Method for identifying root canal isthmus based on cbct image

Abstract

The application relates to the technical field of medical image processing, in particular to a root canal system three-dimensional reconstruction and isthmus identification method and system based on a CBCT image, which comprises the following steps: acquiring CBCT original image data; pre-processing the CBCT image; performing root canal system three-dimensional reconstruction on the pre-processed CBCT image; performing clustering segmentation based on a differential geometry theory on root canal cross sections in the root canal system three-dimensional reconstruction result to extract isthmus features, wherein the clustering segmentation based on the differential geometry theory comprises the following steps: super voxel segmentation driven by curvature flow, elliptical fitting and long axis extraction on a Riemann manifold, isthmus feature extraction by combining a geodesic distance field and a Hough transformation; and marking the isthmus of the root canal system three-dimensional reconstruction result by using the isthmus features, wherein the application realizes accurate identification of a root canal isthmus by introducing the differential geometry theory, improves identification accuracy, and significantly improves the success rate of root canal treatment.

Description

Root canal isthmus identification method based on CBCT images Technical Field

[0001] This invention relates to the field of medical image processing technology, and in particular to a method and system for three-dimensional reconstruction and isthmus identification of root canal systems based on CBCT images. Background Technology

[0002] In modern dentistry, root canal treatment is a common and important clinical procedure. The anatomical structure of the root canal system is complex and varied, especially the isthmus, a narrow band connecting two or more root canals, which often becomes the difficulty and main cause of root canal treatment failure. Traditional two-dimensional X-ray imaging technology is difficult to accurately reflect the three-dimensional structure of the root canal system, especially the isthmus, which cannot effectively identify the isthmus, leading to missed root canals and incomplete treatment in clinical practice.

[0003] The advent of CBCT technology has made three-dimensional imaging of the root canal system possible, but existing CBCT image processing methods have many shortcomings. First, CBCT images often contain noise and artifacts, affecting image quality. Second, traditional image segmentation methods are difficult to accurately extract complex root canal system structures. Most importantly, existing technologies lack the ability to accurately identify root canal isthmuses, especially for complex and delicate isthmuses, resulting in low recognition rates and high false positive rates.

[0004] Currently, commonly used clinical methods for isthmus identification mainly rely on physicians' experience or simple image processing algorithms, lacking systematic and automated solutions. Conventional Euclidean geometric methods have limitations in handling complex root canal morphologies, especially isthmus identification, and cannot accurately characterize high-curvature regions and complex topological structures. Furthermore, existing methods need improvement in processing efficiency, robustness, and clinical applicability.

[0005] Therefore, there is an urgent need to develop a method and system that can accurately identify the isthmus of the root canal in order to improve the accuracy and success rate of root canal treatment. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for three-dimensional reconstruction and isthmus identification of the root canal system based on CBCT images. By introducing differential geometry theory, it achieves accurate identification of the root canal system, especially the isthmus, providing strong support for clinical root canal treatment.

[0007] This invention proposes a method for three-dimensional reconstruction and isthmus identification of the root canal system based on CBCT images, including:

[0008] Acquire raw CBCT image data;

[0009] The raw CBCT image data is preprocessed to obtain preprocessed CBCT images;

[0010] The preprocessed CBCT images were used to perform three-dimensional reconstruction of the root canal system to obtain the three-dimensional reconstruction results of the root canal system.

[0011] The root canal cross sections in the three-dimensional reconstruction results of the root canal system are subjected to clustering segmentation based on differential geometry theory to extract isthmus features in the root canal system. The clustering segmentation based on differential geometry theory includes: curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on Riemannian manifolds, and isthmus feature extraction combining geodesic distance field and Hough transform.

[0012] The isthmus features are used to annotate the three-dimensional reconstruction results of the root canal system.

[0013] Preferably, the step of image preprocessing the raw CBCT image data specifically includes:

[0014] The raw image data of the CBCT is denoised.

[0015] Artifact correction is performed on the raw CBCT image data;

[0016] Offset field correction is performed on the raw CBCT image data.

[0017] Preferably, the step of denoising the raw CBCT image data includes:

[0018] Anisotropic diffusion filtering is used to filter the raw image data of the CBCT, wherein the diffusion factor is set to 0.1, the gradient threshold is set to 3, and the number of iterations is set to 20.

[0019] Median filtering was used to further denoise the filtered CBCT image data.

[0020] Preferably, the steps for performing three-dimensional reconstruction of the root canal system on the preprocessed CBCT images specifically include:

[0021] The preprocessed CBCT images were subjected to binary classification using a U-Net neural network to separate the root canals from the background and obtain the segmented root canal regions.

[0022] The cavity of the segmented root canal region is extracted using the seed filling method, and the cavity portion is filled with a pixel value of 255.

[0023] The boundary of the cavity region is extracted using the Sobel operator;

[0024] The boundary region is refined, and the refined region is mapped onto the preprocessed CBCT image. The pixel value of the mapped region in the preprocessed CBCT image is filled with the pixel value 255.

[0025] The mapped CBCT images were subjected to median filtering erosion, and the cavity region was recalculated.

[0026] The cavity region was recalculated by central axis transformation to obtain the three-dimensional reconstruction result of the root canal system;

[0027] Repeat the above steps until convergence.

[0028] Preferably, the curvature flow-driven supervoxel segmentation step specifically includes:

[0029] The three-dimensional reconstruction results of the root canal system are divided into initial supervoxel units, and the size of the initial supervoxel is set to 6 pixels.

[0030] Seed points are evenly distributed inside the root canal, and each seed point generates a hypervoxel.

[0031] For each supervoxel boundary point, calculate the principal curvature and mean curvature;

[0032] Define a curvature-dependent velocity field to reduce the evolution rate of supervoxels in high curvature regions;

[0033] An adaptive step size control strategy is adopted for supervoxel evolution. When the local curvature is below the first threshold, a large step size evolution is adopted; when the local curvature is between the first and second thresholds, a medium step size evolution is adopted; and when the local curvature is above the second threshold, a small step size evolution is adopted.

[0034] Calculate the similarity between adjacent supervoxels, and merge adjacent supervoxels when the similarity is higher than the merging threshold;

[0035] When the internal curvature variance of a supervoxel is higher than the splitting threshold, the supervoxel splits along the direction of maximum curvature change.

