Three-dimensional quantitative evaluation method and system for periodontitis cone beam CT bone absorption image

Abstract

The present application relates to the technical field of medical image processing, in particular to a periodontitis cone beam CT bone absorption image three-dimensional quantitative evaluation method and system, first, the cone beam CT body data is executed multi-label synchronous segmentation to get three types of masks of alveolar bone, tooth root and periodontal membrane gap and automatically locate the enamel cement boundary and alveolar crest top mark point, then calculate the Hounsfield unit direction gradient tensor field along the buccal, lingual, mesial and distal four directions of the tooth root surface to get the direction gradient anisotropy index, and fuse and output the four-direction three-dimensional distance, bone absorption shape classification label and bone quality index; further, the three-dimensional shape of the tooth root is used as an invariant feature to execute three-dimensional registration on series of follow-up data and output the change rate, and the anisotropy index triggers the closed loop refinement of the segmentation boundary in reverse.

Description

Technical Field

[0001] This invention relates to the field of medical image processing technology, specifically to a three-dimensional quantitative assessment method and system for cone-beam CT bone resorption images in periodontitis. Background Technology

[0002] Periodontitis is a chronic infectious disease characterized by progressive destruction of periodontal supporting tissues, initiated by dental plaque biofilm. Clinically, alveolar bone resorption is the most important objective grading and efficacy assessment criterion. Cone-beam computed tomography (CBCT) offers advantages over traditional periapical radiographs and panoramic X-rays, including three-dimensional imaging, isotropic voxels, and low radiation dose, and has become the mainstream imaging method for assessing the degree of alveolar bone destruction in periodontitis. However, in clinical practice, the assessment of periodontal bone tissue using CBCT images has long relied on radiologists' layer-by-layer visual interpretation of tomographic images and manual measurement of bone resorption height and bone density. This presents significant technical challenges, such as large inter-batch variability due to differences in layer selection and the lack of intuitive spatial representation of the three-dimensional morphological characteristics of vertical and horizontal bone resorption on two-dimensional tomographic images. Therefore, a systematic solution using automated quantitative assessment technology is urgently needed.

[0003] Chinese invention patent application CN113223010A discloses a method and system for fully automatic multi-tissue segmentation of oral images. This method uses a 3D U-net neural network to perform fully automatic multi-tissue segmentation on cone-beam computed tomography (CBCT) images, with labeled categories covering thirteen types of oral anatomical tissues, including dentin, enamel, alveolar cortical bone, alveolar cancellous bone, mandibular nerve canal, periodontal ligament, dental lamina, and pulp chamber. It amplifies training samples using a generative adversarial network and uses a watershed algorithm or region growing algorithm with pulp chamber voxels as seed points to achieve single-tooth segmentation. However, this approach only reaches the morphological level of pixel-level segmentation of multiple tissues and single-tooth segmentation. Downstream interpretation of the segmentation results still relies on visual interpretation by clinicians. It does not disclose automatic measurement of the 3D distance from the cementoenamel junction to the alveolar ridge crest, automatic morphological classification of vertical and horizontal bone resorption, or quantitative indicators of bone quality using Hounsfield unit distribution. Furthermore, it does not address the objective driving loop of segmentation results in the longitudinal tracking scenario of periodontitis.

[0004] Chinese invention patent CN117218450B discloses an AI-based automated fine anatomy method for oral CBCT. This method employs a two-stage cascaded deep learning architecture. The first stage uses the nnUnet model to perform coarse CBCT anatomy and output a coarse pixel-level mask. The second stage uses the Unet++ model to perform fine anatomy to handle fine structures such as periodontal ligament spaces ranging from 0.15 mm to 0.38 mm, and performs quantitative analysis on enamel thickness and labial bone wall thickness. However, the quantitative analysis of this scheme is limited to scalar distance measurements in the thickness direction, lacking directional bone resorption quantification indicators in the buccal, lingual, mesial, and distal anatomical directions, and even more so, lacking Hounsfield unit spatial distribution modeling along the tangential direction of the root surface, the latter being a key diagnostic dimension for asymmetric bone destruction in the early stages of periodontitis.

