Dental and jaw segmentation method based on optimal seed point of harmonic field scalar intensity

Abstract

The present invention belongs to the field of digital stomatology, and in particular relates to a method for tooth and jaw segmentation based on optimal seed points of harmonic field scalar intensity, which can quickly and accurately find the gingival margin line on the tooth and jaw 3D model. The steps include: picking feature points on each tooth 3D model in the tooth and jaw 3D model. Constructing a segmentation domain for each tooth 3D model, and constructing a harmonic field within the segmentation domain, and assigning scalar values ​​to mesh vertices through the harmonic field. Screening is performed based on the scalar values ​​of the mesh vertices to obtain an initial screening area and a final screening area, and the final screening area is clustered to obtain a class area. Interpolating the one-ring neighborhood edges of the mesh vertices in the initial screening area, and adding the interpolation points to the corresponding sets according to the scalar values. Based on the one-ring neighborhood vertices of the mesh vertices in the class area and the scalar values ​​of the interpolation points, the scalar intensity of the mesh vertices in the class area is calculated, and the optimal seed point is obtained. The tooth gingival margin line is extracted based on the optimal seed point and the tooth and jaw segmentation is completed.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital dentistry, and in particular relates to a tooth and jaw segmentation method based on optimal seed points of harmonic field scalar intensity. Background Art

[0002] In recent years, with the rapid development of computer-aided design and 3D measurement technology, digital denture technology has been widely used in the dental field. People's demands for oral health have become more diverse and personalized. In this process, 3D tooth model segmentation is a primary and critical step. Subsequent processes such as restoration, tooth alignment, and tooth posture adjustment all require individual teeth, and the accuracy and efficiency of this 3D tooth model segmentation directly impact subsequent work.

[0003] Currently, the main method for segmenting 3D tooth models is to identify tooth morphological features and segment boundaries based on tooth surface curvature information. This method can achieve good results for high-quality dental models, but due to the limitations of 3D scanner resolution and mesh reconstruction accuracy, 3D scanned dental models often exhibit uneven surfaces, blurred boundaries, and tooth adhesion, leading to problems such as broken segmentation boundaries, under-segmentation, and over-segmentation. Zou et al. (B. Zou, S. Liu, S. Liao, et al. Interactive tooth partition of dental mesh base on tooth-target harmonic field, Computers in Biology and Medicine, 2015, 56:132–144) applied harmonic fields to segment 3D tooth models, achieving good results on lower-quality dental models. However, the method described in this article involves significant manual interaction and requires extensive matrix calculations.

[0004] Jiang et al. (Jian Xiaotong, Xu Benlian, Wei Mingqiang, Wu Ke, Yang Siyuan, Qian Longgen, Liu Ningzhong, Peng Qingjin. C2F-3DToothSeg: Coarse-to-fine 3D tooth segmentation via intuitive single clicks [J]. Computers & Graphics, 2022, 102.) first constructed a concave-aware harmonic field for the local mesh model of the tooth, then generated a series of contour lines and screened them, and finally optimized the optimal contour line to obtain the gingival margin line. However, it is necessary to manually pick feature points in the tooth gap, which is difficult, and the optimal contour line usually cannot meet the segmentation requirements. Summary of the Invention

[0005] In order to overcome the defects in the above-mentioned related technologies, the present invention provides a tooth and jaw segmentation method based on the optimal seed point of the harmonic field scalar intensity, which can quickly and accurately find the gingival margin line in the teeth and gums that need to be segmented in the tooth and jaw 3D model.

[0006] In order to achieve the above-mentioned purpose, the present invention provides a method for tooth and jaw segmentation based on the optimal seed point of the harmonic field scalar intensity. The method for tooth and jaw segmentation based on the optimal seed point of the harmonic field scalar intensity includes the following steps: reading in a tooth and jaw 3D model, and picking up a feature point on each tooth 3D model in the tooth and jaw 3D model. Constructing a segmentation domain for each tooth 3D model, and each segmentation domain includes a tooth 3D model. Calculating the curvature of the mesh vertices of the tooth 3D model in the segmentation domain, and constructing a harmonic field in the segmentation domain, and assigning scalar values ​​to the mesh vertices in the segmentation domain through the harmonic field. Establishing initial screening conditions and obtaining mesh vertices located near the tooth gingival margin line, establishing final screening conditions, obtaining mesh vertices clustered on the tooth gingival margin line from the mesh vertices located near the tooth gingival margin line, the mesh vertices located near the tooth gingival margin line are the initial screening area, and the mesh vertices clustered on the tooth gingival margin line are the final screening area, clustering the final screening area to obtain the class area. Interpolate the edges of a ring of neighborhoods of the mesh vertices within the initial screening area and obtain the scalar value of the interpolation point. Calculate the scalar strength of the mesh vertex in the class region based on the scalar values ​​of the ring of neighborhood vertices and the interpolation point of the mesh vertex in the class region and obtain the optimal seed point. Extract the gum margin based on the optimal seed point, and complete the segmentation of the 3D dental model based on the gum margin.

[0007] Preferably, the method for constructing the segmentation domain of each tooth 3D model includes: establishing a vector between the feature point and only another adjacent feature point. A first plane is established through the starting point of the vector and perpendicular to the vector, and a second plane is established through the end point of the vector and perpendicular to the vector. The feature points include a first feature point and a second feature point, the first feature point is located on the tooth 3D model at the leftmost or rightmost end of the jaw 3D model, the second feature point includes other feature points among the feature points except the first feature point, the area between the first plane or the second plane adjacent to the first feature point and the end of the jaw 3D model, or the area between the first plane or the second plane adjacent to the second feature point is the segmentation domain of the tooth 3D model.

[0008] Preferably, the method for constructing the segmentation domain of each tooth 3D model includes: expanding the ring neighborhood of the feature point, stopping the expansion when the expanded neighborhood is in contact with all the feature points adjacent to the feature point, and the expanded neighborhood is the segmentation domain of the tooth 3D model corresponding to the feature point.

[0009] Preferably, the method of assigning scalar values ​​to the mesh vertices in the segmentation domain comprises: calculating the curvature of each mesh vertex in the segmentation domain of the tooth 3D model by fitting a quadratic surface using a least squares method.

