Techniques for identifying dental anatomical landmarks and related systems and methods - Patents.com

Abstract

A technique is described for automating the placement of anatomical landmarks on a 3D model of a patient's teeth for use in orthodontic treatment planning. The technique involves constructing a statistical model that parameterizes the shape of a reference tooth model and determining parameters that transform the shape of the reference tooth model into a shape that matches the shape of the patient's tooth model. The landmarks are associated with the reference tooth model and transformed in a similar manner based on the determined parameters, thereby allowing the location of the landmarks on the patient's tooth model to be identified. The landmarks of the patient's tooth model can be used for subsequent orthodontic treatment planning.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application No. 63 / 431,863, Attorney Docket No. L0914.70009US00, entitled "TECHNIQUES FOR IDENTIFYING DENTAL ANATOMICAL FEATURES AND RELATED SYSTEMS AND METHODS," filed December 12, 2022, which is incorporated herein by reference in its entirety.

[0002] This application relates generally to determining the location of anatomical landmarks on teeth for use in orthodontic treatment. [Background technology]

[0003] background Orthodontic treatment involves orthodontic appliances, such as braces, that apply static mechanical forces to the teeth to stimulate bone remodeling and promote tooth alignment. Orthodontic treatment planning utilizes a 3D model of the patient's teeth to create a treatment plan for the patient, which may include, for example, determining where to place brackets for a set of braces. During the planning process, it may be advantageous to identify the locations of certain anatomical features on the teeth, allowing the orthodontist or other treatment planner to apply orthodontic rules and / or principles when determining treatment. Summary of the Invention

[0004] overview According to some aspects, there is provided a computer-implemented method for determining positions of a plurality of feature points of a patient's teeth based on a statistical tooth model (hereinafter statistical tooth model), the method including: using at least one processor, determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with the 3D model of the patient's teeth; determining positions of the plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and at least in part on the determined values ​​of the plurality of parameters of the statistical tooth model; and associating the plurality of feature points of the patient's teeth with the 3D model of the patient's teeth according to the determined positions of the plurality of feature points.

[0005] According to some aspects, at least one computer-readable medium is provided, the medium comprising instructions, when executed by at least one processor, for performing a method for determining positions of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method including: determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with the 3D model of the patient's teeth; determining positions of the plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and at least in part on the determined values ​​of the plurality of parameters of the statistical tooth model; and associating the plurality of feature points of the patient's teeth with the 3D model of the patient's teeth according to the determined positions of the plurality of feature points.

[0006] According to some aspects, a system is provided that includes: at least one processor; and at least one computer-readable medium comprising instructions that, when executed by the at least one processor, perform a method for determining positions of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method including: determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with the 3D model of the patient's teeth; determining positions of the plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and at least in part on the determined values ​​of the plurality of parameters of the statistical tooth model; and associating the plurality of feature points of the patient's teeth with the 3D model of the patient's teeth according to the determined positions of the plurality of feature points.

[0007] Aspects of the foregoing apparatus and methods may be implemented in any suitable combination of the aspects, features, and operations described above or in more detail below. These and other aspects, aspects, and features of the present teachings may be more fully understood from the following description taken in conjunction with the accompanying drawings. [Brief explanation of the drawings]

[0008] Various aspects and embodiments are described with reference to the following drawings. It should be understood that the drawings are not necessarily drawn to scale. In the drawings, each identical or nearly identical component shown in various figures is represented by a like numeral. For clarity, not every component is labeled in every drawing.

[0009] [Figure 1] FIG. 1 illustrates a model of a patient's teeth with identified feature points, according to some embodiments;

[0010] [Figure 2] FIG. 2 is a conceptual block diagram illustrating a process for determining the location of feature points on a patient's teeth, according to some embodiments;

[0011] [Figure 3] FIG. 3 is a flow chart of a method for determining the location of a patient's dental feature points;

[0012] [Figure 4] FIG. 4 is a flowchart of a method for constructing a statistical tooth model, according to some embodiments;

[0013] [Figure 5] FIG. 5 is a flowchart of a method for generating a root portion of a patient's tooth, according to some embodiments;

[0014] [Figures 6A-6B] 6A-6B show closure of an open model of a patient's teeth, according to some embodiments;

[0015] [Figure 7] FIG. 7 illustrates a tooth portion and a root portion of a tooth model, according to some embodiments; and

[0016] [Figure 8] FIG. 8 illustrates a block diagram of an exemplary computing device suitable for implementing certain aspects described herein. DETAILED DESCRIPTION OF THE INVENTION

[0017] Detailed Description Orthodontics is widely used in clinics to correct malocclusions and align teeth. Traditional brace techniques use preformed brackets that are bonded to the teeth, with elastic metal wires threaded through slots in the brackets to provide drive. The brackets are adapted to each individual tooth by filling any gaps between the tooth surface and the bracket surface with adhesive. This ensures that the brackets are bonded to the teeth so that the bracket slots lie on a nearly flat surface when the teeth are moved into their final position.

[0018] As described above, when planning orthodontic treatment, such as the placement of brackets for braces, it can be advantageous to identify the locations of certain anatomical features of the teeth. These locations can be, for example, medically significant locations or "landmark points" that serve as reference points useful for orthodontic planning. For example, suitable anatomical feature locations (hereinafter "feature points") can include premolar cusps, molar cusps, facial axis points, marginal points, and / or centroid points. One advantageous use of feature points is to configure an orthodontic treatment planning application to perform various automated operations based on the feature points. For example, in some cases, the orthodontic treatment planning application can generate bracket placements for a patient based on the locations of feature points on a 3D model of the patient's teeth.

[0019] However, identifying the location of feature points can be a time-consuming process, and precise placement of feature points can require a high level of expertise from a medical professional. For example, it may be desirable to identify approximately 6-12 feature point locations for each tooth, resulting in approximately 200-300 feature point locations for all teeth. Each of these feature points may need to be accurately located by a medical professional on a 3D model of each tooth (hereinafter, "model") to within one millimeter. Furthermore, because each tooth is unique, and therefore the placement of feature points on each tooth is also unique, feature points cannot typically be copied from one tooth to another. Therefore, determining feature point locations has traditionally been a laborious, technical, manual process.

[0020] The inventors have recognized and evaluated a technique for automating the placement of feature points on a patient's tooth model. This technique involves building a statistical model that parameterizes the shape of a reference tooth model and determining parameters that transform the shape of the reference tooth model into a shape that matches the shape of the patient's tooth model. The feature points are associated with the reference tooth model and transformed in a similar manner based on the determined parameters, thereby allowing the location of the feature points on the patient's tooth model to be identified. The feature points of the patient's tooth model can be used for subsequent orthodontic treatment planning as described above.