[0005] Chinese invention patent application CN115886863A discloses a method and device for three-dimensional overlap measurement of teeth and facial bones using the entire skull base as a reference plane. This method uses four landmarks—the skull base point, the nasal root point, the bilateral supraorbital notches, and the midpoints of the bilateral infraorbital margins—to determine a standard skull base plane as the reference plane. It performs three-dimensional overlap registration on cone-beam CT data from anterior and posterior phases, measuring the movement distances of the root apex and cusp along the X, Y, and Z axes to quantify the positional changes of the teeth in three dimensions. However, this approach uses skull bony landmarks as the registration reference, and the registration object is tooth movement in orthodontic settings rather than tooth-by-tooth bone resorption in periodontitis settings. It does not provide a processing path for the three-dimensional morphology of the tooth root as a registration-invariant feature, and it does not address core quantitative parameters required for periodontitis diagnosis, such as directional anisotropy, morphological classification, and bone mass index.

[0006] After in-depth analysis of existing technologies, the inventors discovered that the three aforementioned schemes and their derivative methods all follow a unidirectional, serial, isotropic technical path: high-precision multi-label segmentation → geometric landmark localization → Euclidean distance formula → classification threshold. This simplifies bone resorption quantification to a scalar average of distances in each direction, thus revealing a deep bottleneck: in the early stages of periodontitis (distance from the cementoenamel junction to the alveolar ridge crest less than 3 mm), bone resorption exhibits significant directional anisotropy. Osteoclast activity is anatomically directional specific; the buccal bone plate is inherently thinner than the lingual plate; and interproximal spaces where plaque accumulates are preferentially resorbed. The averaging of absolute distances actually masks this anisotropy. Anisotropy of direction is a strong early pathological signal; however, segmentation and geometric measurement are unidirectional serial paths, with segmentation boundary errors directly transmitted to geometric measurement results without feedback correction mechanisms. The classification of vertical and horizontal bone resorption morphology relies solely on post-hoc morphological interpretation and fails to utilize directional priors during the segmentation stage. Therefore, existing technologies have systematic limitations in terms of diagnostic sensitivity for asymmetric bone resorption in early periodontitis, closed-loop accuracy of segmentation-quantification, and objective driving force for morphological classification. A three-dimensional quantitative assessment scheme with directional gradient anisotropy as the underlying signal and closed-loop feedback refinement as the coupling mechanism is urgently needed to achieve a fundamental breakthrough. Summary of the Invention

[0007] To address the core bottleneck in existing cone-beam CT (CBCT) bone resorption image assessment for periodontitis that relies on scalar distance mean while neglecting directional anisotropy, this invention provides a three-dimensional quantitative assessment method and system for CBCT bone resorption images of periodontitis. By explicitly calculating the Hounsfield unit directional gradient tensor field along the buccal, lingual, mesial, and distal anatomical orientations along the tangential direction of the tooth root surface, and using the directional gradient anisotropy index to trigger closed-loop refinement of the segmentation boundary, this method achieves highly sensitive diagnosis of early asymmetric bone resorption in periodontitis, improved segmentation-quantification closed-loop accuracy, and objective automatic classification of vertical and horizontal bone resorption morphologies, based on the principle of directional specificity in bone remodeling biology, without increasing cone-beam CT scanning parameters or hardware costs.

[0008] The technical solution of this invention is: a three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis, comprising the following steps: S1 Data acquisition and multi-label synchronous segmentation step, performing multi-label synchronous segmentation on the cone-beam CT volume data to obtain alveolar bone mask, root mask, and periodontal ligament space mask, and automatically locating anatomical landmarks based on the three-dimensional interface between the root mask and the periodontal ligament space mask to obtain cementoenamel boundary landmarks and alveolar ridge crest landmarks; S2 Directional gradient tensor field calculation step, calculating the Hounsfield unit directional gradient tensor field along the four anatomical orientations of the root mask, and outputting the directional gradient anisotropy index. The four anatomical orientations include buccal, lingual, mesial, and distal orientations; the S3 three-dimensional quantitative analysis and morphological classification step integrates the cementoenamel boundary marker, the alveolar ridge crest marker, and the directional gradient anisotropy index, and outputs the three-dimensional distance from the cementoenamel boundary to the alveolar ridge crest, bone resorption morphological classification labels, and Hounsfield distribution bone quality index for each tooth position; the S4 longitudinal registration and rate of change tracking step performs three-dimensional registration of the alveolar bone mask of the cone-beam CT data from a series of follow-up examinations with the root mask as an invariant feature, and outputs the rate of change of the three-dimensional parameters of bone resorption.

