treatment plan, and / or are indicated by the needs of clinical or esthetic treatment.

[0163] In some instances, ground truth 3D data (or other input data, or generated 3D data) described herein may be decimated, to reduce the complexity and / or data structure size of the respective 3D representations. Decimation may reduce the computational burden of comparing meshes during loss calculation, or other operations. In some implementations, the ground truth data (or other input data, or generated data) described herein may be converted to one or more reference connectivities. A reference connectivity may standardize the data structures that described geometrical aspects of a 3D representation (e.g., an incisal edge or facial surface of a tooth, or a geometrical aspect of an appliance component, etc.). A reference connectivity may standardize which range of values within a vector or matrix representation describe which geometric aspects of a 3D representation. Referenceconnectivities may improve the accuracy of loss calculation, because reference connectivities may facilitate the comparison of corresponding portions of two or more representations.

[0164] The example method 1200 of FIG. 12 describes a method of generating one or more FEA maps which describe the interactions of two or more 3D representations of oral care data. Ground truth data 104 may include one or more transforms to register first 3D representation of oral care data 1202 with second 3D representation of oral care data 1204 (e.g., appliance, fixture model, or other digital workpiece). The one or more transforms may be used to combine (1206) first 3D representation of oral care data 1202 with second 3D representation of oral care data 1204. In some examples, the first representation 1202 may include the patient's 3D dentition, and / or the second representation may include one or more 3D representations of a ground truth appliance. One or more forces may be estimated (1208), such as forces applied by the second representation 1204 on the first representation 1202. A force may include a direction, a magnitude, and / or a location upon which the force acts. In some implementations, mesh collisions (or overlaps) between second representation 1204 and first representation 1202 may be generated using techniques known to one skilled in the art. The overlaps between meshes may be used to estimate forces. For example, forces may be estimated based upon the magnitude of overlap of two or more meshes. When two meshes overlap by a larger magnitude (e.g., volume of overlap, cross-sectional area of overlap, or maximum penetration depth, etc.) then the magnitude of force may be estimated as larger. When two meshes overlap by a smaller magnitude, then the magnitude of force may be estimated to be smaller. Direction of force may be estimated by (e.g., by averaging the normal vectors of the overlapping surfaces, among other techniques). Location of the application of the force may be estimated by the centroid of the overlapping volume, among other examples. The one or more predicted forces 1210 may be provided to FEA module 1212. The combined (or registered) 3D representations of oral care data may be provided to FEA module 1212. FEAmodule 1212 may generate one or more FEA maps 1214.

[0165] The example method 1300 of FIG. 13 describes a method of generating one or more FEA maps which describe the effects of one or more forces (e.g., the downward force of gravity, among others) on a 3D representation of a digital workpiece 1302 and / or 3D printing supports associated with the digital workpiece. Forces may be estimated (1208), such as a uniformly downward force of gravity. The one or more predicted forces 1210 may be provided to FEA module 1212, which may generate one or more FEA maps. In some instances, such an FEA map may describe, at least in part, how well the one or more 3D printing support structures enable the physical workpiece to resist the pull of gravity during the 3D printing process. In some instances, an incomplete portion of the digital workpiece 1302 (and / or associated 3D printing support structures) may be provided to FEA module 1212. For example, the first R layers of the digital workpiece 1302 (and / or associated structures) may be provided to FEA module 1212, to enable FEAmodule 1212 to evaluate how well the digital workpiece 1302 is supported while 3D printing is underway.

[0166] The example method 1400 of FIG. 14 describes a method of computing loss. One or more ground truth 3D representations of oral care data 1402 may be provided to encoder 210, which may generate one or more latent representations of the ground truth data. One or more generated 3D representations of oral care data 1404 may be provided to encoder 210, which may generate one or more latent representations of the generated data. A difference may be computed (1406) between the respective latent representations of ground truth data 1402 and / or generated data 1404. Mean squared error, cross entropy, or other loss calculation methods may be used to compute this difference. The method may output one or more loss values 1408.

[0167] The example method 1500 of FIG. 15 describes a method of computing loss whichinvolves FEA maps. Method 1500 operates similarly to method 1400, except that one or more FEA maps may be compute (1502). Example methods 1200 or 1300 may be used to compute the FEA maps, among other examples.

[0168] 3D oral care representations may include, but are not limited to: 1) a set of mesh element labels which may be applied to the 3D mesh elements of teeth, gums, hardware, or appliance meshes (or point clouds) in the course of mesh segmentation or mesh cleanup; 2) 3D representations) for one or more teeth, gums, hardware, or appliances for which shapes have been modified (e.g., trimmed, distorted, or filled-in) in the course of mesh segmentation or mesh cleanup; 3) one or more coordinate systems (e.g., describing one, two, three or more coordinate axes) for a single tooth or a group of teeth (such as a full arch - as with the LDE coordinate system); 4) 3D representation(s) for one or more teeth for which shapes have been modified or otherwise made suitable for use in dental restoration; 5) 3D representation(s) for one or more dental restoration appliance components; 6) one or more transforms to be applied to one or more of: dental restoration appliance library component placement relative to one or more teeth, a tooth to be placed for an orthodontic setup (either final setup or intermediate stage), a hardware element to be placed relative to one or more teeth or the like; 7) an orthodontic setup; 8) a 3D representation of a hardware element (such as facial bracket, lingual bracket, orthodontic attachment, button, hook, bite ramp, etc.) to be placed relative to one or more teeth, etc.; 8) a 3D representation of a bonding pad for a hardware element (which may be generated for a specific tooth by outlining a perimeter on the tooth, specifying a thickness to form a shell, and then subtracting-out the tooth via a Boolean operation); 9) 3D representation of a clear tray aligner (CT A); 10) the location or shape of a CTA trimline (e.g., described as either a mesh or polyline); 11) archform that describes the contours or layout of an arch of teeth (e.g., described as a 3D polyline or as a 3D mesh or surface), which may follow the incisal edges one or more teeth, which may follow the facial surfaces of one or more teeth, which may in some implementations correspond to the maloccluded arch and in other implementations correspond to the final setup arch (the effects of malocclusion on the shape of the archform may be diminished by smoothing or averaging of the shape of the archform), which may be described by one or more control points and / or a spline; 12) 3D representation of a fixture models (e.g., depictions of teeth and gums for use in thermoforming clear tray aligners, or depictions of teeth, gums,or hardware for use in thermoforming indirect bonding trays); 13) one or more latent space vectors (or latent capsules) produced by the 3D encoder stage of a 3D autoencoder which has been trained on the reconstruction of oral care meshes (e.g., a variational autoencoder which has been trained for tooth reconstruction); 14) one or more oral care metrics values (e.g., such as orthodontic metrics or restoration design generation metrics) for one or more teeth; 15) one or more landmarks (e.g., 3D points) which describe the shapes and / or geometrical attributes of one or more teeth, other dentition structures or hardware structures (e.g., to be used in orthodontic setups creation or restoration appliance component generation or placement); 16) 3D representation created by scanning (e.g., optically scanning, CT scanning or MRI scanning) a 3D printed part corresponding to one or more teeth, gums, hardware, or appliances (e.g., a scanned fixture model); 17) 3D printed aligners (including optionally local thickness, reinforcing rib geometry, flap positioning, or the like); 18) 3D representation of the patient's dentition that was captured chairside by a clinician or medical practitioner (e.g., in a context where the 3D representation is validated chairside, before the patient leaves the clinic, so that errors can be detected and re-scans performed as necessary); 19) dental restoration tooth design (e.g., for veneers, crowns, bridges or dental restoration appliances); 20) 3D representations of one or more teeth for use in digital oral care treatment; 21) other 3D printed parts pertaining to oral care procedures or other fields; 22) IPR cut surfaces; 23) one or more orthodontic setups transforms associated with one or more IPR cut surfaces; 24) a (digital) pontic tooth design which may fill at least a portion of the space between teeth to allow room in an orthodontic setup for an erupting tooth to later emerge from the gums; or 25) a component of a fixture model (e.g., comprising fixture model components such as interproximal webbing, block-out, bite locks, bite ramps, interproximal reinforcement, gingival ridges, torque points, power ridges, pontic tooth or dimples, among others).. In some instances, 3D oral care representations may include a prediction of a patient’s smile, which may show the post-treatment teeth, lips, cheeks, nose, and / or other facial features in relation to each other. In implementations where 3D oral care representations include a prediction of a patient’s smile, the predictions may be presented in several formats, including as 2D images or as 3D representations.