[0021] According to some embodiments, a statistical model can be generated using a training dataset containing multiple models of the same type of tooth (e.g., incisors, canines, premolars, or molars) taken from multiple different patients. The tooth models may have associated feature points with positions determined manually or otherwise. An analysis may be performed to generate parameters that parameterize the shapes of the tooth models in the training dataset, such as a principal component analysis (PCA) analysis or other analysis that reduces the dimensionality of the training dataset. The resulting statistical model and its parameters represent the diversity of tooth shapes observed in the training dataset, and the parameters provide a method for modifying the shape of the reference model to generate any tooth shape (or an approximation thereof) in the training dataset. Feature points may be associated with specific geometric points on this parameterized model; therefore, by transforming the reference model to find parameters that reproduce the shape of the patient's tooth, the location of feature points on this tooth may also be determined.

[0022] According to some embodiments, the statistical model may include or describe a "standard" tooth model that represents the initial state of the reference model, and this "standard" tooth model is used to compare with the patient's tooth model to determine the patient's tooth feature points. This standard tooth model may, for example, represent the average shape of multiple models in the training dataset (e.g., the shape obtained from the average value of all parameters of the statistical model).

[0023] According to some embodiments, the reference tooth model of the statistical model may include root portions. Some orthodontic planning processes may utilize optical scans of the patient's teeth to generate a model that represents only the portions of the teeth that are exposed above the gums. While it may be advantageous to consider the location of the roots in some orthodontic treatments, obtaining a root model of the patient's teeth traditionally requires more complex scans (e.g., panoramic x-rays, cephalometric projections, or CBCT scans). However, using the techniques described herein, root portions can be included in the reference tooth model, allowing 3D models representing the root portions of the patient's teeth to be generated using a statistical model and without the need to perform a scan of the patient's roots. The reference model may include roots generated based on models in a training dataset that include root portions, or roots generated by other methods.

[0024] Various concepts related to techniques for determining the locations of multiple feature points on a patient's dental model and aspects thereof are described in more detail below. It should be understood that the various aspects described herein may be implemented in any of numerous ways. Specific implementation examples are provided herein for illustrative purposes only. Additionally, the various aspects described in the following aspects may be used alone or in any combination, and are not limited to the combinations expressly described herein.

[0025] For illustrative purposes, FIG. 1 shows a model of a patient's teeth with several feature points marked on it. Each feature point is identified by a point in three-dimensional space relative to the tooth, and in the example of FIG. 1, the points are labeled with a numerical identifier. For example, feature point 101 (also labeled "10") is located on the lateral surface of the depicted molar tooth. Feature point 102 (also labeled "5") is located on the cusp of the molar. Feature points 103 and 104 (also labeled "6" and "8," respectively) are marginal ridge points.

[0026] As described above, the locations of the patient's dental feature points can be determined by using a statistical model that parameterizes the shape of the reference tooth model and determining parameter values ​​that transform the shape of the reference tooth model into a shape that matches the shape of the patient's tooth model. Figure 2 is a conceptual block diagram illustrating such a process, according to some embodiments. Figure 3 is a flowchart of a method for determining the locations of the patient's dental feature points, according to some embodiments, and is further described below.

[0027] In the example of FIG. 2 , the positions of the feature points 220 are determined based on the patient's tooth model 201. The statistical tooth model 205 includes a parameterized reference tooth 210 having a plurality of associated parameters, and varying these parameters changes the shape of the reference tooth. Using appropriate analysis techniques, parameter values ​​can be found that produce a reference tooth shape that approximates the shape of the patient's tooth model 201. The statistical model 205 may also include or be associated with a plurality of feature points 214. The feature points 214 may be associated with positions relative to the reference tooth model and / or the feature points 214 may themselves be parameterized by parameters of the reference tooth model 210. Once the parameters of the reference tooth model 210 are determined, the positions of the feature points 214 may be determined according to the determined parameters, and these positions 220 may be associated with the patient's tooth model 201.

[0028] According to some embodiments, the 3D model 201 of the patient's teeth may be generated by capturing images of the patient's teeth using a suitable optical scanner operated by a dental professional, or may be generated based on data obtained from a tooth scan. In some embodiments, the patient's tooth model 201 may be generated by manually and / or automatically selecting geometric data corresponding to a tooth from a plurality of patient's tooth models.

[0029] According to some embodiments, the 3D model 201 of the patient's teeth may not include root portions. For example, if the model is generated from a handheld optical scanner, the model may represent only the portions of the teeth exposed above the gum line and not include root portions. Such a model may be provided in an open configuration as input to the system of FIG. 2 (and utilized in the method of FIG. 3 ) or may be modified to have a closed configuration (exemplary techniques for this are described below). In some embodiments, the 3D model 201 of the patient's teeth may include root portions, as further described below.

[0030] According to some embodiments, the statistical tooth model 205 may correspond to a particular type of tooth. The tooth type here may include broad categories such as incisor, canine, premolar, or molar, as well as narrower categories (e.g., upper incisor, right lower premolar) or specific individual teeth (e.g., upper left central incisor, left lower molar). Because a system may typically include multiple statistical tooth models 205, each corresponding to a different type of tooth, generating feature points for a patient's specific teeth may involve first identifying the patient's tooth type and selecting an appropriate statistical model that matches the tooth type.

[0031] According to some embodiments, the parameters of the parameterized reference tooth model 210 may be or include the principal components of a principal component analysis (PCA) model. Alternatively, the parameters may be parameters of any suitable model that can represent a reduced-dimensionality dataset (in this case, the various shapes of the multiple tooth models in the training dataset).

[0032] A "3D model" (or simply "model") as referred to herein may include any data describing a three-dimensional structure(s), regardless of file format or number of data files. Furthermore, a model may be represented in various ways and may include any method of representing a three-dimensional structure, including but not limited to a polygonal model, a point cloud, a shell model, a volumetric model, or a displacement model, etc.

[0033] 3 is a flowchart of a method for determining the locations of multiple feature points of a patient's teeth based on a statistical tooth model, according to some embodiments. Method 300 can be performed by a suitable computing system, examples of which are described below. Method 300 can be initiated in response to user input provided to the computing system, for example, a user interacting with an appropriate control in a graphical user interface (e.g., clicking a "Calculate Feature Points" button).

[0034] The method 300 is configured as an iterative loop in which operations 302, 304, 306, and 308 are repeated with various different values ​​selected for the parameters of the statistical model until the desired parameter values ​​are obtained. Then, in operation 310, the locations of the feature points of the patient's tooth model are determined according to the determined parameter values.