[0010] A harmonic function is constructed for the mesh vertices in the segmentation domain. The expression of the harmonic function is:

[0011]

[0012] Where, is the scalar value of the mesh vertex with index i, is the scalar value of the mesh vertex with index j, is a set of indices of the neighborhood points of point i. is the weight, and its expression is:

[0013]

[0014] Where, is the average side length of the mesh in the segmentation domain, are the coordinates of the mesh vertex with index i, are the coordinates of the mesh vertex with index j, is the average curvature of the mesh vertex with index i, is the mean curvature of the mesh vertex with index j, is the curvature threshold, is a constant.

[0015] The matrix equation of the harmonic field is constructed according to the harmonic function of each mesh vertex in the segmentation domain, and the scalar value of the feature point in the segmentation domain is set to 1, and the scalar value of the boundary point of the segmentation domain is set to 0 as the constraint conditions of the matrix equation.

[0016] The expression of the matrix equation is:

[0017]

[0018] Where, is the weight matrix, is a vector consisting of 0 and 1, Contains a scalar value for each mesh vertex.

[0019] The scalar value of each mesh vertex in the segmentation domain is obtained by solving the matrix equation.

[0020] Preferably, the method for obtaining the initial screening area includes: establishing T sets s, wherein the T sets s are sets ,gather ,..,gather Each set s corresponds to an initial screening condition, and the initial screening condition includes the screening interval of the scalar value. Each set s includes multiple mesh vertices that meet its corresponding initial screening condition. ,...,gather The mesh vertices in are classified as the initial screening area. The minimum value of the screening interval of the initial screening condition corresponding to each set s increases as the set s serial number increases, and the maximum value of the screening interval of the initial screening condition corresponding to each set s increases as the set s serial number increases. Set and collection Corresponding screening interval ratio set ,...,gather The corresponding screening interval is short, wherein the screening interval is between 0 and 1.

[0021] Preferably, the method for obtaining the final screening area and the class area includes: the final screening conditions include: condition 1, condition 2, condition 3 and condition 4,

[0022] Condition 1:

[0023] Condition 2:

[0024] Condition 3:

[0025] Condition 4:

[0026] Where, A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set The number of A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set The number of A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set ,gather ,..,gather The number of A ring of neighboring points of the grid vertex in the initial screening area belongs to 、 The number of, among which, and is a positive integer. The mesh vertices that meet the final screening conditions in the initial screening area are obtained, and the mesh vertices that meet the final screening conditions are the final screening area. The final screening area is divided into M areas using the FCM clustering algorithm, and the average curvature of the mesh vertices in each area is calculated, wherein the average curvature of the M areas is greater than or equal to The area is the class area, is the class region threshold.

[0027] Preferably, the method for obtaining the interpolation point comprises: interpolating a ring of neighboring edges corresponding to the mesh vertices of the initial screening area to obtain a plurality of interpolation points, and obtaining the coordinates, curvature and scalar value of the interpolation point according to the two mesh vertices corresponding to the interpolation point, and adding the interpolation point to T sets s according to the scalar value, and forming T sets s', wherein the T sets s' are sets ,gather ,..,gather .

[0028] Preferably, the method of calculating the scalar strength of the mesh vertices in the class area and obtaining the optimal seed point includes: obtaining the scalar strength of the mesh vertices and interpolation points within a ring neighborhood of the mesh vertex, and calculating using the following formula:

[0029]

[0030] Where, is the scalar strength of the mesh vertex with index i, is the average length of a ring of neighboring edges of the grid vertex with index i, is the average length of all edges in the segmentation domain, is a set of indices of mesh vertices and interpolation points in a ring neighborhood of the mesh vertex indexed by i. is the number of mesh vertices and interpolation points in the one-ring neighborhood of the mesh vertex indexed by i, is a constant, is the scalar weight of the mesh vertex or interpolation point with index j in the one-ring neighborhood of the mesh vertex with index i. Its value is determined as follows: if the mesh vertex or interpolation point with index j in the one-ring neighborhood of the mesh vertex with index i belongs to the set ,gather ,..,gather A set in , then is the corresponding value in the scalar weight set. The length of the scalar weight set is T, and the values ​​in the scalar weight set show a trend of monotonically increasing first and then monotonically decreasing.

[0031] The scalar intensities of all mesh vertices in any one of the plurality of class regions are calculated, and the mesh vertex with the largest scalar intensity is selected as the optimal seed point in the class region.

[0032] Calculate the scalar strength of all mesh vertices in multiple class areas except the class area where the optimal seed point has been obtained, calculate the scalar strength of the mesh vertices in each class area in the other class areas, and select five mesh vertices in descending order according to the scalar strength value.

[0033] The distances of F mesh vertices to all the obtained optimal seed points are calculated in descending order according to the scalar intensity.

[0034] When the distances between one of the F mesh vertices and all the obtained optimal seed points are greater than R, one of the F mesh vertices is the optimal seed point in the corresponding class area, and the distances between the remaining mesh vertices and the optimal seed point are no longer calculated.

[0035] When the distances between the F grid vertices and all the obtained optimal seed points are no greater than R, there is no optimal seed point in the corresponding class area, and R is the distance threshold.

[0036] Preferably, the method for extracting the gingival margin line of a tooth using the optimal seed point includes: determining the starting point and end point of the first gingival margin line, with the two adjacent and closest optimal seed points among the multiple optimal seed points serving as the starting point and end point of the first gingival margin line, respectively. Determining the starting point and end point of the remaining gingival margin lines except the first gingival margin line and the last gingival margin line. Determining the starting point and end point of the last gingival margin line, with the starting point of the last gingival margin line being the end point of the previous gingival margin line, and the end point of the last gingival margin line being the starting point of the first gingival margin line.

[0037] Based on the heuristic feature line extraction algorithm, the mesh vertices and the interpolation points in the segmentation domain are feasible path points, and a scalar intensity cost function is introduced into the heuristic feature line extraction algorithm. , Represents the relative magnitude of the scalar strength of the candidate path points of the current search center point. The scalar strength cost function The expression is:

[0038]

[0039] Where, 、 Indicates the maximum and minimum scalar intensity values ​​among the candidate path points of the current search center point, A scalar strength representing the current candidate waypoint.

