Automatic determination of a surface representation of a complete tooth

Abstract

Methods and systems for automatic generation of a complete tooth segment are described wherein the method comprises: receiving or determining scanning data, preferably clinical scanning data, representing an incomplete tooth segment, the incomplete tooth segment defining a part of a surface of a dentition representing one tooth of one or more teeth of a dentition, the incomplete tooth segment including one or more missing surface areas; determining contextual tooth information associated with the incomplete tooth segment, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and, determining a complete tooth shape surface of a complete tooth comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of the contextual tooth information and to output the tooth shape surface.

Description

[0001] W041121-Vi / AV

[0002] Automatic determination of a surface representation of a complete tooth

[0003] Technical field

[0004] The disclosure relates to the automatic determination of a surface representation of a complete tooth; , and in particular, though not exclusively, to methods and systems for automatic determination of a surface representation of a complete tooth and a computer program product for executing such methods.

[0005] Background

[0006] In orthodontic and prosthodontic treatments, accurately simulating tooth movement and planning restorative procedures requires a complete 3D representation of the dentition. High-resolution 3D models of teeth are typically obtained through non-invasive intraoral scanners (IOS) or lab-scanned impressions. These technologies efficiently capture exposed tooth surfaces but are limited to the visible crown areas. As a result, certain parts of the tooth — in particular the subgingival areas, surfaces in the interproximal areas blocked by adjacent teeth, or regions missed due to suboptimal scanning — remain unscanned, resulting in an incomplete tooth model. Consequently, there is a need for determining realistic, complete tooth models based on partial IOS scans for accurate treatment planning without relying other modalities, such as CBCT data, which is less accurate, expensive and requires exposure of a patient to radiation.

[0007] Conventionally, surface restauration or completion of missing tooth surfaces has been achieved through computer-aided design (CAD) technology, using tooth templates. This approach allows technicians to select templates from morphology libraries tailored to specific tooth positions, significantly reducing the need to design restorations from scratch. Such approach however requires expert intervention, limiting automation and introducing variability based on technician skill and experience.

[0008] Hence, from the above it follows there is a need in the art for for improved methods and systems for automatic tooth shape completion. In particular, there is a need for methods and system for accurate completion of missing surfaces, such as sub-gingiva and interproximal surfaces, of tooth segments that are segmented from scanned dentitions.Summary

[0009] As will be appreciated by one skilled in the art, aspects of the embodiments in this disclosure may be embodied as a system, method or computer program product. Accordingly, aspects of the embodiments may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system." Functions described in this disclosure may be implemented as an algorithm executed by a microprocessor of a computer. Furthermore, aspects of the embodiments may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied, e.g., stored, thereon.

[0010] Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0011] A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

[0012] Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber, cable, RF, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the embodiments may be writtenin any combination of one or more programming languages, including an object-oriented programming language such as Java(TM), Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0013] Aspects of the embodiments are described below with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments in this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor, in particular a microprocessor or central processing unit (CPU), of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer, other programmable data processing apparatus, or other devices create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0014] These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function / act specified in the flowchart and / or block diagram block or blocks.

[0015] The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. Additionally, the Instructions may be executed by any type of processors, including but not limited to one or more digital signal processors (DSPs), general purpose microprocessors, application specific integrated circuits (ASICs), field programmable logic arrays (FP- GAs), or other equivalent integrated or discrete logic circuitry.The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments in this disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustrations, and combinations of blocks in the block diagrams and / or flowchart illustrations, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

[0016] The embodiments in this disclosure aim to determine a surface representation of a complete tooth based on an incomplete tooth segment comprising missing surface areas, contextual information about the missing surface areas of the incomplete tooth segment and a model that is configured to generate a tooth shape that includes the missing surface areas. The embodiments for determining a surface representation of a complete tooth as described in this disclosure preferably rely on models that are configured to process surface data, such as point clouds or surface meshes, as produced by an optical scanner. A surface representation of a thus completed tooth defines a surface representation of a tooth segment contain areas that are visible during scanning, e.g. parts of the crown and parts that are obscured during scanning by neighbouring teeth, and / or due to inaccessible angles for scanning. In some embodiments, a surface representation of a completed tooth may also contain parts that are obscured during scanning by gingival tissue, in particular parts of the cervical area (the neck) of the tooth.

[0017] In orthodontics, surface representations of complete tooth segments are crucial components for treatment planning. Preferably, a surface representation of complete tooth segment represent the crown and the neck of a tooth. A complete tooth segment provides a detailed and accurate representation of the tooth’s visible geometry, allowing for realistic modelling of a patient’s dentition. During treatment planning movements of one or more teeth in a dentition can be predicted and visualized in a model of the dentition of patient which includes complete tooth segments and gingiva. These simulations ensure that planned tooth movements account for anatomical constraints, such as the surrounding soft tissues, to prevent the tooth from moving out of or beyond the gingival tissue or violating the interproximal spacing. Using the complete toothsegment in treatment planning, orthodontic outcomes can be optimized for both functionality and biological feasibility preventing undesired outcomes, including extrusion beyond the gingiva or interference with adjacent teeth.

[0018] In an aspect, the embodiments may relate to a computer-implemented method for automatically determining a surface representation of a complete tooth, wherein the method may comprise: receiving or determining scanning data, preferably clinical scanning data, representing an incomplete tooth segment, the incomplete tooth segment defining a part of a surface of a dentition representing one tooth of one or more teeth of a dentition, the incomplete tooth segment including one or more missing surface areas; determining contextual tooth information associated with the incomplete tooth segment, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and, determining a complete tooth shape surface of a complete tooth comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of the contextual tooth information and to output the tooth shape surface.

[0019] In an embodiment, the determining of the scanning data representing an incomplete tooth segment may include: receiving scanning data representing a surface of a dentition, the dentition including one or more teeth, the scanning data being obtained by scanning the dentition; and, determining the incomplete tooth segment based on the scanning data representing a surface of a dentition, wherein determining the incomplete tooth segment includes segmenting the dentition in one or more incomplete tooth segments and, optionally, one or more gingiva segments.

[0020] In an embodiment, the one or more missing surface areas may include and / or may consist of one or more subgingival surface areas and / or one or more interproximal surfaces areas.

[0021] In an embodiment, the one or more subgingival surface area may be determined up to a predetermined length below the emergence line of the complete tooth segment, preferably 5 mm below the emergence line, more preferably 3 mm below the emergence line.

[0022] In an embodiment, the method may further include: determining a complete tooth segment, wherein the one or more missing surface areas of the incomplete tooth segment are determined based on the complete tooth shape surface.

[0023] In an embodiment, the determining of the complete tooth segment may include: selecting surface data from the predicted complete tooth shape surface representing the one or more missing surfaces; and, stitching one or more missing surfaces into the missing areas of the incomplete tooth segment.In an embodiment, the contextual tooth information may include information about the gingiva and / or one or more teeth neighbouring the tooth representing the incomplete tooth segment.

[0024] In an embodiment, the contextual tooth information may include information about the tooth type of the incomplete tooth segment, for example a tooth type according to the FDI dental numbering system.

[0025] In an embodiment, the trained tooth model may be trained based on clinical data, the clinical data including surface representations of complete tooth segments, a complete tooth segment representing a surface of a crown including interproximal surfaces and subgingival surfaces.

[0026] In an embodiment, the trained tooth shape model may comprise a trained decoder model, such as a trained SDF deep learning model, configured to receive a shape parameter and a set of coordinates associated with a coordinate space of the incomplete tooth segment at its input and to generate signed distance values for each coordinate of the set of coordinates at its output, the signed distance values representing a complete shape surface.

[0027] In an embodiment, the shape parameter is a latent code.

[0028] In an embodiment, determining a tooth shape surface of a complete tooth may include: optimizing the shape parameter associated with the trained decoder model to determine the tooth shape surface.

[0029] In an embodiment, the optimizing may include determining a trial tooth shape surface using the trained decoder model based on the incomplete tooth segment and based on an initial shape parameter; computing a loss value for the trial tooth shape surface based on the one or more constraints; and, if the loss value does not meet one or more optimization conditions, modifying the shape parameter to determine a further trial tooth shape surface and to compute a further loss value.

[0030] In an embodiment, the initial shape parameter may be determined based one or more shape parameters, e.g. one or more latent codes, that were learned during the training of the decoder model.

[0031] In an embodiment, the determining a tooth shape surface of a complete tooth may include: determining by a trained encoder model, a latent code of a complete tooth shape surface that matches the surface of the incomplete tooth segment; and, determining by a trained decoder model a tooth shape surface based on the latent code and the incomplete tooth shape segment, the trained decoder model being associated with the trained encoder model.

[0032] In an embodiment, the one of the one or more constraints may include that for coordinates inside the scanned surface of the gingiva, the signed distance to thescanned surface of the gingiva is smaller than the signed distance to the tooth shape surface.

[0033] In an embodiment, the one of the one or more constraints may include that for coordinates in the coordinate space of the incomplete tooth segment, the sum of the signed distance of the tooth shape surface and the signed distance of the surface of a tooth neighbouring the incomplete tooth segment is positive.