[0035] In operation 302, the system performing method 300 compares the patient's tooth model with a statistical model of reference teeth. As described above, the patient's tooth model may have been generated by scanning to create a geometric 3D model, and the reference tooth model may be part of (or associated with) the statistical model, whereby adjusting the values ​​of one or more parameters of the statistical model adjusts the shape of the reference teeth. Operation 302 includes identifying, for a plurality of locations on the reference model, the closest locations on the patient's tooth model.

[0036] According to some embodiments, operation 302 can include at least part of an iterative closest point (ICP) process, in which the patient's tooth model and the reference tooth model are represented by respective point clouds. In this process, for each of a plurality of points in the reference tooth point cloud, the closest point in the patient's tooth point cloud is determined. Operation 302 can include generating a point cloud from the patient's tooth model and / or generating a point cloud from the reference model for use in such a process.

[0037] In operation 304, the system performing method 300 selects values ​​for parameters of a statistical model, which may alter the shape of the reference model. These values ​​may be selected based at least in part on values ​​previously selected in previous iterations up to operation 304. According to some aspects, the parameters of the statistical model may be selected by projecting the closest point identified in operation 302 onto the reference model.

[0038] According to some embodiments, the parameters whose values ​​are selected in act 304 may be principal components of a principal component analysis (PCA) model. The values ​​of the parameters (e.g., PCA principal components) may, for example, control the positions of multiple points in a point cloud representing the reference tooth shape. In some embodiments, the parameters may be selected in act 304 by solving the linear equation b=Ax, where b is the vector of closest points identified in act 302, A is a two-dimensional matrix with column vectors that are the principal components of the PCA model, and x is a vector of parameters. In some cases, x can also be determined computationally by performing a matrix multiplication such as x=A'b, where A' is the transpose of A (this may be possible because the principal components are orthonormal to each other).

[0039] In act 306, the system performing method 300 determines a measure reflecting the degree of difference between the reference tooth model with the parameter values ​​selected in act 304 and the patient's tooth model. For example, a relatively small difference measure may reflect more similar models than a relatively large measure. According to some embodiments, this measure may be calculated based on the distance between the closest points identified in act 302. For example, the measure may be calculated as the sum of the squares of each of these distances.

[0040] According to some embodiments, act 306 may include determining the difference between the reference tooth model having the parameter values ​​selected in act 304 and the patient's tooth model at iteration i as the Euclidean distance between two N-dimensional vectors of the two point clouds (representing the reference tooth model and the patient's tooth model): Di = ||Ti - Ri||, where Ti represents the point cloud of the patient's tooth model and Ri represents the point cloud of the reference tooth model.

[0041] In operation 308, the system performing method 300 compares the difference measure determined in operation 306 to a threshold. If the measure is below the threshold, the parameter values ​​selected in operation 304 produced a reference tooth model having a shape sufficiently similar to the patient's tooth model. Otherwise, operations 302, 304, and 306 are repeated iteratively until the difference measure is below the threshold. When operation 302 is repeated, the reference tooth model used to identify the closest point on the patient's tooth model may have its shape adjusted depending on the parameter values ​​selected in operation 304 of the previous iteration of operations 302, 304, and 306. As a result, the set of points identified on the patient's tooth model in operation 302 may differ from the set of points identified in the previous iteration of operation 302 because the shape of the reference model has changed.

[0042] According to some embodiments, operation 308 may include comparing (i) the difference between the reference tooth model and the patient's tooth model with the parameter values ​​selected in operation 304, and (ii) the difference between the reference tooth model and the patient's tooth model with the parameter values ​​selected in a previous iteration of operation 304. That is, operation 308 may determine to what extent the difference between the reference tooth model and the patient's tooth model is decreasing with further iterations. For example, operation 306 may determine the Euclidean difference D i If operation 308 includes calculating D i and D i-1 For example, comparing D i -D i-1 If D is less than the threshold, then the difference may be considered below a desired tolerance in operation 308 (e.g., D i- D i-1 <In the case of x, method 300 returns to operation 302, and in other cases, method 300 proceeds to operation 310).

[0043] In operation 310, the system performing method 3 generates a plurality of featurepoints based optimizing processes of operations 302, 304, 306, and 308 to determine the positions of the plurality of feature points on the patient's dental model.

[0044] In some aspects, the plurality of feature points are associated with a reference dental model (or a point cloud or other data representing the model), and the shape of the reference dental model having a determined value of the parameter of the statistical model can be made to indicate the positions of the feature points on the patient's dental model. For example, a particular vertex or other specified location on the reference model is identified as a feature point, and the position of each of these locations identified on the reference dental model has a shape according to the determined value of the parameter of the statistical model. Thus, determining the positions of the feature points in operation 310 does not necessarily involve additional calculation of the positions of these points, and instead may involve identifying the positions of particular locations within the reference model as the locations of the determined feature points.

[0045] In some aspects, the plurality of feature points are associated with an initial shape of a reference tooth (e.g., the "standard" shape described above), and the positions of these points can be transformed based on the determined values of the parameters of the statistical model. For example, the reference dental model can be represented by a point cloud that includes (or is associated with) points identified as feature points. The positions of these points in the point cloud of the reference model can indicate the positions of the feature points on the patient's dental model if the reference model has a shape according to the determined values of the parameters of the statistical model.

[0046] According to some embodiments, method 300 may include, after act 310, associating the feature points and / or locations determined in act 310 with a patient's tooth model. Such an act may include storing data indicative of the location of each of the plurality of feature points and associating such data with the tooth model so that a suitable orthodontic treatment planning application can utilize the data representing the feature point locations in subsequent treatment planning activities (e.g., displaying the patient's tooth model with the feature points overlaid as shown in FIG. 1 , calculating bracket locations based on the feature point locations, etc.).

[0047] It will be appreciated that method 300 represents an exemplary approach for determining parameter values ​​for a statistical tooth model, and the techniques described herein are not limited to this particular approach. In general, any suitable method for optimizing the values ​​of the parameters controlling the shape of the reference tooth, as shown in FIG. 2 and described above, may be employed.

[0048] 4 is a flowchart of a method for constructing a statistical tooth model, according to some embodiments. The method 400 can be performed by a suitable computing system, examples of which are described below.

[0049] In operation 402, a system performing method 400 acquires a training data set including a plurality of tooth models. In some embodiments, the tooth models are all of a first type, and as a result, the statistical model is constructed for teeth of the first type. For example, the tooth models in the training data set may all be incisor models. Each model acquired in operation 402 may include, for example, a polygon model or a point cloud representing the shape of a tooth.

[0050] In operation 404, the system performing method 400 selects feature point locations for each tooth model in the training data set acquired in operation 402. In some embodiments, the locations may be selected manually by a user. For example, a user may utilize a graphical user interface (GUI) of an appropriate application to place feature points on the tooth models from the training data set. In some cases, the feature point locations may be selected semi-automatically, as described below.