[0009] This invention also provides a three-dimensional quantitative assessment system for cone-beam CT bone resorption images in periodontitis, including a multi-label synchronous segmentation module, a directional gradient tensor field calculation module, a three-dimensional quantitative analysis and morphological classification module, and a longitudinal registration and rate of change tracking module. The multi-label synchronous segmentation module is configured to perform multi-label synchronous segmentation on cone-beam CT volume data and automatically locate the cementoenamel boundary marker and alveolar ridge marker. The directional gradient tensor field calculation module is configured to calculate the Hounsfield unit directional gradient tensor field along the four anatomical orientations of the root mask to obtain the directional gradient anisotropy index. The three-dimensional quantitative analysis and morphological classification module is configured to fuse and output four-directional three-dimensional distances, bone resorption morphological classification labels, and bone mass index. The longitudinal registration and rate of change tracking module is configured to perform three-dimensional registration on a series of follow-up examination data and output the rate of change of three-dimensional parameters of bone resorption.

[0010] The beneficial effects of this invention are as follows. First, it significantly improves the diagnostic sensitivity for early asymmetric bone resorption. This invention calculates the Hounsfield unit gradient tensor field along the four anatomical orientations of the root mask and outputs the directional gradient anisotropy index, which is fundamentally different from simply stopping at pixel-level segmentation and only providing scalar distances in the thickness direction. The mechanism is that osteoclast activity in the early stage of periodontitis has anatomical direction specificity. The difference in directional gradient anisotropy index, as the characteristic value difference of the first-order tensor field, can capture directional asymmetric signals before the three-dimensional distance from the cementoenamel junction to the alveolar ridge crest reaches the pathological threshold, thereby advancing the early diagnostic window. Second, the closed-loop accuracy of segmentation-quantization is systematically enhanced. This invention inputs the directional gradient anisotropy index in reverse to the decoder side of the multi-label synchronous segmentation to trigger the boundary iteration and refinement of the alveolar bone mask, which is fundamentally different from the unidirectional serial path. The mechanism is that segmentation boundary errors cause deviations in the tangential gradient vector calculation, leading to deviations in the directional gradient anisotropy index. This deviation is fed back to the decoder as a reverse gradient, forming a closed-loop drive, allowing segmentation and quantization to converge collaboratively during iteration rather than accumulating errors independently. Third, the invention provides an objective and automatic driving mechanism for the classification of vertical and horizontal bone resorption morphologies. Based on preset vertical and horizontal threshold rules for the directional gradient anisotropy index, this invention automatically determines the bone resorption morphology classification label, which is fundamentally different from existing technologies that rely on post-hoc interpretation by clinicians. The mechanism is that vertical bone resorption is mainly characterized by height differences along the axial direction of the root midline, with a higher directional gradient anisotropy index value and the main anisotropy direction along the axial direction; horizontal bone resorption is mainly characterized by uniform decreases in four directions, with a lower directional gradient anisotropy index value, providing an objective classification basis from a mathematical perspective. Fourth, the invention improves the accuracy of efficacy assessment in longitudinal tracking. This invention uses the three-dimensional morphology of the tooth root mask as a registration-invariant feature, fundamentally different from using skull bony landmarks as a reference. The mechanism is as follows: during the periodontitis treatment cycle, skull bony landmarks introduce errors due to differences in head position scanning, while the three-dimensional morphology of the tooth root remains anatomically stable throughout the treatment cycle. Using this registration-invariant feature, the measurement error of the rate of change of bone resorption three-dimensional parameters can be reduced to the sub-millimeter level. Fifth, the above four beneficial effects form a synergistic strengthening relationship. The directional gradient anisotropy index simultaneously drives the four stages of early diagnosis, closed-loop feedback, morphological classification, and longitudinal tracking. This achieves a nonlinear gain effect where a single indicator connects the four stages of segmentation, quantification, classification, and tracking, providing a systematic technical solution driven by three-dimensional image quantitative analysis for the objective grading of bone destruction in periodontitis and the evaluation of treatment efficacy. Attached Figure Description

[0011] Figure 1 This is a flowchart of a three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis provided in an embodiment of the present invention.