[0169] In some instances, techniques of this disclosure may generate a determination based upon analysis of the patient’ s dentition data that oral care treatment is warranted. The patient’ s dentition data can be presented in several formats, including 2D (e.g., images) or 3D (e.g., meshes, voxels, or point clouds, etc.) representations. In some instances, a determination that oral care treatment is warranted can be based, at least in part, on the presence of one or more restoration indications (as described in more detail elsewhere). Oral care treatments can include automated restoration design generation, automated setups generation, automated fixture model generation, automated mesh segmentation or mesh cleanup, automated coordinate system generation, or others described herein.

[0170] Examples of restoration indication labels include: 1) whether a dark triangle exists between a first tooth and a second tooth; 2) whether a gap exists between a first tooth and a second tooth; 3) whether a target tooth has an uneven incisal edge; 4) whether two or more adjacent teeth have incisaledges that are uneven relative to each other; 5) whether a target tooth has decay (e.g., hypoplastic decay or another type of decay); 6) whether a target tooth has a chip; 7) whether a target tooth has a damaged or broken-down filling; 8) whether a target tooth is too small (e.g., a peg lateral is significantly smaller than the corresponding lateral incisor on the other side of the arch); 9) whether a target tooth’s length is uneven relative to one or more other teeth; 10) whether one or more oral care metrics result in atypical values; or some other indication of an abnormality in the shapes and / or structures of one or more teeth.

[0171] Techniques of this disclosure may, in some implementations, be used to generate one or more treatment outcomes. Generally speaking, a treatment outcome can include an intended or typical result of oral care treatment that is provided to the patient. One such example of a treatment outcome is a taiget dentition.

[0172] A digital fixture model may include 3D representations of the patient’s dentition, with optional fixture model components attached to that dentition. 3D representation generation techniques of this disclosure (e.g., techniques to generate 3D point clouds or 3D voxelized representations) may be trained to generate (or modify) aspects of a digital fixture model, to include treatment-enhancing fixture model components. For example, an ML model that is trained using flow matching may generate one or more vector fields Vt, which may be used to modify 3D representations described herein (e.g., fixture model components, appliance components, etc.). Such a vector field can modify an oral care guide object 308, to shape that guide object 308 into a target shape which is suitable for use in patient treatment. An oral guide object 308 may include a generic or default version of data which is intended for use in treatment of the patient. For example, guide object 308 may include a digital pontic tooth (e.g., a design for a pontic which is generated by averaging the geometries of many examples of the relevant tooth type over a dataset of cohort patient case data, etc.). This generic pontic may be modified by one or more vector fields Vt, such as according to method 900. A vector field Vt which is generated by a normalizing flow-based ML model can be used to modify (or generate) other examples of fixture model components, or appliance components, too. In some implementations, denoising diffusion-based ML models (e.g., a model trained using method 500) can be trained to generate fixture model components, or appliance components. For example, an incomplete fixture model may be included in instant patient case data 416 which is provided to encoder 508, as a part of method 600. Method 600 may provide noisy representation 602 to encoder-decoder structure 614, which may generate one or more predicted noise tensors 616. The one or more predicted noise vectors may be subtracted (or removed) (620) from latent representation 612 for one or more iterations of denoising. After method 600 completes execution, the method may output the fixture model in a modified form which includes blockout (e.g., to fill undercuts), bite ramps, or other fixture model components described herein.

[0173] Fixture model components may include 3D representations (e.g., 3D point clouds, 3D meshes, or voxelized representations) of one or more of the following non-limiting items: 1) interproximal webbing - which may fill-in space or smooth-out the gaps between teeth to ensure aligner removability. 2) blockout - which may be added to the fixture model to remove overhangs that mightinterfere with plastic tray thermoforming or to ensure aligner removability. 3) bite blocks - occlusal features on the molars or premolars intended to prop the bite open. Bite blocks may be applied to open bite cases to intrude the molars. 4) bite ramps - lingual features on incisors and cuspids intended to prop the bite open. Bite ramps may be applied to deep bite cases to intrude the incisors or cuspids. 5) interproximal reinforcement - a structure on the exterior of an oral care appliance (e.g., an aligner tray), which may extend from a first gingival edge of the appliance body on a labial side of the appliance body along an interproximal region between the first tooth and the second tooth to a second gingival edge of the appliance body on a lingual side of the appliance body. The effect of the interproximal reinforcement on the appliance body at the interproximal region may be stiffer than a labial face and a lingual face of the first shell. This may allow the aligner to grasp the teeth on either side of the reinforcement more firmly. 6) gingival ridge structure - a structure which may extend along the gingival edge of a tooth in the mesial-distal direction for the purpose of enhancing engagement between the aligner and a given tooth. Gingival ridge structure may stiffen the aligner tray. 7) torque points - structures which may enhance force delivered to a given tooth at specified locations. Torque points may include hemispherical or conical stmctures, and / or may appear along gingival edge of upper incisors. 8) power ridges - structures which may enhance force delivered to a given tooth at a specified location. 9) dimples - structures which may enhance force delivered to a given tooth at specified locations. Dimples may include hemispherical or conical structures, and / or may be applied to any portion of a tooth. The dimple may intrude upon the tooth space, and / or apply force to the tooth. The dimple may influence which one or more portions of the aligner physically contact one or more teeth. 10) digital pontic tooth - structure which may hold space open or reserve space in an arch for a tooth which is partially erupted, or the like. In aligners, a physical pontic is a tooth pocket that does not cover a tooth when the aligner is installed on the teeth. The tooth pocket may be filled with tooth-colored wax, silicone, or composite to provide a more aesthetic appearance. 11) power bars - blockout added in an edentulous space to provide strength and support to the tray. A power bar may fill-in voids. Abutments or healing caps may be blocked-out with a power bar. 12) trim line - digital path along the digital fixture model, which may approximately follow the contours of the gingiva (e.g., may be biased 1 or 2 mm in the gingival direction). The trimline may define the path along which a clear aligner may be cut or separated from a physical fixture model, after 3D printing. 13) undercut fill - material which is added to the fixture model to avoid the formation of cavities between the fixture model’s height of contour and another boundary (e.g., the gingiva or the plane that the plane that undergirds the physical fixture model after 3D printing).