[0051] In operation 406, the system performing method 400 constructs a statistical model having one or more parameters whose values ​​can be varied to replicate the shapes of the teeth in the training data set. Any suitable statistical shape modeling technique can be applied in operation 406, including, but not limited to, PCA and / or K-means clustering. According to some embodiments, operation 406 can include generating point clouds of one or more models from the training data set.

[0052] According to some aspects, operation 406 comprises determining a plurality of orthonormal eigenvectors by PCA analysis.

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[0053] In operation 408, the system performing method 400 identifies a 3D model of a reference tooth. The reference tooth model may be utilized in determining the location of feature points on the patient's teeth, for example, as described above in connection with method 300 shown in FIG. 3. According to some embodiments, the reference tooth model may be a representative model from a training dataset; in such a case, operation 408 may include selecting an existing model rather than generating a new model. According to some embodiments, the reference tooth may represent an average shape of multiple models in the training dataset (e.g., a shape resulting from the average value of all parameters of a statistical model).

[0054] In some embodiments, method 400 may be performed multiple times in a semi-automated approach, as follows: Initially, method 400 may be performed using a first portion of a training dataset, as described above, to generate a first statistical model. The first statistical model may then be applied to multiple tooth models from a second portion of the training dataset to automatically determine the locations of feature points of the tooth models in the second portion of the training dataset. A user may inspect the automatically determined locations of these feature points and correct them as needed if the feature point locations are inaccurate. Next, method 400 may be performed again using the first and second portions of the training dataset and the feature point locations previously generated in operation 404 to generate a second statistical model. This allows the second statistical model to be generated using the training dataset without having to manually identify every feature point of every tooth model in the training dataset, resulting in a more convenient training process.

[0055] It will be appreciated that method 400 represents an exemplary approach for determining the parameters of a statistical tooth model, and the techniques described herein are not limited to this particular approach. Any suitable method for determining multiple parameters for controlling the shape of the reference tooth can be used to approximate the tooth model from the training data set.

[0056] As described above, the reference tooth model can include a root portion, and a 3D model representing the root portion of a patient's tooth can be generated using a statistical model and without having to perform a scan of the patient's root. Figure 5 is a flowchart of a method for generating a root portion of a patient's tooth, according to some embodiments. Method 500 can be performed by a suitable computing system, examples of which are described below, and utilizes an open-surface model of the patient's tooth (e.g., generated by an optical scan) in addition to a statistical model that includes a parameterized reference tooth model that includes the root portion.

[0057] In operation 502, the system performing method 500 generated a model in which an open-surface model of the patient's teeth is closed. As described above, common scanning techniques may generate a model of the patient's teeth that includes only the portions of the teeth exposed above the gums, and therefore this surface has no underlying boundary surface. Figure 6A shows an illustrative example of such a model. The surfaces may be closed in operation 502 to generate a closed model, for example, including the same surface geometry as the initial model and additional surfaces that close the model. Figure 6B shows an illustrative example of the model shown in Figure 6A closed in this manner.

[0058] According to some embodiments, closing the open model in act 502 may include Poisson surface reconstruction. For example, act 502 may include providing a point cloud of the patient's teeth and estimated normal vectors for each point in the point cloud as inputs to a Poisson surface reconstruction process to generate an estimated surface that closes the model as a smooth extension of the open surface model of the patient's teeth.

[0059] In operation 504, the system performing method 500 segments the parameterized reference model to separate the root portion of the model from the non-root portion of the tooth. FIG. 7 shows an illustrative example of a tooth model including a root, where the upper portion 701 is the tooth portion and the lower portion 702 is the root portion. The segmentation operation may generate a new root model by either modifying the reference model or by generating a new reference model that includes only the root portion. In some embodiments, segmenting the parameterized reference model may include performing one or more mesh segmentation operations.

[0060] According to some embodiments, operation 504 may include determining an edge between the root portion of the reference model and the tooth portion using parameter values ​​of the statistical model determined through analysis of the patient's teeth to which the reference tooth is matched. For example, method 300 may be performed as described above using a reference model having a root portion, and may determine an edge between the root portion of the reference model and the tooth portion based on the determined values ​​of the parameters of the statistical model. In this approach, method 300 may be performed using a set of feature points including multiple feature points along the gum line to determine a new set of parameters for the statistical model.

[0061] According to some embodiments, operation 504 may include generating a point-to-point correspondence between the reference tooth model and the closed model of the patient's teeth generated in operation 502. In some embodiments, such point-to-point correspondence may be generated through a conformal mapping process. For example, the meshes of the reference tooth model and the closed model of the patient's teeth may each be mapped to a unit sphere using spherical conformal mapping, and a mapping between one or more feature points of the reference tooth model on the unit sphere and one or more feature points of the closed model of the patient's tooth model on the unit sphere may be determined.

[0062] Regardless of how the root portion of the reference tooth is identified in operation 504, in operation 506, the system performing method 500 generates a root portion of the patient's tooth model based on the identified root portion of the reference tooth. In some embodiments, generating the root portion of the patient's tooth model may include transforming the root portion of the identified reference tooth based on parameter values ​​of a statistical model determined through analysis of the patient's tooth to which the reference tooth is matched. Although the patient's tooth model may not include a root portion, the root portion of the patient's tooth is expected to differ from the root portion of the reference tooth just as the tooth portion of the patient's tooth differs from the tooth portion of the reference tooth. Thus, the parameter values ​​of the statistical model that enable the closest approximation between the tooth portions of the reference tooth and the patient's tooth model may also enable the root portion of the model generated in operation 504 to be transformed to generate an approximation of the root of the patient's tooth in operation 506.

[0063] According to some embodiments, operation 506 may include generating a root model of the patient's tooth model using a sparse data interpolation algorithm. For example, based on a mapping (e.g., on the unit sphere determined in operation 504) between specific points (e.g., feature points and / or boundary points) on the closed model of the patient's tooth and on the reference model, the remaining points of the reference model may be interpolated to generate the root model of the patient's tooth. Each input point p to be interpolated may be, for example, as follows:

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[0064] In operation 508, the root portion of the patient's tooth model generated in operation 506 is combined with the tooth portion of the patient's tooth model, which may be the initial open version or the closed version generated in operation 502. Combining the two 3D models to generate the new 3D model can be performed in any suitable manner, including using a Boolean combine operation. In some embodiments, the root portion of the patient's tooth model generated in operation 506 is not explicitly combined with the tooth portion of the patient's tooth model, but rather the data are treated together as a single unit.

