A Method for Tooth Three-Dimensional Digital Model Registration and Tooth Neckline Extraction Based on Intraoral Scanning and CBCT

Abstract

The present invention discloses a method for registering three-dimensional digital tooth models and extracting dental cervical lines based on oral scanning and CBCT, which relates to the field of registering three-dimensional digital tooth models. The method includes: respectively obtaining three-dimensional oral cavity images of oral scanning and CBCT, and automatically segmenting the three-dimensional structures of the dental crown and teeth by using the pre-trained V-Net and ToothNet image segmentation models. Then, through the feature extraction network, information exchange network and rigid transformation network, the alignment and registration of the two-modal images are realized. The feature extraction network uses far-point sampling and dynamic graph convolutional neural network to extract local and global features, and the self-attention and cross-attention modules perform feature enhancement and information exchange between the same modality and different modalities. Based on this registration result, the dental cervical line is further extracted and optimized. This method can not only quickly and accurately register three-dimensional digital tooth models, provide high-precision dental cervical line extraction results, but also reduce the labor and time costs of medical institutions and improve medical efficiency.

Description

Technical Field

[0001] The present invention relates to the field of three-dimensional digital model registration of teeth, and specifically to a method for three-dimensional digital model registration of teeth and extraction of dental cervical lines based on intraoral scanning and CBCT. Background Art

[0002] With the continuous progress of oral medicine and dental technology, intraoral scanning (IOS) and cone beam computed tomography (CBCT) have become indispensable tools for modern dental diagnosis and treatment. Intraoral scanning technology can quickly and non-invasively obtain three-dimensional digital models of patients' teeth, providing high-precision tooth morphology information. However, relying solely on intraoral scanning has certain limitations. For example, when dealing with problems such as complex periodontal structures, bone mass assessment, and apical lesions, the images obtained by intraoral scanning may not be sufficient to provide comprehensive anatomical information. At the same time, CBCT technology can provide more detailed three-dimensional images, especially in terms of the positional relationship between bone structures and soft tissues, and can effectively reveal the anatomical characteristics of teeth and their surrounding tissues.

[0003] However, fusing and effectively registering intraoral scanning and CBCT images remains a challenging task. Due to the modal differences in the images acquired by these two technologies, intraoral scanning mainly focuses on the surface structure of the dental crown, while CBCT provides more in-depth three-dimensional information. Such modal differences bring difficulties to the registration process, especially in the feature extraction and matching stages. Traditional methods often rely on manual features or simple transformations, resulting in low registration accuracy and being easily affected by noise and artifacts. Therefore, how to efficiently register multi-modal images and extract key tooth features (such as dental cervical lines) has become a current research hotspot.

[0004] Therefore, in order to solve the above technical problems, it is necessary to provide a new method for three-dimensional digital model registration of teeth and a method for extraction of dental cervical lines.

[0005] In the prior art, the disclosure number CN114974523A discloses a method for fusing three-dimensional digital models of teeth, which specifically includes: obtaining a first three-dimensional digital model representing the crown of a first tooth, a second three-dimensional digital model representing the whole of the first tooth, and a first segmentation scheme. The first segmentation scheme divides the second three-dimensional digital model into a first part and a second part corresponding to the crown and the root respectively; performing point cloud registration on the first three-dimensional digital model and the first part of the second three-dimensional digital model; based on the result of the point cloud registration, calculating a set of points on the second three-dimensional digital model that are closest to the points on the edge of the first three-dimensional digital model, and deleting the part of the second three-dimensional digital model corresponding to the first three-dimensional digital model based on the set of the closest points to obtain a third part of the second three-dimensional digital model; performing surface stitching on the first three-dimensional digital model and the third part of the second three-dimensional digital model to obtain a fused three-dimensional digital model. However, this method fuses multi-dimensional digital models with relatively high requirements for the quality and accuracy of the input overall model. If there is noise, defect or inaccuracy in any of the models, it will directly affect the accuracy of the final fused model. At the same time, multiple point cloud registrations and geometric processes are required, and the processing time is relatively long. Therefore, this solution requires a large amount of computing resources and also reduces the real-time performance and effectiveness of model fusion.

[0006] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present disclosure, and thus it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for registering three-dimensional digital models of teeth and extracting the cementoenamel junction based on oral scanning and CBCT to solve the problems raised in the above background art.

[0008] To achieve the above purpose, the present invention provides the following technical solutions:

[0009] A method for registering three-dimensional digital models of teeth and extracting the cementoenamel junction based on oral scanning and CBCT, the specific steps include:

[0010] S1, collecting three-dimensional oral images and CBCT oral slice images of several different tooth morphologies in historical oral scans, marking the crown contour in the three-dimensional oral images of the historical oral scans by manual marking, and recording the grid information of the crown contour at the same time. Marking the tooth contour in the CBCT oral slice images by manual marking and recording the voxel information of tooth segmentation. The grid information of the crown contour includes: vertex data, face data, edge data, and segmentation label data of the crown in the image; the voxel information of tooth segmentation includes: coordinate data, class label, gray value, and resolution of the voxels in the tooth image;

[0011] S2. Establish a first segmentation model and a second segmentation model. Use the three-dimensional oral cavity image marked with the crown contour and its mesh information to train the first segmentation model, and use the CBCT oral cavity slice image marked with tooth segmentation and its voxel information to train the second segmentation model;

[0012] S3. Input the three-dimensional oral cavity image to be registered in the oral cavity scan into the trained first segmentation model, and input the CBCT oral cavity slice image into the trained second segmentation model to output the three-dimensional crown image of the first modality and its mesh information, the three-dimensional reconstructed tooth image of the second modality and the corresponding voxel information, and convert the obtained mesh information and voxel information into point cloud data;

[0013] S4. Based on the converted point cloud data, perform feature extraction and registration on the two groups of point cloud data to accurately align the three-dimensional crown image of the first modality in the space of the three-dimensional tooth image of the second modality, obtain the transformed three-dimensional crown image of the first modality, and perform extraction and optimization of the cementoenamel junction based on the transformed three-dimensional crown image of the first modality, and finally obtain an accurate cementoenamel junction contour.