[0034] In a further aspect, the embodiments may relate to a system for automatically determining a surface representation of a complete tooth, wherein the system comprises comprising: a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium, wherein responsive to executing the computer readable program code, the processor is configured to perform executable operations comprising: receiving or determining scanning data, preferably clinical scanning data, representing an incomplete tooth segment, the incomplete tooth segment defining a part of a surface of a dentition representing one tooth of one or more teeth of a dentition, the incomplete tooth segment including one or more missing surface areas; determining contextual tooth information associated with the incomplete tooth segment, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and, determining a complete tooth shape surface of a complete tooth comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of the contextual tooth information and to output the tooth shape surface.

[0035] In an embodiment, the executable operations may further comprise any of the steps as described with reference to the embodiments above.

[0036] In a further aspect, the embodiments may relate to a computer-implemented method for automatically determining a surface representation of a complete tooth. In an embodiment, the method may include determining an incomplete tooth segment based on scanning data, preferably clinical scanning data, representing a surface of part of a dentition comprising one or more teeth, the incomplete tooth segment including one or more missing surface areas; determining contextual tooth information associated with the incomplete tooth segment based on the scanning data, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and, determining a predicted complete tooth shape surface comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of the contextual tooth information and to output the predicted tooth shape surface comprising the one or more missing surface areas.In an embodiment, scanning data may be obtained by scanning a dentition. In an embodiment, the incomplete tooth segment may be determined by segmenting the scanning data representing part of the dentition in one or more incomplete tooth segments and, optionally, one or more gingiva segments.

[0037] In an embodiment, the one or more missing surface areas may include and / or consist of one or more subgingival surface areas, e.g. surface areas representing the neck of the tooth, and / or one or more interproximal surfaces areas.

[0038] In an embodiment, the method may further include: determining a complete tooth segment based on the incomplete tooth segment and the predicted complete tooth shape surface; preferably, the determining of the complete tooth segment including: selecting surface data from the predicted complete tooth shape surface representing the one or more missing surfaces; and, stitching selected surface data representing the one or more missing surfaces into the missing areas of the incomplete tooth segment.

[0039] In an embodiment, a complete tooth segment may comprise a completed subgingival surface area up to a predetermined length below the emergence line of the complete tooth segment, preferably 5 mm below the emergence line, more preferably 3 mm below the emergence line.

[0040] In a further aspect, the embodiments may relate to a system for automatically determining a surface representation of a complete tooth comprising: a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium, wherein responsive to executing the computer readable program code, the processor is configured to perform executable operations comprising: determining an incomplete tooth segment based on scanning data, preferably clinical scanning data, representing a surface of part of a dentition comprising one or more teeth, the incomplete tooth segment including one or more missing surface areas; determining contextual tooth information associated with the incomplete tooth segment based on the scanning data, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and, determining a predicted complete tooth shape surface comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of the contextual tooth information and to output the predicted tooth shape surface comprising the one or more missing surface areas.

[0041] In an embodiment, the executable operations further comprise any of the steps as described in the embodiments described in this disclosure.The embodiments may also relate to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry the method steps as described with reference to the embodiments above.

[0042] The embodiments will be further illustrated with reference to the attached drawings, which schematically will show embodiments in this disclosure. It will be understood that these embodiments are not in any way restrictive.

[0043] Brief Description of the drawings

[0044] Fig. 1A-1C depict examples of optical scans of a dentition including teeth and surrounding tissue such as gingiva;

[0045] Fig. 2 depicts a system for determining a surface representation of a complete tooth according to an embodiment;

[0046] Fig. 3A-3C depict complete tooth segments according to an embodiment;

[0047] Fig. 4A-4E depict details of a collision between surface representation of a complete tooth segment and gingiva;

[0048] Fig. 5A-5D illustrates a tooth segment that is determined based on the embodiments in this disclosure with and without a gingiva constraint;

[0049] Fig. 6A and 6B depict complete tooth segments which are determined without taking into account collisions with a neighbouring tooth;

[0050] Fig. 7A-7C depict details of collision between complete tooth and neighbouring tooth;

[0051] Fig. 8 depicts a system for determining a surface representation of a complete tooth according to an embodiment;

[0052] Fig. 9 depicts a system for determining a surface representation of a complete tooth according to another embodiment;

[0053] Fig. 10 illustrates a flow diagram of a method for determining a surface representation of a complete tooth according to an embodiment;

[0054] Fig. 11 illustrates factors influencing a latent code optimization process for determining a surface representation of a complete tooth according to various embodiments;

[0055] Fig. 12 Illustrates a training process for a tooth shape model that is trained to generate complete tooth shapes based on incomplete tooth segments according to an embodiment;

[0056] Fig. 13 depicts an example of a latent code optimization process for a tooth shape model during inference according to an embodiment;Fig. 14 depicts an inference phase for a tooth shape model that trained to generate complete tooth shapes based on incomplete tooth segments;

[0057] Fig. 15 depicts a flow process of a method for determining an initial latent code that may be used in a process for determining a surface representation of a complete tooth according to an embodiment;

[0058] Fig. 16 illustrates a process of forming a complete tooth based on an incomplete tooth segment according to an embodiment;

[0059] Fig. 17 demonstrates the impact of incorporating the gingiva constraint during inference.

[0060] Fig. 18 is a block diagram illustrating exemplary data processing systems described in this disclosure.

[0061] Description of the embodiments

[0062] Tooth segments determined based on segmenting a surface model of a scanned 3D maxillofacial data, such as dentition, typically include one or more missing surface areas, especially around the interproximal areas and / or the areas around to the emergence line, i.e. the line determining the intersection of the crown and the gingiva of a scanned dentition, and the subgingival areas of a tooth. Hence, the surface of tooth segments that are obtained by segmenting surface data representing a dentition acquired by an optical scanning system may be incomplete in the sense that certain surface areas are missing. In order to use these tooth segments in clinical dentition models that are used in digital treatment planning applications surface models of a complete teeth are needed in the sense that these surface models include subgingival and interproximal surface areas.

[0063] Fig. 1 A illustrates scanned surface data representing the surface of a maxillofacial structure, e.g. a dentition 102, which may be captured using an optical scanner, such as an intra-oral scanner (IOS). The scanned surface may include one or more teeth 104 and surrounding tissue such as gingiva, providing a detailed 3D representation of the visible portions of the dentition. The surface of the dentition may be represented as a point cloud or a mesh, e.g. a triangulated mesh, including vertices, edges, and faces interconnected to model the scanned surfaces. During the scanning process the portions of the teeth that are optically visible and accessible to the scanner, such as areas above the gingiva.

[0064] Fig. 1B shows an example of a tooth segment 103 which is the result of a segmentation process of the scanned dentition 102 depicted in Fig. 1A. Accurate segmentation and classification of 3D maxillofacial surface data may be based on one or more trained neural network systems. Examples of such trained neural network systemsare described in WO2021009258, which is hereby incorporated by reference in this application. Based on such segmentation and classification scheme, a set of tooth segments may be determined, wherein each tooth segment of the set of tooth segments may be associated with a tooth type. Teeth may be categorized based on their specific shape using a classicisation system such as the FDI (Federation Dentaire Internationale) notation. In the FDI system, each tooth is assigned a two-digit identifier: the first digit denotes the quadrant of the dentition where the tooth is located, and the second digit specifies the tooth's position within that quadrant, such as categories defined by the FDI notation.

[0065] As shown in Fig. 1B, the tooth segment is a surface representation of an individual tooth, that has been segmented from a 3D scan of the dentition. Due to the scanning process, a tooth segment may be incomplete in that sense that certain surface areas, such as (part of the) interproximal surfaces areas and / or (part of) the subgingival surface areas, are missing. In this disclosure, such tooth segment may be referred to as an incomplete tooth segment. The incomplete tooth segment may include visible portions of the tooth, typically those above the gingiva and captured by the scanning process. It excludes areas obscured by neighbouring teeth, gingival tissue, or areas inaccessible due to scanning limitations or occlusions.

[0066] Fig. 1C provides a more detailed view of tooth 103 in the scanned dentition 102 of Fig. 1A. When comparing Fig. 1B and 1C, a clear relationship exists between surface of the segmented tooth 104 and the dental tissue surrounding tooth 104, e.g. neighbouring teeth 108i,2and associated gingiva 106. These dental elements may provide contextual information about the missing surface areas of the incomplete tooth segment.

[0067] The embodiments in this disclosure aim to determine a complete tooth segment based on the incomplete tooth segment, contextual information about the missing surface areas of the incomplete tooth segment and a model that is configured to generate a tooth shape that includes the missing surface areas. The embodiments for determining surface representations of complete tooth as described in this disclosure preferably rely only on surface data as produced by an optical scanner. A surface representations of complete tooth defines a surface representation of a tooth segment that contains areas that are obscured during scanning by gingival tissue, neighbouring teeth, and / or inaccessible angles.