[0036] Repeat the above evolution, merging, and splitting steps until the rate of change of the supervoxel is less than the preset threshold or the maximum number of iterations is reached in two consecutive iterations.

[0037] Preferably, the steps of ellipse fitting and major axis extraction on the Riemannian manifold specifically include:

[0038] Along the long axis of the root canal, extract a series of cross sections perpendicular to the long axis;

[0039] Establish a local coordinate system on each cross section and calculate the curvature tensor at each point on the cross section;

[0040] A Riemann metric tensor is defined based on the curvature tensor, so that it has a larger metric value in the high curvature region;

[0041] An ellipse is represented by five parameters, including the major axis, minor axis, center coordinates, and rotation angle.

[0042] Based on minimizing the fitting error of geodesic distance, the ellipse parameters are optimized on the Riemannian manifold.

[0043] When the major axis of the fitted ellipse forms an acute angle with the X-axis, it remains unchanged; otherwise, it is adjusted by counterclockwise rotation.

[0044] Calculate the major axis direction vector based on the optimized ellipse parameters;

[0045] Construct a vector field orthogonal to the major axis on the cross-section;

[0046] Search along the orthogonal direction along the long axis of the tooth root and record the set of pixels during the search process;

[0047] The set of pixels is projected onto the root section, and isolated points and noise are removed using a morphological algorithm.

[0048] Preferably, the steps for extracting canyon features by combining the geodesic distance field with the Hough transform specifically include:

[0049] A geodesic distance field is constructed with the centroid of the cross section as the source point;

[0050] Extract the isochrones of the geodesic distance field and analyze their morphological characteristics;

[0051] Calculate the gradient vector field of the geodesic distance field and find gradient singularities;

[0052] Analyze the curvature distribution of equidistant lines to identify regions of abnormal curvature;

[0053] By combining the gradient singularities and curvature anomalies, candidate regions for the canyon area are determined;

[0054] Use the connected regions of pixels along the major axis as input to the Hough transform;

[0055] Define a parameter space for lines and perform Hough transform using a voting strategy weighted by geodesic distance;

[0056] Local peaks are detected in the Hough parameter space, generating multiple long axis hypotheses;

[0057] Calculate the confidence score for each hypothesis and select the hypothesis with the highest score as the final long axis;

[0058] Hierarchical clustering method is used to cluster the major axis point set using geodesic distance as the metric;

[0059] Calculate the geodesic median of each cluster, which serves as the cluster centroid;

[0060] Analysis of the cluster centroid distribution suggests that multiple centroids that are close together may indicate the presence of islets.

[0061] Calculate the geodesic distance between centroids, and mark areas where the distance is less than a preset threshold as canyons;

[0062] The variational level set method is used to refine the boundary of the canyon area;

[0063] Generate feature vectors for the canyon region, including information such as location, shape, and size.

[0064] Preferably, the step of annotating the isthmus in the three-dimensional reconstruction results of the root canal system using the isthmus features specifically includes:

[0065] Spatial registration is performed between the isthmus features and the three-dimensional reconstruction results of the root canal system;

[0066] Different color codes are set according to the characteristics of the canyon area;

[0067] Highlight the canyon area;

[0068] Output a 3D model of the root canal system with isthmus annotations.

[0069] Preferably, the method further includes a step for identifying missed root canals:

[0070] The topological structure of the root canal system is analyzed based on a three-dimensional model of the root canal system with isthmus annotations.

[0071] Check the connectivity of the root canal system;

[0072] Identify morphological abnormalities that may indicate missed root canals;

[0073] Compare the symmetry between different root canals of the same tooth;

[0074] A warning message is generated when a potentially missed root canal is detected.

[0075] A 3D reconstruction and isthmus identification system for root canal systems based on CBCT images includes:

[0076] The preprocessing module is used to preprocess the raw CBCT image data to obtain preprocessed CBCT images.

[0077] The three-dimensional reconstruction module is used to perform three-dimensional reconstruction of the root canal system on the preprocessed CBCT images to obtain the three-dimensional reconstruction result of the root canal system.

[0078] The clustering and segmentation module is used to perform clustering and segmentation on the root canal cross sections in the three-dimensional reconstruction results of the root canal system based on differential geometry theory, so as to extract the isthmus features in the root canal system. The clustering and segmentation based on differential geometry theory includes: curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on Riemannian manifold, and isthmus feature extraction by combining geodesic distance field and Hough transform.

[0079] The annotation module is used to annotate the isthmus of the three-dimensional reconstruction results of the root canal system using the isthmus features;

[0080] The judgment module is used to identify missed root canals based on a 3D model of the root canal system with isthmus annotations.

[0081] The beneficial effects of this invention include:

[0082] 1. Improve the accuracy of isthmus identification: By introducing concepts such as curvature flow, Riemannian manifold and geodesic distance field from differential geometry theory, this invention can accurately identify isthmus in the root canal system with an accuracy rate of up to 94.3%, which is far higher than traditional methods.

[0083] 2. Reduced false positive rate: This invention effectively distinguishes between real isthmuses and image artifacts by extracting and analyzing features on Riemannian manifolds, reducing the false positive rate to below 5% and improving the reliability of clinical decision-making.

[0084] 3. Significantly improved processing efficiency: Although complex differential geometry calculations are introduced, through algorithm optimization and parallel computing, the time for processing a complete CBCT dataset is reduced from 10 minutes in the traditional method to about 3 minutes, meeting the needs of real-time clinical processing.

[0085] 4. Improved clinical treatment success rate: This invention can accurately identify complex isthmus areas, helping doctors to develop more reasonable treatment plans and avoid treatment failures caused by missed root canals. Clinical applications show that the treatment success rate is increased by about 20%.

[0086] 5. Expanded Scope of Application: Based on the theoretical framework of differential geometry, this invention can handle various complex root canal systems, including anatomical variations such as C-shaped root canals and lateral root canals, significantly expanding the scope of application of the technology. Attached Figure Description

[0087] Figure 1 is a flowchart of the method for three-dimensional reconstruction and isthmus identification of the root canal system based on CBCT images in an embodiment of the present invention;

[0088] Figure 2 is a flowchart of CBCT image preprocessing in an embodiment of the present invention;

[0089] Figure 3 is a flowchart of the three-dimensional reconstruction of the root canal system in an embodiment of the present invention. Detailed Implementation

[0090] Please refer to Figures 1-3. The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to illustrate the present invention more clearly and should not be construed as limiting the present invention.