[0014] Furthermore, the first segmentation model uses a V-Net structure, and the second segmentation model uses ToothNet to realize automatic segmentation and recognition of teeth. Among them, the second segmentation model completes the segmentation and recognition of teeth by extracting the feature information of each slice edge map, connecting the edge map feature information with the original image feature information, and then putting the feature information into the corresponding network.

[0015] Furthermore, step S3 further includes the following steps:

[0016] The logic for converting the obtained mesh information into point cloud data is as follows:

[0017] Realize the conversion of point cloud data through a rotation matrix and a translation vector:

[0018] S31. Extract the vertex coordinates in the mesh information to generate initial point cloud data:

[0019] The mesh data contains several mesh faces, and each mesh face is defined by multiple vertices. First, extract all vertices P from the mesh data, which is represented as an N×3 matrix:

[0020]

[0021] Among them, N is the number of vertices, and each row represents the coordinates (x i , y i , z i ) of a vertex in three-dimensional space, where i = 1, 2,..., N;

[0022] Transform the coordinates of each grid vertex using a rotation matrix and a translation vector to generate new point cloud data. The specific steps are as follows:

[0023] S32. Calculation of the rotation matrix: Generate a random number between 0 and 1, and multiply this random number by π / 4 to obtain the Euler angle θ x , θ y , θ z ;

[0024] Use the function euler2mat to convert the Euler angle to a 3×3 rotation matrix R, which is used to describe the rotation of the object around each axis:

[0025] R = euler2mat(θ x , θ y , θ z )

[0026] In the formula, θ x , θ y , θ z represents the Euler angle, specifically the rotation angles around the x, y, and z axes, in radians; Calculate the rotation matrices around the x, y, and z axes respectively based on the rotation matrix formula. Remember R x , R y and R z . Then the formula for the final rotation matrix R′ is:

[0027] R′ = R x ·R y ·R z

[0028] Perform a rotation operation on all the extracted vertices P according to the generated rotation matrix R′. The specific formula is:

[0029] P rotated = (R′ × P T ) T

[0030] In the formula, P rotated represents the rotated point cloud, with a shape of N×3, and T represents the transpose;

[0031] S33. The steps for performing a translation transformation on the coordinates of each grid vertex include: Generate three random numbers between -5 and 5, combine them into a three-dimensional vector G, and then translate the rotated point cloud to move it from the origin to the target position. The specific formula is:

[0032] P IOS = P rotated + G

[0033] where, P IOS represents the translated point cloud;

[0034] S34. Generate a point cloud dataset. For each mesh surface, repeat the above rotation and translation steps to generate the required number of point cloud data, and merge all the generated points into a point cloud dataset to finally obtain a complete point cloud set, where the point cloud set is the set of point clouds within all mesh surfaces;

[0035] The logic for converting the obtained voxel information into point cloud data is as follows: Extract all non-zero voxels, multiply their coordinates by the scaling factor s, convert them into actual physical coordinates to obtain point cloud data, and then only retain the voxels that meet the boundary conditions to obtain the boundary part of interest. The specific expression of the point cloud dataset converted from voxel data is:

[0036] P CBCT ={(x i ·s, y i ·s, z i ·s)|(x i , y i , z i ) ∈ F}

[0037] where, P CBCT represents the point cloud dataset converted from CBCT voxel data, and F is the set of voxel coordinates that meet the boundary conditions.

[0038] Furthermore, in step S4, the process of registering two sets of point cloud data includes:

[0039] S41. Construct a feature extraction network, and respectively extract features from the point cloud data of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality, extract their surface edge features, textures, geometric structures, and global geometric shape features, and generate corresponding feature descriptors;

[0040] S42. Use an information exchange network to respectively perform feature matching on the two sets of feature descriptors, identify corresponding feature point pairs based on the anatomical features of the dental crown and the tooth, achieve feature alignment between the two sets of feature descriptors, and output the feature descriptors after feature alignment;

[0041] S43. Through a rigid transformation network, based on the feature descriptors after feature alignment, calculate the rigid transformation matrix for transforming the three-dimensional dental crown image of the first modality into the coordinate system of the three-dimensional tooth image of the second modality. The rigid transformation matrix includes a rotation matrix and a translation vector, so that the three-dimensional dental crown image of the first modality is precisely aligned with the three-dimensional tooth image of the second modality in space to obtain the transformed three-dimensional dental crown image of the first modality.

[0042] Further, the step S41 includes the following steps:

[0043] S411. The step of feature extraction from the point cloud data includes: downsampling the point cloud of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality by using the farthest point sampling algorithm, and extracting features from the downsampled point cloud data of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality by using a dynamic graph convolutional neural network with shared weights to obtain local point cloud feature descriptors;

[0044] Wherein the specific logic of the farthest point sampling algorithm is: randomly select an initial point from the point cloud data of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality respectively to generate a sampling set, and put the selected initial point into the sampling set. The specific expression of the sampling set is:

[0045] S IOS ={P IOS1}, P IOS1 ∈P IOS

[0046] S CBCT ={P CBCT1}, P CBCT1 ∈P CBCT

[0047] In the formula, S IOS represents the grid point cloud sampling set, S CBCT is the CBCT voxel point cloud sampling set, P IOS1 and P CBCT1 are respectively a point in the point cloud after grid translation and the point cloud dataset converted from the CBCT voxel data;

[0048] Select the point farthest from the selected sampling set among the remaining points and add it to the sampling set, and repeat the above steps until a predetermined number of points are selected.