[0068] In orthodontics, complete tooth segments are crucial components for treatment planning. A complete tooth segment provides a detailed and accurate representation of the tooth’s visible geometry, allowing for realistic modelling of a patient’s dentition. During treatment planning movements of one or more teeth in a dentition can be predicted and visualized in the model of the dentition which includes complete toothsegments and gingiva. These simulations ensure that planned tooth movements account for anatomical constraints, such as the surrounding soft tissues, to prevent the tooth from moving out of or beyond the gingival tissue or violating the interproximal spacing. Using the complete tooth segment in treatment planning, orthodontic outcomes can be optimized for both functionality and biological feasibility preventing undesired outcomes, including extrusion beyond the gingiva or interference with adjacent teeth.

[0069] Various data representations exist for representing surfaces of objects, such as maxillofacial structures. A well-known representation is a 3D triangulated mesh, which provides a precise depiction of the surface geometry. Mesh representations as shown in Fig. 1A-1C include ordered arrangements of interconnected vertices (typically ranging from 100 to 10,000) that accurately captures the tooth's geometry. The surface orientation of a surface mesh may be defined by the normal vectors of the triangles, which may also be used to distinguish between the inside and outside of the tooth. Typically, the basic teeth shapes may be defined as 3D meshes, i.e. a 3D model of polygons. The polygons that are used to model a 3D dental object are geometric shapes, such as quadrangles or triangles, which can be further broken down into vertices (defined by x,y,z coordinates of the coordinate system of a 3D mesh) and lines. A mesh representation may be a standard output format for an intraoral scanner.

[0070] Fig. 2 illustrates a system for determining a surface representation of a complete tooth according to an embodiment. The system may be configured to generate an accurate surface representation of a complete tooth segment including subgingival surface areas and interproximal surfaces areas that may be used in digital dental treatment planning application. To that end, the system may include a model that is configured to generate the missing surface areas of the incomplete tooth segment. Data that is input to the system may include data representing an optical scan of a part of a dentition 210, which may include gingiva. The data may be obtained by an optical scanner which is configured to generate surface data that captures the visible portions of the teeth and the gingival tissue. The scanned data may be processed to generate one or more tooth segments. However, as previously discussed, these tooth segments are incomplete due to occlusions or limitations in the scanning process as discussed with reference to Fig. 1.

[0071] A segmentation process may be used to separate data of the dentition into one or more separate incomplete tooth segments 206, where each incomplete tooth segment may represent a specific scanned tooth with missing surface areas, such as one or more missing surface areas associated with the interproximal part of the tooth segment and / or one or more missing surface areas that is covered by gingiva close to the crown emergence line.Contextual tooth information 212 may be derived from the surface data representing the scanned dentition. In an embodiment, the contextual tooth information may include information, e.g. points or sets of points, associated with the scanned gingiva and teeth neighbouring an incomplete tooth. In a further embodiment, it may include information about a spatial relationship between an incomplete tooth segment and one or more teeth neighbouring the incomplete tooth segment. In another embodiment, the contextual information may include information about a spatial relation between the gingiva and the incomplete tooth segment. For example, the contextual information may include information about the position of a crown emergence line, which identifies the intersection between the crown and the gingiva. In yet a further embodiment, contextual information may include information about the tooth type, e.g. the FDI number.

[0072] A surface representation of the incomplete tooth segment 206 and, optionally, at least part of the contextual tooth information 212 may be input into a tooth shape model 202. This model may be trained to receive the surface representation of the incomplete tooth comprising one or more missing surface areas and, optionally, the contextual information and to generate a tooth shape surface 208 of a complete tooth, including the one or more missing surface areas. This model may be trained based on surface data. In particular, the model may be trained based on surface representations of complete tooth segments that include the subgingival and interproximal surface areas. In contrast to known models no other data modalities, such as (CB)CT data, are needed to train the model.

[0073] The embodiments in this disclosure use the contextual tooth information derived from surface representations of dentitions as one or more constraints 214 in the process to generate a predicted tooth shape surface of a complete tooth. These constraints may include clinical information about the surrounding gingiva 216 and / or one or more neighbouring teeth 218, which provide anatomical context and boundary conditions necessary for an accurate tooth surface prediction that is needed for determining the complete tooth segment.

[0074] In an embodiment, the thus obtained surface representation may be used as a complete tooth segment in a digital dental workflow application.

[0075] In another embodiment, one or more parts of the predicted tooth shape surface 208 may be combined with the incomplete tooth segment 206 to produce a complete tooth segment 212. In particular, the one or more missing surface areas, i.e. the subgingival and / or interproximal surfaces areas, in the incomplete tooth segment may be repaired 210 based on the parts of the predicted tooth surface that represent the one or more missing surface areas. This step may include determining the one or more missing surfaces in the predicted tooth shape surface, selecting surface data representing the one or more missing surfaces from the predicted tooth shape surface and stitching theselected surface data representing the one or more missing surfaces into the missing areas of the incomplete tooth segment. This way, a complete tooth segment is determined that is a complete and an anatomically accurate representation of the tooth which is suitable for use in orthodontic treatment planning software or other digital dental applications.

[0076] Fig. 3A-3C illustrate examples of surface models of a dentition comprising complete tooth segments according to various embodiments. In particular, Fig. 3A illustrates an arrangement of complete teeth segments forming a surface model of a dentition of a patent. The model may be determined by segmenting a surface representation of a dentition obtained by optically scanning a dentition as explained with reference to Fig. 1 into incomplete tooth segments and gingiva, wherein each incomplete tooth segment may be associated with a location in the dentition. Each incomplete tooth segment and, optionally, the associated contextual tooth information of each incomplete tooth segment may be input to a system for completing an incomplete tooth segment into a complete tooth segment as described with reference to Fig. 2.

[0077] The complete tooth segments and the segmented gingiva may then be used to construct a surface model of the dentition comprising complete tooth segments may be obtained as shown in Fig. 3A. In this figure, the gingiva is illustrated as semitransparent so that the subgingival surface of each complete tooth segment is visible. This is illustrated in more detail in Fig. 3B, which is an zoomed-in part of a region 302 of the dentition of Fig. 3A. Fig. 3B shows a complete teeth segment including a visible surface part 304 and a subgingival surface part 306 that is normally not visible because it is covered by gingiva.

[0078] In the embodiment of Fig. 3A and 3B, the tooth completion may be determined without using the gingiva as a constraint in the tooth shape generation process. In certain situations however irregularities in the predicted missing surfaces may appears if the local tooth context of an incomplete tooth segment is not taken into account. Fig. 3C depicts a model of the dentition comprising complete tooth segments and gingiva of a dentition of another patient than the one shown in Fig. 3A and 3B. As shown in this figure, because the gingiva is not taken into account as a constraint in the tooth completion, a part 302 of the modelled subgingival surface area may collide with the gingiva.

[0079] Fig. 4A-4E depict further detail of the collision between the complete tooth segment and gingiva as shown in Fig. 3C. Fig. 4A depicts a close-up of the complete tooth segment 402 which includes a surface area 404 that collides at a certain position with the gingiva. As shown in this figure, surface area 404 of the subgingival surface of the complete tooth segment protrudes through the gingival surface indicating that at least part of the complete subgingival surface area is anatomically inaccurate. Fig. 4B and 4Cprovide different view of the complete tooth segment wherein the other neighbouring complete tooth segments are removed. Fig. 4D and 4E illustrate cross-sectional representations of the complete tooth segment as depicted in Fig. 4B and 4C, wherein 406 represents a cross-section of the tooth and 408 represents a cross-section of the gingiva. These cross-sections highlight how the tooth surface intersects with the gingival surface, indicating an area 410 which violates anatomical constraints. In an embodiment, such collisions may be addressed during the tooth surface completion process to ensure that the complete tooth segment is both anatomically realistic and biologically feasible.

[0080] Fig. 5A-5D depicts details of a tooth segment that is determined without taking into account gingiva constraints (Fig. 5A and 5B) and with gingiva constraints (Fig.

[0081] 5C and 5D). These figures clearly show that the gingiva constraints allow generation of a complete tooth segment that is anatomically more accurate compared with the generation of a complete tooth segments in which the constraints are not taken into account.

[0082] Fig. 6A and 6B depict a model comprising tooth segments that are determined without taking into account collisions with neighbouring teeth. Here, Fig. 6A depicts the model including the gingiva and Fig. 6B depicts the model without the gingiva. When completing the interproximal surface areas of an incomplete tooth segment, predicted areas of a complete tooth segment 602 may occlude and / or collide with part of a surface of a neighbouring tooth 606 in an interproximal area 604. Part of the tooth surface experiences a collision with the surface of a neighboring tooth due to occlusion. This condition arises during the scanning process, where the proximity of the adjacent tooth obscures or occludes portions of the scanned surface, leading to an incomplete surface representation of the tooth segment.

[0083] Fig. 7A-7C depict a more detailed view of collision between a complete tooth segment and neighbouring tooth as shown in Fig. 6B. In particular, Fig. 7A and 7B provide a side view and a top view of the complete tooth segment 702 and its neighbouring tooth segment 704. The occluding neighboring tooth obstructs portions of the surface, resulting in gaps or overlaps in the scanned data. Fig. 7C provides a cross-sectional view of the collision area, illustrating how the neighboring tooth intersects with the tooth being scanned. The cross-section clearly shows a collision region 710 wherein the surface lines of the complete tooth segment 706 and its neighboring tooth segment 708 overlap. This figure emphasizes the need for using constraints during the tooth completion process to resolve such intersections and restore the missing tooth surface accurately.