[0040] Finally, the gum margin of each tooth is extracted according to the heuristic feature line extraction algorithm, and then the complete gum margin line is obtained and the jaw segmentation is completed.

[0041] Preferably, the method for determining the starting point and end point of the remaining gingival margin lines except the first gingival margin line segment and the last gingival margin line segment includes: the starting point of the current gingival margin line is the end point of the previous gingival margin line segment. The end point of the current gingival margin line is the point in the set E that is shortest from the starting point of the current gingival margin line.

[0042] The set E stores points P that meet the following conditions:

[0043] Condition 5: Point P is the optimal seed point that has not yet been used as the starting point or end point of the gingival margin line;

[0044] Condition 6: Point P satisfies the following formula:

[0045]

[0046] Where, The starting point of the upper gingival margin line. The end point of the previous gingival margin line. The starting point of the current gingival margin line.

[0047] The beneficial effects of the present invention are:

[0048] The present invention requires little manual interaction, and the selected feature points only need to be within a certain range, which effectively reduces the interaction difficulty for users.

[0049] The present invention introduces the concept of scalar strength, which effectively improves the accuracy and stability of selecting seed points and extracting gingival margin lines.

[0050] The present invention has good robustness and high efficiency, and is of great significance for improving the effect of digital orthodontic treatment of dentures. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] Figure 1 This is a diagram showing the steps of the tooth and jaw segmentation method based on the optimal seed point of the harmonic field scalar intensity according to the present invention;

[0053] Figure 2 are the characteristic points on the dental 3D model described in the present invention;

[0054] Figure 3 Establishing a structural diagram of segmented domains on the 3D model of the tooth and jaw described in the present invention;

[0055] Figure 4 A structural diagram of another segmentation domain is established on the 3D model of the tooth and jaw described in the present invention;

[0056] Figure 5 Establishing an initial screening area within the segmentation domain described in the present invention;

[0057] Figure 6 Establishing a final screening area within the segmentation domain described in the present invention;

[0058] Figure 7 Establishing a class region within the segmentation domain described in the present invention;

[0059] Figure 8 is the location map of the optimal seed point described in the present invention;

[0060] Figure 9 The structural diagram of the gingival margin line obtained by the present invention;

[0061] Figure 10 This is the segmentation result diagram of the present invention. DETAILED DESCRIPTION

[0062] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following is a collection of drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0063] In some embodiments of the present invention, Figure 1 As shown, a method for tooth and jaw segmentation based on optimal seed points of harmonic field scalar intensity is provided. The method for tooth and jaw segmentation based on optimal seed points of harmonic field scalar intensity includes the following steps:

[0064] S1. Read in a 3D jaw model, and pick a feature point on each 3D tooth model in the 3D jaw model.

[0065] S2. Construct a segmentation domain for each tooth 3D model, where each segmentation domain includes a tooth 3D model.

[0066] S3. Calculate the curvature of the mesh vertices of the tooth 3D model in the segmented domain, construct a harmonic field in the segmented domain, and assign scalar values ​​to the mesh vertices in the segmented domain through the harmonic field.

[0067] S4. Establish initial screening conditions and obtain mesh vertices located near the gum line of the teeth, establish final screening conditions, obtain mesh vertices clustered on the gum line of the teeth from the mesh vertices located near the gum line of the teeth, the mesh vertices located near the gum line of the teeth are the initial screening area, the mesh vertices clustered on the gum line of the teeth are the final screening area, cluster the final screening area to obtain the class area.

[0068] S5. Interpolate the neighborhood edges of the mesh vertices in the initial screening area and obtain the scalar value of the interpolation point according to the scalar value of the interpolation point.

[0069] S6. Calculate the scalar strength of the mesh vertex in the class area according to the scalar values ​​of a ring of neighboring vertices and interpolation points of the mesh vertex in the class area, and obtain an optimal seed point.

[0070] S7. Extracting the gum margin line based on the optimal seed point, and completing the segmentation of the dental jaw 3D model according to the gum margin line.

[0071] In some examples, the scanned jaw 3D model is read into the corresponding processing software, and a point in the middle area of ​​each tooth 3D model in the jaw 3D model is selected as a feature point, such as Figure 2 As shown in the figure, the tooth sockets of premolars and molars, and the middle position at the junction of the lingual and buccal sides of canines, lateral incisors, and central incisors can usually be selected as feature point 1. Segmentation domains are constructed based on feature point 1, and each segmentation domain includes a tooth 3D model. In this way, the gingival margin line can be extracted from a single tooth 3D model.

[0072] The tooth 3D model is an STL file, which is composed of multiple triangular facets. The three vertices of each triangular facet are mesh vertices in the tooth 3D model, and the triangular facet edges that are in direct contact with the mesh vertices are the neighborhood edges of the mesh vertices.

[0073] The present invention constructs a harmonic field for the segmentation domain and sets concave perception weights and constraints, so that the mesh vertices corresponding to a large range of scalar values ​​can be gathered at the gum line of the teeth. The scalar values ​​of the mesh vertices in the tooth 3D model can be filtered according to the scalar value range to obtain the mesh vertices near the gum line of the teeth.

[0074] It can be understood that in order to improve the accuracy of the tooth gum margin line, a ring of neighborhood edges of the obtained mesh vertices near the tooth gum margin line can be interpolated, and the optimal seed point of the mesh vertex near the tooth gum margin line is preferably obtained. Based on the optimal seed point, a smooth tooth gum margin line is extracted, and the tooth and jaw 3D model segmentation is completed according to the tooth gum margin line.

[0075] In some embodiments, as Figure 3 As shown, the method for constructing the segmentation domain H of each tooth 3D model includes the following steps:

[0076] S21: Establish a vector between the feature point and only one adjacent feature point.

[0077] S22. Establish a first plane passing through the starting point of the vector and perpendicular to the vector, and establish a second plane passing through the end point of the vector and perpendicular to the vector.