[0049] Further, the dynamic graph convolutional neural network with shared weights includes four convolutional layers, a normalization layer, an activation layer, a pooling layer, and one convolutional layer, a normalization layer, a fully connected layer, and an output layer. The local and global features at different levels of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality are gradually extracted through the convolutional layers. Each layer of convolutional operation starts from local features and gradually extracts geometric structures of higher dimensions. Specifically, it includes:

[0050] The first convolutional layer, with 6 input channels and 64 output channels, extracts low-level surface edge features for detecting and aligning the surface edges of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality respectively before registration:

[0051] X1=ReLU(BatchNorm(W1*X+b1))

[0052] Where X∈R N×3 Represents the original point cloud data, W1 represents the weight matrix of this layer, W1∈R 6×64 , X1 represents the point cloud data after the first convolutional layer, X1∈R N×64 , b1 represents the bias term of this layer, and ReLU represents the activation function;

[0053] The second convolutional layer, with 128 input channels and 64 output channels, further extracts surface texture information and identifies local geometric features and shapes on the first modality 3D crown image and the second modality 3D tooth image, respectively, retaining their local features:

[0054] X2=ReLU(BatchNorm(W2*X1+b2))

[0055] Where W2∈R 64×64 , X2∈R N×64 ;

[0056] The third convolutional layer has 128 input channels and 128 output channels, extracting the deep geometric structure information of the first modality 3D crown image and the second modality 3D tooth image, respectively, and identifying the surface morphology of the crown and tooth:

[0057] X3=ReLU(BatchNorm(W3*X2+b3))

[0058] Where W3∈R 64×128 , X3∈R N×128 ;

[0059] The fourth convolutional layer has 256 input channels and 256 output channels, capturing the global geometric morphology of the entire first modality 3D crown image and the second modality 3D tooth image, respectively, and identifying the overall spatial relationship:

[0060] X4=ReLU(BatchNorm(W4*X3+b4))

[0061] Where W4∈R 128×256 , X4∈R N×256 ;

[0062] Finally, the features at different levels are processed through the fully connected layer to output a feature vector with geometric information of the accurate tooth model:

[0063] X final =W fc *X4+b fc

[0064] Where, Xfinal A feature vector representing the geometric information of an accurate tooth model, W fc is the weight matrix of the fully connected layer, b fc is the bias vector of the fully connected layer, W fc ∈R 256×1024 , X final ∈R N×1024 .

[0065] Furthermore, in step S42, the information exchange network includes a self-attention algorithm and a cross-attention algorithm, and the feature alignment and fusion of two data modalities are completed through the two attention algorithms, specifically including:

[0066] The self-attention mechanism is used to enhance the feature expression within each modality. By calculating the correlation between each point in the point cloud data and other points, it focuses on the most representative features in the tooth image, ensuring that the most critical geometric features and boundary information are extracted in each modality;

[0067] The cross-attention mechanism is used to exchange information between different modalities, including intraoral scan images and CBCT images. By calculating the degree of association of the feature correlation between one modality and another modality, it captures the common features in the two images and enhances the accuracy of fusion.

[0068] Furthermore, in step S43, the logic for obtaining the transformed three-dimensional crown image of the first modality through the rigid transformation network is as follows:

[0069] Based on the feature descriptors of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality after feature alignment, calculate the feature Euclidean distance between the point clouds of the two modality images and generate a matching matrix;

[0070] The logic for generating the matching matrix is: calculate the Euclidean distance between the feature points in the source point cloud and the feature points in the target point cloud to obtain a similarity matrix between each feature point, use the softmax function to normalize all distances to obtain a probability distribution, and then obtain the matching matrix M, which describes the matching strength between the source point and the target point; through the matching matrix M, select the point pair with the highest similarity between each source point and the target point as the candidate matching point pair, and take the similarity in the matching matrix to calculate the weight of each point pair. The formula for calculating the weight of each point pair is:

[0071] ω k = M[p,q], (p,q) ∈ TopK(M)

[0072] In the formula, TopK(M) represents selecting the top u optimal matching point pairs according to the similarity matrix M, ω k represents the weight of the k-th point pair, and k is the index of the point pair;

[0073] Calculate the covariance matrix using the weights of the matching point pairs: Calculate the weighted centroids of the point cloud data of the three-dimensional dental crown image of the first modality and the three-dimensional dental image of the second modality respectively; then remove the respective centroids from the source point cloud and the reference point cloud, and calculate the covariance matrix H through the decentralized point cloud; use SVD to perform singular value decomposition on the covariance matrix, and calculate the rigid transformation matrix R and the translation matrix t; based on the rigid transformation matrix R and the translation matrix t, transform the three-dimensional dental crown image of the first modality to overlap with the three-dimensional dental image of the second modality, and obtain the transformed three-dimensional dental crown image of the first modality.

[0074] Further, the method for extracting and optimizing the dental neck line based on the transformed three-dimensional dental crown image of the first modality is: Extract the boundary points of the teeth from the transformed three-dimensional dental crown image of the first modality;

[0075] Find the nearest points of these boundary points in the three-dimensional dental image of the second modality, connect the nearest points to generate the dental neck line, process the dental neck line, remove the outliers in the curve, and use the remaining points as key points, and use the breadth-first search algorithm to determine the shortest path between adjacent key points; Interpolate the dental neck line based on the points in the shortest path to obtain an accurate dental neck line contour.