[0084] Fig. 3-7 above collectively emphasize the advantageous use of constrains for accurately determining surface representation of a complete tooth while preventing collisions with the gingiva or neighbouring teeth. These constraints may be derived from contextual tooth information that is associated with an incomplete tooth segment that forwhich a surface representation of a complete tooth needs to be determined. Additionally, they emphasize the need to maintain functional and anatomical integrity in the complete tooth segments, which is essential for achieving accurate and realistic outcomes in applications such as orthodontic treatment planning.

[0085] Fig. 8 illustrates a system 802 for automatically determining a surface representation of a complete tooth according to an embodiment. Surface data 810 representing the surface of a dentition comprising one or more teeth may be segmented to determine one or more incomplete tooth segments 806. The surface data may be obtained by optically scanning the dentition of a patient. The incomplete tooth segment represents part of a tooth surface with one or more missing areas due to scanning limitations or occlusions.

[0086] As previously discussed, the segmentation and classification may be based on one or more trained neural network systems. In addition to determining one of the one or more teeth segments in the scanned dentition, contextual tooth information 812 may be derived from the scanned data. Contextual information may include information about neighbouring teeth 818 and gingiva 816. The contextual information may be used during tooth segment completion as optimization constraints such that the complete tooth segment conforms to realistic anatomical and spatial relationships within the dentition.

[0087] The system may include a parameterized tooth shape model 804 that is configured to predict on the basis of an incomplete tooth segment, a tooth shape surface comprising missing surface areas of the incomplete tooth segment, wherein the missing surface areas are clinically accurate.

[0088] In an embodiment, the tooth shape model may be implemented as a decoder model that is parameterized by a latent code that encodes various realistic tooth shapes. The latent code provides a low-dimensional representation that encodes the variability of realistic tooth shapes in the scanned dentition and may serve as an additional input to the tooth shape model 804. Hence, in that case the latent code may be regarded as a shape parameter that is provided to the input of the tooth shape model.

[0089] A set of point-distance pairs may be used as a representation of a surface shape of a dentition or a tooth. In such representation, 3D surface points may be distributed throughout a 3D space, typically near or on the surface of a tooth. Each point is associated with a signed distance indicating its proximity to the nearest point on the surface. The signed distance is positive if the point lies outside the tooth, and negative if it is inside. As such, each point-distance pair may include four values: three representing the point's 3D coordinates and one for the signed distance.

[0090] Point-distance pairs can be generated from a mesh by first sampling a point on the mesh. A small offset, such as one derived from a 3D uniform distribution, is then applied to the sampled point. Finally, the signed distance between the offset pointand the nearest point on the mesh may be calculated. Conversely, it is possible to reconstruct a mesh from a set of point-distance pairs. A commonly used method for this purpose is Marching Cubes (Lorensen et al. Marching cubes: A high resolution 3d surface construction algorithm. In SIGGRAPH, volume 21, pages 163-169. ACM, 1987.), which generates a mesh by processing point-distance pairs arranged within a 3D grid.

[0091] An extension of the set of point-distance pairs is the signed distance function (SDF). This function takes a 3D point as input and outputs a signed distance indicating the point's position relative to the surface. The SDF provides a continuous and smooth representation of the surface, capable of achieving virtually an unlimited resolution. By applying the SDF to a 3D grid of points, a corresponding set of pointdistance pairs can be generated, which can then be used to reconstruct a mesh representation of the surface.

[0092] Hence, in an embodiment, a complete tooth segment may be represented using signed distance function (SDF) values, and consequently, the predicted decoder values are also expressed as SDF values. This data representation offers the flexibility to handle any form of input data, such as incomplete tooth segments with a variable number of vertices in any mesh format. This approach provides an advantage over the traditional auto-encoder frameworks, where the encoder requires the input during inference to closely resemble the training data. For a tooth segment represented as SDF values, the completed tooth segment may be converted into a mesh format by applying the Marching Cubes algorithm to the set of point-distance pairs.

[0093] The system may execute a tooth completion process that involves determining an optimal latent code that best represents the incomplete tooth segment, received as input. To that end, the system may be configured to execute an optimization process wherein an optimizer 824 may iteratively adjust the shape parameter (e.g. the latent code) 826 that is provided to the input of the parameterized tooth shape model to minimize a loss function 820, which measures the difference between the predicted decoder output and the input data, subject to the contextual constraints 814. When the computed loss meets a stopping criteria, the optimization process is stopped. This way, an accurate tooth shape surface may be obtained. In an embodiment, the thus obtained surface representation may be used as a complete tooth segment in a digital dental workflow application.

[0094] In another embodiment, one or more parts of the predicted tooth shape surface 808 may be combined with the incomplete tooth segment 806 to produce a complete tooth segment 812. In particular, the one or more missing surface areas, i.e. the subgingival and / or interproximal surfaces areas, in the incomplete tooth segment may be repaired 810 based on the parts of the predicted tooth surface that represent the one or more missing surface areas in a similar way as described with reference to Fig. 2. Thisway, a complete tooth segment is determined that is a complete and an anatomically accurate representation of the tooth which is suitable for use in orthodontic treatment planning software or other digital dental applications.

[0095] The optimization scheme illustrated in Fig. 8 is a non-limiting example and many different implementations may be possible without departing from the teaching of the embodiments. Collision losses may be computed based on point-to-surface distance as described in the article of Engelmann et al, From points to multi-object 3D reconstruction, htps: / / arxiv.org / abs / 2012.11575v3, which is hereby incorporated by reference into this application.

[0096] Different machine learning models may be used in the scheme as illustrated in Fig. 8. These machine learning models have in common that they are trained to produce a complete tooth shape based on one or more shape parameters that may be provided to the input of the machine learning model. Further, these machine learning models are associated with a loss function that may compute a loss value that provides a measure how well a tooth shape meets the tooth constraints.

[0097] In an embodiment, a trained SDF deep learning model may be used which is configured to represent a wide variety of realistic complete tooth segments, wherein each tooth shape is associated with a specific latent code. The trained SDF model may be parameterized by a set of trainable parameters (e.g. weights), which may be implemented using neural networks such as multi-layer perceptrons (MLPs) or other deep neural networks. Alternative neural network architectures, such as convolutional neural networks (CNNs) or transformer-based models, could also be employed depending on the spatial resolution or complexity of the input data. The parameters of the SDF model are trained on a comprehensive (e.g. including diverse complete tooth segments, which may be categorized by FDI types) dataset of realistic surface representations of complete tooth segments, enabling the model to learn intricate geometric patterns and generalize across diverse tooth morphologies.

[0098] Various known SDF-based machine learning models may be used for efficiently generating complete tooth segments, including but not limited to DeepSDF (DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation, htps: / / arxiv.org / abs / 1901.05103v1), Deformed Implicit Field by Deng et al. (Modeling 3D Shapes with Learned Dense Correspondence. arXiv preprint, arXiv:2003.12299), or ToothDIT by Chen et al. These models have been employed to encode and reconstruct 3D shapes.

[0099] Fig. 9 depicts a system for the automatically determining a surface representation of a complete tooth according to an embodiment. An optical scan of part of a dentition 910 is used to obtain data representing an incomplete tooth segment 906. This optical scan may also capture relevant contextual information 912 about the scannedteeth, including surrounding anatomical structures such as gingiva tissue. The contextual information 912 may be used as additional constraints for generating a tooth shape surface that can be used to determine a complete tooth shape. These constraints may include details about the gingiva 916 and / or the positioning of neighboring teeth 918, ensuring the reconstruction adheres to anatomical consistency.

[0100] In one embodiment, the contextual information and the incomplete tooth segment may be processed by using encoder-decoder model 902. The encoder model 920 may be configured to compute a latent representation (latent code) of a complete tooth shape surface that accurately matches the surface of the incomplete tooth segment, effectively encoding the features required for the tooth shape completion. The tooth shape model which is configured to generate the tooth shape surface, includes a trained decoder 922, which maps the latent code back to the data space, so that a predicted toot shape surface 908 can be determined. In an embodiment, the thus obtained surface representation may be used as a complete tooth segment in a digital dental workflow application.

[0101] In another embodiment, one or more parts of the predicted tooth shape surface 908 may be combined with the incomplete tooth segment 906 to produce a complete tooth segment 912. In particular, the one or more missing surface areas, i.e. the subgingival and / or interproximal surfaces areas, in the incomplete tooth segment may be repaired 810 based on the parts of the predicted complete tooth surface that represent the one or more missing surface areas in a similar way as described with reference to Fig.

[0102] 2. This way, a complete tooth segment is determined that is a complete and an anatomically accurate representation of the tooth which is suitable for use in orthodontic treatment planning software or other digital dental applications.

[0103] This encoder-decoder scheme as shown in Fig. 9 ensures efficient tooth segment completion without the need for an iterative optimization. During training, the encoder and decoder are optimized together using a dataset of complete tooth segments. The encoder is trained to generate meaningful latent codes, while the decoder is trained to reconstruct realistic tooth shapes from these latent representations. The training process may minimize a reconstruction error, ensuring that a tooth shape surface generated by the decoder closely matches a ground-truth complete tooth segment.

