Tooth segmentation method and system and computer equipment

Abstract

The invention discloses a tooth segmentation method and system and computer equipment, and relates to the technical field of digital oral cavity, and the method comprises the following steps: obtaining a tooth local area on a 3D dental grid model; constructing a depression sensing harmonic field in the tooth local area, and calculating scalar intensity of grid vertexes in the tooth local area through the depression sensing harmonic field; optimal seed points located on the segmentation boundary are screened out according to the scalar intensity; according to the optimal seed point, a path search algorithm is adopted to extract a segmentation boundary; segmenting the teeth based on the segmentation boundary; the method can realize accurate and efficient tooth segmentation, has relatively high stability and robustness, and can meet clinical requirements.

Description

Technical Field

[0001] The present invention relates to the field of digital dentistry, and particularly to a tooth segmentation method, system and computer device. Background Art

[0002] With the rapid development of computer technology and three-dimensional scanning technology, computer-aided design (CAD) is widely used in the field of oral medicine. In a CAD orthodontic system, a three-dimensional dental arch mesh model is input, and dentists perform treatment procedures such as posture adjustment, tooth arrangement, and tooth restoration, and provide a set of treatment plans and expected results to patients. Since most operations are based on individual single teeth, and the tooth quality is directly related to the subsequent treatment results, how to accurately and efficiently segment teeth has become a research hotspot in this field.

[0003] Constructing a surface curvature field on a dental arch model and performing tooth segmentation through morphological skeleton technology is one of the common methods. However, this method is very sensitive to noise and cannot well segment complex dental arch models. Some other methods generate multiple contour lines on the surface of the dental arch model by constructing a depression-aware harmonic field and select the optimal contour line as the segmentation boundary. This method is accurate for segmenting general dental arch models, but the results of the harmonic field on deformed models are often abnormal, resulting in a large error in the optimal contour line. Methods based on deep learning are also applied to tooth segmentation. However, the common problem of this method is that the segmentation accuracy depends on the quantity, authenticity, and diversity of the training data. If the data set is small, it is difficult to ensure the reliability of the segmentation method. However, it is an extremely huge and difficult task for researchers to collect thousands of clinical data from different populations and make a data set. Summary of the Invention

[0004] Aiming at the deficiency that the existing technology is accurate for segmenting general dental arch models, but the results of the harmonic field on deformed models are often abnormal, resulting in a large error in the optimal contour line, the present invention proposes a tooth segmentation method, system and computer device. By constructing a depression-aware harmonic field in the local tooth area, calculating the scalar intensity of the grid vertices in the local tooth area, screening out the optimal seed points located on the segmentation boundary according to the scalar intensity, and using a path search algorithm to extract the segmentation boundary to segment the teeth, thus solving the problem that the results of the harmonic field on deformed models in the existing technology are often abnormal, resulting in a large error in the optimal contour line.

[0005] A tooth segmentation method includes the following steps:

[0006] Obtain the local tooth area on a 3D dental arch mesh model, where the local tooth area includes a complete single tooth and part of the gingiva and adjacent teeth;

[0007] Construct a dent depression perception harmonic field in a local tooth area, and calculate the scalar intensity of grid vertices in the local tooth area through the dent depression perception harmonic field;

[0008] Screen out the optimal seed points located on the segmentation boundary of the local tooth area according to the scalar intensity;

[0009] Extract the segmentation boundary by using a path search algorithm according to the optimal seed points;

[0010] Segment the tooth based on the segmentation boundary.

[0011] Further, the obtaining of the local tooth area specifically includes the following steps:

[0012] Use the PCA technique to reduce the point cloud data of the 3D dental arch grid model to two dimensions, and obtain two-dimensional feature points corresponding to the feature points;

[0013] Assign an ellipse to each tooth, and the ellipse equation is:

[0014]

[0015] where x0 and y0 are the abscissa and ordinate of the two-dimensional feature point p0 corresponding to the tooth to which the currently required ellipse is assigned, θ is the angle between the vector formed by p0 and the two-dimensional feature point p1 closest to p0 and the y-axis, r is |p1p2|, and r1 and r2 are parameters;

[0016] The local 3D grid generated by the points inside the ellipse is the local tooth area;

[0017] Or assign a sphere to each tooth, and the sphere equation is:

[0018] (x - a) 2 +(y - b) 2 +(z - c) 2 =r′ 2

[0019] where a, b, and c correspond one-to-one with the coordinate values, p is the feature point on the tooth to which the currently required sphere is assigned, n is the outward unit normal vector of p, and r′ are parameters;

[0020] The local 3D grid inside the sphere is the local tooth area.