[0076] Compared with the prior art, the beneficial effects of the present invention are:

[0077] This method automatically segments the three-dimensional structures of the dental crown and teeth by obtaining the three-dimensional oral images of oral scanning and CBCT respectively, using the pre-trained V-Net and ToothNet image segmentation models. Then, through the feature extraction network, information exchange network and rigid transformation network, the alignment and registration of the two-modal images are realized. The feature extraction network uses farthest point sampling (FPS) and dynamic graph convolutional neural network (DGCNN) to extract local and global features. By introducing self-attention and cross-attention modules, it can achieve effective information exchange between the same modality and different modalities, further improving the accuracy and stability of registration. Based on this registration result, the dental neck line is further extracted and optimized. This method only requires two oral images and only performs one cloud point registration, saving computational resources. In addition, the way of combining farthest point sampling and dynamic graph convolutional neural network in the feature extraction network enables the model to better capture local details and global features, so as to more accurately perform feature correspondence and information integration between modalities. It can not only quickly and accurately register the three-dimensional digital model of teeth, provide high-precision dental neck line extraction results, but also reduce the labor and time costs of medical institutions, improve medical efficiency, and is applicable to orthodontic treatment and the precise construction of dental models. Description of the Drawings

[0078] Figure 1Schematic diagram of the overall method flow of the present invention;

[0079] Figure 2 Schematic diagram of the three-dimensional digital model obtained by oral scanning and the annotation of the crown contour;

[0080] Figure 3 Three-dimensional crown digital image of the first modality output by the first segmentation model from the three-dimensional digital image of intraoral scanning;

[0081] Figure 4 Three-dimensional reconstructed tooth digital image of the second modality output by the second segmentation model from the CBCT oral slice image;

[0082] Figure 5 Schematic diagram of the tooth neck line extraction effect. Detailed implementation manners

[0083] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with specific embodiments.

[0084] It should be noted that unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this term cover the elements or objects listed after this term and their equivalents, without excluding other elements or objects. The terms such as "connected" or "linked" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left" and "right" are only used to represent relative position relationships. When the absolute position of the object to be described changes, the relative position relationship may also change accordingly.

[0085] Embodiment:

[0086] Please refer to Figures 1 - 5 , the present invention provides a technical solution:

[0087] A method for registering a three-dimensional digital model of teeth and extracting a tooth neck line based on oral scanning and CBCT, the specific steps include:

[0088] S1, collecting a number of three-dimensional oral images and CBCT oral slice images of different tooth morphologies from historical oral scans, manually marking the tooth crown contours in the three-dimensional oral images of the historical oral scans, and recording the mesh information of the tooth crown contours, manually marking the tooth contours in the CBCT oral slice images, and recording the tooth segmentation voxel information, wherein the mesh information of the tooth crown contours includes: vertex data, face data, edge data, and segmentation label data of the tooth crown in the image; and the voxel information of the tooth segmentation includes: coordinate data, category label, grayscale value, and resolution of the voxels in the tooth image;

[0089] The first segmentation model uses a V-Net architecture, while the second segmentation model utilizes ToothNet for automatic tooth segmentation and recognition. The second segmentation model extracts feature information from the edge map of each slice, connects this edge map feature information with the original image feature information, and then feeds this feature information into the corresponding network to complete tooth segmentation and recognition. V-Net and ToothNet are commonly used network models, and their specific structures are not detailed here.

[0090] S2, establishing a first segmentation model and a second segmentation model, training the first segmentation model using a three-dimensional oral image with marked crown contours and mesh information, and training the second segmentation model using a CBCT oral slice image with marked tooth segmentation and voxel information;

[0091] The inputs are three-dimensional oral images from oral scans and CBCT oral slice images. The segmentation model can identify and extract three-dimensional images of crowns and teeth, and obtain image data of crown and tooth contours. These data are stored in the form of a grid to form crown grid information and voxel information for tooth segmentation.

[0092] S3, inputting the 3D oral image to be registered in the oral scan into the trained first segmentation model, inputting the CBCT oral slice image into the trained second segmentation model, outputting the 3D crown image and its mesh information of the first modality, the 3D reconstructed tooth image of the second modality and its corresponding voxel information, and converting the obtained mesh information and voxel information into point cloud data;

[0093] The step S3 further comprises the following steps:

[0094] The logic for converting the obtained grid information into point cloud data is as follows:

[0095] The transformation of point cloud data is achieved through rotation matrix and translation vector:

[0096] S31, extract the vertex coordinates in the grid information and generate the initial point cloud data:

[0097] The grid data contains several grid faces, and each grid face is defined by multiple vertices. First, extract all the vertices P from the grid data, which is represented as an N×3 matrix:

[0098]

[0099] where N is the number of vertices, and each row represents the coordinates (x i , y i , z i ) of a vertex in three-dimensional space, where i = 1, 2, …, N;

[0100] Transform the coordinates of each grid vertex through a rotation matrix and a translation vector to generate new point cloud data. The specific steps include:

[0101] S32. Calculation of the rotation matrix: Generate a random number between 0 and 1, and multiply this random number by π / 4 to obtain the Euler angle θ x , θ y , θ z ;

[0102] Use the function euler2mat to convert the Euler angle to a 3×3 rotation matrix R, which is used to describe the rotation of an object around each axis:

[0103] R = euler2mat(θ x , θ y , θ z )

[0104] In the formula, θ x , θ y , θ z represents the Euler angle, specifically the rotation angles around the x, y, and z axes, in radians; Calculate the rotation matrices around the x, y, and z axes respectively based on the rotation matrix formula. Remember R x , R y and R z . Then the formula for the final rotation matrix R′ is:

[0105] R′ = R x ·R y ·R z

[0106] where the specific formula of the euler2mat function is:

[0107]

[0108] Perform a rotation operation on all the extracted vertices P according to the generated rotation matrix R′. The specific formula is:

[0109] Protated =(R'×P T ) T

[0110] Wherein, P rotated represents the rotated point cloud, with the shape of N×3, and T represents the transpose;

[0111] For S33, the steps of performing translational transformation on the coordinates of each grid vertex include: generating three random numbers between -5 and 5, combining them into a three-dimensional vector G, and then translating the rotated point cloud to move it from the origin to the target position. The specific formula is:

[0112] P IOS =P rotated +G

[0113] Wherein, P IOS represents the translated point cloud;

[0114] For S34, generate a point cloud dataset. For each grid face, repeat the above rotation and translation steps to generate the required number of point cloud data, and merge all the generated points into a point cloud dataset to finally obtain a complete point cloud set, where the point cloud set is the set of point clouds within all grid faces;

[0115] The logic for converting the obtained voxel information into point cloud data is: extract all non-zero voxels, multiply their coordinates by the scaling factor s, convert them into actual physical coordinates to obtain the point cloud data, and then only retain the voxels that meet the boundary conditions to obtain the boundary part of interest. The specific expression of the point cloud dataset converted from the voxel data is:

[0116] P CBCT ={(x i ·s, y i ·s, z i ·s)|(x i , y i , z i ) ∈ F}

[0117] Wherein, P CBCT represents the point cloud dataset converted from the CBCT voxel data, and F is the set of voxel coordinates that meet the boundary conditions.