[0078] S23. The feature points include a first feature point and a second feature point, the first feature point is located on the tooth 3D model at the leftmost or rightmost end of the dental jaw 3D model, the second feature point includes other feature points among the feature points except the first feature point, the area between the first plane or the second plane adjacent to the first feature point and the end of the dental jaw 3D model, or the area between the first plane or the second plane adjacent to the second feature point is the segmentation domain of the tooth 3D model.

[0079] For example, four consecutive tooth 3D models are selected in the dental jaw 3D model, and a point is selected on each tooth 3D model as feature point 1. The first vector is established with feature point 1 on the first tooth 3D model as the starting point and feature point 1 on the second tooth 3D model as the end point. The second vector is established with feature point 1 on the third tooth 3D model as the starting point and feature point 1 on the fourth tooth 3D model as the end point.

[0080] A first plane A is established perpendicular to the first vector and passes through the feature point 1 on the first tooth 3D model, a second plane B is established perpendicular to the first vector and passes through the feature point 1 on the second tooth 3D model, and a first plane A' is established perpendicular to the second vector and passes through the feature point 1 on the third tooth 3D model.

[0081] When the first tooth 3D model corresponds to the first tooth on the jaw 3D model, the feature point 1 on the first tooth 3D model is the first feature point 1', that is, the area between the second plane B and the end of the jaw 3D model is the segmentation domain corresponding to the first tooth 3D model, wherein the end of the jaw 3D model refers to the end of the jaw 3D model closest to the first feature point 1'.

[0082] The feature point 1 on the second tooth 3D model is a second feature point 1 ″, that is, the area between the first plane A and the first plane A′ is the segmentation domain H corresponding to the second tooth 3D model.

[0083] In other embodiments, Figure 4As shown, the method for constructing the segmentation domain of each tooth 3D model includes: expanding the ring neighborhood of the feature point 1, stopping the expansion when the expanded neighborhood G is in contact with all the feature points 1 adjacent to the feature point 1, and the expanded neighborhood G is the segmentation domain of the tooth 3D model corresponding to the feature point.

[0084] Exemplarily, three consecutive tooth 3D models are selected from the jaw 3D model, and a point is selected on each tooth 3D model as a feature point 1. Among them, when one of the three tooth 3D models corresponds to the first tooth on the jaw 3D model, the feature point 1 on the tooth 3D model is the first feature point, and the feature points 1 on the other tooth 3D models are the second feature points. The first feature point is adjacent to only one feature point 1, and the first feature point is expanded in a ring neighborhood. When it contacts the adjacent feature point 1, the expanded neighborhood G corresponding to the first feature point can completely contain the tooth 3D model corresponding to the first feature point. The second feature point is adjacent to two feature points 1, and the second feature point is expanded in a ring neighborhood. When it contacts the two adjacent feature points, the expanded neighborhood G corresponding to the second feature point can completely contain the tooth 3D model corresponding to the second feature point.

[0085] In some embodiments, the method of assigning scalar values ​​to the mesh vertices within the segmentation domain comprises the following steps:

[0086] S31. Calculate the curvature of each mesh vertex in the segmentation domain of the 3D tooth model by fitting a quadratic surface using the least squares method.

[0087] S32. Construct a harmonic function for the mesh vertices within the segmentation domain. The harmonic function has a smooth characteristic and can make the mesh surface diffuse along the specified constraint. The expression of the harmonic function is:

[0088]

[0089] Where, is the scalar value of the mesh vertex with index i, is the scalar value of the mesh vertex with index j, is a set of indices of the neighborhood points of point i. is the weight, and its expression is:

[0090]

[0091] Where, is the average side length of the mesh in the segmentation domain, are the coordinates of the mesh vertex with index i, are the coordinates of the mesh vertex with index j, is the average curvature of the mesh vertex with index i, is the mean curvature of the mesh vertex with index j, is the curvature threshold, is a constant. For example: It can be 0.05, It can be 0.0001.

[0092] S33. Construct a matrix equation of the harmonic field based on the harmonic function of each mesh vertex in the segmentation domain, set the scalar value of the feature point in the segmentation domain to 1, and set the scalar value of the boundary point of the segmentation domain to 0 as the constraint conditions of the matrix equation. The expression of the matrix equation is:

[0093]

[0094] Where, is the weight matrix, is a vector consisting of 0 and 1, Contains the scalar value of each mesh vertex, and the scalar value of each mesh vertex is obtained by solving the matrix equation.

[0095] In some embodiments, the method for obtaining the initial screening area includes the following steps:

[0096] Establish T sets s, which are sets ,gather ,..,gather , each set s corresponds to an initial screening condition, and the initial screening condition includes the screening interval of the scalar value.

[0097] Among them, each set s includes multiple mesh vertices that meet its corresponding initial screening conditions. ,...,gather The mesh vertices in are classified as the initial screening area.

[0098] For example, ten sets can be established: Set to , among which, Figure 5As shown, the initial screening condition of the set s0 is the mesh vertex 2 whose scalar value is between 0 and 0.1 in the segmentation domain, the initial screening condition of the set s1 is the mesh vertex 2 whose scalar value is between 0.1 and 0.2 in the segmentation domain, the initial screening condition of the set s2 is the mesh vertex 2 whose scalar value is between 0.2 and 0.3 in the segmentation domain, the initial screening condition of the set s3 is the mesh vertex 2 whose scalar value is between 0.3 and 0.4 in the segmentation domain, and the initial screening condition of the set s4 is the mesh vertex 2 whose scalar value is between 0.4 and 0.5 in the segmentation domain. The initial screening condition of the set s5 is the mesh vertex 2 whose scalar value in the segmentation domain is between 0.5 and 0.6, the initial screening condition of the set s6 is the mesh vertex 2 whose scalar value in the segmentation domain is between 0.6 and 0.7, the initial screening condition of the set s7 is the mesh vertex 2 whose scalar value in the segmentation domain is between 0.7 and 0.8, the initial screening condition of the set s8 is the mesh vertex 2 whose scalar value in the segmentation domain is between 0.8 and 0.9, and the initial screening condition of the set s9 is the mesh vertex 2 whose scalar value in the segmentation domain is between 0.9 and 1. The set s8 constitutes the initial screening area 3, that is, The mesh vertices in the set s8 are mesh vertices located near the gum line of the tooth.