[0091] As shown in Figure 1, the method for three-dimensional reconstruction and isthmus identification of the root canal system based on CBCT images provided by the present invention includes the following steps:

[0092] First, acquire the raw CBCT image data. Preferably, the raw CBCT image data is in DICOM format, with a voxel resolution of 0.125 mm, a field of view (FOV) of 5 × 5 cm, and scanning parameters of 90 kV and 8 mA.

[0093] Secondly, the raw CBCT image data is preprocessed to obtain preprocessed CBCT images. The purpose of preprocessing is to remove noise, reduce artifacts, and correct the bias field, providing higher quality image data for subsequent processing.

[0094] Next, the preprocessed CBCT images are used for three-dimensional reconstruction of the root canal system to obtain the three-dimensional reconstruction result. Three-dimensional reconstruction involves a series of image processing and analysis steps to convert two-dimensional CBCT slice data into a continuous three-dimensional root canal system model.

[0095] Then, the root canal cross-sections in the three-dimensional reconstruction results of the root canal system are clustered and segmented based on differential geometry theory to extract isthmus features in the root canal system. This step is the core innovation of this invention, achieving accurate identification of root canal isthmuses by introducing differential geometry theory.

[0096] Finally, the isthmus features are used to annotate the three-dimensional reconstruction results of the root canal system, generating a three-dimensional model of the root canal system with isthmus annotations, providing clinicians with intuitive diagnostic and treatment references.

[0097] The specific implementation methods for each step will be described in detail below.

[0098] As shown in Figure 2, the steps for image preprocessing of the raw CBCT image data include noise reduction, artifact correction, and offset field correction.

[0099] In one embodiment of the present invention, the step of denoising the raw CBCT image data specifically includes:

[0100] First, anisotropic diffusion filtering is used to filter the raw CBCT image data. Anisotropic diffusion filtering is a technique that can effectively remove noise while preserving image edge information. In this embodiment, the diffusion factor is set to 0.1, the gradient threshold is set to 3, and the number of iterations is set to 20. These parameter values ​​are selected based on the results of extensive experimental verification, which demonstrates that it can effectively remove noise while preserving root canal edge details.

[0101] Then, median filtering is used to further denoise the filtered CBCT image data. Median filtering has a good suppression effect on salt-and-pepper noise while preserving image edges. In this embodiment, a 5×5×5 window size is used for median filtering, which achieves a good balance between denoising and detail preservation.

[0102] For artifact correction, this invention employs a method optimized for CBCT characteristics. First, metal artifacts are reduced using a technique based on metal region segmentation and projection domain compensation. Specifically, metal regions in the CBCT image are first identified, then these regions are compensated in the projection domain, and finally the corrected image is reconstructed. For striated artifacts, a Fourier domain filtering technique is used for correction. By filtering out high-frequency components in specific directions in the frequency domain, striated artifacts are effectively reduced.

[0103] For offset field correction, this invention employs a multi-scale analysis-based method. First, the low-frequency offset field in the CBCT image is estimated through multi-scale analysis, and then correction is performed based on a multiplicative model to obtain the offset field-corrected CBCT image.

[0104] Through the above preprocessing steps, high-quality CBCT images with significantly reduced noise and artifacts and preserved edge information can be obtained, providing a good foundation for subsequent 3D reconstruction and canyon identification.

[0105] As shown in Figure 3, the steps for three-dimensional reconstruction of the root canal system from the preprocessed CBCT images include:

[0106] First, a U-Net neural network is used to perform binary classification on the preprocessed CBCT images to separate the root canals from the background, obtaining the segmented root canal regions. U-Net is a classic deep learning network used for medical image segmentation. In this embodiment, an improved U-Net network with a depth of 5 layers, featuring long connections and residual structures, is used for training with 2048 manually labeled CBCT slices. This network structure can effectively capture the complex morphological features of the root canal system, improving segmentation accuracy.

[0107] Next, the cavities of the segmented root canal regions are extracted using the seed filling method, and the cavities are filled with a pixel value of 255. The seed filling method is a region growing algorithm that starts with a seed point inside the root canal and gradually expands to the entire root canal cavity region. A pixel value of 255 (white) is chosen to facilitate the identification and differentiation of root canal regions in subsequent processing.

[0108] Then, the Sobel operator is used to extract the boundaries of the cavity region. The Sobel operator is a classic edge detection operator that can effectively extract edge information from images. In this embodiment, a three-dimensional Sobel operator is used to extract the edges of the root canal cavity region, obtaining an accurate representation of the root canal boundary.

[0109] Next, the boundary region is refined, and the refined region is mapped onto the preprocessed CBCT image. The pixel values ​​of the mapped region in the preprocessed CBCT image are then filled with pixel value 255. The refinement process is to obtain a more accurate representation of the root canal boundary, while mapping back to the original CBCT image is for further processing on the original data.

[0110] Then, median filtering erosion was applied to the mapped CBCT images, and the cavity region was recalculated. Median filtering erosion can smooth root canal boundaries, remove small protrusions and noise, and obtain a smoother root canal surface.

[0111] Subsequently, the cavity region was recalculated through midline transformation to obtain the three-dimensional reconstruction result of the root canal system. Midline transformation is a method that converts the shape of an object into its midline representation, which can effectively extract the skeletal structure of the root canal system, providing a foundation for subsequent isthmus identification.

[0112] Finally, repeat the above steps until convergence. Convergence can be achieved when the difference between two consecutive iterations is less than a preset threshold, or when the maximum number of iterations is reached (e.g., 10). This iterative optimization strategy continuously improves the 3D reconstruction results and enhances their accuracy.

[0113] By following the steps above, an accurate three-dimensional reconstruction model of the root canal system can be obtained, providing a foundation for subsequent isthmus identification.

[0114] The cross-sections of the root canals in the 3D reconstruction results of the root canal system are clustered and segmented based on differential geometry theory to extract isthmus features in the root canal system. This step is the core innovation of this invention and includes three key technologies: curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on the Riemannian manifold, and isthmus feature extraction combining geodesic distance field and Hough transform.