[0118] For S4, based on the converted point cloud data, perform feature extraction and registration on the two sets of point cloud data to accurately align the three-dimensional crown image of the first modality in the space of the three-dimensional tooth image of the second modality, obtain the transformed three-dimensional crown image of the first modality, and perform extraction and optimization of the gingival margin based on the transformed three-dimensional crown image of the first modality to finally obtain an accurate gingival margin contour.

[0119] In step S4, the process of registering the two sets of point cloud data includes:

[0120] S41. Construct a feature extraction network to extract features from the point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality respectively, extract their surface edge features, textures, geometric structures, and global geometric shape features, and generate corresponding feature descriptors;

[0121] S42. Use an information exchange network to perform feature matching on the two sets of feature descriptors respectively. Based on the anatomical features of the crown and the tooth, identify the corresponding feature point pairs, achieve feature alignment between the two sets of feature descriptors, and output the feature descriptors after feature alignment;

[0122] S43. Through a rigid transformation network, based on the feature descriptors after feature alignment, calculate the rigid transformation matrix for transforming the three-dimensional crown image of the first modality into the coordinate system of the three-dimensional tooth image of the second modality. The rigid transformation matrix includes a rotation matrix and a translation vector, so that the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality are accurately aligned in space, and the transformed three-dimensional crown image of the first modality is obtained.

[0123] The step S41 includes the following steps:

[0124] S411. The steps of extracting features from the point cloud data include: using the farthest point sampling algorithm to downsample the point clouds of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality, and using a dynamic graph convolutional neural network with shared weights to extract features from the downsampled point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality to obtain local point cloud feature descriptors;

[0125] The specific logic of the farthest point sampling algorithm is: randomly select an initial point from the point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality respectively to generate a sampling set, and put the selected initial point into the sampling set. The specific expression of the sampling set is:

[0126] S IOS ={P IOS1},P IOS1 ∈P IOS

[0127] S CBCT ={P CBCT1},P CBCT1 ∈P CBCT

[0128] In the formula, S IOS represents the grid point cloud sampling set, S CBCTis the CBCT voxel point cloud sampling set, P IOS1 and P CBCT1 are respectively the point cloud after grid translation and a point in the point cloud dataset converted from the CBCT voxel data;

[0129] Select the point farthest from the selected sampling set among the remaining points and add it to the sampling set. The formula for calculating the farthest point is:

[0130]

[0131] P iosnew = argmaxd i

[0132] In the formula, d i is the minimum Euclidean distance between P iosi and P iosj ||P iosi - P iosj ||2 represents the Euclidean distance between P iosi and P iosj P iosi and P iosj are the i-th and j-th point cloud data in the point cloud set after grid translation, P iosnew is the point farthest from the selected sampling set, and argmax represents the independent variable that makes a certain function reach the maximum value;

[0133] Repeat the above steps until a predetermined number of points are selected. The establishment method of the CBCT voxel point cloud sampling set is the same.

[0134] The dynamic graph convolutional neural network with shared weights includes four convolutional layers, a normalization layer, an activation layer, a pooling layer, a fully connected layer, and an output layer. It gradually extracts different levels of local and global features of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality through the convolutional layers. Each layer of convolutional operation starts from local features and gradually extracts higher-dimensional geometric structures, specifically including:

[0135] The first convolutional layer, with 6 input channels and 64 output channels, extracts low-level surface edge features for detecting and aligning the surface edges of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality before registration:

[0136] X1 = ReLU(BatchNorm(W1 * X + b1))

[0137] In the formula, X ∈ R N×3 represents the original point cloud data, W1 represents the weight matrix of this layer, W1 ∈ R 6×64 , X1 represents the point cloud data after passing through the first convolutional layer, X1 ∈ R N×64, b1 represents the bias term of this layer, and ReLU represents the activation function;

[0138] The second convolutional layer, with 128 input channels and 64 output channels, further extracts surface texture information, respectively identifies the local geometric features and shapes on the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality, and retains its local features:

[0139] X2 = ReLU(BatchNorm(W2 * X1 + b2))

[0140] Among them, W2 ∈ R 64×64 , X2 ∈ R N×64 ;

[0141] The third convolutional layer, with 128 input channels and 128 output channels, respectively extracts the deep geometric structure information of the three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality, and identifies the surface morphology of the dental crown and the tooth:

[0142] X3 = ReLU(BatchNorm(W3 * X2 + b3))

[0143] Among them, W3 ∈ R 64×128 , X3 ∈ R N×128 ;

[0144] The fourth convolutional layer, with 256 input channels and 256 output channels, respectively captures the global geometric morphology of the entire three-dimensional dental crown image of the first modality and the three-dimensional tooth image of the second modality, and identifies the overall spatial relationship:

[0145] X4 = ReLU(BatchNorm(W4 * X3 + b4))

[0146] Among them, W4 ∈ R 128×256 , X4 ∈ R N×256 ;

[0147] Finally, the features of different levels are processed through the fully connected layer, and a feature vector with geometric information of the precise tooth model is output:

[0148] X final = W fc * X4 + b fc

[0149] In the formula, X final represents the feature vector with geometric information of the precise tooth model, W fc is the weight matrix of the fully connected layer, b fc is the bias vector of the fully connected layer, W fc ∈ R 256×1024 , X final ∈ R N×1024 ;

[0150] The point cloud after translating the grid and the point cloud data set converted from CBCT voxel data are respectively used as the inputs of the dynamic graph convolutional neural network with shared weights, and the feature vectors with the geometric information of the accurate tooth model are obtained through the dynamic graph convolutional neural network.