[0065] As a result of method 500, the root portions of the patient's tooth models can be approximated using the statistical model described above. The patient's tooth models, including the root portions, can be utilized in subsequent orthodontic treatment planning processes, including planning tooth movement. For example, the process of determining bracket placement on the patient's teeth can be based on one or more patient's tooth models, including the root portions.

[0066] In some embodiments, the systems and techniques described herein may be implemented using one or more computing devices. In particular, the computing device may be operated to perform method 300, method 400, and / or method 500, which include determining parameter values ​​of a statistical model, as described above. However, embodiments are not limited to operating using a particular type of computing device. By way of further explanation, FIG. 8 is a block diagram of an exemplary computing device 800. The computing device 800 may include one or more processors 802 and one or more tangible, non-transitory, computer-readable storage media (e.g., memory 804). The memory 804 may store computer program instructions on the tangible, non-transitory, computer-recordable medium that, when executed, implement any of the functions described above. The processor(s) 802 are coupled to the memory 804 and can execute such computer program instructions to realize and perform functions.

[0067] Computing device 800 may also include a network input / output (I / O) interface 806 that allows the computing device to communicate with other computing devices (e.g., over a network), and may also include one or more user I / O interfaces 808 that allow the computing device to provide output to a user and receive input from a user. User I / O interfaces may include devices such as a keyboard, a mouse, a microphone, a display device (e.g., a monitor or touchscreen), speakers, a camera, and / or various other types of I / O devices.

[0068] The above-described aspects can be implemented in various ways. By way of example, aspects can be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor (e.g., a microprocessor) or collection of processors, whether located on a single computing device or distributed across multiple computing devices. It should be noted that any component or collection of components that perform the functions described above can be generally considered to be one or more controllers that control the functions described above. The one or more controllers can be implemented in various ways, such as dedicated hardware or general-purpose hardware (e.g., one or more processors) that are programmed using microcode or software to perform the functions described above.

[0069] In some embodiments, the software-based application may be connected to one or more components of the computing device (e.g., via a wired or wireless connection). In an embodiment, for example, computing device 800 may be controlled at least in part by the software-based application. In some cases, a user may interact with a graphical user interface to perform one or more operations of methods 300, 400, and / or 500 via the software-based application (e.g., identify the location of the feature points in operation 404). In some cases, the software-based application may store information (e.g., the location of the feature points) generated based on user input.

[0070] In this regard, it should be understood that one implementation of the aspects described herein includes at least one computer-readable storage medium (e.g., RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage, or other tangible, non-transitory computer-readable storage medium) encoded with a computer program (i.e., a plurality of executable instructions) that, when executed on one or more processors, performs the above-described functions of one or more aspects. The computer-readable medium may be portable such that the program stored thereon can be loaded onto any computing device to implement aspects of the technology described herein. Furthermore, it should be understood that references to a computer program that, when executed, performs any of the above-described functions are not limited to an application program running on a host computer. Rather, the terms computer program and software are used herein in a generic sense to refer to any type of computer code (e.g., application software, firmware, microcode, or other form of computer instructions) that can be used to program one or more processors to implement aspects of the technology described herein.

[0071] Having described several aspects of at least one embodiment of this invention, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art.

[0072] Such changes, modifications, and improvements are intended to be part of this disclosure and are intended to be within the spirit and scope of the invention. Moreover, while advantages of the invention have been described, it should be understood that not all aspects of the technology described herein include all of the described advantages. Some aspects may not implement any of the features described as advantageous herein, and in some cases, one or more of the described features may be implemented to achieve further aspects. Accordingly, the foregoing description and drawings are merely illustrative.

[0073] The above aspects of the technology described herein can be implemented in various ways. For example, aspects can be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can run on any suitable processor or collection of processors, whether on a single computer or distributed across multiple computers. Such processors can be implemented as integrated circuits, where one or more processors are included within an integrated circuit component; this includes commercially available integrated circuit components known in the art by names such as CPU chips, GPU chips, microprocessors, microcontrollers, or coprocessors. Alternatively, the processor can be implemented in a custom circuit, such as an ASIC, or a semi-custom circuit resulting from the configuration of a programmable logic device. As yet another alternative, the processor can be part of a larger circuit or semiconductor device, whether commercially available, semi-custom, or custom. As a specific example, some commercially available microprocessors have multiple cores, one or a subset of those cores may constitute a processor. However, a processor may be implemented using any suitable form of circuitry.

[0074] Various aspects of the present invention can be used alone, in combination, or in various arrangements not specifically described in the above embodiments, and therefore, its application is not limited to the details and arrangements of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment can be combined in any manner with aspects described in other embodiments.

[0075] The present invention may also be embodied as a method, an example of which is shown. The acts performed as part of the method may be ordered in any suitable manner. As such, embodiments may be constructed in which acts are performed in an order different from that shown, which may include performing some acts simultaneously even though the exemplary embodiments show acts as sequential.

[0076] Additionally, some actions are described as being performed by a "user." It should be understood that a "user" need not necessarily be a single individual, and that in some embodiments actions attributed to a "user" may be performed by a team of individuals and / or an individual in combination with computer-assisted tools or other mechanisms.

[0077] The use of ordinal numbers such as "first," "second," "third," etc. to modify claim elements in a claim does not, by itself, imply that a claim element has priority, precedence, or order over other claim elements, or the chronological order in which method operations are performed, but is merely used as a label to distinguish a claim element having a particular name from another element having the same name (except for the use of the ordinal number), thereby distinguishing the claim elements.

[0078] The terms "approximately" and "about" can be used in some embodiments to mean within ±20% of a target value, in some embodiments within ±10% of a target value, in some embodiments within ±5% of a target value, and even in some embodiments within ±2% of a target value. The terms "approximately" and "about" can include the target value. The term "substantially equal" can be used to refer to values ​​in some embodiments within ±20% of each other, in some embodiments within ±10% of each other, in some embodiments within ±5% of each other, and even in some embodiments within ±2% of each other.

[0079] The term "substantially" can be used to refer to values ​​that are within ±20%, within ±10%, within ±5%, and even within ±2% of a comparative measurement in some embodiments. For example, a first direction that is "substantially" perpendicular to a second direction refers to a first direction that is within ±20% of making a 90-degree angle with the second direction in some embodiments, within ±10% of making a 90-degree angle with the second direction in some embodiments, within ±5% of making a 90-degree angle with the second direction in some embodiments, and within ±2% of making a 90-degree angle with the second direction in some embodiments.

[0080] Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of "including," "comprising," "having," "containing," "involving," and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof, as well as additional items.

[0081] This disclosure describes various aspects, including but not limited to the following aspects.