[0174] Method 100 may generate fixture models in accordance with the ground truth data 104 which are used in the training method 100. Method 100 may include any number of cascaded ML models, such as ML models trained by method 500, or method 800. For example, when training method 500 trains encoder-decoder structure 522 using ground tmth data 104 that includes gingival trimlines from many cohort patient cases, then the method 500 may be trained to generate gingival trimlines. Similarly, when training method 500 trains encoder-decoder structure 522 using ground truth data 104that includes mold parting surfaces (e.g. or other appliance components, etc.) from many cohort patient cases, then the method 500 may be trained to generate mold parting surfaces (e.g. or other appliance components, etc.). In other words, the ML models of this disclosure may be trained to generate certain structures based on the presence (or absence) of those structures in the ground truth data 104. This approach enables ML models to be trained to generate output that is customized to the patient’ s dentition and / or treatment needs by adjusting the distribution of data samples in the training dataset.

[0175] Techniques of this disclosure (e.g., diffusion models, continuous normalizing flows, transformer-based, or autoencoder-based models) may be trained to generate the custom appliance components which are customized to the shape and / or structure of the patient's dentition. For example, an ML model that is trained using flow matching may generate one or more vector fields Vt, which may be used to modify a 3D representation of an appliance component, or to modify a transform (e.g., a transform which positions an appliance component or fixture model component into a pose that is suitable for patient treatment). Such a vector field can modify an oral care guide object 308, causing that guide object 308 to take-on a modified shape and / or structure which is suitable for patient treatment. A vector field Vt which is generated by a normalizing flow-based ML model can be used to modify (or generate) other examples of appliance components or transforms, too.

[0176] Examples of custom appliance components include a mold parting surface, a gingival trim surface, a shell, a facial ribbon, a lingual shelf (also referred to as a “stiffening rib”), a door, a window, an incisal ridge, a case frame sparing, or a diastema matrix wrapping, a spline, among others. A spline refers to a curve that passes through a plurality of points or vertices, such as a piecewise polynomial parametric curve. A mold parting surface refers to a 3D representation that bisects two sides of one or more teeth of the patient's dentition (e.g., separates the facial side of one or more teeth from the lingual side of the one or more teeth). A gingival trim surface refers to a 3D representations that trims an encompassing shell along the gingival margin. A shell refers to a body of nominal thickness. In some examples, an inner surface of the shell matches the surface of the dental arch and an outer surface of the shell is a nominal offset of the inner surface. The facial ribbon refers to a stiffening rib of nominal thickness that is offset facially from the shell. A window refers to an aperture that provides access to the tooth surface so that dental composite can be placed on the tooth. A window (or port) may be located along the facial or occlusal surface of a tooth. A door refers to a structure that covers the window. An incisal ridge provides reinforcement at the incisal edge of dental appliance and may be derived from an arch form. A case frame sparing refers to connective material that couples parts of a dental appliance (e.g., the lingual portion of a dental appliance, the facial portion of a dental appliance, and subcomponents thereof) to the manufacturing case frame. In this way, the case frame sparing may tie the parts of a dental appliance to the case frame during manufacturing, protect the various parts from damage or loss, and / or reduce the risk of mixing-up parts. These appliance components and others are described in PCT patent applications W02020240351A1 and W02021240290A1, both of which are incorporated herein by reference in their entirety.

[0177] A mold parting surface refers to a 3D representation that bisects two sides of one or more teeth (e.g., by separating the facial side of one or more teeth from the lingual side of the one or more teeth). A gingival trim surface refers to a 3D representation that trims an encompassing shell along the gingival margin. A shell refers to a body of nominal thickness. In some examples, an inner surface of the shell matches the surface of the dental arch and an outer surface of the shell is a nominal offset of the inner surface.

[0178] The facial ribbon refers to a stiffening rib of nominal thickness that is offset facially from the shell. A window refers to an aperture that provides access to the tooth surface so that dental composite can be placed on the tooth. A door refers to a structure that covers the window. An incisal ridge provides reinforcement at the incisal edge of a dental restoration appliance and may be derived from the archform. The case frame sparing refers to connective material that couples parts of a dental restoration appliance (e.g., the lingual portion of a dental restoration appliance, the facial portion of a dental restoration appliance, and subcomponents thereof) to the manufacturing case frame. In this way, the case frame sparing may tie the parts of a dental restoration appliance to the case frame during manufacturing, protect the various parts from damage or loss, and / or reduce the risk of mixing up parts.

[0179] In some implementations, the generative ML models of this disclosure may generate transforms which are configured to place 3D representations oral care data relative to each other. The transforms may be used to place a tooth relative to one or more other teeth of the patient's dentition. The transforms may be configured to place one or more appliance components, fixture model components, or hardware elements (e.g., brackets, etc.), relative to the patient's dentition. Appliance components (e.g., components which form parts of dental restoration appliances, etc.) may be drawn from a library of standardized part designs. Examples of appliance components which may be drawn from a standardized library, and / or places relative to the patients dentition include the following: a center clip registration tab (or “beak”), door hinges, door snaps, door vents, rear snap clamps, among others. A center clip registration tab may be placed into a pose (e.g., including position and / or orientation) which is proximate to the two maxillary central incisors. Door hinges may be configmed to pivotably couple a door to a dental appliance. Door snaps may include an indentation or protuberance which functions to keep a door secured in place (or to keep the door closed). Door vents may include an hole or aperture in the appliance. A door vent may transport excess dental composite out of the dental appliance. A door vent may be located along the incisal or facial surface of a tooth, or along the facial surface of the tooth. Rear snap clamps may be attached to the digital representation of the patient's dentition (e.g., near the posterior teeth) and / or may enable the physical fixture model to be gripped or handled.

[0180] Techniques of this disclosure may, in some implementations, use PointNet, PointNet++, or derivative neural networks (e.g., networks trained via transfer learning using either PointNet or PointNet++ as a basis for training) to extract local or global neural network features from a 3D point cloud or other 3D representation (e.g., a 3D point cloud describing aspects of the patient’s dentition -such as teeth or gums). Techniques of this disclosure may, in some implementations, use U-Nets to extract local or global neural network features from a 3D point cloud or other 3D representation.

[0181] Techniques of this disclosure may use transfer learning to train, at least in part, generative ML models. For example, a UNet which has been trained to perform denoising (e.g., to predict noise tensors) for fixture model generation may then be used as an initial configuration in the training of a UNet for the denoising of tooth restoration designs. Generally, a first ML model which has been trained to generate a first 3D oral care representation may be used as an initial configuration for the training of a second ML model (e.g., a second ML model which is trained to generate a second 3D oral care representation). The benefits of transfer learning include that learnings from a first domain area can then be applied to a second domain area.