[0151] In step S42, the information exchange network includes a self-attention algorithm and a cross-attention algorithm, and the feature alignment and fusion of the two data modalities are completed through the two attention algorithms, specifically including:

[0152] The self-attention mechanism is used to enhance the feature expression within each modality. By calculating the correlation between each point in the point cloud data and other points, it focuses on the most representative features in the tooth image to ensure that the most critical geometric features and boundary information are extracted in each modality.

[0153] The cross-attention mechanism is used to exchange information between different modalities, including oral scan images and CBCT images. By calculating the correlation degree of the feature association between one modality and another modality, it captures the common features in the two images and enhances the accuracy of fusion.

[0154] Aggregate the global context information of the local feature descriptors of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality extracted by the dynamic graph convolutional neural network (DGCNN) through the self-attention module;

[0155] Exchange information between the feature descriptors of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality after aggregating the global context information through the cross-attention module to enhance the discrimination ability of the feature descriptors.

[0156] The self-attention and cross-attention modules include:

[0157] The self-attention module calculates the feature vectors within the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality respectively to enhance the feature expression within each modality image;

[0158] The cross-attention module calculates between the feature vectors of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality to promote the feature alignment and fusion of the two data modalities;

[0159] The attention module specifically includes:

[0160] Perform a linear transformation on each feature vector to generate query, key, and value matrices;

[0161] Calculate the dot product between the query matrix and the key matrix, and normalize it using the softmax function to obtain the attention weight matrix;

[0162] Use the attention weight matrix to perform a weighted sum on the value matrix, thereby obtaining an enhanced feature representation;

[0163] Concatenate the results of multiple attention heads and perform a transformation through a linear layer to output the final feature descriptor;

[0164] Introduce positional encoding and a feed-forward neural network to ensure that the feature vectors capture local information while maintaining the integrity of the global context.

[0165] In step S43, the logic for obtaining the transformed first-modal three-dimensional dental crown image through the rigid transformation network is as follows:

[0166] Based on the feature descriptors of the three-dimensional dental crown image of the first modality and the three-dimensional dental image of the second modality after feature alignment, calculate the feature Euclidean distance between the point clouds of the two modality images and generate a matching matrix;

[0167] The logic for generating the matching matrix is as follows: Calculate the Euclidean distance between the feature points in the source point cloud and the feature points in the target point cloud to obtain a similarity matrix between each feature point. Use the softmax function to normalize all distances to obtain a probability distribution, and then obtain the matching matrix M, which describes the matching strength between the source point and the target point. Through the matching matrix M, select the point pairs with the highest similarity between each source point and target point as candidate matching point pairs, and take the similarity in the matching matrix to calculate the weight of each point pair. The formula for calculating the weight of each point pair is:

[0168] ω k = M[p,q], (p,q) ∈ TopK(M)

[0169] In the formula, TopK(M) represents selecting the top u optimal matching point pairs according to the similarity matrix M, and ω k represents the weight of the kth point pair, and k is the index of the point pair;

[0170] Calculate the covariance matrix using the weights of the matching point pairs: calculate the weighted centroids of the point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality respectively; then remove the respective centroids from the source point cloud and the reference point cloud, and calculate the covariance matrix H through the decentralized point cloud; use the SVD algorithm to perform singular value decomposition on the covariance matrix, and calculate the rigid transformation matrix R and the translation matrix t; based on the rigid transformation matrix R and the translation matrix t, transform the three-dimensional crown image of the first modality to overlap with the three-dimensional tooth image of the second modality, and obtain the transformed three-dimensional crown image of the first modality.

[0171] The method for extracting and optimizing the gingival margin based on the transformed three-dimensional crown image of the first modality is as follows: extract the boundary points of the tooth from the transformed three-dimensional crown image of the first modality;

[0172] Find the nearest points of these boundary points in the three-dimensional tooth image of the second modality, connect the nearest points to generate the gingival margin, process the gingival margin, remove the outliers in the curve, and use the remaining points as key points, and use the breadth-first search algorithm to determine the shortest path between adjacent key points; interpolate the gingival margin based on the points in the shortest path to obtain an accurate gingival margin contour.

[0173] Statistical methods (such as mean and standard deviation) or clustering-based methods (such as DBSCAN) can be used to identify and remove the outliers in the curve. Spline interpolation (such as B-spline or Catmull-Rom spline) methods can be used to interpolate the key points in the shortest path to obtain a finer gingival margin contour. The breadth-first search (BFS) algorithm is a mature existing technology and will not be elaborated here.

[0174] The above formulas are all dimensionless and take their numerical values for calculation. The formulas are obtained by collecting a large amount of data for software simulation to get a formula closest to the actual situation. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0175] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by the combination of computer software and electronic hardware. Whether these functions are executed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0176] The unit described as a separation component may or may not be physically separated. The component displayed as a unit may or may not be a physical unit, and it may be located in one place or distributed across multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0177] As described above, the above are only specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or substitutions, which should all be covered within the protection scope of the present application.

Claims

1. A method for three-dimensional digital model registration of teeth and extraction of dental cervical lines based on intraoral scanning and cone-beam computed tomography (CBCT), characterized in that, The specific steps include: S1. Collect three-dimensional oral images and CBCT oral slice images of several different tooth morphologies in historical oral data. Manually mark the crown contour in the three-dimensional oral image of the historical oral scan, and record the mesh information of the crown contour at the same time. Manually mark the tooth contour in the CBCT oral slice image, and record the voxel information of tooth segmentation. The mesh information of the crown contour includes: vertex data, face data, edge data, and segmentation label data of the crown in the image; the voxel information of tooth segmentation includes: coordinate data, class label, gray value, and resolution of the voxels in the tooth image. S2. Establish a first segmentation model and a second segmentation model. Use the three-dimensional oral image with the marked crown contour and its mesh information to train the first segmentation model, and use the CBCT oral slice image with the marked tooth segmentation and its voxel information to train the second segmentation model. S3. Input the three-dimensional oral image to be registered in the oral scan into the trained first segmentation model, and input the CBCT oral slice image into the trained second segmentation model to output the three-dimensional crown image of the first modality and its mesh information, the three-dimensional reconstructed tooth image of the second modality and the corresponding voxel information, and convert the obtained mesh information and voxel information into point cloud data. S4. Based on the converted point cloud data, perform feature extraction and registration on the two sets of point cloud data to accurately align the three-dimensional crown image of the first modality in the space of the three-dimensional tooth image of the second modality, obtain the transformed three-dimensional crown image of the first modality, and perform extraction and optimization of the gingival margin based on the transformed three-dimensional crown image of the first modality to finally obtain an accurate gingival margin contour.