[0104] At inference, the trained encoder processes the input data (the incomplete tooth segment and contextual constraints) in a single step, generating a latent code. The decoder then uses this latent code to produce a tooth shape surface which is used to determine a complete tooth segment. This one-step approach eliminates the need for iterative optimization of the latent code as described with reference to Fig. 8, allowing for fast and deterministic reconstructions suitable for real-time or automated dental workflows.The internal structure of the encoder and / or decoder is primarily determined by the chosen tooth segment representation. As previously highlighted various representations, such as voxels, raw point clouds, meshes, SDF values are known common representations of scanned dentition. Each representation influences the design of the encoder and decoder. For instance, voxel-based representations are well-suited for 3D CNNs, while raw point clouds are effectively processed using architectures like PointNet or PointNet++. Similarly, mesh-based representations often leverage Graph Neural Networks (GNNs) to capture the geometric and topological relationships inherent in the data. The decoder's design also adapts to the output format representation, using techniques like Signed Distance Functions (SDF) for continuous surfaces, point cloud decoders for discrete reconstructions, or mesh based decoders for outputting meshes with vertices and faces.

[0105] In an embodiment, the system for completing an incomplete tooth segment may leverage a full auto-encoder architecture only during training. For the inference process, only the decoder is retained, and the optimal latent vector corresponding to a given tooth segment is determined through an iterative optimization process. This process involves initializing a latent vector and refining it iteratively by minimizing a loss function. The loss function may be configured to quantify the difference between the reconstructed complete tooth shape surface, generated by the decoder, and the ground-truth completed tooth segment. The optimization process may be guided by constraints derived from scanned contextual information 912, ensuring that the completed tooth shape conforms to realistic dental anatomy and maintains compatibility with surrounding structures, such as adjacent teeth 918 and gingiva 916.

[0106] Fig. 10 outlines a method for determining a surface representation of a complete tooth based on scanning data of a dentition according to an embodiment. The process may start by receiving scanning data representing a surface of a dentition (step 1002), the dentition including one or more teeth. The scanning data may be obtained by optically scanning a dentition of a patient. In an embodiment, the scanned data is obtained using an IOS scanner.

[0107] Based on the scanned data, an incomplete tooth segment is determined, with the segment defining part of the surface of the dentition that represents one tooth of the one or more teeth of the dentition (step 1004). The incomplete tooth segment may include one or more missing surface areas. In an embodiment, one or more missing surface areas include (or represent) one or more subgingival surface areas and / or one or more interproximal surfaces areas.

[0108] The method then involves determining contextual information associated with the incomplete tooth segment (step 1006). In an embodiment, contextual information may be used to determine one or more constraints for predicting the one or more missingsurface areas. Based on the incomplete tooth segment and the contextual information, a complete tooth shape surface is determined (step 1008), comprising the one or more missing surface areas, by using a trained tooth shape model. The trained tooth shape model may be configured to receive the incomplete tooth segment and contextual information and to output a surface representation of a complete tooth shape. The thus obtained surface representation may be used as a complete tooth segment in digital dental workflow applications.

[0109] In an embodiment, a completed tooth segment is determined wherein the one or more missing surface areas of the incomplete tooth segment are reconstructed (repaired) based on the tooth shape surface (step 1010). The method thus enables completion of missing parts of an incomplete tooth segment to create a surface representation of a realistic, complete tooth segment.

[0110] Fig. 11 illustrates the factors that may influence the optimization process of the latent code (i.e. , tooth shape parameters) used to complete an incomplete tooth segment, in accordance with an embodiment. In this embodiment, the incomplete tooth segment may be derived by segmenting 1104 an optical scan of part of a dentition 1102.

[0111] The incomplete tooth segment may be classified and categorized 1106 based on a taxonomy, such as its Federation Dentaire Internationale (FDI) type. The incomplete tooth segmentation and classification may be based on one or more trained neural network systems.

[0112] Once the class (e.g. FDI label) of a tooth segment is identified, the initial latent code values are determined based on the learned latent codes for similar teeth obtained during the training of the tooth shape model, serving as the starting point for the latent space optimization 1108. The similar teeth may be identified based on their FDI categorization. In an embodiment, the initial latent code values for an input incomplete tooth segment may be computed based on metrics derived from similar tooth segments. These metrics could include the averages of learned latent codes corresponding to similar tooth segments, median values, or other statistical measures that capture the general characteristics of the latent codes associated with the same or comparable tooth types.

[0113] The latent code optimization may also leverage contextual information determined from the optical scan. The contextual information is associated with each incomplete tooth segment and may comprise one or more constraints for predicting the one or more missing surface areas of the incomplete tooth segment. These constraints may be integrated into the latent code optimization loss as additional loss factors to penalize anatomical inconsistencies. In one embodiment, the constraints are represented as additional loss functions designed to penalize collisions between the tooth segment and neighbouring teeth or gingiva 1110.In an embodiment, where the incomplete tooth segment is represented as a signed distance function, the gingiva constraint loss ensures that the reconstructed surface of the completed tooth surface does not intrude into the gingiva. An example of a colliding completed tooth segment and gingiva surface is presented in Fig. 4A-4E.

[0114] Avoiding this collision may be achieved by penalizing cases where the predicted SDF values by the tooth shape model 504 incorrectly indicate that points are inside the gingiva.

[0115] To compute this loss, during the latent code optimization, a set of 3D points (x) is sampled near or on the gingiva surface, each associated with its true signed distance value (s) to the gingiva surface. Points located exactly on the gingiva surface have a signed distance of zero, while points outside the gingiva have positive signed distances. For each sampled point, the loss is computed as the maximum of zero or the difference between the true signed distance (s), i.e. the signed distance to the scanned surface, and the predicted SDF value (SDF(x)). In other words, in an embodiment, a gingiva constraint may be formulated as the signed distance to the scanned surface of the gingiva should be smaller than the signed distance to the modelled tooth surface. This ensures that the predicted SDF values remain non-negative for points located on or outside the gingiva. Accordingly, the loss for each sample point x is defined by equation 1:

[0116] ^gingiva HiaX (0, S SDF(x^) (1)

[0117] This formula ensures that the predicted SFD(x) value should not be negative when the true signed distance value (s) is 0 or positive. Also, for points outside the gingiva (s > 0), the loss similarly penalizes predictions where SDF(x) < s, encouraging the reconstructed tooth segment surface to respect gingival boundaries.

[0118] In another embodiment, where the incomplete tooth segment is represented as a signed distance function, the neighbouring teeth collision loss ensures that the reconstructed tooth segment does not collide with adjacent teeth. An example of colliding adjacent teeth is presented in Fig. 7A-7C. This may be accomplished by penalizing cases where the predicted SDF values of the completed tooth surface and a neighbouring tooth surface indicate overlapping regions.

[0119] To achieve this, the loss penalizes configurations where during inference, the surface of the completed tooth segment and its neighbouring tooth surface overlap. Specifically, if two neighbouring teeth surfaces are represented by SDFA(x) and SDFB(x) a collision is detected when there exists at least one point x for which the sum of the signed distances from the two SDFs is negative, i.e., SDFA(x) + SDFB(x) < 0. This condition implies that the point x lies within or in the neighbourhood the intersecting region of the two surfaces. The loss is derived by sampling a set of points x in the vicinity of the surface of the incomplete tooth segment that requires completion.To express this constraint, a neighbouring-teeth collision loss is defined as:

[0120]

[0121] where Z represents a set of sampled 3D points around the reconstructed and neighbouring teeth. The ‘max’ operator ensures that only sampled points indicating collisions contribute to the loss, while points that lie outside the teeth surface or on the surfaces are ignored.

[0122] Efficiently sampling 3D points is critical for the implementation. Sampling should focus on regions where collisions are likely, such as near the expected contact points of the neighbouring teeth based on their segments. This avoids unnecessary computations for points far from the considered incomplete tooth, which would invariably have large, non-colliding SDF values. If the SDFs are not defined in the same reference frame, the points must be appropriately transformed to a canonical pose to ensure alignment for accurate evaluation.

[0123] For example, if the two SDFs are based on different orientations or positions of the teeth in 3D space, the points being checked for collisions need to be aligned (transformed to a standardized or "canonical" pose) 1114 before their distances are computed. This alignment ensures that the SDF values accurately reflect the spatial relationships between the teeth and prevent incorrect results due to misaligned coordinate systems.

[0124] In orthodontic treatment, the pose of a tooth refers to the position and orientation of the tooth relative to a reference coordinate system shared among all teeth in the dentition. To define this pose, a specific reference frame for each tooth is established. Typically, the origin of this reference frame is positioned near the geometric center of the portion of the tooth that has erupted above the gingiva.

[0125] The axes of the reference frame are generally aligned along three primary directions: the occlusal direction, the buccal direction, and the distal direction. Depending on the tooth, this reference frame may be configured as either right-handed or lefthanded. This specific configuration, commonly referred to as the canonical pose of the tooth, allows for a consistent and comparable representation of tooth shapes across the dentition. Accurate determination of the canonical pose of 3D maxillofacial data may be based on one or more trained neural network systems. Examples of such trained neural network systems are described in W02020007941 , which is hereby incorporated by reference in this application.