[0182] 3D oral care representations are described herein as such because 3-dimensional representations are currently state of the art. Nevertheless, 3D oral care representations are intended to be used in a non-limiting fashion to encompass any representations of 3-dimensions or higher orders of dimensionality (e.g., 4D, 5D, etc.), and it should be appreciated that machine learning models can be trained using the techniques disclosed herein to operate on representations of higher orders of dimensionality. For example, a 3D mesh (e.g., of a tooth, etc.) may include vertices whose locations may be described by X, Y, and / or Z coordinate axes. Each vertex may additionally have data values, such as one or more mesh element labels (e.g., which describe the classification or category of object to which the vertex belongs). In this sense, the 3D mesh can be interpreted to occupy Q-dimensional space, where Q is the number of vertices (or other mesh elements, etc.). Stated another way, the set of mesh element labels corresponding to the mesh may be interpreted as a Q-dimensional data structure, which the first three dimensions correspond to the X, Y, and Z coordinate axes, and the remaining dimensions correspond to other data associated with the oral care representation (e.g., oral care arguments, or other data).

[0183] This disclosure pertains to digital oral care, which encompasses the fields of digital dentistry and digital orthodontics. This disclosure generally describes methods of processing three- dimensional (3D) representations of oral care data, and / or associated transforms. It should be understood, without loss of generality, that there are various types of 3D representations. One type of 3D representation is a 3D geometry. A 3D representation may include, be, or be part of one or more of a 3D polygon mesh, a 3D Although the term “mesh” is used frequently throughout this disclosure, the term should be understood, in some implementations, to be interchangeable with other types of 3D representations. A 3D representation may describe elements of the 3D geometry and / or 3D structure of an object, point cloud (e.g., such as derived from a 3D mesh), a 3D voxelized representation (e.g., a collection of voxels - for sparse processing), or 3D representations which are described by mathematical equations. 3D data may be generated using intraoral scanners, computed tomography (e.g., CBCT), cameras, or other 2D or 3D devices. In some examples, the data may be stored in the Digital Imaging and Communications in Medicine (DICOM) format.

[0184] In some instances, input data may include 3D mesh data, 3D point cloud data, 3D surface data, 3D polyline data, 3D voxel data, or data pertaining to a spline (e.g., control points). An encoderdecoder structure may comprise one or more encoders, or one or more decoders. In some implementations, the encoder may take as input mesh element feature vectors for one or more of the inputted mesh elements. By processing mesh element feature vectors, the encoder is trained in a manner to generate more accurate representations of the input data. For example, the mesh element feature vectors may provide the encoder with more information about the shape and / or structure of the mesh, and therefore the additional information provided allows the encoder to make better-informed decisions and / or generate more-accurate latent representations of the mesh. Examples of encoder-decoder structures include U-Nets, autoencoders or transformers (among others). A representation generation module may comprise one or more encoder-decoder structures (or portions of encoders-decoder structures - such as individual encoders or individual decoders). A representation generation module may generate an information-rich (optionally reduced-dimensionality) representation of the input data, which may be more easily consumed by other generative or discriminative machine learning models.

[0185] A U-Net may comprise an encoder, followed by a decoder. The architecture of a U-Net may resemble a “U” shape. The encoder may extract one or more global neural network features from the input 3D representation, zero or more intermediate-level neural network features, or one or more local neural network features (at the most local level as contrasted with the most global level). The output from each level of the encoder may be passed along to the input of corresponding levels of a decoder (e.g., by way of skip connections). Like the encoder, the decoder may operate on multiple levels of global-to-local neural network features. For instance, the decoder may output a representation of the input data which may contain global, intermediate or local information about the input data. For example, when the input data includes a 3D representation of a tooth of the patient, global neural network features may be generated which describe the overall shape, dominant texture, or color of the tooth. Intermediate neural network feature may be generated which describe specific sub-regions of the tooth, or patterns in the shape of the tooth which include comers, edges, or small portions of anatomy (e.g., cusp tips, incisal edges, etc.). Local neural network features may be generated which include vectors of data which describe small regions of the tooth (e.g., key points, etc.). The U-Net may, in some implementations, generate an information-rich (optionally reduced-dimensionality) representation of the input data, which may be more easily consumed by other generative or discriminative machine learning models.

[0186] An autoencoder may be configured to encode the input data into a latent form. An autoencoder may train an encoder to reformat the input data into a reduced-dimensionality latent form in between the encoder and the decoder, and then train a decoder to reconstruct the input data from that latent form of the data. A reconstruction error may be computed to quantify the extent to which the reconstructed form of the data differs from the input data. The latent form may, in some implementations, be used as an information-rich reduced-dimensionality representation of the inputdata which may be more easily consumed by other generative or discriminative machine learning models. In most scenarios, an autoencoder may be trained to input a 3D representation, encode that 3D representation into a latent form (e.g., a latent embedding), and then reconstruct a close facsimile of that input 3D representation at the output.

[0187] A transformer may be trained to use self-attention to generate, at least in part, representations of its input. A transformer may encode long-range dependencies (e.g., encode relationships between a large number of inputs). A transformer may comprise an encoder or a decoder. Such an encoder may, in some implementations, operate in a bi-directional fashion or may operate a self-attention mechanism. Such a decoder may, in some implementations, may operate a masked selfattention mechanism, may operate a cross-attention mechanism, or may operate in an auto-regressive manner. The self-attention operations of the transformers described herein may, in some implementations, relate different positions or aspects of an individual 3D oral care representation in order to compute a reduced-dimensionality representation of that 3D oral care representation. The crossattention operations of the transformers described herein may, in some implementations, mix or combine aspects of two (or more) different 3D oral care representations. The auto-regressive operations of the transformers described herein may, in some implementations, use previously generated aspects of 3D oral care representations (e.g., previously generated points, point clouds, transforms, etc.) as additional input when generating a new or modified 3D oral care representation. The transformer may, in some implementations, generate a latent form of the input data, which may be used as an informationrich reduced-dimensionality representation of the input data, which may be more easily consumed by other generative or discriminative machine learning models.

[0188] In some implementations, an encoder-decoder structure may first be trained as an autoencoder. In deployment, one or more modifications may be made to the latent form of the input data. This modified latent form may then proceed to be reconstructed by the decoder, yielding a reconstructed form of the input data which differs from the input data in one or more intended aspects. Oral care arguments, such as oral care parameters or oral care metrics may be provided to the encoder, the decoder, or may be used in the modification of the latent form, to influence the encoder-decoder structure in generating a reconstructed form that has desired characteristics (e.g., characteristics which may differ from that of the input data).

[0189] Techniques of this disclosure may, in some instances, be trained using federated learning. Federated learning may enable multiple remote clinicians to iteratively improve a machine learning model, while protecting data privacy (e.g., the clinical data may not need to be sent “over the wire” to a third party). Data privacy is particularly important to clinical data, which is protected by applicable laws. A clinician may receive a copy of a machine learning model, use a local machine learning program to further train that ML model using locally available data from the local clinic, and then send the updated ML model back to the central hub or third party. The central hub or third party may integrate the updated ML models from multiple clinicians into a single updated ML model which benefits fromthe learnings of recently collected patient data at the various clinical sites. In this way, a new ML model may be trained which benefits from additional and updated patient data (possibly from multiple clinical sites), while those patient data are never actually sent to the 3rd party. Training on a local in-clinic device may, in some instances, be performed when the device is idle or otherwise be performed during off-hours (e.g., when patients are not being treated in the clinic). Devices in the clinical environment for the collection of data and / or the training of ML models for techniques described herein may include intra-oral scanners, CT scanners, X-ray machines, laptop computers, servers, desktop computers or handheld devices (such as smart phones with image collection capability). In addition to federated learning techniques, in some implementations, contrastive learning may be used to train, at least in part, the ML models described herein. Contrastive learning may, in some instances, augment samples in a training dataset to accentuate the differences in samples from difference classes and / or increase the similarity of samples of the same class.