[0021] Further, the constructing of the dent depression perception harmonic field in the local tooth area and calculating the scalar intensity of grid vertices in the local tooth area through the dent depression perception harmonic field specifically include the following steps:

[0022] Construct a harmonic function according to the grid vertices in the local tooth area;

[0023] Take the f-ring neighborhood points of the feature points on the local area of the tooth and the boundary points of the local area of the tooth as the constraint conditions of the dent depression perception harmonic field; construct a matrix equation according to the harmonic function and the constraint conditions, and then solve to obtain the scalar value of the grid vertex; the feature points are the points selected at the center area of each tooth.

[0024] Based on the scalar values, divide the grid vertices into multiple sets, evaluate the aggregation and centrality of the grid vertices, and construct an aggregation function and a central function respectively.

[0025] According to the aggregation function and the central function, calculate the scalar intensity of the grid vertices in the local area of the tooth.

[0026] Further, the expression of the harmonic function is:

[0027]

[0028] where u i and u j are the scalar values of grid vertex i and grid vertex j, N(i) is the set of one-ring neighborhood points of point i, ω ij is the weight of edge ij, and its expression is:

[0029]

[0030] where e max is the maximum side length of the local area of the tooth, v i and v j are grid vertex i and grid vertex j, and δ is a constant.

[0031] Further, for constructing the matrix equation according to the harmonic function and the constraint conditions, and then solving to obtain the scalar value of the grid vertex; taking the f-ring neighborhood points of the feature points on the local area of the tooth and the boundary points of the local area of the tooth as the constraint conditions of the dent depression perception harmonic field, and setting their constraint values to 1 and 0 respectively, then its matrix equation is expressed as:

[0032] Lu = b

[0033] where L is the weight matrix, b is a vector composed of 0 and 1, and u contains the scalar values of the grid vertices;

[0034] Obtain the scalar values of the grid vertices by solving the matrix equation.

[0035] Further, for calculating the scalar intensity of the grid vertices in the local area of the tooth according to the aggregation function and the central function, it specifically includes the following steps:

[0036] The aggregation function is expressed as:

[0037]

[0038] Among them, N is the number of one-ring neighborhood points of vertex v, and n is the number of one-ring neighborhood points of vertex v in different sets;

[0039] The central function is expressed as:

[0040]

[0041] Among them, N(v) is the one-ring neighborhood point of vertex v, and u i is the scalar value of vertex v i and ε is the centrality parameter;

[0042] Then the calculation formula of the scalar intensity is expressed as:

[0043]

[0044] Furthermore, screening out the optimal seed points located on the segmentation boundary according to the scalar intensity specifically includes the following steps:

[0045] Select the grid vertices with scalar values in [u1, u2] as the screening area;

[0046] Judge the connectivity of the screening area, and select the largest connected domain as the new screening area;

[0047] Calculate the evaluation value e(v) of each vertex in the new screening area, and its calculation formula is expressed as:

[0048]

[0049] Among them, h(v) is the curvature of vertex v;

[0050] Screen out two optimal seed points. If the Euclidean distance between two grid vertices and the included angles between the vectors formed by the two grid vertices and the feature points are both greater than the threshold, and the sum of the evaluation values of the two grid vertices is the largest, then they are used as the two optimal seed points.