2. The method for three-dimensional digital model registration of teeth and gingival margin extraction based on intraoral scanning and CBCT according to claim 1, wherein: The first segmentation model uses a V-Net structure, and the second segmentation model uses ToothNet to achieve automatic segmentation and recognition of teeth. Among them, the second segmentation model extracts the feature information of each slice edge map, connects the edge map feature information with the original image feature information, and then puts the feature information into the corresponding network to complete the segmentation and recognition of teeth.

3. A method for registering a three-dimensional digital model of teeth and extracting the dental cervical line based on oral scanning and CBCT according to claim 1, characterized in that: Step S3 further includes the following steps: The logic for converting the obtained mesh information into point cloud data is: The conversion of point cloud data is achieved through a rotation matrix and a translation vector: S31. Extract the vertex coordinates in the mesh information to generate initial point cloud data: The mesh data contains several mesh faces, and each mesh face is defined by multiple vertices. First, extract all vertices P from the mesh data, which is represented as an N×3 matrix: where N is the number of vertices, and each row represents the coordinates (x i , y i , z i ) of a vertex in three-dimensional space, where i = 1, 2, …, N; The coordinates of each mesh vertex are transformed through a rotation matrix and a translation vector to generate new point cloud data. The specific steps include: S32, Calculation of the rotation matrix: Generate a random number between 0 and 1, and multiply this random number by π / 4 to obtain the Euler angle θ x , θ y , θ z ; Use the function euler2mat to convert the Euler angles into a 3×3 rotation matrix R, which is used to describe the rotation of the object around each axis: R = euler2mat(θ x , θ y , θ z ) where θ x , θ y , θ z represent Euler angles, specifically the rotation angles about the x, y, and z axes, in radians; based on the rotation matrix formula, the rotation matrices about the x, y, and z axes are calculated respectively. Denote R x , R y , and R z . Then the formula for the final rotation matrix R' is: R′ = R x ·R y ·R z Perform a rotation operation on all the extracted vertices P according to the generated rotation matrix R′. The specific formula is: P rotated = (R' × P T ) T Where P rotated represents the rotated point cloud with a shape of N×3, and T represents the transpose; The steps of performing a translation transformation on the coordinates of each grid vertex in S33 include: generating three random numbers between -5 and 5, combining them into a three-dimensional vector G, and then translating the rotated point cloud to move it from the origin to the target position. The specific formula is as follows: P IOS = P rotated + G where P IOS represents the translated point cloud; S34, Generate a point cloud data set. For each grid face, repeat the above rotation and translation steps to generate the required number of point cloud data, and merge all the generated points into a point cloud data set to finally obtain a complete point cloud set, where the point cloud set is the set of point clouds within all grid faces; The logic for converting the obtained voxel information into point cloud data is: extract all non-zero voxels, multiply their coordinates by the scaling factor s, convert them into actual physical coordinates to obtain point cloud data, and then only retain the voxels that meet the boundary conditions to obtain the boundary part of interest. The specific expression of the point cloud data set converted from voxel data is: P CBCT = {(x i · s, y i · s, z i · s) | (x i , y i , z i ) ∈ F} Where P CBCT represents the point cloud data set converted from the CBCT voxel data, and F is the set of voxel coordinates that meet the boundary conditions.

4. A method for registering a three-dimensional digital model of teeth and extracting the dental cervical line based on oral scanning and CBCT according to claim 1, characterized in that: In step S4, the process of registering two sets of point cloud data includes: S41, Construct a feature extraction network, and perform feature extraction on the point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality respectively, extract their surface edge features, textures, geometric structures, and global geometric shape features, and generate corresponding feature descriptors; S42, Use an information exchange network to perform feature matching on the two sets of feature descriptors respectively, identify corresponding feature point pairs based on the anatomical features of the crown and the tooth, achieve feature alignment between the two sets of feature descriptors, and output the feature descriptors after feature alignment; S43, Through a rigid transformation network, based on the feature descriptors after feature alignment, calculate the rigid transformation matrix for transforming the three-dimensional crown image of the first modality into the coordinate system of the three-dimensional tooth image of the second modality. The rigid transformation matrix includes a rotation matrix and a translation vector, so that the three-dimensional crown image of the first modality is precisely aligned with the three-dimensional tooth image of the second modality in space to obtain the transformed three-dimensional crown image of the first modality.

5. A method for three-dimensional digital model registration of teeth and extraction of dental cervical lines based on intraoral scanning and cone beam computed tomography (CBCT) according to claim 4, characterized in that: The step S41 includes the following steps: S411, The steps of performing feature extraction on point cloud data include: using the farthest point sampling algorithm to downsample the point clouds of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality, and using a dynamic graph convolutional neural network with shared weights to perform feature extraction on the downsampled point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality to obtain local point cloud feature descriptors; The specific logic of the farthest point sampling algorithm is: randomly select an initial point from the point cloud data of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality respectively to generate a sampling set, and put the selected initial point into the sampling set. The specific expression of the sampling set is: S IOS = {P IOS1}, P IOS1 ∈ P IOS S CBCT = {P CBCT1}, P CBCT1 ∈ P CBCT Where, S IOS represents the grid point cloud sampling set, S CBCT is the CBCT voxel point cloud sampling set, P IOS1 and P CBCT1 are respectively a point in the point cloud after grid translation and the point cloud dataset converted from the CBCT voxel data; Select the point farthest from the selected sampling set among the remaining points and add it to the sampling set, and repeat the above steps until a predetermined number of points are selected.