[0190] One or more oral care meshes (e.g., teeth arranged in one or more dental arches) may be provided to techniques of this disclosure. Each of these meshes may undergo pre-processing before being provided to the predictive architectures (e.g., an encoder, decoder, pyramid encoder-decoder, or U-Net, among others). In some implementations, this pre-processing may include the encoding of the mesh into latent form. In some implementations, the pre-processing may include the conversion of the mesh into lists of mesh elements, such as vertices, edges, faces or in the case of sparse processing - voxels. For the chosen mesh element type or types, (e.g., vertices), feature vectors may be generated. In some examples, one feature vector is generated per vertex of the mesh (or per edge or per face). Each feature vector may contain a combination of spatial and / or structural features, as specified in Table 3.Table 3

[0191] Table 3 discloses non-limiting examples of mesh element features. In some implementations, color (or other visual cues / identifiers) may be considered as a mesh element feature in addition to the spatial or structural mesh element features described in Table 3. As used herein (e.g., in Table 3), a point differs from a vertex in that a point is part of a 3D point cloud, whereas a vertex is part of a 3D mesh and may have incident faces or edges. A dihedral angle (which may be expressed in either radians or degrees) may be computed as the angle (e.g., a signed angle) between two connected faces (e.g., two faces which are connected along an edge). A sign on a dihedral angle may reveal information about the convexity or concavity of a mesh surface. For example, a positively signed angle may, in some implementations, indicate a convex surface. Furthermore, a negatively signed angle may, in some implementations, indicate a concave surface. To calculate the principal curvature of a mesh vertex, directional curvatures may first be calculated to each adjacent vertex around the vertex. These directional curvatures may be sorted in circular order (e.g., 0, 49, 127, 410, 305 degrees) in proximity to the vertex normal vector and may comprise a subsampled version of the complete curvature tensor. Circular order means: sorted in by angle around an axis. The sorted directional curvatures may contribute to a linear system of equations amenable to a closed form solution which may estimate thetwo principal curvatures and directions, which may characterize the complete curvature tensor. Consistent with Table 3, a voxel may also have features which are computed as the aggregates of the other mesh elements (e.g., vertices, edges and faces) which either intersect the voxel or, in some implementations, are predominantly or fully contained within the voxel. Rotating the mesh may not change structural features but may change spatial features. And, as described elsewhere in this disclosure, the term “mesh” should be considered in a nonlimiting sense to be inclusive of 3D mesh, 3D point cloud and 3D voxelized representation.

[0192] Techniques of this disclosure may require a training dataset of hundreds or thousands of cohort patient cases, to ensure that the neural network is able to encode the distribution of patient cases which are likely to be encountered in clinical treatment. A cohort patient case may include a set of tooth crown meshes, a set of tooth root meshes, or a data file containing attributes of the case (e.g., a JSON file). A typical example of a cohort patient case may contain up to 32 crown meshes (e.g., which may each contain tens of thousands of vertices or tens of thousands of faces), up to 32 root meshes (e.g., which may each contain tens of thousands of vertices or tens of thousands of faces), multiple gingiva mesh (e.g., which may each contain tens of thousands of vertices or tens of thousands of faces) or one or more JSON files which may each contain tens of thousands of values (e.g., objects, arrays, strings, real values, Boolean values or Null values).

[0193] Turning now FIG. 16, an example computer-based system 1600 for training an ML model, using a fully trained ML model, or for implementing any one of the computer-implemented methods described herein is shown. For example, the system 1600 can be configured to perform one or more of the methods 100, 200, 300, 400, 500, 600, 800, 900, 1000, 1100 (or others described herein) according to some implementations. The system 1600 includes a data collection component 1602, a computation component 1604, and one or more input / output devices 1610.

[0194] The data collection component 1602 is configured to capture one or more data which may be provided as input to the ML models described herein. The data collection component 1602 may include devices for the capture of images, 3D representations, among other data structures. In some embodiments, the data collection component 1602 can include, for example, intraoral scanners, CBCT scanners, PRT scanners, digital cameras (e.g., of mobile phones), IR cameras, etc.

[0195] In the embodiment of FIG. 16, the computation component 1604 includes a processor 1606 and a memory 1608. The computation component 1604 is functionally connected to the data collection component 1602 (e.g., an intraoral scanner, etc.), and receives signals related to 3D dentition meshes which are captured by the data collection component 1602. The processor 1606 can then use the 3D dentition meshes to train, at least in part, ML models described herein. The training of an ML model, or the use of a fully trained ML model may include running a computer program in any suitable programming language (e.g., Python), by implementing one or more of the methods 100, 200, 300, 400, 500, 600, 800, 900, 1000, 1100 (or others described herein), according to some implementations.

[0196] The trained ML models can be stored in the memory 1608. In some embodiments, the memory 1608 may contain data files to store the outputs of training ML models, and / or 3D oral care representations including, for example, 3D dentition meshes.

[0197] The memory 1608 stores information. In some embodiments, the memory 1608 can store instructions for performing the methods or processes described herein. In some embodiments, 3D dentition data, partially trained ML model data, or fully trained ML model data can be pre-stored in the memory 1608.

[0198] The memory 1608 may include any volatile or non-volatile storage elements. Examples may include random access memory (RAM) such as synchronous dynamic random access memory (SDRAM), read-only memory (ROM), non-volatile random access memory (NVRAM), electrically erasable programmable read-only memory (EEPROM), or FLASH memory.

[0199] Examples may also include hard-disk, magnetic tape, a magnetic or optical data storage media, a compact disk (CD), a digital versatile disk (DVD), a Blu-ray disk, and a holographic data storage medium.

[0200] The processor 1606 may include, for example, one or more general-purpose microprocessors, specially designed processors, application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), a collection of discrete logic, and / or any type of processing device capable of executing the techniques described herein. In some embodiments, the processor 1606 (or any other processors described herein) may be described as a computing device.

[0201] In some embodiments, the memory 1608 may be configured to store program instructions (e.g., software instructions) that are executed by the processor 1606 to carry out the processes or methods described herein. In other embodiments, the processes or methods described herein may be executed by specifically programmed circuitry of the processor 1606. In some embodiments, the processor 1606 may thus be configmed to execute the digital oral care techniques described herein. The processor 1606 (or any other processors described herein) may include one or more processors.

[0202] Input / output device 1610 may include one or more devices configured to input or output information from or to a user or other device. For instance, the input / output device 1610 may include one or more display devices communicatively coupled to the computation component 1604 (including the processor 1606). In some embodiments, the input / output device 1610 may present a graphical user interface (GUI) 1612 where a user may control the digital oral care automation processes described herein. For example, the GUI 1612 may include a display screen for presenting visual information to a user. In some embodiments, the display screen includes a touch sensitive display. In some embodiments, the GUI 1612 may include one or more different types of devices for presenting information to a user. The GUI 1612 may include, for example, any number of visual (e.g., display devices, lights, etc.), audible (e.g., one or more speakers), and / or tactile (e.g., keyboards, touch screens, or mice) feedback devices. In some embodiments, the input / output devices 1610 may represent one or more of a display screen (e.g., a liquid crystal display or light emitting diode display) and / or a printer (e.g., a printingdevice or component for outputting instructions to a printing device). In some embodiments, the input / output device 1610 may be configured to accept or receive program instructions (e.g., software instructions) that are executed by the processor 1606 to carry out the embodiments described herein.