[0082] 1. A computer-implemented method for determining the positions of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method including, using at least one processor: determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with the 3D model of the patient's teeth; determining the positions of the plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and at least in part on the determined values ​​of the plurality of parameters of the statistical tooth model; and associating the plurality of feature points of the patient's teeth with the 3D model of the patient's teeth according to the determined positions of the plurality of feature points.

[0083] 2. The method of aspect 1, wherein determining a plurality of parameter values ​​of the statistical tooth model includes, for each of a plurality of points on the 3D model of the reference tooth, identifying a point on the 3D model of the patient's tooth that is closest to the point on the 3D model of the reference tooth.

[0084] 3. The method of aspect 2, wherein determining a plurality of parameter values ​​of the statistical tooth model further includes measuring a difference between the 3D model of the patient's teeth and the 3D model of the reference teeth by comparing a plurality of points on the 3D model of the reference teeth with a plurality of identified points on the 3D model of the patient's teeth.

[0085] 4. The method of aspect 3, wherein determining multiple parameter values ​​of the statistical tooth model further includes optimizing multiple parameters of the statistical tooth model based on measured differences between the 3D model of the patient's teeth and the 3D model of the reference teeth.

[0086] 5. The method of any one of aspects 1 to 4, wherein the plurality of parameters of the statistical tooth model comprises a plurality of principal components of a principal component analysis (PCA) model.

[0087] 6. The method of any of aspects 1-5, wherein determining the locations of the plurality of feature points of the patient's teeth includes transforming the plurality of feature points associated with the statistical tooth model according to determined values ​​of the plurality of parameters.

[0088] 7. The method of any of aspects 1-6, wherein determining the positions of the plurality of feature points of the patient's teeth includes identifying relative positions of the plurality of feature points associated with the statistical tooth model with respect to the 3D model of the reference teeth, whereby the 3D model of the reference teeth has a shape according to the determined values ​​of the plurality of parameters.

[0089] 8. The method of any of aspects 1-7, wherein the plurality of feature points of the patient's teeth include one or more premolar cusps, molar cusps, facial axis points, marginal ridge points, fossa points, and / or central points.

[0090] 9. The method of any of aspects 1-8, further comprising generating a statistical tooth model by: obtaining a plurality of reference 3D tooth models; and determining a plurality of parameters based on the plurality of reference 3D tooth models.

[0091] 10. The method of aspect 9, wherein determining the plurality of parameters includes performing a principal component analysis (PCA) of the plurality of reference 3D tooth models.

[0092] 11. The method of any of aspects 1-10, wherein the statistical tooth model is defined for an incisor, canine, premolar, or molar, and wherein the reference tooth and the patient's tooth are incisors, canines, premolars, or molars.

[0093] 12. The method of any of aspects 1-11, further comprising generating a root model of the 3D model of the patient's tooth based on the statistical tooth model and the determined values ​​of the plurality of parameters of the statistical tooth model.

[0094] 13. The method of aspect 12, wherein generating the root model includes transforming a 3D model of a reference tooth including a root portion according to a plurality of parameters of the statistical tooth model.

[0095] 14. The method of any of aspects 1-13, further comprising determining one or more orthodontic treatments based on the 3D model of the patient's teeth and the associated plurality of feature points.

[0096] 15. At least one computer-readable medium comprising instructions that, when executed by at least one processor, perform a method for determining positions of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method comprising: determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with the 3D model of the patient's teeth; determining positions of the plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and based at least in part on the determined values ​​of the plurality of parameters of the statistical tooth model; and associating the plurality of feature points of the patient's teeth with the 3D model of the patient's teeth according to the determined positions of the plurality of feature points.

[0097] 16. At least one computer-readable medium of aspect 15, wherein determining the plurality of parameter values ​​of the statistical tooth model includes, for each of the plurality of points on the 3D model of the reference tooth, identifying a point on the 3D model of the patient's tooth that is closest to the point on the 3D model of the reference tooth.

[0098] 17. At least one computer-readable medium of aspect 16, wherein determining a plurality of parameter values ​​of the statistical tooth model further includes measuring a difference between the 3D model of the patient's teeth and the 3D model of the reference teeth by comparing a plurality of points on the 3D model of the reference teeth with a plurality of identified points on the 3D model of the patient's teeth.

[0099] 18. At least one computer-readable medium of aspect 17, wherein determining multiple parameter values ​​of the statistical tooth model further includes optimizing multiple parameters of the statistical tooth model based on measured differences between the 3D model of the patient's teeth and the 3D model of the reference teeth.

[0100] 19. At least one computer-readable medium of any of aspects 15-18, wherein the plurality of parameters of the statistical tooth model comprises a plurality of principal components of a principal component analysis (PCA) model.

[0101] 20. At least one computer-readable medium of any of aspects 15-19, wherein determining the positions of a plurality of feature points of the patient's teeth includes transforming a plurality of feature points associated with the statistical tooth model according to determined values ​​of a plurality of parameters.

[0102] 21. At least one computer-readable medium described in any of aspects 15-20, wherein determining the positions of the plurality of feature points of the patient's teeth includes identifying relative positions of the plurality of feature points associated with the statistical tooth model with respect to the 3D model of the reference teeth, whereby the 3D model of the reference teeth has a shape according to the determined values ​​of the plurality of parameters.

[0103] 22. At least one computer-readable medium described in any of aspects 15-21, wherein the plurality of feature points of the patient's teeth include one or more premolar cusps, molar cusps, facial axis points, marginal ridge points, fossa points, and / or central points.

[0104] 23. At least one computer-readable medium described in any of aspects 15 to 22, wherein the method further includes generating a statistical tooth model by: obtaining a plurality of reference 3D tooth models; and determining a plurality of parameters based on the plurality of reference 3D tooth models.

[0105] 24. At least one computer-readable medium of aspect 23, wherein determining the plurality of parameters includes performing a principal component analysis (PCA) of the plurality of reference 3D tooth models.

[0106] 25. At least one computer-readable medium of any of aspects 15-24, wherein the statistical tooth model is defined for an incisor, canine, premolar, or molar, and wherein the reference tooth and the patient's tooth are incisors, canines, premolars, or molars.

[0107] 26. At least one computer-readable medium of any of aspects 15-25, wherein the method further includes generating a root model of the 3D model of the patient's tooth based on the statistical tooth model and the determined values ​​of the plurality of parameters of the statistical tooth model.

[0108] 27. At least one computer-readable medium of aspect 26, wherein generating the root model includes transforming a 3D model of a reference tooth including a root portion according to a plurality of parameters of the statistical tooth model.

[0109] 28. At least one computer-readable medium of any of aspects 15-27, further comprising determining one or more orthodontic treatments based on the 3D model of the patient's teeth and the associated plurality of feature points.