[0099] According to the above example, the minimum value of the screening interval of the initial screening condition corresponding to each set s increases as the set s serial number increases, and the maximum value of the screening interval of the initial screening condition corresponding to each set s increases as the set s serial number increases. For example, the minimum value of the screening interval of the initial screening condition of set s0 is 0, the minimum value of the screening interval of the initial screening condition of set s1 is 0.1, ..., the minimum value of the screening interval of the initial screening condition of set s9 is 0.9, and so on. The minimum value of the screening interval of the initial screening condition of set s increases as its serial number increases. Similarly, the maximum value of the screening interval of the initial screening condition of set s increases as its serial number increases.

[0100] gather and collection Corresponding screening interval ratio set ,...,gather The corresponding filtering intervals are short. For example, the initial filtering condition for set s0 has a filtering interval of 0 to 0.1, and the initial filtering condition for set s9 has a filtering interval of 0.9 to 1. Compared with the initial filtering condition intervals for sets s1 to s8, the filtering intervals for sets s0 and s9 are shorter.

[0101] The screening interval is between 0 and 1. That is, the initial screening conditions of the above set S are all between 0 and 1.

[0102] In some embodiments, the method for obtaining the final screening area includes:

[0103] A final screening condition is established, and mesh vertices in the initial screening area that meet the final screening condition are obtained, and the mesh vertices that meet the final screening condition are the final screening area.

[0104] The final screening conditions include: condition 1, condition 2, condition 3 and condition 4.

[0105] Condition 1:

[0106] Condition 2:

[0107] Condition 3:

[0108] Condition 4:

[0109] Where, A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set The number of A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set The number of A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set ,gather ,..,gather The number of A ring of neighboring points of the grid vertex in the initial screening area belongs to 、 The number of, among which, and Is a positive integer.

[0110] It should be noted that the collection and For two consecutive serial numbers, that is, when T is an odd number, the set and The serial number can be selected as a positive integer in ascending or descending order. For example, when T is 5, the set Can be S2 or S3, Can be S3 or S4.

[0111] For example, create an empty set S, such as Figure 6As shown, if the mesh vertex 2 exists in the initial screening area and satisfies the four conditions at the same time, the mesh vertex 2 is added to the set S, and the mesh vertices in the set S are the final screening area 4:

[0112] The four conditions include condition 1, condition 2, condition 3 and condition 4.

[0113] Condition 1:

[0114] Condition 2:

[0115] Condition 3:

[0116] Condition 4:

[0117] Where, A ring of neighboring points of the mesh vertex 2 belongs to the set The number of A ring of neighboring points of the mesh vertex 2 belongs to the set The number of is the number of neighboring points of the mesh vertex 2 belonging to the set s1, set s2, set s3, and set s4, is the number of neighboring points of the mesh vertex 2 that belong to set s5, set s6, set s7, and set s8.

[0118] In some embodiments, the method for obtaining the class region includes: using the FCM clustering algorithm to divide the final screening area into M regions, and calculating the average curvature of the grid vertices in each region, wherein the average curvature of the M regions is greater than or equal to The area is the class area, is the class region threshold.

[0119] For example, Figure 7 As shown, the FCM clustering algorithm is used to divide the set S into 8 regions 5, and the average curvature of the mesh vertices in each region 5 is calculated, wherein the average curvature of the 8 regions 5 is greater than or equal to The area is the class area, is the class region threshold, for example, It can be 0.35.

[0120] In some embodiments, the process of obtaining a class region according to assigning scalar values ​​to the mesh vertices within the segmentation domain may include:

[0121] S41. Obtain an initial screening area.

[0122] S42: Establish final screening conditions, screen the mesh vertices in the initial screening area again and obtain a final screening area.

[0123] S43. Cluster the final screened area and obtain the class area.

[0124] The method for obtaining the initial screening area, the final screening area, and the method for obtaining the class area have been described in detail in the above embodiments, and will not be repeated here.

[0125] In some embodiments, the method for obtaining interpolation points includes:

[0126] Interpolate the neighboring edges of the mesh vertices corresponding to the initial screening area to obtain multiple interpolation points, and obtain the coordinates, curvature and scalar values ​​of the interpolation points according to the two mesh vertices corresponding to the interpolation points, and add the interpolation points to T sets s according to the scalar values, and form T sets s', which are sets ,gather ,..,gather .

[0127] Exemplarily, the method for obtaining interpolation points may include the following steps:

[0128] A plurality of points are interpolated on a ring of neighborhood edges of the grid vertices in the initial screening area. For example, 2 to 3 points may be interpolated. The coordinates, curvature, and scalar values ​​of the interpolation points are obtained based on the grid vertices at both ends of the ring of neighborhood edges where the interpolation points are located. The interpolation points are added to the sets s0 to s9 according to the scalar values ​​to form new sets s0' to s9'. It can be understood that the scalar values ​​of the interpolation points meet the initial screening conditions corresponding to sets s0 to s9.

[0129] Specifically, the one-ring neighborhood edges of the grid vertices in the initial screening area are interpolated, and interpolation points are made at equal intervals according to the length of each one-ring neighborhood edge, and the threshold is set. , such as the threshold It can be 0.3. If the length of a ring's neighboring edge is greater than , three interpolation points are made on the edge of a ring neighborhood; otherwise, two interpolation points are made on the edge of a ring neighborhood. The coordinates, curvature, and scalar value of the interpolation point are determined by the two mesh vertices on the edge of the ring neighborhood where it is located. The interpolation formula is:

[0130]

[0131] Where, and are the coordinates of two mesh vertices of the interpolated ring neighborhood edge, are the interpolation point coordinates, for The curvature of for The curvature of for The curvature of for scalar value of , for scalar value of , for scalar value. When interpolating 2 interpolation points, m is 3 and k is 1 or 2. When interpolating 3 interpolation points, m is 4 and k is 1, 2, or 3.

[0132] The interpolation points are sequentially classified into the initial screening area according to the scalar value to form new sets s0', ..., s9'.