[0203] The system 1600 may also include other components and the functions of any of the illustrated components including the processor 1606, the memory 1608, and the input / output devices 1610 may be distributed across multiple components and separate devices such as, for example, computers. The system 1600 may be configured as a workstation, desktop computing device, notebook computer, tablet computer, mobile computing device, or any other suitable computing device or collection of computing devices. The system 1600 may operate on or be collected to a local network or be hosted in a Cloud computing environment 1614. The illustrated components of FIG. 16 are shown merely to explain various aspects of the present disclosure and the addition or removal of components would be apparent to one of skill in the art. Additionally, while FIG. 16 depicts individual components, it should be appreciated that system 1600 may include more than one of those components, e.g., one or more processors 1606, one or more input / output devices 1610, and the like.

[0204] The example method 100 described in FIG. 1 (or other ML models described herein) may generate (or modify) digital designs for oral care appliances. For example, the ML models may be trained to generate digital designs for orthodontic aligner trays. The digital designs can be 3D printed, resulting in physical aligner trays. In some implementations, a digital aligner tray may be designed to include one or more geometrical features which enable the corresponding physical aligner tray to integrate with a physical pontic tooth. A physical pontic tooth may be selected from a library of available physical designs. A physical pontic tooth may be formed using curable, flowable, or packable material which is deposited into the indentations for one or more teeth within the physical aligner tray. A physical pontic tooth may be directly 3D printed into the physical aligner tray using a 3D printing resin which differs in appearance (e.g., color or translucency) from the 3D printing resin used in printing the aligner tray. A physical pontic tooth may be integrated with a physical aligner tray to fill-in a gap in the patient’s dentition (e.g., for aesthetic reasons, etc.). The digital aligner tray may be designed to include one or more keyholes, slots, or other inter-locking feature pairs which enable a physical pontic tooth to snap securely into a physical aligner tray. The digital aligner tray may be designed to include one or more pontic securement apparatuses, such as pontic securement apparatuses 1702 (see FIGs. 17A-17B), recessed textures 1802 (see pattern in FIGs. 18A-18B), embossed or debossed patterns, bumps, protrusions, indentations, holes, or other pontic secmement apparatuses. The pontic securement apparatuses enable a physical pontic tooth to be securely held within the physical aligner tray (e.g., when a paste or polymer material is extruded into the indentation corresponding to a tooth in the physical aligner tray, and / or subsequently cured).

[0205] Pontic securement apparatuses may include one or more protrusions from a first object which interface with one or more cavities in a second object. Pontic securement apparatuses may include one or more protmding textures 1804 on one or more teeth of arch 1800. The arch 1800 maybe customized to the dentition of the patient, and / or may be used to define aspects of the shape of aligner tray 1700. The one or more protruding textures 1804 in arch 1800 lead directly to corresponding recessed textures 1802 in aligner 1700. One or more of the tooth cavities which include recessed texture 1802 may be filled using flowable and / or curable substrate (e.g., a substrate which is used to form the physical pontic tooth). The aligner 1700 may, in some instances, be generated to include barriers or dams within one or more interproximal spaces. The barriers or dams may contain the flowable and / or curable material, so that the material fills-in the intended one or more tooth slots. A 3D representation of a digital pontic tooth may be selected from a library of available designs (e.g., designs which have different shapes, styles, and / or designs, etc.). The selection may be determined, at least in part, based on the specification included within oral care arguments 136. For example, when the patient is missing a particular tooth (e.g., an upper left canine, etc.), then a digital pontic tooth may be specified by the oral care arguments 136 which is compatible with the size, shape, and / or style of one or more existing teeth in the arch (e.g., compatible with an existing upper right canine, etc.). Likewise, a physical pontic tooth may be selected from a library of available designs.

[0206] Pontic securement apparatuses may include recessed geometries. In some implementations, the protrusions or texture apparatuses may be located along the lingual portions of the aligner tray (among other locations), to hide the geometry of the securement apparatuses from casual view when the aligner tray is worn by the patient.

[0207] In some implementations, oral care arguments 136 may indicate which one or more tooth locations of the patient’s dentition (e.g., dentition included within 3D oral care representations 102) are to be replaced, filled or designed with digital pontic teeth. Generative module 118a may be trained to generate transforms for the a final setup that describes the target poses of the patient’s teeth (or to generate an intermediate stage). The example generative module 118a may include one or more representation generation modules (e.g., encoders, etc.) which encode the patient’s dentition into one or more latent representations. The example generative module 118a may also include one or more transform-generation neural networks (e.g., MLPs, or others described herein). The one or more latent representations of the patient’s teeth may be provided to the one or more transform-generation neural networks, which may generate one or more transforms which place the patient’s teeth into poses for the final stage (or an intermediate stage) of orthodontic treatment. Those transforms may be provided to the example generative module 118b, which may generate one or more digital designs for orthodontic aligner trays. In some implementations, the example generative module 118b may generate one ormore transforms which place one or more digital representations of pontic securement apparatuses relative to one or more digital representations of teeth in the patient’s dentition (or place one or more holes, indentations or openings corresponding to one or more pontic securement apparatuses relative to a digital design for an orthodontic aligner tray). The generated digital aligner tray and / or the one or more pontic securement apparatuses may be combined, to generate a modified aligner tray which has slots or knobs to support the attachment of physical pontics to the physical aligner tray. Ground truth data 104may include ground truth data pertaining to the placement of pontic securement apparatuses (or pontic attachment apparatuses). For example, ground truth data 106b may include transforms for pontic securement apparatuses, and / or generated data 120b may include corresponding generated transforms. In some implementations, ground truth data 104 may include one or more examples of aligner trays which already have protrusions, notches, or other pontic secmement apparatuses built-in to the shapes and / or structures of those trays. Loss may be computed by comparing generated data and / or corresponding ground truth data, and then be used to train, at least in part, the generative modules described herein (e.g., the generative modules of method 100, etc.). In some implementations, a generative module of example method 100 may include the diffusion model of example method 600, the normalizing flow model of method 900, the autoencoder-based model of method 1100, the transformer-based model of method 1000, or others described herein.

[0208] Any of generative modules 118a-118n may include ML models for automatic orthodontic setups generation. An automated setups generation ML model may encode input data 102 into one or more latent representations using one or more representation generation modules (e.g., encoders, etc.), and then provide the one or more latent representations to one or more ML models that generate transforms for the teeth. The transforms may include transforms which place one or more teeth of the patient’s dentition (e.g., included as part of input data 102, etc.) into poses which are suitable for use in orthodontic treatment (e.g., for intermediate stages, or final setups, etc.). The one or more transforms of a generated orthodontic setup may be used to transform the poses of the patient’s teeth. For example, an automated final setups generationML model (e.g., included in any of generative modules 118a-l 18n, etc.) may place the patient’s teeth into poses which minimize crowding, minimize collisions, are arranged with alignments which are orthodontically correct, or the like.