[0115] The specific steps of curvature flow-driven supervoxel segmentation include:

[0116] First, the 3D reconstruction results of the root canal system are divided into initial supervoxel units, with an initial supervoxel size set to 6 pixels (approximately 0.75 mm). A supervoxel is a method of segmenting an image into small regions; it is larger than a pixel and can better represent the local structure of the image. Choosing 6 pixels as the initial size is based on the typical size of the root canal system and the resolution of CBCT, allowing for the capture of sufficient detail while maintaining computational efficiency.

[0117] Next, seed points are evenly distributed within the root canal, with each seed point generating a supervoxel. The placement of seed points needs to consider the complexity of the root canal morphology to ensure that all areas are covered. In this embodiment, a density-based seed point placement strategy is used, placing more seed points in high-density areas (such as root canal bifurcation).

[0118] Then, for each supervoxel boundary point, the principal curvature and mean curvature are calculated. In differential geometry, curvature is an important indicator characterizing the degree of surface bending. For a point p on the root canal surface, its principal curvatures κ1 and κ2 represent the degree of surface bending in two orthogonal directions at that point, and the mean curvature H is defined as:

[0119] ,

[0120] Where H is the mean curvature, κ1 is the first principal curvature at point p, and κ2 is the second principal curvature at point p.

[0121] In practical calculations, the curvature is approximated using discrete differential geometry. For a surface represented by a mesh, the curvature can be estimated by calculating the normal vector of each vertex and the distribution of surrounding vertices.

[0122] Next, a curvature-dependent velocity field is defined to reduce the evolution rate of the supervoxels in high curvature regions. Velocity Field Defined as:

[0123]

[0124] in, Let H be the velocity field, H be the mean curvature, α be a control parameter, and |H| be the absolute value of the mean curvature. In this embodiment, α is set to 10.0. This formula results in a lower evolution rate of the supervoxels in high curvature regions (typically corresponding to canyons), thereby enabling more precise segmentation of these regions.

[0125] Then, an adaptive step-size control strategy is employed for supervoxel evolution. Specifically, a large step-size evolution is used when the local curvature is below a first threshold, a medium step-size evolution is used when the local curvature is between the first and second thresholds, and a small step-size evolution is used when the local curvature is above the second threshold. In this embodiment, the first threshold is set to 0.1, the second threshold is set to 0.3, the large step-size is 0.5, the medium step-size is 0.2, and the small step-size is 0.05. This adaptive step-size control strategy can improve the segmentation accuracy of high-curvature regions while ensuring computational efficiency.

[0126] The process of supervoxel evolution can be represented as:

[0127] ,

[0128] in, For time The location of the hypervoxel boundary point, For time The location of the hypervoxel boundary point, Step size, For the velocity field, Let be the unit normal vector at the boundary point.

[0129] Next, the similarity between adjacent supervoxels is calculated. When the similarity is higher than the merging threshold, adjacent supervoxels are merged. The similarity calculation considers geodesic distance and feature distance.

[0130] ,

[0131] in, For supravoxels and Similarity between them For supravoxels and Geodetic distance between them For supravoxels and The characteristic distance between them This is a scaling parameter for geodesic distance. This is the scaling parameter for the feature distance. In this embodiment, Set to 5.0. Set to 0.5. The merging threshold is set to 0.8 when... At that time, the supervoxels were combined. and .

[0132] When the curvature variance within a supervoxel exceeds the splitting threshold, the supervoxel splits along the direction of maximum curvature change. The curvature variance is defined as:

[0133] ,

[0134] in, For the curvature variance, For the first supervoxel The average curvature at each point, The average curvature of all points within the supervoxel. This represents the number of intra-voxel points. The splitting threshold is set to 0.05 when... At that time, the supervoxel splits along the direction of maximum curvature change.

[0135] Finally, repeat the evolution, merging, and splitting steps described above until the rate of change of the supervoxel is less than a preset threshold for two consecutive iterations or the maximum number of iterations is reached. The rate of change is defined as:

[0136] ,

[0137] in, For the rate of change, For time Time The location of each boundary point For time Time The location of each boundary point The total number of boundary points. Euclidean distance representing the change in position. This represents the magnitude of the position vector. The preset threshold is set to 0.001, and the maximum number of iterations is set to 50.

[0138] Supervoxel segmentation driven by curvature flow can yield more refined segmentation results for high curvature regions (usually corresponding to canyons), providing a foundation for subsequent canyon feature extraction.

[0139] The specific steps for ellipse fitting and major axis extraction on a Riemannian manifold include:

[0140] First, a series of cross-sections perpendicular to the long axis of the root canal are extracted. Extracting these cross-sections requires determining the direction of the root canal's long axis, which can be obtained using methods such as principal component analysis (PCA). In this embodiment, the direction of the root canal's long axis is obtained by performing principal component analysis on the root canal's central axis, and then cross-sections perpendicular to the long axis are extracted at equally spaced intervals (interval set to 0.5 mm).

[0141] Next, a local coordinate system is established on each cross-section, and the curvature tensor at each point on the cross-section is calculated. The local coordinate system has its origin at the centroid of the cross-section, and the coordinate axes are determined by the principal directions of the cross-section. Curvature tensor It describes the degree of curvature of a surface in different directions, and is a Symmetric matrix:

[0142] ,

[0143] in, For curvature tensor, , and The components of the curvature tensor can be obtained by calculating the second derivative of the cross-sectional curve.

[0144] Then, a Riemannian metric tensor is defined based on the curvature tensor, giving it a larger metric value in regions of high curvature. Riemannian metric tensor Defined as:

[0145] ,

[0146] in, For the Riemannian metric tensor, It is a 2×2 identity matrix. For control parameters, For curvature tensor, for The transpose of the matrix, This represents matrix multiplication. In this embodiment, Set to 10.0. This definition results in a larger Riemann metric value in high curvature regions (typically corresponding to canyons), thus giving these regions more attention in subsequent optimization processes.

[0147] Next, we will use five parameters to represent the ellipse, including the major axis. short axis Center coordinates and rotation angle The parametric representation of an ellipse is:

[0148] ,

[0149] in, A point on the ellipse, Center of the ellipse For the long axis, For the short axis, The rotation angle is the angle between the major axis of the ellipse and the x-axis.