6. A method for registering a three-dimensional digital dental model and extracting a dental cervical line based on oral scanning and CBCT according to claim 5, characterized in that: The dynamic graph convolutional neural network with shared weights includes four convolutional layers, a normalization layer, an activation layer, a pooling layer, a fully connected layer, and an output layer. It gradually extracts local and global features at different levels from the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality through the convolutional layers. Each layer of convolutional operation starts from local features and gradually extracts geometric structures of higher dimensions. Specifically, it includes: The first convolutional layer has 6 input channels and 64 output channels, extracting low-level surface edge features for detecting and aligning the surface edges of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality before registration: X1 = ReLU(BatchNorm(W1 * X + b1)) where \(X\in R\) N×3 represents the original point cloud data, \(W_1\) represents the weight matrix of this layer, \(W_1\in R\) 6×64 , \(X_1\) represents the point cloud data after the first convolutional layer, \(X_1\in R\) N×64 , \(b_1\) represents the bias term of this layer, ReLU represents the activation function; The second convolutional layer has 128 input channels and 64 output channels, further extracting surface texture information, respectively identifying local geometric features and shapes on the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality, and retaining their local features: X2 = ReLU(BatchNorm(W2 * X1 + b2)) where, W2 ∈ R 64×64 , X2 ∈ R N×64 ; The third convolutional layer has 128 input channels and 128 output channels, respectively extracting deep geometric structure information of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality, and identifying the surface morphology of the crown and the tooth: X3 = ReLU(BatchNorm(W3 * X2 + b3)) where, W3 ∈ R 64×128 , X3 ∈ R N×128 ; The fourth convolutional layer has 256 input channels and 256 output channels, respectively capturing the global geometric morphology of the entire three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality, and identifying the overall spatial relationship: X4 = ReLU(BatchNorm(W4 * X3 + b4)) where, W4 ∈ R 128×256 , X4 ∈ R N×256 ; Finally, features at different levels are processed through the fully connected layer to output a feature vector with geometric information of an accurate tooth model: X final = W fc * X4 + b fc Wherein, X final represents the feature vector with geometric information of the precise tooth model, W fc is the weight matrix of the fully connected layer, b fc is the bias vector of the fully connected layer, W fc ∈R 256×1024 , X final ∈R N×1024 .

7. A method for registering a three-dimensional digital dental model and extracting a dental cervical line based on oral scanning and CBCT according to claim 4, characterized in that: In step S42, the information exchange network includes a self-attention algorithm and a cross-attention algorithm, and completes feature alignment and fusion of the two data modalities through the two attention algorithms. Specifically, it includes: The self-attention mechanism is used to enhance the feature expression within each modality. By calculating the correlation between each point in the point cloud data and other points, it focuses on the most representative features in the tooth image to ensure that the most critical geometric features and boundary information are extracted in each modality; The cross-attention mechanism is used to perform information exchange between different modalities, including intraoral scan images and CBCT images. By calculating the correlation degree of feature association between one modality and another modality, it captures the common features in the two images and enhances the accuracy of fusion.

8. A method for three-dimensional digital model registration of teeth and extraction of dental cervical lines based on intraoral scanning and CBCT according to claim 4, characterized in that: In step S43, the logic for obtaining the transformed three-dimensional crown image of the first modality through the rigid transformation network is: Based on the feature descriptors of the three-dimensional crown image of the first modality and the three-dimensional tooth image of the second modality after feature alignment, calculate the feature Euclidean distance between the point clouds of the two modality images and generate a matching matrix; The logic for generating the matching matrix is as follows: Calculate the Euclidean distance between the feature points in the source point cloud and the feature points in the target point cloud to obtain a similarity matrix between each feature point. Use the softmax function to normalize all distances to obtain a probability distribution, and then obtain the matching matrix M, which describes the matching strength between the source points and the target points. Based on the matching matrix M, select the point pairs with the highest similarity between each source point and target point as candidate matching point pairs, and take the similarity in the matching matrix to calculate the weight of each point pair. The formula for calculating the weight of each point pair is as follows: ω k = M[p, q], (p, q) ∈ TopK(M) where TopK(M) represents selecting the top u optimal matching point pairs according to the similarity matrix M, and ω k represents the weight of the k-th point pair, where k is the index of the point pair; Calculate the covariance matrix using the weights of the matching point pairs: Calculate the weighted centroids of the point cloud data of the first-modal three-dimensional dental crown image and the three-dimensional dental image of the second modality respectively. Then, remove the respective centroids from the source point cloud and the reference point cloud, and calculate the covariance matrix H through the centered point cloud. Use the SVD algorithm to perform singular value decomposition on the covariance matrix, and calculate the rigid transformation matrix R and the translation matrix t. Based on the rigid transformation matrix R and the translation matrix t, transform the first-modal three-dimensional dental crown image to overlap with the three-dimensional dental image of the second modality, and obtain the transformed first-modal three-dimensional dental crown image.

9. A method for registering a three-dimensional digital model of teeth and extracting the dental cervical line based on oral scanning and CBCT according to claim 1, characterized in that: The method for extracting and optimizing the gingival margin based on the transformed first-modal three-dimensional dental crown image is as follows: Extract the boundary points of the teeth from the transformed first-modal three-dimensional dental crown image. Find the nearest points of these boundary points in the three-dimensional dental image of the second modality, connect the nearest points to generate the gingival margin, process the gingival margin to remove the outliers in the curve, and use the remaining points as key points. Use the breadth-first search algorithm to determine the shortest path between adjacent key points. Interpolate the gingival margin based on the points in the shortest path to obtain an accurate gingival margin contour.

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