[0012] Figure 2This is an architecture diagram of the three-dimensional quantitative assessment system for cone-beam CT bone resorption images in periodontitis provided in this embodiment of the invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of the invention.

[0014] This embodiment provides a three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis. (See [link to relevant documentation]). Figure 1 The method includes steps S1 to S4. The specific implementation of each step will be explained below.

[0015] Step S1: Data Acquisition and Multi-Label Synchronous Segmentation. Step S1 performs multi-label synchronous segmentation on the cone-beam CT data to obtain alveolar bone mask, root mask, and periodontal ligament space mask. Based on the three-dimensional interface between the root mask and the periodontal ligament space mask, anatomical landmarks are automatically located to obtain cementoenamel boundary landmarks and alveolar ridge crest landmarks.

[0016] Cone-beam CT volume data were acquired using clinically common cone-beam CT scanning equipment. The preferred scanning field of view was a full arch view or a partial view of the dental arch. The preferred voxel isotropic resolution was 0.2 mm to 0.4 mm. The preferred tube voltage was 80 kV to 120 kV, and the preferred tube current was 4 mA to 10 mA. The cone-beam CT volume data was imported into the processing flow in DICOM format and sent to a multi-label synchronous segmentation network after being normalized to a spatial coordinate system. Specifically, a spatial coordinate system was established with the occlusal plane as the XOY plane and the left and right symmetry planes as the XOZ planes. The Hounsfield unit gray values ​​of all voxels were linearly normalized to the interval [0, 1].

[0017] Multi-label synchronous segmentation is performed using a 3D fully convolutional encoder-decoder segmentation network. The encoder portion of the network extracts multi-scale voxel features from the cone-beam CT volume data through four levels of 3D convolutional downsampling, with the number of feature channels at each downsampling level being 32, 64, 128, and 256 respectively. Each downsampling level is followed by two 3×3×3 3D convolutional layers, a batch normalization layer, and a ReLU activation layer. The decoder portion restores the original resolution of the volume data through corresponding four levels of 3D transposed convolutional upsampling, with the number of feature channels at each upsampling level being 256, 128, 64, and 32 respectively. The encoder and decoder portions are connected via skip connections to pass shallow detail voxel features. The output layer of the network synchronously outputs the voxel-level probability distributions of three tissue types—alveolar bone mask, root mask, and periodontal ligament space mask—using a softmax activation function. During the training phase, the total loss is calculated by weighting the Dice loss function and the cross-entropy loss function, with an optimal weight ratio of 0.7 to 0.3. The Adam optimizer is used, with an initial learning rate of 1×10⁻⁶. -4 The batch size is 2, and the number of iterations is 300.

[0018] After multi-label synchronous segmentation, automatic anatomical landmark localization is performed based on the three-dimensional interface between the root mask and the periodontal ligament space mask. Specifically, the three-dimensional interface between the root mask and the periodontal ligament space mask is the voxel-level adjacent region between the root surface and the periodontal ligament space, which anatomically corresponds to the cementum surface. The cementoenamel boundary landmark is the coronalmost dividing point of this interface along the root midline, corresponding to the anatomical position of the transition between enamel and cementum; the alveolar ridge crest landmark is the coronalmost adjacent point between this interface and the alveolar bone mask in the buccal, lingual, mesial, and distal anatomical directions. The automatic localization of the cementoenamel boundary landmark and the alveolar ridge crest landmark is achieved using a landmark detection network based on heatmap regression. The input is the three-dimensional interface region between the root mask and the periodontal ligament space mask, and the output is the three-dimensional spatial coordinates of each landmark. Output the coordinates of one cementoenamel boundary marker and four alveolar ridge crest markers for each tooth position, one each for the buccal, lingual, mesial, and distal sides.

[0019] Step S2: Calculation of the directional gradient tensor field. Step S2 calculates the Hounsfield unit directional gradient tensor field along the four anatomical orientations of the tooth root mask, and outputs the directional gradient anisotropy index. The four anatomical orientations include the buccal orientation, lingual orientation, mesial orientation, and distal orientation.