[0126] Additionally, a tooth segment may be scaled to a uniform size, standardizing its dimensions relative to other tooth segments segmented from the scanned dentition. An alternative strategy may involve leveraging backpropagation toiteratively refine the sampling process by identifying 3D points most likely to contribute to the loss, further improving computational efficiency and accuracy.

[0127] Fig. 12 illustrates an example of a training process for a parameterized tooth shape model based on a Signed Distance Function (SDF) approach. The model, referred to as the SDF model, is designed to generate complete tooth shapes surfaces for partial intraoral scans that represent incomplete tooth segments.

[0128] Optionally, the complete tooth segment used as input to the SDF model, may be pre-processed 1216 to standardize its representation in the 3D space. This may involve determining a canonical pose, which establishes a consistent reference frame for the tooth based on its orientation and position in the dentition. Once the canonical pose is identified, the tooth segment may be transformed to align with this reference frame.

[0129] Further details regarding the determination of the canonical pose are provided in reference to Fig. 11. Additionally, normalization may be applied by scaling the input tooth segment to a uniform size. These steps ensure that the input tooth segments are standardized, reducing variability and improving the robustness of the SDF model during training or inference.

[0130] The input to the SDF model comprises 3D spatial points 1204 sampled from the tooth shape surface, and, optionally from the surrounding surface area of the completed tooth segment received as input. Each 3D sampled point is paired with its corresponding ground truth signed distance value 1214, which indicates the distance of the point from the tooth surface with negative values for points inside the tooth and positive values for points outside the tooth surface.

[0131] The completed tooth segments used as inputs to the SDF model are derived from a labelled clinical dataset 1202 comprising a diverse collection of completed tooth segments. This dataset may include samples from various tooth types (e.g., FDI categories), ensuring a comprehensive representation of different tooth morphologies and geometries.

[0132] Each 3D sampled point is paired with its ground truth signed distance value 1214, creating a set of point-distance pairs that serve as training data for the SDF model. The process of converting a tooth segment from a mesh representation to an SDF representation, and vice versa, is further detailed with reference to Fig. 1.

[0133] The SDF model is further parameterized by an additional input: a latent code 1206, that encodes the unique shape characteristics of a complete tooth segment. The latent code serves as a descriptor of the overall tooth morphology, enabling the model to generalize across varying tooth shapes and types. By combining spatial information (3D points) with the latent code, the model can accurately reconstruct complete tooth shape surfaces from incomplete segments. The latent code effectivelyencapsulates the shape characteristics of a tooth, serving as a concise representation of its surface geometry

[0134] The SDF model described in the embodiment of Fig. 12, operates as a decoder-only model. In this configuration, the neural network directly predicts the signed distance value for any 3D point given its latent code as input, eliminating the need for an explicit encoder. The SDF model may employ a deep neural network 1208 trained with clinical data of complete tooth segments 1202. These complete tooth segments serve as the ground truth for the SDF representation and SDF model optimization.

[0135] The objective of the SDF model is to accurately predict the signed distance value at any given spatial point (x, y, z), which indicates the distance of that point to the nearest surface of the tooth segment.

[0136] During training, a set of 3D points 1204 is sampled from the surface and surrounding region of each training tooth segment. These sampled points are associated with their ground truth distance values 1214, creating point-distance pairs that describe the spatial relationship between each point and the tooth shape surface. Along with these point-distance pairs, the network also takes as input a latent code 1206 that encodes the unique shape characteristics of the complete tooth. In an embodiment, the latent code may be represented as a fixed-size vector and may be randomly initialized using a Gaussian distribution. Other initialization strategies such as zero-mean values and other distributions may be used for the latent code initialization. The latent code serves as a compact representation of the tooth's morphology, allowing the model to generalize across a wide variety of tooth shapes.

[0137] The SDF model (i.e. the deep neural network) predicts a signed distance value 1210 for each 3D input point, based the latent code 1206 and the 3D spatial coordinates 1204 provided as inputs.

[0138] The predicted SDF values are compared to the ground truth distances 1214, and a loss function 1212 calculates an error. In an embodiment, the loss function may be defined as:

[0139]

[0140] where X represents the sampled set of point-distance pairs (x,s), with x representing the 3D point and s the ground-truth distance. This loss function quantifies the difference between the predicted and true SDF distances for all sampled 3D points. Alternatively, other loss functions, such as the L2 norm, may be also utilized to quantify the error. The deep neural network may minimize the loss through backpropagation, iteratively updating the network parameters and latent code to improve the accuracy of SDF value predictionsfor the input data. This optimization process continues until the SDF model can reliably reproduce the SDF field of the complete tooth shapes based on the training set.

[0141] This approach builds upon the principles of the DeepSDF method outlined in Park et al. (DeepSDF: Learning continuous signed distance functions for shape representation." Proceedings of the IEEE / CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 165-174. DOI: 10.1109 / CVPR.2019.00025), adapting and extending it for application in the context of automatic generation of completed teeth segments.

[0142] An advantage of this approach is the ability to embed multiple tooth shapes into a shared latent space, enabling the network to generalize across different morphologies. During inference, the latent code is optimized to match the available data from an incomplete tooth segment, allowing the system to reconstruct the most likely complete tooth shape surface.

[0143] Fig. 13 illustrates a latent code optimization process, focusing on reconstructing a complete tooth shape surface from an incomplete tooth segment 1302 using a Signed Distance Function (SDF) model. The process begins with the incomplete tooth segment 1302, which is represented as a mesh, which may be obtained from the segmentation of an optical scan of part of dentition. Optionally, the incomplete tooth segment may undergo pre-processing steps similar to those applied to the training data used for training the SDF model. These steps standardize its representation in 3D space. A set of 3D sample points 1304 is extracted from the tooth surface, and, optionally from the surrounding regions. The latent code 1306 is initialized and provided as input to the SDF model, serving as the starting point for the latent code optimization process. This latent code is a compact vector representation of the tooth's shape, and its initialization plays a critical role in ensuring fast convergence and accurate tooth surface shape reconstructions. In one embodiment, the initial latent code is derived from the average latent code of tooth shapes within the same FDI category. These average latent codes are precomputed and learned during the training of the SDF model, leveraging prior knowledge of similar tooth shapes to provide a well-informed starting point for optimization. Hence, this initialization leverages prior knowledge of similar tooth types, reducing the computational complexity and improving the likelihood of generating anatomically plausible reconstructions.

[0144] The extracted sample points 1304 and the initialized latent code 1306 are fed into the SDF model which operates with fixed parameters 1308. Here, 'fixed' means that the parameters of the SDF model were pre-trained during the training phase and remain unchanged during the inference process, ensuring that only the latent code is optimized to reconstruct the tooth shape surface. The model predicts a signed distance value 1310 for each sample point, which is then compared to the expected ground truth.Additional constraints, such as gingiva boundaries or neighbouring teeth collision avoidance, are incorporated into the loss function 1312, contributing to the final loss calculation. These constraints (i.e. mapped as additional loss terms) ensure that the reconstructed tooth surface adheres to anatomical and spatial requirements The optimization process may iteratively adjusts the latent code through backpropagation to minimize the loss and improve the accuracy of the predicted SDF values.

[0145] Several constraints may be incorporated during optimization to ensure that the reconstructed tooth surface shape adheres to anatomical and spatial requirements. The loss functions are further explained with reference to Fig. 11, equations (1) and (2). The gingiva constraint (equation (1)) ensures that the reconstructed tooth surface does not encroach into the gingiva. The loss for this constraint penalizes cases where the predicted signed distance value for a point on or near the gingiva becomes negative or falls below the true distance.

[0146] Similarly, the neighbouring-teeth collision constraint (equation (2)) prevents overlap between the reconstructed tooth surface and adjacent teeth. This is achieved by penalizing configurations where the sum of the signed distances to the reconstructed tooth and neighbouring teeth surfaces is negative, indicating a collision. Therefore, the combined loss function for a sampled point x may incorporate three components: the reconstruction loss, the gingiva constraint loss, and the neighbouring-teeth collision loss, may be given by:

[0147]

[0148] The first term |s - SDF(x)\ measures the error between the predicted signed distance value and the ground truth signed distance (s) for the point x. The second term, max(o,s - SDF(x)), penalizes cases where the predicted SDF(x) is less than s (e.g., for points on or outside the gingiva). The third term ,max (0, ~(SDFA(x) + S£>Fs(x)), penalizes collisions between the reconstructed tooth surface (SDFA(x) and a neighbouring tooth surface SDFB(x).gingivaandcouisionare weighting factors that balance the importance of the gingiva and collision constraints relative to the reconstruction loss.

[0149] The combination of these constraints during latent code optimization ensures that the reconstructed tooth shape surface is both anatomically accurate and spatially consistent with its surrounding structures. The iterative process continues until the SDF model reliably predicts signed distance values that accurately represent the completed tooth surface. This approach highlights the adaptability of the SDF model andits latent space representation in handling incomplete tooth segments while respecting critical anatomical and spatial boundaries.