[0110] 29. A system comprising: at least one processor; and at least one computer-readable medium comprising instructions that, when executed by the at least one processor, perform a method for determining positions of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method comprising: determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with the 3D model of the patient's teeth; determining positions of the plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and at least in part on the determined values ​​of the plurality of parameters of the statistical tooth model; and associating the plurality of feature points of the patient's teeth with the 3D model of the patient's teeth according to the determined positions of the plurality of feature points.

[0111] 30. The system of aspect 29, wherein determining the plurality of parameter values ​​of the statistical tooth model includes, for each of the plurality of points on the 3D model of the reference tooth, identifying a point on the 3D model of the patient's tooth that is closest to the point on the 3D model of the reference tooth.

[0112] 31. The system of aspect 30, wherein determining the plurality of parameter values ​​of the statistical tooth model further includes measuring a difference between the 3D model of the patient's teeth and the 3D model of the reference teeth by comparing the plurality of points on the 3D model of the reference teeth with the plurality of identified points on the 3D model of the patient's teeth.

[0113] 32. The system of aspect 31, wherein determining multiple parameter values ​​of the statistical tooth model further includes optimizing multiple parameters of the statistical tooth model based on measured differences between the 3D model of the patient's teeth and the 3D model of the reference teeth.

[0114] 33. The system of any of aspects 29-32, wherein the plurality of parameters of the statistical tooth model comprises a plurality of principal components of a principal component analysis (PCA) model.

[0115] 34. The system of any of aspects 29-33, wherein determining the locations of the plurality of feature points of the patient's teeth includes transforming the plurality of feature points associated with the statistical tooth model according to determined values ​​of the plurality of parameters.

[0116] 35. The system of any of aspects 29-34, wherein determining the positions of the plurality of feature points of the patient's teeth includes identifying relative positions of the plurality of feature points associated with the statistical tooth model with respect to the 3D model of the reference teeth, whereby the 3D model of the reference teeth has a shape according to the determined values ​​of the plurality of parameters.

[0117] 36. The system of any of aspects 29-35, wherein the plurality of feature points of the patient's teeth include one or more premolar cusps, molar cusps, facial axis points, marginal ridge points, fossa points, and / or central points.

[0118] 37. The system of any of aspects 29-36, wherein the method further includes generating a statistical tooth model by: obtaining a plurality of reference 3D tooth models; and determining a plurality of parameters based on the plurality of reference 3D tooth models.

[0119] 38. The system of aspect 37, wherein determining the plurality of parameters includes performing a principal component analysis (PCA) of the plurality of reference 3D tooth models.

[0120] 39. The system of any of aspects 29-38, wherein the statistical tooth model is defined for an incisor, canine, premolar, or molar, and wherein the reference tooth and the patient's tooth are incisors, canines, premolars, or molars.

[0121] 40. The system of any of aspects 29-39, wherein the method further includes generating a root model of the 3D model of the patient's tooth based on the statistical tooth model and the determined values ​​of the plurality of parameters of the statistical tooth model.

[0122] 41. The system of aspect 40, wherein generating the root model includes transforming a 3D model of the reference tooth including the root portion according to a plurality of parameters of the statistical tooth model.

[0123] 42. The system of any of aspects 29-41, further comprising determining one or more orthodontic treatments based on the 3D model of the patient's teeth and the associated plurality of feature points.

Claims

1. 1. A computer-implemented method for determining the location of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method comprising: With at least one processor: determining values ​​of a plurality of parameters of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with a 3D model of the patient's tooth; determining locations of a plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and based at least in part on the determined values ​​of a plurality of parameters of the statistical tooth model; and Associating the plurality of feature points of the patient's teeth with a 3D model of the patient's teeth according to the determined locations of the plurality of feature points; The method comprising:

2. 2. The method of claim 1, wherein determining a plurality of parameter values ​​of the statistical tooth model comprises, for each point of the plurality of points on the 3D model of the reference tooth, identifying a point on the 3D model of the patient's tooth that is closest to the point on the 3D model of the reference tooth.

3. 3. The method of claim 2, wherein determining the plurality of parameter values ​​of the statistical tooth model further comprises measuring a difference between the 3D model of the patient's teeth and the 3D model of the reference teeth by comparing the plurality of points on the 3D model of the reference teeth with the plurality of identified points on the 3D model of the patient's teeth.

4. 4. The method of claim 3, wherein determining values ​​of the plurality of parameters of the statistical tooth model further comprises optimizing the plurality of parameters of the statistical tooth model based on measured differences between the 3D model of the patient's teeth and the 3D model of the reference teeth.

5. The method of claim 1 , wherein the plurality of parameters of the statistical tooth model comprises a plurality of principal components of a principal component analysis (PCA) model.

6. 10. The method of claim 1, wherein determining the locations of the plurality of feature points of the patient's teeth comprises transforming the plurality of feature points associated with the statistical tooth model in response to determined values ​​of the plurality of parameters.

7. 10. The method of claim 1, wherein determining the positions of the plurality of feature points of the patient's teeth comprises identifying relative positions of the plurality of feature points associated with the statistical tooth model with respect to the 3D model of the reference teeth, whereby the 3D model of the reference teeth has a shape according to the determined values ​​of the plurality of parameters.

8. The method of claim 1 , wherein the plurality of feature points of the patient's teeth comprises one or more premolar cusps, molar cusps, facial axis points, marginal ridge points, fossa points, and / or central points.

9. Obtaining multiple reference 3D tooth models; Determining a plurality of parameters based on a plurality of reference 3D tooth models; The method of claim 1 , further comprising generating a statistical tooth model by:

10. 10. The method of claim 9, wherein determining the plurality of parameters comprises performing a principal component analysis (PCA) of the plurality of reference 3D tooth models.

11. 2. The method of claim 1, wherein the statistical tooth model is defined for an incisor, canine, premolar, or molar, and wherein the reference tooth and the patient's tooth are incisors, canines, premolars, or molars.

12. The method of claim 1 , further comprising generating a root model of the 3D model of the patient's tooth based on the statistical tooth model and the determined values ​​of the plurality of parameters of the statistical tooth model.

13. The method of claim 12 , wherein generating the root model comprises transforming a 3D model of the reference tooth including the root portion according to a plurality of parameters of the statistical tooth model.

14. The method of claim 1 , further comprising determining one or more orthodontic treatments based on the 3D model of the patient's teeth and the associated plurality of feature points.