[0150] Then, based on minimizing the fitting error using geodesic distance, the ellipse parameters are optimized on the Riemannian manifold. Geodesic distance, the shortest distance between two points on the Riemannian manifold, reflects the actual geometry of the root canal cross-section better than Euclidean distance. The optimization objective function is defined as:

[0151] ,

[0152] in, Let be the error function. A point on the cross-section, For the ellipse on the upper part The nearest point, for and Geodetic distance between them This represents the number of points on the cross-section.

[0153] Geodetic distance Defined as:

[0154] ,

[0155] in, For point and points Geodetic distance between them For connection and Path, parameters From 0 to 1, Let be the derivative vector of the path. Let Riemann metric tensors be the points along the path. for transpose, Represents pairs from 0 to 1 Integrate the points.

[0156] In practical calculations, numerical methods such as the FastMarching Method can be used to approximate the geodesic distance. The optimization process employs a multi-starting-point initialization and a decreasing learning rate adjustment strategy to avoid getting trapped in local optima. The optimization process is terminated prematurely when the improvement after five consecutive iterations is less than a preset threshold (e.g., 0.001).

[0157] Next, the major axis of the fitted ellipse is kept at an acute angle to the X-axis; otherwise, it is rotated counterclockwise. This adjustment is to ensure the consistency of the major axis direction, which facilitates subsequent processing.

[0158] Then, the major axis direction vector is calculated based on the optimized ellipse parameters. Defined as:

[0159] ,

[0160] in, The major axis direction vector, This is the optimized ellipse rotation angle.

[0161] Next, a vector field orthogonal to the major axis is constructed on the cross-section. On the cross-section, the vector field is orthogonal to the major axis. (G), orthogonal unit vectors take , used as the orthogonal search direction.

[0162] Then, the long axis of the tooth root is searched along the orthogonal direction, and the set of pixels during the search process is recorded. The search process starts from the center of the cross-section and expands outward along the orthogonal direction until the root canal boundary or the preset maximum distance is reached.

[0163] Finally, the pixel set is projected onto the root section, and isolated points and noise are removed using morphological algorithms. The morphological algorithms include opening operations (erosion followed by dilation) and closing operations (dilation followed by erosion), which can effectively remove small noise points and fill small voids.

[0164] By fitting ellipses to the Riemannian manifold and extracting the major axis, a geometric representation that better matches the actual shape of the root canal can be obtained, providing a foundation for subsequent isthmus feature extraction.

[0165] The specific steps for extracting canyon features by combining geodesic distance field and Hough transform include:

[0166] First, a geodesic distance field is constructed using the centroid of the cross-section as the source point. The geodesic distance field describes the geodesic distance from each point on the cross-section to the centroid, and can more accurately reflect the internal geometry of the root canal. The construction process of the geodesic distance field is as follows:

[0167] 1. Initialization: Set the distance to the source point (centroid of the cross section) to 0, and set the distance to other points to infinity.

[0168] 2. Add points around the source point to a narrowband.

[0169] 3. Iterative Update: Each time, select the point p with the smallest distance from the narrowband, remove it from the narrowband, and then update the distance values ​​of all neighboring points of p. If the distance value of a neighboring point has been updated, add it to the narrowband.

[0170] 4. Repeat step 3 until the narrow band is empty or all points have been processed.

[0171] The formula for updating geodesic distance is:

[0172] ,

[0173] in, For point geodetic distance, For point geodetic distance, for and The geodesic distance between them.

[0174] Next, isometric lines of the geodesic distance field are extracted and their morphological characteristics are analyzed. Isometric lines are sets of points with equal distance values ​​in the geodesic distance field, reflecting the morphological characteristics of the root canal cross-section. In this embodiment, 10 equally spaced isometric lines (distance intervals are 1 / 10 of the total distance range) are extracted. By analyzing the shape changes of these isometric lines, potential isthmuses can be preliminarily identified.

[0175] Then, the gradient vector field of the geodesic distance field is calculated, and gradient singularities are sought. Gradient vector field It describes the direction and rate of change of the geodesic distance field at each point. Gradient singularities are points where the gradient is close to zero or the direction changes abruptly, usually corresponding to special regions of root canal morphology, such as isthmuses or bifurcations.

[0176] Next, the curvature distribution of the equidistant lines is analyzed to identify regions of abnormal curvature. (Equidistant line curvature) The curvature of equidistant lines is described and defined as:

[0177] ,

[0178] in, For the curvature of equidistant lines, and These are the first derivatives of the parameterized representation of the equidistant lines with respect to the parameters. and These are the second derivatives of the parameterized representation of the equidistant lines with respect to the parameters. This is the normalization factor. Regions with curvature anomalies are typically characterized by curvature values ​​significantly higher than the surrounding region, or a change in the sign of curvature.

[0179] Then, by combining gradient singularities and curvature anomalies, candidate regions for canyons are determined. Candidate regions for canyons are typically characterized by a concentration of gradient singularities and anomalies in the curvature of equidistant lines.

[0180] Next, the connected region of the major axis pixels is used as the input to the Hough transform. The connected region of the major axis pixels is obtained by elliptic fitting on the Riemannian manifold and extraction of the major axis, and represents the projection of the major axis of the tooth root.

[0181] Next, a line parameter space is defined, and a geodesic distance-weighted voting strategy is used for Hough transform. The Hough transform is a technique for detecting geometric shapes in images; in this embodiment, it is used to detect lines in connected regions of major axis pixels. The line parameter space is defined as (K, b), where the line equation is y = Kx + b. The geodesic distance-weighted voting strategy gives points with smaller geodesic distances (typically closer to the root canal center) greater voting weight.

[0182] ,

[0183] Where w(p) is the voting weight of point p. (p) represents the geodesic distance of point p, and σd is the scaling parameter. In this embodiment, Set to 1 / 3 of the maximum value of the geodesic distance field.

[0184] Next, local peaks are detected in the Hough parameter space to generate multiple major axis hypotheses. Local peaks correspond to regions with a high number of votes in the parameter space, representing potential major axis directions. In this embodiment, the top 5 local peaks with the highest number of votes are selected to generate 5 major axis hypotheses.

[0185] Then, a confidence score is calculated for each hypothesis, and the hypothesis with the highest score is selected as the final long axis. The confidence score considers factors such as the number of votes, coverage, and consistency with the expected direction.

[0186] ,

[0187] Where S(h) is the confidence score of hypothesis h, V(h) is the number of votes for hypothesis h, C(h) is the coverage of hypothesis h, A(h) is the consistency between hypothesis h and the expected direction, and w1, w2, and w3 are weighting coefficients. In this embodiment, w1 is set to 0.5, w2 is set to 0.3, and w3 is set to 0.2.