[0133] Among them, set s0' includes set s0 and points that satisfy the interpolation of scalar values ​​between 0 and 0.1; set s1' includes set s1 and points that satisfy the interpolation of scalar values ​​between 0.1 and 0.2; set s2' includes set s2 and points that satisfy the interpolation of scalar values ​​between 0.2 and 0.3; set s3' includes set and points that satisfy the interpolation of scalar values ​​between 0.3 and 0.4; set s4' includes the set and points that satisfy the interpolation of scalar values ​​between 0.4 and 0.5; set s5' includes the set and points that satisfy the interpolation of scalar values ​​between 0.5 and 0.6; set s6' includes the set and points that satisfy the interpolation of scalar values ​​between 0.6 and 0.7; set s7' includes the set and points that satisfy the interpolation of scalar values ​​between 0.7 and 0.8; set s8' includes the set and points that satisfy the interpolation of scalar values ​​between 0.8 and 0.9; set s9' includes the set and the points that satisfy the interpolation of scalar values ​​between 0.9 and 1.

[0134] In some embodiments, the method of calculating the scalar strength of the mesh vertices and obtaining the optimal seed point comprises the following steps:

[0135] S61. Obtain the scalar strength of the mesh vertices and interpolation points in a ring neighborhood of the mesh vertex, and calculate using the following formula:

[0136]

[0137] Where, is the scalar strength of the mesh vertex with index i, is the average length of a ring of neighboring edges of the grid vertex with index i, is the average length of all edges in the segmentation domain, is a set of indices of mesh vertices and interpolation points in a ring neighborhood of the mesh vertex indexed as i, N is the number of mesh vertices and interpolation points in a ring neighborhood of the mesh vertex indexed as i, is a constant, is the scalar weight of the mesh vertex or interpolation point with index j in the one-ring neighborhood of the mesh vertex with index i. The value is determined as follows: if the mesh vertex or interpolation point with index j in the one-ring neighborhood of the mesh vertex with index i belongs to the set ,gather ,..,gather A set in , then is the corresponding value in the scalar weight set. The length of the scalar weight set is T, and the values ​​in the scalar weight set show a trend of monotonically increasing and then monotonically decreasing.

[0138] A large number of numerical experiments show that the middle position of the class region tends to the position of the gingival margin. By calculating the scalar strength of the mesh vertices in the class region, the mesh vertices located in the middle position of the class region, that is, the mesh vertices located on the gingival margin, can be optimized.

[0139] For example, the scalar weight set can be {0, 0.01, 0.05, 0.2, 1, 1, 0.8, 0.1, 0.01, 0}, then the mesh vertex with index j belongs to s0', The corresponding value is 0; the mesh vertex with index j belongs to s1', The corresponding value is 0.01; the mesh vertex with index j belongs to s2', The corresponding value is 0.05; the mesh vertex with index j belongs to s3', The corresponding value is 0.2; the mesh vertex with index j belongs to s4', The corresponding value is 1; the mesh vertex with index j belongs to s5', The corresponding value is 1; the mesh vertex with index j belongs to the set s6', The corresponding value is 0.8; the mesh vertex with index j belongs to the set s7', The corresponding values ​​are 0.1; the mesh vertex with index j belongs to the set s8', The corresponding value is 0.01; the mesh vertex with index j belongs to the set s9', The corresponding value is 0.

[0140] S62 , calculating the scalar strengths of all mesh vertices in any one of the plurality of class regions, and selecting the mesh vertex with the largest scalar strength as the optimal seed point in the class region.

[0141] S63. Calculate the scalar strengths of all mesh vertices in the other class areas except the class area where the optimal seed point has been obtained, calculate the scalar strengths of the mesh vertices in each class area in the other class areas, and select five mesh vertices in descending order according to the scalar strength values.

[0142] S64. Calculate the distances of the F mesh vertices to all the acquired optimal seed points in descending order of scalar strength. When the distances of one of the F mesh vertices to all the acquired optimal seed points are greater than R, one of the F mesh vertices is the optimal seed point in the corresponding class region, and the distances of the remaining mesh vertices to the optimal seed points are no longer calculated. When the distances of the F mesh vertices to all the acquired optimal seed points are no greater than R, there is no optimal seed point in the corresponding class region, and R is the distance threshold. For example, R can be 2.

[0143] For example, Figure 8 As shown, first, a class region is selected from all class regions, the scalar strength of all mesh vertices in this class region is calculated, and the mesh vertex with the largest scalar strength is selected as the optimal seed point x of this class region.

[0144] Then select one class area from the remaining class areas, calculate the scalar strength of all mesh vertices in this class area, and select five mesh vertices in descending order according to the scalar strength: mesh vertex , mesh vertices , mesh vertices , mesh vertices and mesh vertices , first calculate the mesh vertices The distance from the optimal seed point x; if it is greater than or equal to R, the mesh vertex is the optimal seed point for this type of area, and the grid vertex , mesh vertices , mesh vertices and mesh vertices Discard, selection ends; if it is less than R, the mesh vertex is discarded , from the mesh vertex Start selecting until the optimal seed point of the region is obtained. The optimal seed point of the region is recorded as y. If the grid vertex , mesh vertices , mesh vertices , mesh vertices and mesh vertices If none of them are optimal seed points, then there is no optimal seed point in this type of region.

[0145] Then, perform the same steps as above for the class region that has not been selected for the optimal seed point. For example, select five mesh vertices in a class region that has not been selected for the optimal seed point. 、 、 、 and , first calculate The distance from the optimal seed point x and the optimal seed point y; if both are greater than or equal to R, then is the optimal seed point for this type of region, 、 、 and Discard, selection ends; if less than R, discard ,from Start selecting until the optimal seed point is found in this type of area. The optimal seed point in this type of area is recorded as z. 、 、 、 and If none of them are optimal seed points, then there is no optimal seed point for this class region. The above steps are executed in sequence for the remaining class regions until all class regions are executed.

[0146] In some embodiments, the method for extracting the gingival margin line using the optimal seed point comprises the following steps:

[0147] S71. Determine the starting point and the end point of the first gingival margin line. The two adjacent and closest optimal seed points among the multiple optimal seed points are used as the starting point and the end point of the first gingival margin line respectively.

[0148] S72. Determine the starting points and ending points of the remaining gingival margin lines except the first gingival margin line segment and the last gingival margin line segment.