15. At least one computer-readable medium comprising instructions that, when executed by at least one processor, perform a method for determining locations of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method comprising: determining a plurality of parameter values ​​of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with a 3D model of the patient's tooth; determining locations of a plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and based at least in part on the determined values ​​of a plurality of parameters of the statistical tooth model; and Associating the plurality of feature points of the patient's teeth with a 3D model of the patient's teeth according to the determined locations of the plurality of feature points; the at least one computer-readable medium comprising:

16. 16. At least one computer-readable medium according to claim 15, wherein determining the plurality of parameter values ​​of the statistical tooth model comprises, for each point of the plurality of points on the 3D model of the reference tooth, identifying a point on the 3D model of the patient's tooth that is closest to the point on the 3D model of the reference tooth.

17. 17. At least one computer-readable medium according to claim 16, wherein determining the plurality of parameter values ​​of the statistical tooth model further comprises measuring a difference between the 3D model of the patient's teeth and the 3D model of the reference teeth by comparing the plurality of points on the 3D model of the reference teeth with the plurality of identified points on the 3D model of the patient's teeth.

18. 20. At least one computer-readable medium according to claim 17, wherein determining the plurality of parameter values ​​of the statistical tooth model further comprises optimizing the plurality of parameters of the statistical tooth model based on measured differences between the 3D model of the patient's teeth and the 3D model of the reference teeth.

19. 16. At least one computer-readable medium according to claim 15, wherein the plurality of parameters of the statistical tooth model comprises a plurality of principal components of a principal component analysis (PCA) model.

20. 16. At least one computer-readable medium according to claim 15, wherein determining the locations of the plurality of feature points of the patient's teeth comprises transforming the plurality of feature points associated with the statistical tooth model according to determined values ​​of the plurality of parameters.

21. 16. At least one computer-readable medium according to claim 15, wherein determining the positions of the plurality of feature points of the patient's teeth comprises identifying relative positions of the plurality of feature points associated with the statistical tooth model with respect to the 3D model of the reference teeth, whereby the 3D model of the reference teeth has a shape according to the determined values ​​of the plurality of parameters.

22. 16. At least one computer-readable medium according to claim 15, wherein the plurality of feature points of the patient's teeth comprises one or more premolar cusps, molar cusps, facial axis points, marginal ridge points, fossa points, and / or central points.

23. 16. At least one computer-readable medium as recited in claim 15, wherein the method further comprises: Obtaining multiple reference 3D tooth models; Determining a plurality of parameters based on a plurality of reference 3D tooth models; generating a statistical tooth model by

24. 24. At least one computer-readable medium according to claim 23, wherein determining the plurality of parameters comprises performing a principal component analysis (PCA) of the plurality of reference 3D tooth models.

25. 16. At least one computer-readable medium according to claim 15, wherein the statistical tooth model is defined for an incisor, a canine, a premolar, or a molar, and wherein the reference tooth and the patient's tooth are an incisor, a canine, a premolar, or a molar.

26. 16. At least one computer-readable medium according to claim 15, wherein the method further comprises generating a root model of the 3D model of the patient's tooth based on the statistical tooth model and the determined values ​​of the plurality of parameters of the statistical tooth model.

27. 27. At least one computer-readable medium according to claim 26, wherein generating the root model comprises transforming a 3D model of a reference tooth including a root portion according to a plurality of parameters of the statistical tooth model.

28. 16. The at least one computer-readable medium of claim 15, further comprising determining one or more orthodontic treatments based on the 3D model of the patient's teeth and the associated plurality of feature points.

29. The system includes: at least one processor; and At least one computer-readable medium comprising instructions that, when executed by at least one processor, perform a method for determining locations of a plurality of feature points of a patient's teeth based on a statistical tooth model, the method comprising: determining a plurality of parameter values ​​of the statistical tooth model by comparing a three-dimensional (3D) model of a reference tooth having a shape parameterized by a plurality of parameters with a 3D model of the patient's tooth; determining locations of a plurality of feature points of the patient's teeth based at least in part on the plurality of feature points associated with the statistical tooth model and based at least in part on the determined values ​​of a plurality of parameters of the statistical tooth model; and Associating the plurality of feature points of the patient's teeth with a 3D model of the patient's teeth according to the determined locations of the plurality of feature points; the at least one computer-readable medium comprising:

30. 30. The system of claim 29, wherein determining the plurality of parameter values ​​of the statistical tooth model comprises, for each point of the plurality of points on the 3D model of the reference tooth, identifying a point on the 3D model of the patient's tooth that is closest to the point on the 3D model of the reference tooth.

31. 31. The system of claim 30, wherein determining the plurality of parameter values ​​of the statistical tooth model further comprises measuring a difference between the 3D model of the patient's teeth and the 3D model of the reference teeth by comparing the plurality of points on the 3D model of the reference teeth with the plurality of identified points on the 3D model of the patient's teeth.

32. 32. The system of claim 31 , wherein determining the plurality of parameter values ​​of the statistical tooth model further comprises optimizing the plurality of parameters of the statistical tooth model based on measured differences between the 3D model of the patient's teeth and the 3D model of the reference teeth.

33. 30. The system of claim 29, wherein the plurality of parameters of the statistical tooth model comprises a plurality of principal components of a principal component analysis (PCA) model.

34. 30. The system of claim 29, wherein determining the locations of the plurality of feature points of the patient's teeth comprises transforming the plurality of feature points associated with the statistical tooth model in response to determined values ​​of the plurality of parameters.

35. 30. The system of claim 29, wherein determining the positions of the plurality of feature points of the patient's teeth comprises identifying relative positions of the plurality of feature points associated with the statistical tooth model with respect to the 3D model of the reference teeth, whereby the 3D model of the reference teeth has a shape according to the determined values ​​of the plurality of parameters.

36. 30. The system of claim 29, wherein the plurality of feature points of the patient's teeth include one or more premolar cusps, molar cusps, facial axis points, marginal ridge points, fossa points, and / or central points.

37. The method further Obtaining multiple reference 3D tooth models; Determining a plurality of parameters based on a plurality of reference 3D tooth models; 30. The system of claim 29, comprising generating the statistical tooth model by:

38. 38. The system of claim 37, wherein determining the plurality of parameters comprises performing a principal component analysis (PCA) of the plurality of reference 3D tooth models.

39. 30. The system of claim 29, wherein the statistical tooth model is defined for an incisor, canine, premolar, or molar, and wherein the reference tooth and the patient's tooth are incisors, canines, premolars, or molars.

40. 30. The system of claim 29, wherein the method further comprises generating a root model of the 3D model of the patient's tooth based on the statistical tooth model and the determined values ​​of the plurality of parameters of the statistical tooth model.

41. 41. The system of claim 40, wherein generating the root model comprises transforming the 3D model of the reference tooth including the root portion according to a plurality of parameters of the statistical tooth model.

42. 30. The system of claim 29, further comprising determining one or more orthodontic treatments based on the 3D model of the patient's teeth and the associated plurality of feature points.

Images