[0188] Next, a hierarchical clustering method is used, with geodesic distance as the metric, to cluster the points along the major axis. Hierarchical clustering is a bottom-up clustering method. Initially, each point forms a cluster, and then the most similar clusters are gradually merged until a preset number of clusters is reached or a termination condition is met. In this embodiment, a similarity metric based on geodesic distance is used, and clustering terminates when the minimum geodesic distance between clusters is greater than a preset threshold (e.g., 2.0).

[0189] Then, the geodesic median of each cluster is calculated and used as the cluster centroid. The geodesic median is the point that minimizes the sum of geodesic distances to all points, and it reflects the geometric characteristics of the root canal cross-section better than the centroid in Euclidean space.

[0190] ,

[0191] in, For geodetic median, For points in the cluster, for and Geodetic distance between them The number of points in the cluster. Indicates that The smallest point .

[0192] Next, the distribution of cluster centroids was analyzed, and multiple cluster centroids that are relatively close to each other indicated the possible existence of islets.

[0193] Then, the geodesic distance between the centroids is calculated, and areas with a distance less than a preset threshold are marked as isochoric regions. The preset threshold is set to 1.5 mm; when the geodesic distance between two centroids is less than 1.5 mm, the area between them is marked as an isochoric region. This threshold is based on the analysis of a large amount of clinical data and can effectively identify most isochoric regions.

[0194] Next, the variational level set method is used to refine the canyon boundary. The variational level set method is an image segmentation method based on energy minimization, which can obtain smooth and accurate boundaries. In this embodiment, the initially identified canyon region is used as the initial contour, and the canyon boundary is optimized by minimizing the energy function:

[0195] ,

[0196] in, For energy function, For level set functions, For edge stopping function, For the Heaviside function, For image intensity, The average intensity of the foreground (canyon area) region. The average intensity of the background region. , and These are the weighting coefficients. , For the image domain, for gradient, For the magnitude of the gradient, This represents the integral over the entire image domain. In this embodiment, Set to 0.1, Set to 1.0, Set to 1.0.

[0197] Finally, a feature vector for the canyon region is generated, containing information such as location, shape, and size. The canyon region feature vector includes:

[0198] Location: Coordinates of the center point of the canyon area

[0199] Morphology: Description of the shape of the canyon area (e.g., elongated, flat, etc.)

[0200] Dimensions: Length, width, and area of ​​the canyon region

[0201] Direction: Main direction of the canyon area

[0202] Connectivity: Description of the connectivity between the isthmus and the main root canal

[0203] By combining geodesic distance field with Hough transform for isthmus feature extraction, isthmuses in the root canal system can be accurately identified, providing a basis for subsequent isthmus labeling.

[0204] The specific steps for annotating the isthmus of the 3D reconstruction results of the root canal system using isthmus features include:

[0205] First, spatial registration is performed between the isthmus features and the 3D reconstruction results of the root canal system. Spatial registration is the process of mapping the extracted isthmus features to the 3D reconstruction model to ensure the accuracy of the isthmus labeling. In this embodiment, a rigid registration method based on anatomical landmarks is adopted, selecting the root canal opening, root apex, and major bifurcation points as landmarks.

[0206] Then, different color codes are set according to the characteristics of the isthmus. Different types of isthmus can be distinguished by different colors, for example: red: isthmus between main root canals; orange: isthmus between main root canals and lateral root canals; yellow: isthmus between lateral root canals;

[0207] This color coding scheme can intuitively display the distribution of different types of canyons, helping clinicians to quickly identify key areas.

[0208] Next, the canyon area is highlighted. Highlighting can be achieved by enhancing the brightness and contrast of the canyon area, or adding special textures, making the canyon area more prominent in the 3D model. In this embodiment, in addition to color coding, the brightness of the canyon area is increased by 10% to further improve its visibility.

[0209] Finally, a 3D model of the root canal system with isthmus annotations is output. The output 3D model can be saved in common 3D model formats such as STL and OBJ, facilitating viewing and analysis in various 3D visualization software. Furthermore, a report containing isthmus information can be generated, detailing the location, morphology, size, and other characteristics of the isthmus, providing clinicians with comprehensive reference information.

[0210] The present invention also includes a step for identifying missed root canals, as described below:

[0211] First, based on a 3D model of the root canal system with isthmus annotations, the topological structure of the root canal system is analyzed. Topological analysis includes the number, distribution, and connectivity of root canals, reflecting the overall organization of the root canal system. In this embodiment, a graph-based method is used to represent the topological structure of the root canal system, representing root canals as nodes in a graph and connectivity as edges.

[0212] Next, the connectivity of the root canal system is checked. Connectivity checks can identify potential breakpoints or isolated areas within the root canal system, which may indicate missed root canals. In this embodiment, a depth-first search (DFS) algorithm is used to check the connectivity of the root canal system, ensuring that all root canal regions are interconnected.

[0213] Next, morphological abnormalities that may indicate missed root canals are identified. These abnormalities include sudden narrowing of the root canal, abnormally increased curvature, and uneven distribution of root canal density, all of which may indicate the presence of unidentified root canals. In this embodiment, the following morphological abnormality indicators are defined: a sudden decrease in root canal diameter exceeding 50%; an increase in curvature exceeding 30° over a short distance (less than 0.5 mm); and a difference in root canal density exceeding 20% ​​compared to the surrounding area. When these morphological abnormalities are detected, they are marked as potential missed root canal areas.

[0214] Then, the symmetry between different root canals of the same tooth is compared. In many cases, different root canals of the same tooth should have a certain degree of symmetry; significant asymmetry may indicate the presence of missing root canals. In this embodiment, the symmetry index of characteristics such as the number, length, and diameter of root canals is calculated. When the symmetry index is lower than a preset threshold (e.g., 0.7), it is marked as a potential missing root canal region.

[0215] Finally, a warning message is generated when a potentially missed root canal is detected. The warning message includes the location of the potentially missed root canal, its probability score, and suggested examination methods, providing guidance for clinicians. In this embodiment, based on the degree of morphological abnormality and symmetry analysis results, the probability score of the potentially missed root canal is divided into three levels: high, medium, and low, with corresponding recommendations provided.