[0150] Fig. 14 illustrates the inference phase of the process, during which a complete tooth surface is reconstructed from a latent code and subsequently transformed from a Signed Distance Function (SDF) representation into a mesh representation. This way a completed tooth segment suitable for orthodontic treatment planning may be generated.

[0151] The process may start with a grid of 3D points 1402 representing the 3D spatial domain of the incomplete tooth segment. These points, along with the optimized latent code 1404, are provided as inputs to the SDF model, which operates using fixed parameters 1406 that were pre-trained during the SDF model's training phase (reference to Fig. 12). The optimized latent code for an input incomplete tooth segment 1404 is the result of the latent code optimization process described in Fig. 13. As discussed before, the optimized latent code encapsulates the unique morphological characteristics of the tooth segment and guides the SDF model in predicting the appropriate complete tooth shape surface.

[0152] For each input point sampled from the 3D grid, the SDF model predicts a corresponding SDF value 1408, which represents the signed distance of that point relative to the surface of the tooth. The predicted SDF values are processed in a conversion step 1410, where the continuous SDF representation is converted into a surface representation, for example a discrete mesh representation using techniques such as the Marching Cubes algorithm. The thus obtained surface representation may be used as a complete tooth segment in a digital dental workflow application.

[0153] In an embodiment, a completed tooth segment may obtained by merging the mesh of the incomplete tooth segment (received as input) with the mesh of the predicted tooth segment based on the SDF model. In this process, the original mesh of the incomplete tooth segment is preserved as it represents accurate clinical data obtained from an optical scan. The predicted mesh, generated by the SDF model, may be used only to complete the missing surface areas of the completed tooth surface. The merging or stitching process involves seamlessly integrating the predicted tooth mesh with the incomplete tooth segment mesh, ensuring alignment and continuity at their boundaries.

[0154] In an embodiment, stitching may be based on raytracing. Rays which represent surface and / or vertex normals are cast from the predicted tooth segment mesh through the 3D space of the tooth segment to determine where the predicted mesh intersects with the incomplete tooth segment mesh. At these intersections, the mesh of the incomplete segment is preserved to ensure the original, accurate data remains unaltered. The predicted mesh is then used to fill in the missing surface area, seamlessly extending and completing the incomplete tooth surface mesh. This process results in asingle, unified model where the incomplete and predicted meshes are seamlessly merged, creating a smooth, representation of the complete tooth geometry.

[0155] Therefore, the output of the inference pipeline is the completed tooth segment 1412, reconstructed as a watertight 3D mesh that faithfully represents the full tooth surface geometry, filling in the gaps from the incomplete tooth segment. This mesh is suitable for downstream applications such as orthodontic treatment planning or prosthetics manufacturing.

[0156] Teeth sharing the same second digit generally exhibit similar surface shapes when aligned in their canonical pose. Using the FDI categorization may be particularly beneficial for learning tooth surface shape generation, as it allows for grouping teeth with similar characteristics, such as shape and surface features. This grouping ensures consistency and enables tooth surface shape generation modelling techniques to better generalize across teeth of the same type.

[0157] Fig. 15 illustrates the steps for determining an initial latent code to be used in the latent code optimization process during the reconstruction of an incomplete tooth segment, according to an embodiment of this disclosure. In step 1502, scanning data representing the surface of a dentition is received, and an incomplete tooth segment is identified along with its associated tooth type (e.g., based on its FDI category). In step 1504, an SDF model is trained using labelled clinical data of complete tooth segments, the model being parameterized by a latent code that encodes the shape of the tooth. In step 1506, an initial latent code is computed for optimization during inference. This initial latent code is determined using statistical metrics derived from the latent codes learned during the SDF model training and the FDI categories of the teeth segments included in the training data.

[0158] Fig. 16 illustrates a process of forming a completed tooth based on an incomplete tooth segment and a predicted tooth shape surface according to an embodiment. The incomplete tooth segment and the tooth shape surface may be fused into complete tooth segment. For example, a part of a tooth shape surface associated with the missing surface areas may be separated from the tooth shape surface and stitched to the incomplete tooth segment. To that end, the incomplete tooth segment 1602 and the complete shoot shape surface 1604 may serve as inputs to a separation module 1606. The separation module may employ a collision algorithm 1612, which may be configured to determine surface normals at vertex position of the surfaces of incomplete tooth segment. For example, in an embodiment, for each vertex, edge and / or face, of the mesh a surface normal may be determined. The surface normals of the incomplete tooth segment may be projected in positive and / or negative direction onto the tooth shape surface. Surface parts (defined by vertices, edges and faces) of the tooth shape surface for which the surface normals intersect with incomplete tooth segment may be removed.The use of the direction of the surface normals for determining which parts of the tooth shape surface need to be removed may be regarded as a raytracing process using the direction of the surface normals.

[0159] This process may be repeated until all surface parts of the incomplete tooth segment that have a normal that is intersecting with the surface of the tooth shape surface are removed. This way, the separation module removes part of the tooth shape surface that overlaps with the incomplete tooth segment. The technique of using surface normals to separate a part of a mesh into a separated mesh part without resampling and / or change position of points so that the separated mesh part can be accurately merged, i.e. fused, with another mesh. The separation module 1606 may further include a data storage for storing the separated parts 1614.

[0160] A stitching module 1608 may be employed to fuse the incomplete tooth segment with the separated part of tooth shape surface into a surface representation of a complete tooth segment 1610. This part of the tooth shape surface may be referred to as the missing surface part. The stitching module may be configured to execute steps including cleaning and repairing 1616 the mesh of the missing surface part and the incomplete tooth segment around the region where the two meshes are fused. This region may be referred to as the seam region, representing a transitional area where the meshes of the first modality and the separated part of the second modality are fused. The cleaning and repairing may include techniques such as described in the article by Liepa, Filling holes with meshes, Eurographics Symposium on Geometry Processing(2003).

[0161] In embodiment, the seam region may be triangulated (meshed) 1618 to ensure a smooth meshing between the missing surface part and the incomplete tooth part. In an embodiment, a graph algorithm may be used that defines triangles and / or polygons from the mesh boundaries. Polygons may be further split into triangles. The output for this process is a mesh including the incomplete tooth segment, the missing part surface and the seam region connecting the incomplete tooth segment, the missing part surface.

[0162] In a further embodiment, one or more filtering steps 1620 may be applied to the seam region and the resulting fused structure. For example, in an embodiment, a smoothing technique, such as Laplacian smoothing, may be used to reshape the seam region to fit the correct topology of the tooth. In particular, Laplacian smoothing method may be used to further smooth the seam mesh. In an embodiment, during smoothing some point displacement may be allowed to ensure topology consistency with the context. The context from the seam point of view is the topology of the incomplete tooth meshes and the missing part surface meshes. The Laplacian regularization ensures that the seam mesh is deformed and smoothed in a way that follows the context topology.Fig. 17 illustrates the steps of a tooth segment completion process according to the embodiments in this disclosure. Each step of the process from the incomplete segment to the final post-processed completed tooth segment is highlighted.

[0163] Fig. 17A depicts the initial incomplete tooth segment is shown as a mesh that is obtained by segmenting a scanned surface of a dentition. As shown in this figure, subgingival surface areas that are part of the cervical part (the neck) of the tooth and interproximal surface areas of the crown are missing. The incomplete tooth segment represents the starting point for the reconstruction process.

[0164] Fig. 17B depicts a prediction of a completed tooth segment generated by a trained SDF model as described with reference to the embodiments in this disclosure. The predicted tooth shape surface may be based on an optimized latent code obtained during inference so that the pre-trained latent code parameters of the SDF model can be leveraged. The predicted tooth shape surface may include accurate predictions of surface regions that are missing in the incomplete tooth segments. These predictions are based on the shape geometries of surface representations of complete tooth that were used for training the SDF model.

[0165] Fig. 17C shows a complete tooth shape segment that was formed based on the incomplete tooth segment and the predicted tooth shape surface. The figure illustrates the incomplete tooth segment 1702 which is merged with part of the surface 1704 of the predicted tooth shape that coincides with the missing surface of the incomplete tooth segment. This part may be referred to as missing surface part 1704. As explained with reference to Fig. 14 and Fig. 16, the missing surface part may be identified by comparing the incomplete tooth segment with the predicted tooth shape. After identifying the part of the predicted tooth shape surface that hat coincides with the missing surface of the incomplete tooth segment, the missing surface part may be separated from the predicted tooth shape and merged, i.e. fused, with the original incomplete tooth segment. Hence, the black surface region 1704 in the figure represent the areas of the SDF model prediction that have been integrated with the incomplete tooth segment (gray mesh 1702) to create a cohesive tooth segment. Fusion techniques as explained with reference to Fig. 16 may be used to ensure that the transition region 1706 between the incomplete tooth segment and the missing surface part is smooth and anatomically accurate.

[0166] Fig. 17D presents a complete tooth segment, which is post-processed. Here, the end part of the subgingival surface of the completed tooth segment as shown in Fig. 17C may be adjusted. For example, in an embodiment, the subgingival surface of the completed tooth segment may be elongated. A certain percentage of elongation may be required when using the complete tooth segments in dental models that are used for dental and / or orthodontic treatment planning. The elongation reflects clinical requirementsfor ensuring proper alignment and fit within the dental arch. A surface model of a dentition comprising such post-processed completed tooth segments is shown in Fig. 17E. Similar to Fig. 3A the gingiva is made semi-transparent so that the subgingival surface areas of the completed tooth segments are visible as well as the parts of the tooths segments stick out of the gingiva.