[0209] Subsequent to automated setups generation, gaps between the patient’s teeth may be reduced or eliminated using an automated tooth packing module. In some implementations, an automated tooth packing module may pack the tooth meshes of an arch along a spline (e.g., a spline which passes through the origins of the tooth coordinate systems, or the tooth centroids, etc.). After automated setups generation and / or automated tooth packing, arch lengths may be generated. For example, the maxillary arch length may be computed along a spline that passes through tooth coordinate systems of the maxillary teeth. The mandibular arch length may be computed along a spline that passes through the tooth coordinate systems of the mandibular teeth. In some implementations, an arch length may be computed by summing the widths of the teeth within an arch. In some implementations, an arch length may be measured between two (or more) teeth of the arch (e.g., measured along a spline that runs between the 1stmolars of the arch, or between other teeth).

[0210] An arch length metric may be generated based on the dentition of this predicted orthodontic setup. An arch length metric may be generated based on the patient’s maloccluded dentition. An arch length discrepancy metric may be computed by computing the difference between the maloccluded andpredicted setup arch lengths. A Bolton metric may be generated by dividing the mandibular arch length by the maxillary arch length.

[0211] In some implementations, Bolton metrics, arch length metrics, and / or 3D representations of the patient’s dentition (or latent representations of the patient’s dentition) may be provided to an automated interproximal reduction (IPR) prediction module. For example, an automated IPR prediction module may be configured to perform the techniques disclosed in PCT Patent Application No. PCT / IB2024 / 062592, which is incorporated herein by reference. An IPR prediction module may generate one or more predictions for IPR to be applied to one or more teeth of the patient’s dentition. An IPR prediction module may be implemented using any of the ML models described herein. An IPR prediction module may determine a total quantity of IPR which is to be applied to the patient’s dentition. In instances when a Bolton discrepancy exists in the patient’s dentition (e.g., when the Bolton ratio is larger or smaller than an ideal range), then a total amount of IPR may be designated to resolve the Bolton discrepancy. The IPR module may generate a total quantity of IPR (e.g., in millimeters, etc.) that is to be assigned, allocated, or applied to the patient’s teeth. The IPR may be divided up among the anterior teeth of an arch, and / or divided up among the posterior teeth of an arch. Upon the application of the IPR, the patient’s teeth may be brought into an orthodontically acceptable Bolton ratio. Oral care arguments 136 may include IPR limits (e.g., limits to the quantity of IPR which is to be applied to each tooth, etc.). Method 1900 of FIG. 19 may generate orthodontic setups which include the application of interproximal reduction (IPR) to generate space within an arch, and alleviate crowding, to name two examples. Patient dentition data 1916 may be provided to an automated setups generation module. For example, an automated setups generation module may be configured to perform the techniques disclosed in U.S. Patent Application No. US 18 / 713,011, which is incorporated herein by reference. The method may run (1902) automated setups generation. An ML model for automatic setups prediction may include one or more representation generation modules (e.g., which may generate one or more latent representations of teeth), and / or one or more transform generation modules. The one or more latent representations of teeth may be provided to the transform generation module, which may generate one or more transforms to place the patient’s teeth into poses which are suitable for orthodontic treatment. Mesh element feature vectors for one or more mesh elements of the patient’s teeth may be provided to the ML model. One or more oral care metrics may be included with oral care arguments 136, which may be provided to the ML model.

[0212] The method may run (1904) tooth packing. The method may perform tooth packing by first fitting a spline through one or more control points. The method may then move the tooth meshes along the spline to remove spaces or gaps between the teeth (e.g. , thereby packing the teeth) . The control points of the spline may include landmarks, such as the origins of the one or more tooth coordinate systems for the one or more teeth of an arch.

[0213] The method may generate splines that are based upon control points. The control points may include landmarks in the teeth of an arch. The method may generate (1906) arch lengths. In someimplementations, arch length may be generated as the sum of the widths of one or more teeth. In some implementations, arch length may be measured along a portion of a spline. A spline may be fitted through the tooth coordinate system origins of the teeth in an arch. The distance along the spline may be measured between two or more landmarks. For example, the distance may be measured along the spline between the most distal mesh elements of the two 1stmolars (or another pair of teeth). In some implementations, the sum of tooth widths may be computed for the teeth in an arch. In some implementations, the distances between two or more landmarks may be measured, and the sum of those distances may be used to approximate an arch length.

[0214] The method may generate oral care metrics, such as Bolton index or arch length discrepancy. For example, the method may generate (1908) a Bolton index metric by dividing the mandibular arch length by the maxillary arch length. In some implementations, the computed Bolton index metric may be further scaled by a scaling factor, for instance, by multiplying the Bolton index metric by 100 (or another scaling factor).

[0215] The method 1900 may assign or allocate how much IPR is to be performed on each tooth of the patient’s dentition. An allocation of IPR may include the assigning of how much IPR is to be applied to the mesial side of the tooth and / or how much IPR is to be applied to the distal side of the tooth. The method may generate IPR allocations for the arch (the total IPR), and / or IPR allocations for one or more individual teeth. For example, the method may generate (1910) the total intended IPR (e.g., in millimeters, or another unit) which is to be applied to the dentition. Oral care arguments 136 may designate one or more teeth to receive IPR, such as the anterior teeth and / or posterior teeth of the arch. Atotal IPR amount for an arch may be computed (e.g., the amount of IPR in mm which is required to generate a correct ratio of arch lengths and / or to correct a Bolton discrepancy, etc.). IPR may, in some implementations, be computed to correct asymmetry between teeth. For example, when the left central incisor is wider than the right central incisor of an arch, then IPR may be applied to that left central incisor to remove the asymmetry in the widths of corresponding teeth. This asymmetry correction may be performed for pairs of teeth within the arch, such as central incisors, lateral incisors, cuspids, 1stbicuspids, 2ndbicuspids, 1stmolars, etc. In some implementations, an ML model may generate one or more IPR magnitudes, or one or more IPR cut surfaces, for application to one or more teeth of the arch (e.g,. as described in PCT Patent Application No. PCT / IB2024 / 062592).

[0216] The method may apply (1912) the predicted IPR to one or more 3D representations of teeth of the patient’s dentition. For example, the method 1900 may generate IPR cut surfaces using a trained ML model, or generate IPR cut planes which trim a designated number of millimeters of material off the mesial or distal sides of designated teeth. The method 1900 may perform Boolean mesh processing operations known to one skilled in the art to subtract the portions of a tooth which are cut or intersected by the IPR cut surfaces. In such a manner, the method 1900 may modify one or more representations of the patient’s teeth, to alleviate crowding and / or generate space within one or both arches. These modified teeth may be provided to an automated setups prediction module, and / or enable that moduleto generate setups which are more accurate, because the reduction in crowding enables better tooth alignments to be generated.