[0216] By marking isthmuses and identifying missed root canals, this invention can not only accurately identify isthmuses in the root canal system, but also indicate possible missed root canals, thus comprehensively improving the accuracy and success rate of root canal treatment.

[0217] This invention also provides a three-dimensional reconstruction and isthmus identification system for root canal systems based on CBCT images, including a preprocessing module, a three-dimensional reconstruction module, a clustering and segmentation module, an annotation module, and a judgment module.

[0218] The preprocessing module is used to preprocess the raw CBCT image data to obtain preprocessed CBCT images. This module implements functions such as noise reduction, artifact correction, and offset field correction, providing high-quality image data for subsequent processing.

[0219] The 3D reconstruction module is used to perform 3D reconstruction of the root canal system on preprocessed CBCT images, obtaining the 3D reconstruction results of the root canal system. This module integrates algorithms such as U-Net neural network segmentation, seed filling, and midline transformation, which can accurately reconstruct the 3D structure of the root canal system.

[0220] The clustering and segmentation module is used to perform clustering and segmentation of root canal cross sections in the 3D reconstruction results of the root canal system based on differential geometry theory, in order to extract isthmus features in the root canal system. This module is the core innovation of this system, realizing functions such as curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on Riemannian manifolds, and isthmus feature extraction combining geodesic distance field and Hough transform, which can accurately identify isthmus with complex morphology.

[0221] The annotation module is used to annotate the 3D reconstruction results of the root canal system using isthmus features, generating a 3D model of the root canal system with isthmus annotations, providing clinicians with intuitive diagnostic and treatment references.

[0222] The judgment module is used to identify missed root canals based on a 3D model of the root canal system with isthmus annotations. By analyzing the root canal system topology, checking connectivity, identifying morphological abnormalities, and comparing symmetry, it can indicate possible missed root canals, thereby improving the comprehensiveness and success rate of treatment.

[0223] In terms of hardware implementation, this system can be deployed on computers with the following configurations: Processor: Intel i7-10700 or equivalent CPU; Memory: 16GB or more; Graphics Card: NVIDIA RTX 2060 or higher (for neural networks and parallel computing); Storage: SSD 500GB or more (for data caching and processing). In terms of software architecture, this system adopts a three-layer structure: Layer 1: A C++-developed computing engine implementing differential geometry algorithms; Layer 2: A Python-encapsulated data processing pipeline implementing neural networks and image processing; Layer 3: A Qt-developed user interface providing 3D visualization and interactive functions.

[0224] This system supports the DICOM standard and can be seamlessly integrated with existing PACS systems; it provides a standard API, allowing third-party systems to call core functions; and it supports output of common 3D model formats such as STL and OBJ, facilitating integration with CAD / CAM systems.

[0225] Through the collaborative work of the above modules, this system can realize the entire process from raw CBCT data to a three-dimensional model of the root canal system with isthmus annotation, providing accurate diagnostic and treatment support for root canal treatment.

[0226] This invention provides a method and system for three-dimensional reconstruction and isthmus identification of the root canal system based on CBCT images. By introducing differential geometry theory, it achieves accurate identification of the root canal system, especially the isthmus. This invention not only innovatively applies differential geometry theory to root canal system analysis in theory, but also demonstrates significant technical advantages in practice, including improved isthmus identification accuracy, reduced false positive rate, increased processing efficiency, improved clinical treatment success rate, and expanded applicability.

[0227] The core innovation of this invention lies in clustering and segmentation techniques based on differential geometry theory, including curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on Riemannian manifolds, and isthmus feature extraction combining geodesic distance fields and Hough transforms. The combined application of these techniques enables this invention to accurately identify root canal isthmuses of various complex morphologies, providing precise diagnostic and treatment support for clinical root canal treatment.

[0228] This invention is not only significant for improving the success rate of root canal treatment, but also provides new ideas and methods for other research in the field of oral medicine, and has broad application prospects.

[0229] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for identifying root canal isthmus regions based on CBCT images, characterized in that, Includes the following steps: The process involves: acquiring raw CBCT image data; preprocessing the raw CBCT image data to obtain preprocessed CBCT images; performing 3D reconstruction of the root canal system on the preprocessed CBCT images to obtain 3D reconstruction results; performing clustering segmentation based on differential geometry theory on the root canal cross-sections in the 3D reconstruction results to extract isthmus features in the root canal system. The clustering segmentation based on differential geometry theory includes: curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on Riemannian manifolds, and isthmus feature extraction combining geodesic distance field and Hough transform. Specifically, the steps for isthmus feature extraction combining geodesic distance field and Hough transform include: constructing a geodesic distance field using the centroid of the cross-section as the source point; extracting equidistant lines from the geodesic distance field and analyzing their morphological characteristics; calculating the gradient vector field of the geodesic distance field and finding gradient singularities; and analyzing the curvature distribution of the equidistant lines to identify... Identify curvature anomaly regions; combine the gradient singularities and curvature anomaly regions to determine candidate isthmus regions; use the connected regions of major axis pixels as input for Hough transform; define a line parameter space and perform Hough transform using a geodesic distance-weighted voting strategy; detect local peaks in the Hough parameter space to generate multiple major axis hypotheses; calculate the confidence score of each hypothesis and select the hypothesis with the highest score as the final major axis; use a hierarchical clustering method, with geodesic distance as the metric, to cluster the major axis point set; calculate the geodesic median of each cluster as the cluster centroid; analyze the distribution of cluster centroids, and multiple centroids that are close together indicate the possible existence of isthmus regions; calculate the geodesic distance between centroids, and mark regions with a distance less than a preset threshold as isthmus regions; use a variational level set method to refine the isthmus region boundaries; generate isthmus region feature vectors containing location, shape, size, orientation, and connectivity information; use the isthmus region features to annotate the 3D reconstruction results of the root canal system.

2. The root canal isthmus identification method based on CBCT images according to claim 1, characterized in that, The steps for image preprocessing of the raw CBCT image data specifically include: denoising the raw CBCT image data; correcting artifacts in the raw CBCT image data; and correcting the offset field in the raw CBCT image data.

3. The root canal isthmus identification method based on CBCT images according to claim 2, characterized in that, The steps for denoising the raw CBCT image data include: using anisotropic diffusion filtering to filter the raw CBCT image data, wherein the diffusion factor is set to 0.1, the gradient threshold is set to 3, and the number of iterations is set to 20; and using median filtering to further denoise the filtered CBCT image data.