[0149] S73. Determine the starting point and end point of the last gingival margin line, wherein the starting point of the last gingival margin line is the end point of the previous gingival margin line, and the end point of the last gingival margin line is the starting point of the first gingival margin line.

[0150] S74, the heuristic feature line extraction algorithm is to realize the path search from one seed point to another sub-point by defining a cost function between two sub-points. Based on the heuristic feature line extraction algorithm, the mesh vertices and the interpolation points in the segmentation domain are feasible path points, and a scalar intensity cost function is introduced into the heuristic feature line extraction algorithm. , Represents the relative magnitude of the scalar strength of the candidate path points of the current search center point. The scalar strength cost function The expression is:

[0151]

[0152] Where, 、 Respectively represent the maximum and minimum scalar values ​​of the next feasible points (vertices and interpolation points) of the current path point, A scalar value representing the current feasible point.

[0153] Finally, the gum margin of each tooth is extracted according to the heuristic feature line extraction algorithm, and then the complete gum margin line is obtained and the jaw segmentation is completed. The segmentation results are as follows: Figure 10 shown.

[0154] In some embodiments, as Figure 9 As shown, the method for determining the starting point and the end point of the remaining gingival margin lines 6 except the first gingival margin line 6 and the last gingival margin line 6 includes the following steps:

[0155] S721 . The starting point of the current gingival margin line 6 is the end point of the previous gingival margin line 6 .

[0156] S721 The end point of the current gingival margin line 6 is the optimal seed point in the set E that has the shortest distance to the starting point of the current gingival margin line 6 .

[0157] The set E stores points P that meet the following conditions:

[0158] Condition 5: Point P is an optimal seed point that has not yet been used as the starting point or the end point of the gingival margin line 6 .

[0159] Condition 6: Point P satisfies the following formula:

[0160]

[0161] Where, It is the starting point of the previous gingival margin line 6. It is the end point of the previous gingival margin line 6. It is the starting point of the current gingival margin line 6.

[0162] In some embodiments, an optimal seed point is obtained, and then the first gingival margin line 6, the remaining gingival margin lines 6, and the last gingival margin line 6 are sequentially determined based on the optimal seed point. The starting point and the end point of each gingival margin line 6 are both optimal seed points.

[0163] In order to improve the accuracy of the gingival margin line 6, a heuristic feature line extraction algorithm can be used. Specifically, the gingival margin line 6 can be obtained by using a tooth biological feature line extraction technique based on a heuristic search strategy. A heuristic feature line extraction algorithm is introduced, and interpolation points are added to feasible path points, which are points that the gingival margin line 6 can pass through. The obtained feasible path points are sequentially connected to obtain each segment of the gingival margin line 6.

[0164] The above are only specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity, characterized in that: The following steps are involved: Reading a 3D model of the jaw, and picking a feature point on each 3D model of teeth in the 3D model of the jaw; Constructing a segmentation domain for each tooth 3D model, where each segmentation domain includes a tooth 3D model; Calculating the curvature of the mesh vertices of the tooth 3D model within the segmented domain, constructing a harmonic field within the segmented domain, and assigning scalar values ​​to the mesh vertices within the segmented domain through the harmonic field; Establishing initial screening conditions and obtaining mesh vertices located near the gum margin line of the teeth, establishing final screening conditions, obtaining mesh vertices clustered on the gum margin line from the mesh vertices located near the gum margin line of the teeth, the mesh vertices located near the gum margin line of the teeth being the initial screening area, the mesh vertices clustered on the gum margin line of the teeth being the final screening area, clustering the final screening area to obtain a class area; Interpolating the grid vertex-ring neighborhood edges within the initial screening area; Calculating the scalar strength of the mesh vertex in the class region according to a ring of neighboring vertices and the scalar value of the interpolation point of the mesh vertex in the class region, and obtaining an optimal seed point; Extracting the gum margin line based on the optimal seed point, and completing the segmentation of the 3D model of the jaw according to the gum margin line; The method for extracting the gingival margin line based on the optimal seed point includes: Determine the starting point and the end point of the first gingival margin line, and use the two adjacent and closest optimal seed points among the multiple optimal seed points as the starting point and the end point of the first gingival margin line respectively; Determine the starting points and ending points of the remaining gingival margin lines except the first gingival margin line and the last gingival margin line; Determine the starting point and end point of the last gingival margin line, wherein the starting point of the last gingival margin line is the end point of the previous gingival margin line, and the end point of the last gingival margin line is the starting point of the first gingival margin line; Based on the heuristic feature line extraction algorithm, the mesh vertices and the interpolation points in the segmentation domain are feasible path points, and a scalar intensity cost function is introduced into the heuristic feature line extraction algorithm. , Represents the relative magnitude of the scalar strength of the candidate path points of the current search center point. The scalar strength cost function The expression is: ； Where, 、 Indicates the maximum and minimum scalar intensity values ​​among the candidate path points of the current search center point, scalar strength representing the current candidate path point; Finally, the gum margin of each tooth is extracted according to the heuristic feature line extraction algorithm, and then the complete gum margin line is obtained and the jaw segmentation is completed.

2. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 1, characterized in that: The method for constructing the segmentation domain of each tooth 3D model includes: Establishing a vector between the feature point and only another adjacent feature point; A first plane is established through the starting point of the vector and perpendicular to the vector, and a second plane is established through the end point of the vector and perpendicular to the vector; The feature points include a first feature point and a second feature point, the first feature point is located on the tooth 3D model at the leftmost or rightmost end of the dental jaw 3D model, the second feature point includes other feature points among the feature points except the first feature point, the area between the first plane or the second plane adjacent to the first feature point and the end of the dental jaw 3D model, or the area between the first plane or the second plane adjacent to the second feature point is the segmentation domain of the tooth 3D model.

3. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 1, characterized in that: The method for constructing the segmentation domain of each tooth 3D model includes: The ring neighborhood of the feature point is expanded, and the expansion is stopped when the expanded neighborhood contacts all the feature points adjacent to the feature point. The expanded neighborhood is the segmentation domain of the tooth 3D model corresponding to the feature point.

4. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to any one of claims 1 to 3, characterized in that: The method of assigning scalar values ​​to the mesh vertices within the segmentation domain comprises: Calculating the curvature of each mesh vertex within the segmentation domain of the 3D tooth model by fitting a quadratic surface using the least squares method; A harmonic function is constructed for the mesh vertices in the segmentation domain. The expression of the harmonic function is: ； Where, is the scalar value of the mesh vertex with index i, is the scalar value of the mesh vertex with index j, is a set of indices of the neighborhood points of point i. is the weight, and its expression is: ； Where, is the average side length of the mesh in the segmentation domain, are the coordinates of the mesh vertex with index i, are the coordinates of the mesh vertex with index j, is the average curvature of the mesh vertex with index i, is the mean curvature of the mesh vertex with index j, is the curvature threshold, is a constant; Constructing a matrix equation of the harmonic field according to the harmonic function of each mesh vertex in the segmentation domain, setting the scalar value of the feature point in the segmentation domain to 1 and the scalar value of the boundary point of the segmentation domain to 0 as constraints of the matrix equation; The expression of the matrix equation is: ； Where, is the weight matrix, is a vector consisting of 0 and 1, Contains the scalar value of each mesh vertex; The scalar value of each mesh vertex in the segmentation domain is obtained by solving the matrix equation.

5. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 4, characterized in that: The mesh vertices located near the gum line are the initial screening area. The method for obtaining the initial screening area includes: establishing T sets s, and the T sets s are sets ,gather ,..,gather , each set s corresponds to an initial screening condition, and the initial screening condition includes the screening interval of the scalar value; Each set s includes multiple mesh vertices that meet its corresponding initial screening conditions. ,...,gather The mesh vertices in are classified as the initial screening area; The minimum value of the screening interval of the initial screening condition corresponding to each set s increases as the sequence number of the set s increases, and the maximum value of the screening interval of the initial screening condition corresponding to each set s increases as the sequence number of the set s increases; gather and collection Corresponding screening interval ratio set ,...,gather The corresponding screening interval is short; The screening interval is between 0 and 1.

6. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 5, characterized in that: The mesh vertices clustered on the gum line are the final screening area, the final screening area is clustered to obtain the class area, and the method for obtaining the final screening area and the class area includes: The final screening conditions include: condition 1, condition 2, condition 3 and condition 4, Condition 1: ; Condition 2: ; Condition 3: ; Condition 4: ; Where, A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set The number of A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set The number of A ring of neighborhood points of the grid vertices in the initial screening area belongs to the set ,gather ,..,gather The number of A ring of neighboring points of the grid vertex in the initial screening area belongs to 、 The number of, among which, and is a positive integer; Obtaining mesh vertices in the initial screening area that meet the final screening conditions, and the mesh vertices that meet the final screening conditions are the final screening area, The final screening area is divided into M areas using the FCM clustering algorithm, and the average curvature of the grid vertices in each area is calculated, wherein the average curvature of the M areas is greater than or equal to The area is the class area, is the class region threshold.

7. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 6, characterized in that: The method of interpolating the mesh vertex-ring neighborhood edges within the initial screening area to obtain interpolation points includes: Interpolate the neighboring edges of the mesh vertices corresponding to the initial screening area to obtain multiple interpolation points, and obtain the coordinates, curvature and scalar values ​​of the interpolation points according to the two mesh vertices corresponding to the interpolation points, and add the interpolation points to T sets s according to the scalar values, and form T sets s', which are sets ,gather ,..,gather .

8. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 7, characterized in that: The method of calculating the scalar strength of the mesh vertices in the class area and obtaining the optimal seed point includes: The scalar strength of the mesh vertex is obtained based on the mesh vertices and interpolation points in a ring neighborhood of the mesh vertex, and is calculated using the following formula: ； Where, is the scalar strength of the mesh vertex with index i, is the average length of a ring of neighboring edges of the grid vertex with index i, is the average length of all edges in the segmentation domain, is a set of indices of mesh vertices and interpolation points in a ring neighborhood of the mesh vertex indexed by i. is the number of mesh vertices and interpolation points in the one-ring neighborhood of the mesh vertex indexed by i, is a constant, is the scalar weight of the mesh vertex or interpolation point with index j in the one-ring neighborhood of the mesh vertex with index i. Its value is determined as follows: if the mesh vertex or interpolation point with index j in the one-ring neighborhood of the mesh vertex with index i belongs to the set ,gather ,..,gather A set in , then is the corresponding value in the scalar weight set; The length of the scalar weight set is T, and the values ​​in the scalar weight set show a trend of first monotonically increasing and then monotonically decreasing; Calculating the scalar strength of all mesh vertices in any one of the plurality of class regions, and selecting the mesh vertex with the largest scalar strength as the optimal seed point in the class region; Calculating the scalar strength of all mesh vertices in the other class areas except the class area where the optimal seed point has been obtained, calculating the scalar strength of the mesh vertices in each class area of ​​the other class areas, and selecting F mesh vertices in descending order according to the scalar strength values; The distances of F mesh vertices to all the obtained optimal seed points are calculated in descending order according to the scalar intensity; When the distances between one of the F mesh vertices and all the obtained optimal seed points are greater than R, one of the F mesh vertices is the optimal seed point in the corresponding class area, and the distances between the remaining mesh vertices and the optimal seed point are no longer calculated; When the distances between the F grid vertices and all the obtained optimal seed points are no greater than R, there is no optimal seed point in the corresponding class area, and R is the distance threshold.

9. The method for tooth and jaw segmentation based on optimal seed point selection based on harmonic field scalar intensity according to claim 8, characterized in that: The method for determining the starting point and the ending point of the remaining gingival margin lines except the first gingival margin line and the last gingival margin line comprises: The starting point of the current gingival margin line is the end point of the previous gingival margin line; The end point of the current gingival margin line is the point in set E that is shortest in distance to the starting point of the current gingival margin line; The set E stores points P that meet the following conditions: Condition 5: Point P is the optimal seed point that has not yet been used as the starting point or end point of the gingival margin line; Condition 6: Point P satisfies the following formula: ； Where, It is the starting point of the upper gingival margin line. The end point of the previous gingival margin line. The starting point of the current gingival margin line.

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