[0051] Furthermore, extracting the segmentation boundary by using the path search algorithm and segmenting the teeth based on the segmentation boundary specifically includes the following steps:

[0052] Take the new screening area after k-ring neighborhood expansion as the graph G of the Dijkstra algorithm;

[0053] Take any one of the two optimal seed points as the starting point of the Dijkstra algorithm and the other as the end point;

[0054] Define a boundary perception function as the edge weight in the Dijkstra algorithm, and its expression is:

[0055]

[0056] In the formula, w ij is the perception weight of edge ij, and λ1 and λ2 are parameters;

[0057] Use the Dijkstra algorithm to perform the first path search to obtain a part of the initial segmentation boundary l0;

[0058] After blocking the direction of a part of the initial segmentation boundary l0, perform path search again to obtain another part of l0;

[0059] For the path points (m0, m1,..., m n ) of l0, perform continuous sampling at equal intervals t to obtain multiple groups of new starting points and ending points (m0, m t-1 ), (m t-1 , m 2t-2 )...;

[0060] Similarly, based on the new starting points and ending points, obtain multiple new segmentation boundaries (l1, l2...);

[0061] Count the number of path points of all the segmentation boundaries in (l0, l1, l2...), find the segmentation boundary with the most frequent same number of path points, and select any one of them as the final segmentation boundary;

[0062] Based on the feature points on the local area of the tooth, perform neighborhood expansion until it stops when reaching the final segmentation boundary. The expanded triangular mesh is the segmented tooth.

[0063] Furthermore, a tooth segmentation system includes:

[0064] An acquisition module, configured to acquire the local area of the tooth on the 3D dental arch mesh model, where the local area of the tooth includes a complete single tooth and part of the gingiva and adjacent teeth;

[0065] A calculation module, configured to construct a depression perception harmonic field in the local area of the tooth, and calculate the scalar intensity of the grid vertices in the local area of the tooth through the depression perception harmonic field;

[0066] A screening module, configured to screen out the optimal seed points located on the segmentation boundary of the local area of the tooth according to the scalar intensity;

[0067] An extraction module, configured to extract the segmentation boundary according to the optimal seed points by using a path search algorithm;

[0068] A segmentation module, configured to segment the tooth based on the segmentation boundary.

[0069] Furthermore, a tooth segmentation computer device includes: a memory, a processor, and a computer program stored in the memory. When the processor executes the computer program, the steps of the tooth segmentation method are implemented.

[0070] The present invention provides a tooth segmentation method, system, and computer device, having the following beneficial effects:

[0071] In the present invention, a dent depression perception harmonic field is constructed in a local tooth region, the scalar intensity of grid vertices in the local tooth region is calculated, the optimal seed points located on the segmentation boundary are selected according to the scalar intensity, and a path search algorithm is used to extract the segmentation boundary to segment the teeth. By proposing a tooth segmentation framework of harmonic field - point - line, the robustness and reliability of tooth segmentation are ensured. At the same time, a new attribute of grid vertices, called scalar intensity, is proposed, which can accurately evaluate the ability of vertices on the segmentation boundary. The accuracy of tooth segmentation is improved for both general dental models and deformed models, which is of great significance for digital orthodontics. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 is a step diagram of a tooth segmentation method in an embodiment of the present invention;

[0073] Figure 2 is a position diagram of feature points and spheres in an embodiment of the present invention;

[0074] Figure 3 is a position diagram of the image, ellipse, and two - dimensional feature points after dimensionality reduction in an embodiment of the present invention;

[0075] Figure 4 is a mapping diagram of the scalar values of grid vertices of the dent depression perception harmonic field on the local tooth region in an embodiment of the present invention;

[0076] Figure 5 is a mapping diagram of the scalar intensity of grid vertices on the local tooth region in an embodiment of the present invention;

[0077] Figure 6 is a position diagram of the optimal seed points and the final segmentation boundary in an embodiment of the present invention;

[0078] Figure 7 is a segmentation result diagram in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0079] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0080] As Figure 1As shown in the figure, the present invention provides a tooth segmentation method, which specifically includes the following steps:

[0081] S1: Read in a 3D dental arch mesh model and select a feature point in the approximate center area of each tooth. Among them, the 3D dental arch mesh model is an stl file, the model surface is composed of multiple triangular patches stitched together, and the vertices of each triangular patch are the mesh vertices of the 3D dental arch mesh model.