[0217] The method 1900 may, in some implementations, proceed to re-run (1904) tooth packing. The method 1900 may then regenerate (1908) a Bolton index metric, or one or more other oral care metrics. The method 1900 may output the resulting IPR-modified dentition 1914 (e.g., the mal dentition which has been modified by IPR, among other examples of dentitions which may be modified). The IPR-modified dentition 1914 may be provided to an automated setups generation module, for instance, as described above. The method 1900 may re-mn (1920) automated setups generation. This second iteration of setups generation benefits from the increased space within one or more interproximal spaces (e.g., space generated by the application of IPR to modify the shapes of one or more teeth). In some implementations, the resulting orthodontic setup may again be provided to the input of the automated setups generation module, which may improve upon that orthodontic setup. Stated another way, the second application of automated setups generation may improve upon the output of the first application of automated setups generation, because the teeth are in better initial poses (e.g., poses which are more orthodontically correct than the maloccluded poses). The method may, in some implementations, perform (1904) tooth packing on the orthodontic setup. The resulting IPR-adjusted dentition 1918 may be provided to downstream processing methods, ultimately resulting in the generation of one or more digital designs for oral care appliances, and / or the 3D printing of those digital designs.

[0218] Aspects of the present disclosure can provide a technical solution to the technical problem of automatically generating 3D designs for oral care appliances, and the subsequent 3D printing thereof. In particular, by practicing techniques disclosed herein computing systems specifically adapted to automate the generation of 3D oral care representations using ML models (e.g., for generating digital designs for oral care appliances, such as aligner trays which are configmed for use with pontic teeth, etc.) which have been trained using flow matching are improved. For example, aspects of the present disclosure improve the performance of a computing system having a 3D representation of the patient’s dentition by reducing the consumption of computing resources. In particular, aspects of the present invention reduce computing resource consumption by decimating 3D representations of the patient’s dentition (e.g., reducing the counts of mesh elements used to describe aspects of the patient’s dentition) so that computing resources are not unnecessarily wasted by processing excess quantities of mesh elements. Additionally, decimating the meshes does not reduce the overall predictive accuracy of the computing system (and indeed may actually improve predictions because the input provided to the ML model after decimation is a more accurate (or better) representation of the patient’s dentition). For example, noise or other artifacts which are unimportant (and which may reduce the accuracy of the predictive models) are removed. That is, aspects of the present invention provide for more efficient allocation of computing resources.

[0219] Furthermore, aspects of the present disclosure may need to be executed in a time- constrained manner, such as when an oral care appliance (e.g., a dental restoration appliance, such asFILTEK Matrix, or an orthodontic aligner tray, etc.) must be generated for a patient in close relation to the intraoral scanning (e.g., while the patient waits in the clinician’s office). As such, aspects of the present disclosure are necessarily rooted in the underlying computer technology of training one or more machine learning models to generate one or more oral care appliance designs using continuous normalizing flows (or denoising diffusion models), and cannot be performed by a human, even with the aid of pen and paper. For instance, implementations of the present disclosure must be capable of: 1) storing thousands or millions of mesh elements of the patient’s dentition in a manner that can be processed by a computer processor; 2) performing calculation on thousands or millions of mesh elements, e.g., to quantify aspects of the shape and or / structure of an individual tooth in the 3D representation of the patient’s dentition; 3) computing one or more mesh element feature vectors including hundreds or thousands of dimensions for each of the thousands or millions of mesh elements; 4) encoding the thousands or millions of mesh elements into one or more latent representations using one or more encoders; 5) concatenate the resulting one or more latent representations with one or more latent representations 820, one or more latent representations 818, or one or more latent representations 502, resulting in one or more latent representations 808; 6) applying one or more vector fields Vt 810, which contains thousands or millions of elements, to each of the hundreds or thousands of dimensions of the one or more latent representations 808; 7) generating one or more flow gradients 814, and using the one or more flow gradients to update the thousands or millions of elements of the one or more vector fields Vt 810, and do so during the course of a short office visit.

Claims

WHAT IS CLAIMED IS:

1. A system comprising: one or more computer processors; non-transitory computer-readable storage communicatively coupled with the one or more processors, the computer readable storage having instructions stored thereon that when executed by the one or more processors causes the one or more processors to: receive a first distribution of data samples defining one or more 3D oral care representations in initial configurations receive one or more corresponding ground truth 3D oral care representations in respective final configurations; generate a second distribution which includes one or more samples from the one or more ground truth 3D oral care representations; iteratively train, using flow matching, one or more first generative models to predict one or more mappings between the first distribution and the second distribution, the training comprising: for each of the one or more data samples in the first distribution, generate an estimated vector field which defines one or more transformations wherein the one or more transformations, when iteratively applied, transform the data sample from the first distribution into a respective final configuration; combine each of the generated estimated vector fields into an aggregate representation; use the aggregate representation to define one or more trained first generative models output the one or more trained first generative models.

2. The system of claim 1, further comprising instructions that when executed by the one or more processors where generating the estimated vector field cause the one or more processors to: provide, to one or more trained second neural networks, one or more representations of the patient’s dentition; and generate, by one or more trained second neural networks using the one or more representations of the patient’s definition, the one or more of the estimated vector fields.

3. The system of claim 2, wherein the one or more fully trained second neural networks includes an encoder-decoder structure.

4. The system of claim 1, further comprising instructions that when executed by the one or more processors where generating the estimated vector field cause the one or more processors to: provide, to one or more ordinary differential equation solvers, one or more representations of the patient’s dentition; and generate, by the one or more ordinary differential equation solvers and using the one or more representations of the patient’s dentition, one or more vector fields.

5. The system of claim 1, wherein the one or more trained first generative models are configured to generate one or more tooth restoration designs.

6. The system of claim 5, wherein the one or more tooth restoration designs includes one or more layered tooth restoration designs.

7. The system of claim 1, wherein the one or more trained first generative models are configured to generate one or more transforms which place one or more corresponding 3D representations of teeth into poses which are suitable for inclusion in an orthodontic setup.

8. The system of claim 1, wherein the one or more trained first generative models are configured to generate one or more fixture model components.

9. The system of claim 8, wherein the one or more fixture model components is used in the generation of one or more fixture models.

10. The system of claim 1, wherein the one or more trained first generative models are configured to generate one or more appliance components, and the one or more appliance components.

11. The system of claim 1, wherein the one or more trained first generative models are configured to generates one or more transforms which describe, at least in part, the local coordinate systems for one or more teeth of the patient.

12. The system of claim 1, wherein the patient's dentition includes one or more 3D representations, and the one or more trained first generative models are configmed to generate one or more mesh element labels for one or more mesh elements of the patient's 3D dentition.

13. The system of claim 12, further comprising instructions that when executed by the one or more processors to segment, using the one or more mesh element labels, the one or more 3D representations of the patient's dentition.

14. The system of claim 12, further comprising instructions that when executed by the one or more processors to perform, using the one or more mesh element labels, one or more cleanup operations on the one or more 3D representations of the patient's dentition.

15. The system of claim 1, wherein the one or more trained first generative models includes one or more normalizing flow-based models.

16. The system of claim 1, wherein the one or more trained first generative models includes one or more denoising diffusion-based models.

17. The system of claim 1, wherein the one or more trained first generative models includes one or more cascade-based machine learning models.

18. The system of claim 1, further comprising instructions that cause the one or more processors to: receive one or more oral care arguments; and wherein iteratively training the one or more first generative models include generating one or more partially trained generative models based at least in part on output generated by one or more previous iterations of training the one or more generative models and the one or more oral care arguments influence the output of the one or more partially trained generative models.

19. The system of claim 18, wherein the one or more oral care arguments specify one or more customizations and the one or more trained generative models use the one or more oral care arguments to generate output customized for the patient’s dentition.

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