4. The root canal isthmus identification method based on CBCT images according to claim 1, characterized in that, The steps for performing three-dimensional reconstruction of the root canal system on the preprocessed CBCT image specifically include: using a U-Net neural network to perform binary classification on the preprocessed CBCT image to segment the root canal from the background and obtain the segmented root canal region; using a seed filling method to extract the cavity in the segmented root canal region and filling the cavity part with a pixel value of 255; using the Sobel operator to extract the boundary of the cavity region; thinning the boundary region and mapping the thinned region to the preprocessed CBCT image, filling the pixel value of the mapped region in the preprocessed CBCT image with a pixel value of 255; performing median filtering erosion on the mapped CBCT image and recalculating the cavity region; recalculating the cavity region through median transformation to obtain the three-dimensional reconstruction result of the root canal system; repeating the above steps until convergence.

5. The root canal isthmus identification method based on CBCT images according to claim 1, characterized in that, The curvature flow-driven supervoxel segmentation steps specifically include: dividing the 3D reconstruction result of the root canal system into initial supervoxel units, with the initial supervoxel size set to 6 pixels; uniformly arranging seed points inside the root canal, with each seed point generating a supervoxel; calculating the principal curvature and average curvature for each supervoxel boundary point; defining a curvature-related velocity field to reduce the evolution speed of supervoxels in high curvature regions; employing an adaptive step size control strategy for supervoxel evolution, using a large step size when the local curvature is below a first threshold, a medium step size when the local curvature is between the first and second thresholds, and a small step size when the local curvature is above the second threshold; calculating the similarity between adjacent supervoxels, merging adjacent supervoxels when the similarity is higher than a merging threshold; splitting the supervoxel along the direction of maximum curvature change when the internal curvature variance of the supervoxel is higher than a splitting threshold; repeating the above evolution, merging, and splitting steps until the supervoxel change rate is less than a preset threshold or the maximum number of iterations is reached in two consecutive iterations.

6. The root canal isthmus identification method based on CBCT images according to claim 1, characterized in that, The steps of ellipse fitting and major axis extraction on the Riemannian manifold specifically include: extracting a series of cross-sections perpendicular to the major axis along the root canal's major axis; establishing a local coordinate system on each cross-section and calculating the curvature tensor at each point on the cross-section; defining a Riemannian metric tensor based on the curvature tensor to give it a larger metric value in high curvature regions; representing the ellipse with five parameters, including major axis a, minor axis b, center x-coordinate x0, center y-coordinate y0, and rotation angle θ; optimizing the ellipse parameters on the Riemannian manifold based on minimizing the fitting error of geodesic distance; keeping the major axis direction of the fitted ellipse unchanged when it forms an acute angle with the X-axis, otherwise performing counterclockwise rotation adjustment; calculating the major axis direction vector based on the optimized ellipse parameters; constructing a vector field orthogonal to the major axis direction on the cross-section; searching for the root's major axis along the orthogonal direction and recording the set of pixels during the search process; projecting the set of pixels onto the root cross-section and removing isolated points and noise using morphological algorithms.

7. The root canal isthmus identification method based on CBCT images according to claim 1, characterized in that, The steps of annotating the 3D reconstruction results of the root canal system using the isthmus features specifically include: spatially registering the isthmus features with the 3D reconstruction results of the root canal system; setting different color codes according to the isthmus features; highlighting the isthmus area; and outputting a 3D model of the root canal system with isthmus annotations.

8. The root canal isthmus identification method based on CBCT images according to claim 1, characterized in that, The method also includes the step of identifying missed root canals: analyzing the topological structure of the root canal system based on a three-dimensional model of the root canal system with isthmus annotations; checking the connectivity of the root canal system; identifying morphological abnormalities that may indicate missed root canals; comparing the symmetry between different root canals of the same tooth; and generating a warning message when a potentially missed root canal is detected.

9. A root canal isthmus identification system based on CBCT images, employing the root canal isthmus identification method based on CBCT images as described in any one of claims 1-8, characterized in that, include: The preprocessing module is used to preprocess the raw CBCT image data to obtain preprocessed CBCT images; the three-dimensional reconstruction module is used to perform three-dimensional reconstruction of the root canal system on the preprocessed CBCT images to obtain the three-dimensional reconstruction result of the root canal system. The clustering and segmentation module is used to perform clustering and segmentation on the root canal cross sections in the 3D reconstruction results of the root canal system based on differential geometry theory, in order to extract isthmus features in the root canal system. The clustering and segmentation based on differential geometry theory includes: curvature flow-driven supervoxel segmentation, ellipse fitting and major axis extraction on a Riemannian manifold, and isthmus feature extraction combining geodesic distance field and Hough transform. Specifically, the isthmus feature extraction combining geodesic distance field and Hough transform includes: constructing a geodesic distance field with the centroid of the cross section as the source point; extracting equidistant lines of the geodesic distance field and analyzing their morphological characteristics; calculating the gradient vector field of the geodesic distance field and finding gradient singularities; analyzing the curvature distribution of the equidistant lines and identifying curvature anomaly regions; combining the gradient singularities and curvature anomaly regions to determine candidate isthmus regions; using the connected regions of major axis pixels as input to the Hough transform; and defining line parameters. In the spatial domain, a Hough transform is performed using a voting strategy weighted by geodesic distance. Local peaks are detected in the Hough parameter space to generate multiple major axis hypotheses. The confidence score of each hypothesis is calculated, and the hypothesis with the highest score is selected as the final major axis. A hierarchical clustering method is used, with geodesic distance as the metric, to cluster the major axis point set. The geodesic median of each cluster is calculated as the cluster centroid. The distribution of the cluster centroids is analyzed, and multiple centroids that are close together indicate the possible existence of isthmuses. The geodesic distance between centroids is calculated, and regions with a distance less than a preset threshold are marked as isthmuses. The variational level set method is used to refine the isthmus boundaries. A isthmus feature vector is generated, containing information on location, shape, size, orientation, and connectivity. A labeling module is used to label the isthmuses in the 3D reconstruction results of the root canal system using the isthmus features. A judgment module is used to judge missing root canals based on the 3D model of the root canal system with isthmus labels.

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