[0082] S2: Obtain the local tooth area. The local tooth area contains a complete single tooth and part of the gingiva and adjacent teeth. After obtaining the local tooth area, each subsequent operation is performed on a local tooth area, and finally all teeth are segmented. Among them, step S2 includes two implementation methods, and one of the implementation methods specifically includes:

[0083] S11: Use the PCA technology to reduce the point cloud data of the 3D dental arch mesh model to two dimensions, and at the same time obtain the two-dimensional feature points corresponding to the feature points.

[0084] S12: Assign an ellipse to each tooth, and the ellipse equation is:

[0085]

[0086] In the formula, x0 and y0 are respectively the abscissa and ordinate of the two-dimensional feature point p0 corresponding to the tooth for which the current ellipse needs to be assigned, θ is the angle between the vector formed by p0 and the two-dimensional feature point p1 closest to p0 and the y-axis, r is |p1p2|, and r1 and r2 are parameters. For example: r1 can be 0.8 and r2 can be 0.9.

[0087] S13: The local 3D mesh generated by the points inside the ellipse is the local tooth area.

[0088] Exemplarily, after PCA dimensionality reduction, the two-dimensional feature points corresponding to all feature points are obtained. The two-dimensional feature point corresponding to the feature point on the second molar on the 3D dental arch mesh model is p0'. On the two-dimensional image, the two-dimensional feature point p1' of the first molar closest to p0' is obtained. Therefore, the center of the ellipse matched by the second molar is p0', the rotation angle is The angle between the vector and the y-axis, and the major axis and minor axis are r1|p0'p1'| and r2|p0'p1'| respectively. The local 3D mesh generated by the three-dimensional points before dimensionality reduction corresponding to the two-dimensional points inside the ellipse is the local tooth area of the second molar. Similarly, the local tooth areas of other teeth are obtained in the same way, which will not be elaborated here.

[0089] Another implementation method of step S2 specifically includes:

[0090] S21. Assign a sphere to each tooth. The equation of the sphere is:

[0091] (x - a) 2 +(y - b) 2 +(z - c) 2 =r′ 2

[0092] where a, b, and c correspond one-to-one with the coordinate values of p- , p is a feature point on the tooth to which the sphere is currently to be assigned, n is the outward unit normal vector of p, and r′ are parameters. For example: can be 1.5 and r′ can be 9.5.

[0093] S22. The local 3D grid within the sphere is the local area of the tooth. Exemplarily, if the outward unit normal vector of the feature point p′ on the second molar is n′, then the center of the sphere matched to the second molar is with a radius of r′. The local 3D grid generated by the three-dimensional points within the sphere is the local area of the second molar. Similarly, the local areas of other teeth can be obtained in the same way and will not be elaborated here.

[0094] S3: Construct a dent depression perception harmonic field on the local area of the tooth. Step S3 specifically includes:

[0095] S31. Construct a harmonic function for the grid vertices within the local area of the tooth. The expression of the harmonic function is:

[0096]

[0097] where u i and u j are the scalar values of grid vertex i and grid vertex j, N(i) is the set of one-ring neighboring points of point i, ω ij is the weight of edge ij, and its expression is:

[0098]

[0099] where e max is the maximum side length of the local area of the tooth, v i and v j are grid vertex i and grid vertex j, and δ is a constant. For example: δ can be 0.0001.

[0100] S32. Take the f-ring neighboring points of the feature points on the local area of the tooth and the boundary points of the local area of the tooth as the constraint positions of the dent depression perception harmonic field, and set the constraint values to 1 and 0 respectively. For example: f can be 5.

[0101] S33. Construct a matrix equation based on the harmonic function and the constraint conditions, and its expression is:

[0102] Lu = b

[0103] Where L is the weight matrix, b is a vector composed of 0 and 1, and u contains the scalar values of the grid vertices.

[0104] S34. Obtain the scalar values of the grid vertices by solving the matrix equation.