[0167] This figure demonstrates the effectiveness of embodiments in this closure in reconstructing anatomically accurate, seamless, and treatment-ready tooth segments using incomplete tooth segments and contextual tooth information as input to a tooth shape model. It highlights the reconstruction, integration, and refinement stages in producing a watertight and clinically applicable result.

[0168] The methods and system for determining a surface representation of a complete tooth segment as described with reference to the embodiments in this disclosure may be used in a digital treatment planning workflow, in which a treatment plan can be generated based on an accurate virtual 3D model of a dentition of a patient that is displayed on a screen, wherein the teeth of the 3D model are represented by complete tooth segments as described with reference to the embodiments in this disclosure.

[0169] Fig. 18 is a block diagram illustrating exemplary data processing systems described in this disclosure. Data processing system 1800 may include at least one processor 1802 coupled to memory elements 1804 through a system bus 1806. As such, the data processing system may store program code within memory elements 1804. Further, processor 1802 may execute the program code accessed from memory elements 1804 via system bus 1806. In one aspect, data processing system may be implemented as a computer that is suitable for storing and / or executing program code. It should be appreciated, however, that data processing system 1800 may be implemented in the form of any system including a processor and memory that is capable of performing the functions described within this specification.

[0170] Memory elements 1804 may include one or more physical memory devices such as, for example, local memory 1808 and one or more bulk storage devices 1810. Local memory may refer to random access memory or other non-persistent memory device(s) generally used during actual execution of the program code. A bulk storage device may be implemented as a hard drive or other persistent data storage device. The processing system 1800 may also include one or more cache memories (not shown) that provide temporary storage of at least some program code in order to reduce the number of times program code must be retrieved from bulk storage device 1810 during execution.

[0171] Input / output (I / O) devices depicted as key device 1812 and output device 1814 optionally can be coupled to the data processing system. Examples of key device may include, but are not limited to, for example, a keyboard, a pointing device such as a mouse, or the like. Examples of output device may include, but are not limited to, forexample, a monitor or display, speakers, or the like. Key device and / or output device may be coupled to data processing system either directly or through intervening I / O controllers. A network adapter 1816 may also be coupled to data processing system to enable it to become coupled to other systems, computer systems, remote network devices, and / or remote storage devices through intervening private or public networks. The network adapter may comprise a data receiver for receiving data that is transmitted by said systems, devices and / or networks to said data and a data transmitter for transmitting data to said systems, devices and / or networks. Operation modems, cable operation modems, and Ethernet cards are examples of different types of network adapter that may be used with data processing system 1800.

[0172] As pictured in FIG. 18, memory elements 1804 may store an application 1818. It should be appreciated that data processing system 1800 may further execute an operating system (not shown) that can facilitate execution of the application. Application, being implemented in the form of executable program code, can be executed by data processing system 1800, e.g., by processor 1802. Responsive to executing application, data processing system may be configured to perform one or more operations to be described herein in further detail.

[0173] In one aspect, for example, data processing system 1800 may represent a client data processing system. In that case, application 1818 may represent a client application that, when executed, configures data processing system 1800 to perform the various functions described herein with reference to a "client". Examples of a client can include, but are not limited to, a personal computer, a portable computer, a mobile phone, or the like.

[0174] In another aspect, data processing system may represent a server. For example, data processing system may represent an (HTTP) server in which case application 1818, when executed, may configure data processing system to perform (HTTP) server operations. In another aspect, data processing system may represent a module, unit or function as referred to in this specification.

[0175] Various components, modules, or units are described in this disclosure to emphasize functional aspects of devices configured to perform the disclosed techniques, but do not necessarily require realization by different hardware units. Rather, as described above, various units may be combined in a hardware unit or provided by a collection of interoperative hardware units, including one or more processors as described above, in conjunction with suitable software and / or firmware.

[0176] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting for the embodiments. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms"comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0177] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the embodiments has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the embodiments in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the claimed subjected matter. The embodiments were chosen and described in order to best explain the principles and practical applications, and to enable persons of ordinary skill in the art to understand the embodiments with various modifications as being suited to the particular uses and applications contemplated.

Claims

35CLAIMS1. A computer-implemented method for automatically determining a surface representation of a complete tooth, the method comprising:determining an incomplete tooth segment based on scanning data, preferably clinical scanning data, representing a surface of part of a dentition comprising one or more teeth, the incomplete tooth segment including one or more missing surface areas;determining contextual tooth information associated with the incomplete tooth segment based on the scanning data, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and,determining a predicted complete tooth shape surface comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of the contextual tooth information and to output the predicted tooth shape surface comprising the one or more missing surface areas.

2. Method according to claim 1 wherein the scanning data is obtained by scanning a dentition; and, wherein the incomplete tooth segment is determined by segmenting the scanning data representing part of the dentition in one or more incomplete tooth segments and, optionally, one or more gingiva segments.

3. Method according to claim 1 or 2 wherein the one or more missing surface areas include and / or consist of one or more subgingival surface areas, e.g. surface areas representing the neck of the tooth, and / or one or more interproximal surfaces areas.

4. Method according to any of claims 1-3 wherein the method further includes:determining a complete tooth segment based on the incomplete tooth segment and the predicted complete tooth shape surface; preferably, the determining of the complete tooth segment including:selecting surface data from the predicted complete tooth shape surface representing the one or more missing surfaces; and,stitching selected surface data representing the one or more missing surfaces into the missing areas of the incomplete tooth segment.

365. Method according to claim 3 wherein the complete tooth segment comprises a completed subgingival surface area up to a predetermined length below the emergence line of the complete tooth segment, preferably 5 mm below the emergence line, more preferably 3 mm below the emergence line.

6. Method according to any of claims 1-5 wherein the contextual tooth information includes information about the gingiva and / or one or more teeth neighbouring the tooth representing the incomplete tooth segment.

7. Method according to any of claims 1-6 wherein the contextual tooth information includes information about the tooth type of the incomplete tooth segment, preferably a tooth type according to the FDI dental numbering system.

8. Method according to an of claims 1-7 wherein the trained tooth model is trained based on clinical data, the clinical data including surface representations of complete tooth segments, a complete tooth segment representing a surface of a crown including interproximal surfaces and subgingival surfaces.

9. Method according to any of claims 1-8 wherein the trained tooth shape model comprises a trained decoder model, preferably a trained SDF deep learning model, configured to receive a shape parameter, preferably a latent code representing a tooth shape, and a set of coordinates associated with a coordinate space of the incomplete tooth segment at its input and to generate signed distance values for each coordinate of the set of coordinates at its output, the signed distance values representing a complete tooth shape surface .

10. Method according to claim 9 wherein determining a predicted tooth shape surface includes:optimizing the shape parameter associated with the trained decoder model to determine the tooth shape surface, the optimizing including:determining a trial tooth shape surface using the trained decoder model based on the incomplete tooth segment and based on an initial shape parameter, preferably the initial shape parameter being based one or more shape parameters, e.g. one or more latent codes, that were learned during the training of the decoder model;computing a loss value for the trial tooth shape surface based on the one or more constraints; and,if the loss value does not meet one or more optimization conditions, modifying the shape parameter to determine a further trial tooth shape surface and to compute a further loss value.

11. Method according to any of claims 1-9 wherein determining a tooth shape surface of a complete tooth includes:determining by a trained encoder model, a latent code of a complete tooth shape surface that matches the surface of the incomplete tooth segment;determining by a trained decoder model a tooth shape surface based on the latent code and the incomplete tooth shape segment, the trained decoder model being associated with the trained encoder model.

12. Method according to any of claims 1-11 wherein one of the one or more constraints includes that for coordinates inside the scanned surface of the gingiva, the signed distance to the scanned surface of the gingiva is smaller than a signed distance to the tooth shape surface; and / or, that for coordinates in the coordinate space of the incomplete tooth segment, the sum of a signed distance of the tooth shape surface and a signed distance of the surface of a tooth neighbouring the incomplete tooth segment is positive.

13. System for automatically determining a surface representation of a complete tooth comprising:a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium, wherein responsive to executing the computer readable program code, the processor is configured to perform executable operations comprising:determining an incomplete tooth segment based on scanning data, preferably clinical scanning data, representing a surface of part of a dentition comprising one or more teeth, the incomplete tooth segment including one or more missing surface areas;determining contextual tooth information associated with the incomplete tooth segment based on the scanning data, at least part of the contextual tooth information being used as one or more constraints for predicting the one or more missing surface areas; and,determining a predicted complete tooth shape surface comprising the one or more missing surface areas using a trained tooth shape model, the trained tooth shape model being configured to receive the incomplete tooth segment and at least part of thecontextual tooth information and to output the predicted tooth shape surface comprising the one or more missing surface areas.

14. System according to claim 13 wherein the executable operations further comprise any of the steps according to claims 2-12.

15. Computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry the method steps according to any of claims 1-12.

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