[0105] S4: Propose the concept of variable intensity and calculate the scalar intensity of the grid vertices in the local area of the tooth. The scalar intensity is an attribute of the grid vertex, and its magnitude can be used to evaluate the ability of the grid vertex to be located on the segmentation boundary. Step S4 specifically includes:

[0106] S41. Divide the grid vertices into multiple sets based on the magnitude of the scalar values. For example: It can be divided into ten sets.

[0107] S42. Define an aggregation function to evaluate the aggregation of the grid vertices, and the aggregation function is:

[0108]

[0109] Where N is the number of one-ring neighborhood points of vertex v, and n is the number of one-ring neighborhood points of vertex v in different sets.

[0110] S43. Define a centrality function to evaluate the centrality of the grid vertices, and the centrality function is:

[0111]

[0112] Where N(v) is the one-ring neighborhood points of vertex v, u i is the scalar value of vertex v i and ε is the centrality parameter. For example: ε can be 0.5.

[0113] S44. Combine the aggregation function and the centrality function to define the scalar intensity, and the scalar intensity calculation formula is:

[0114]

[0115] S45. Calculate the scalar intensity of the grid vertices in the local area of the tooth.

[0116] S5: Design a seed point screening scheme and screen out two optimal seed points located on the segmentation boundary. Step S5 specifically includes:

[0117] S51. Select the grid vertices whose scalar values are within [u1, u2] as the screening area. For example, u1 can be 0.1 and u2 can be 0.9.

[0118] S52. Judge the connectivity of the screening area, and select the largest connected domain as the new screening area.

[0119] S53. Calculate the evaluation value e(v) of each vertex in the new screening area. The calculation formula is:

[0120]

[0121] In the formula, h(v) is the curvature of vertex v.

[0122] S54. Screen out two optimal seed points. If the Euclidean distance between two grid vertices and the angles between the vectors formed by the two grid vertices and the feature point are both greater than the threshold, and the sum of the evaluation values of the two grid vertices is the largest, then they are used as the two optimal seed points.

[0123] S6: Design a boundary perception function, and combine it with a path search algorithm to complete the extraction of the segmentation boundary. Finally, segment the teeth based on the segmentation boundary. Step S6 specifically includes:

[0124] S61. Use the new screening area after k-ring neighborhood expansion as the graph G of the Dijkstra algorithm. For example, k can be 6.

[0125] S62. Use any one of the two optimal seed points as the starting point of the Dijkstra algorithm, and the other as the end point.

[0126] S63. Define a boundary perception function as the edge weight in the Dijkstra algorithm. Its expression is:

[0127]

[0128] In the formula, w ij is the perception weight of edge ij, and λ1 and λ2 are parameters. For example, λ1 can be 0.7 and λ2 can be 0.3.

[0129] S64. Use the Dijkstra algorithm to perform the first path search to obtain a part of the initial segmentation boundary l0.

[0130] S65. Block the direction of a part of the initial segmentation boundary l0 and then perform path search again to obtain another part of l0.

[0131] S66. For the path points (m0, m1,..., m n)Sampling continuously at equal intervals of t, multiple new starting points and ending points (m0, m t-1 ) are obtained, (m t-1 , m 2t-2 )... For example, t can be 20.

[0132] S67. Similar to the step of obtaining l0, multiple new segmentation boundaries (l1, l2...) are obtained based on the new starting points and ending points.

[0133] S68. Count the number of path points of all the segmentation boundaries in (l0, l1, l2...), find out those segmentation boundaries with the most frequent same number of path points, and select any one of them as the final segmentation boundary.

[0134] S69. Perform neighborhood expansion based on the feature points on the local tooth region until it stops at the final segmentation boundary. The expanded triangular mesh is the segmented tooth.

[0135] In some examples, the scanned 3D dental jaw mesh model is read into the corresponding processing software, and a point is selected as the feature point in the approximate center region of each tooth in the 3D dental jaw mesh model. As Figure 2 shown, usually, the tooth sockets of premolars and molars, and the middle positions on the upper part of the lingual sides of canines, lateral incisors, and central incisors can be selected as the feature points.

[0136] Based on the same inventive concept, the present invention proposes a tooth segmentation system, including:

[0137] An acquisition module for acquiring the local tooth region on the 3D dental jaw mesh model, where the local tooth region includes a complete single tooth and part of the gingiva and adjacent teeth.

[0138] A calculation module for constructing a depression perception harmonic field in the local tooth region and calculating the scalar intensity of the mesh vertices in the local tooth region through the depression perception harmonic field.

[0139] A screening module for screening out the optimal seed points located on the segmentation boundary of the local tooth region according to the scalar intensity.

[0140] An extraction module for extracting the segmentation boundary according to the optimal seed points by using a path search algorithm.

[0141] A segmentation module for segmenting the tooth based on the segmentation boundary.

[0142] Based on the same inventive concept, the present invention also proposes a tooth segmentation computer device, including: a memory, a processor, and a computer program stored in the memory. When the processor executes the computer program, the steps of the tooth segmentation method are implemented.

[0143] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes should be covered within the protection scope of the present invention.

Claims

1. A method for tooth segmentation, characterized in that, Including the following steps: Obtain the local tooth region on the 3D dental jaw mesh model, where the local tooth region contains a complete single tooth, part of the gingiva, and adjacent teeth; Construct a depression-sensing harmonic field in the local tooth region, and calculate the scalar intensity of the mesh vertices in the local tooth region through the depression-sensing harmonic field; Select the optimal seed points located on the segmentation boundary in the local tooth region according to the scalar intensity; Extract the segmentation boundary using a path search algorithm based on the optimal seed points; Segment the teeth based on the segmentation boundary.

2. The tooth segmentation method according to claim 1, wherein The obtaining of the local tooth region specifically includes the following steps: Use the PCA technique to reduce the point cloud data of the 3D dental jaw mesh model to two dimensions, obtaining two-dimensional feature points corresponding to the feature points; Assign an ellipse to each tooth, and the ellipse equation is: where x0 and y0 are the abscissa and ordinate of the two-dimensional feature point p0 corresponding to the tooth for which the ellipse is currently to be assigned, θ is the angle between the vector formed by p0 and the two-dimensional feature point p1 closest to p0 and the y-axis, r is |p1p2|, and r1 and r2 are parameters; The local 3D mesh generated by the points inside the ellipse is the local tooth region; Or assign a sphere to each tooth, and the sphere equation is: (x - a) 2 +(y - b) 2 +(z - c) 2 = r' 2 where a, b, and c correspond one-to-one with the coordinate values of , p is a feature point on the tooth of the sphere to be currently allocated, n is the outward unit normal vector of p, and r' are parameters; The local 3D mesh inside the sphere is the local tooth region.

3. A tooth segmentation method according to claim 1, characterized in that, The constructing of the depression-sensing harmonic field in the local tooth region and calculating the scalar intensity of the mesh vertices in the local tooth region through the depression-sensing harmonic field specifically includes the following steps: Construct a harmonic function according to the mesh vertices in the local tooth region; Use the f-ring neighborhood points of the feature points on the local tooth region and the boundary points of the local tooth region as the constraint conditions of the depression-sensing harmonic field; construct a matrix equation according to the harmonic function and the constraint conditions, and then solve to obtain the scalar values of the mesh vertices; the feature points are the points selected at the central region of each tooth; Divide the mesh vertices into multiple sets based on the scalar values, and evaluate the clustering and centrality of the mesh vertices, respectively constructing a clustering function and a central function; Calculate the scalar intensity of the mesh vertices in the local tooth region according to the clustering function and the central function.

4. A tooth segmentation method according to claim 3, characterized in that The expression of the harmonic function is: where u i and u j are scalar values of grid vertices i and j, N(i) is the set of first-ring neighboring points of point i, and ω ij is the weight of edge ij, and its expression is: Among them, e max is the maximum side length of the local area of the tooth, v i and v j are the mesh vertices i and mesh vertex j, and δ is a constant.

5. A method for tooth segmentation according to claim 3, characterized in that, The constructing of the matrix equation according to the harmonic function and the constraint conditions, and then solving to obtain the scalar values of the mesh vertices; using the f-ring neighborhood points of the feature points on the local tooth region and the boundary points of the local tooth region as the constraint conditions of the depression-sensing harmonic field, and setting their constraint values to 1 and 0 respectively, then its matrix equation is expressed as: Lu = b where L is the weight matrix, b is a vector composed of 0 and 1, and u contains the scalar values of the mesh vertices; Obtain the scalar values of the mesh vertices by solving the matrix equation.

6. The tooth segmentation method according to claim 3, wherein, The calculating of the scalar intensity of the mesh vertices in the local tooth region according to the clustering function and the central function specifically includes the following steps: The clustering function is expressed as: where N is the number of one-ring neighborhood points of vertex v, and n is the number of one-ring neighborhood points of vertex v in different sets; The central function is expressed as: where N(v) is the one-hop neighborhood of vertex v, and u i is the scalar value of vertex v i , and ε is the centrality parameter; Then the calculation formula of the scalar intensity is expressed as:

7. A tooth segmentation method according to claim 1, wherein, The selecting of the optimal seed points located on the segmentation boundary according to the scalar intensity specifically includes the following steps: Select the mesh vertices with scalar values in [u1, u2] as the screening region; Judge the connectivity of the screening area, and select the largest connected component as the new screening area; Calculate the evaluation value e(v) of each vertex in the new screening area, and its calculation formula is expressed as: Among them, is the curvature of vertex v; Screen out two optimal seed points. If the Euclidean distance between two grid vertices and the angles between the vectors formed by the two grid vertices and the feature points are both greater than the threshold, and the sum of the evaluation values of the two grid vertices is the largest, then they are used as the two optimal seed points.

8. A method for tooth segmentation according to claim 7, wherein The path search algorithm is used to extract the segmentation boundary, and the teeth are segmented based on the segmentation boundary. The specific steps are as follows: Take the new screening area after k-ring neighborhood expansion as the graph G of the Dijkstra algorithm; Take any one of the two optimal seed points as the starting point of the Dijkstra algorithm, and the other as the end point; Define a boundary perception function as the edge weight in the Dijkstra algorithm, and its expression is: In the formula, is the perception weight of edge ij, and λ1 and λ2 are parameters; Use the Dijkstra algorithm to perform the first path search to obtain a part of the initial segmentation boundary l0; Block the direction of a part of the initial segmentation boundary l0 and then perform path search again to obtain another part of l0; Uniformly sample the path points (m0, m1,..., m n ) of l0 at intervals of t continuously, obtaining multiple new sets of starting and ending points (m0, m t-1 ), (m t-1 , m 2t-2 )...; Similarly, obtain multiple new segmentation boundaries (l1, l2...) based on the new starting point and end point; Count the number of path points of all segmentation boundaries in (l0, l1, l2...), find the segmentation boundary with the most frequent same number of path points, and select any one of them as the final segmentation boundary; Perform neighborhood expansion based on the feature points on the local area of the tooth until it stops when expanding to the final segmentation boundary. The expanded triangular mesh is the segmented tooth.

9. A tooth segmentation system, characterized in that, Including: An acquisition module for acquiring the local area of the tooth on the 3D dental arch mesh model, where the local area of the tooth includes a complete single tooth and part of the gingiva and adjacent teeth; A calculation module for constructing a depression perception harmonic field in the local area of the tooth, and calculating the scalar intensity of the grid vertices in the local area of the tooth through the depression perception harmonic field; A screening module for screening out the optimal seed points located on the segmentation boundary of the local area of the tooth according to the scalar intensity; An extraction module for extracting the segmentation boundary by using the path search algorithm according to the optimal seed points; A segmentation module for segmenting the tooth based on the segmentation boundary.

10. A dental segmentation computer device, characterized in that, Including: A memory, a processor, and a computer program stored in the memory. When the processor executes the computer program, the steps of the tooth segmentation method described in any one of claims 1-8 are implemented.

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