[0020] The four-directional anatomical orientations are established using the root midline of the tooth corresponding to the root mask as a reference to establish a local anatomical coordinate system. The buccal orientation is the anatomical orientation ray pointing from the root midline to the buccal mucosa; the lingual orientation is the anatomical orientation ray pointing from the root midline to the lingual mucosa; the mesial orientation is the anatomical orientation ray pointing from the root midline to the adjacent middle tooth position; and the distal orientation is the anatomical orientation ray pointing from the root midline to the adjacent distal tooth position. The specific implementation of the directional gradient tensor field calculation is then described in four sub-steps: sub-step S2.1 is the extraction of the root midline; sub-step S2.2 is the parameterization of the cylindrical coordinate system of the root surface; sub-step S2.3 is the calculation of the tangential gradient vector and four-directional projection; and sub-step S2.4 is the calculation of the directional gradient anisotropy index.

[0021] Sub-step S2.1: Root midline extraction. The root midline is extracted by performing multi-view principal component axial fitting on the root mask. This extraction process incorporates the curved morphology prior of the root mask, reducing the axial deviation at root curvatures compared to single principal component axial fitting, and is particularly suitable for multi-rooted teeth (molars) and slightly curved roots of anterior teeth.

[0022] First, principal component analysis is performed on the voxel coordinate point set of the root mask to obtain the three principal axis directions. The voxel coordinate point set of the root mask... ,in The first tooth root mask The three-dimensional spatial coordinates of an individual element. Let this be the total number of voxels within the root canal mask. Calculate the covariance matrix of the voxel coordinate point set. as follows:

[0023] ,in: Let be the covariance matrix of the voxel coordinate point set of the root mask, representing the divergence of the voxel coordinates in the three spatial dimensions. A symmetric positive semi-definite matrix, a real matrix whose values ​​are in the range of non-negative diagonal elements, with units of mm², is obtained by statistical calculation of the voxel coordinate point set described in this formula, and is used to support the subsequent solution of the principal component axial direction; The first tooth root mask The three-dimensional spatial coordinates of the voxels are three-dimensional column vectors. The range of values ​​is determined by the field of view and voxel resolution of cone-beam CT scanning. The unit is mm. The voxel index of the root mask is converted by spatial resolution and used as the input data points for the covariance matrix. Let be the arithmetic mean, or centroid, of the set of voxel coordinates, and be a three-dimensional column vector whose values ​​range from . Same domain, unit is mm, from The calculated value serves as the centralized benchmark for the covariance matrix. The total number of voxels within the root canal mask is a positive integer scalar with a value range of [value range missing]. The magnitude, dimensionless, is obtained from the voxel count of the root mask and serves as the range for summation and normalization; superscript. This is the matrix transpose operator, which transposes a column vector into a row vector to construct an outer product matrix; The variable is the summation of voxel indices, and its value range is... A positive integer, dimensionless, is used as a pointer for summation traversal. Then, eigenvalue decomposition is performed on the covariance matrix to obtain three eigenvalues ​​and their corresponding eigenvectors:

[0024] ,in: The first covariance matrix is ​​the first... The eigenvalues ​​are arranged in descending order, are non-negative real scalars, and take values ​​ranging from 1 to 2. The unit is mm², calculated by the eigenvalue decomposition algorithm, representing the root mask in the first... The magnitude of the variance along the principal axis, and the direction corresponding to the largest eigenvalue, is the principal extension direction of the root mask; The first covariance matrix is ​​the first... Each eigenvector is a three-dimensional unit column vector, taking values ​​within the unit sphere, dimensionless, and calculated by the eigenvalue decomposition algorithm, satisfying the following conditions. As a root mask in the first Geometric direction indication of the main axis direction; The eigenvalue index is an integer, and its value is... Dimensionless, representing an enumeration of the three principal axes. The principal axis with the largest cumulative variance contribution rate is selected. As a preliminary axial direction, it is denoted as .

[0025] Then, using the initial axial direction as a reference, least-squares curve fitting is performed on the centroid point set of the root mask along multiple cross-sections perpendicular to the initial axial direction to obtain the root midline. Specifically, the core axis is set at equal intervals along the initial axial direction with a preset step size (preferably 0.5 mm). cross-section Each cross-sectional plane is perpendicular to the initial axis. In the first... Extract the set of elements at the intersection of the root mask and the cross-section on each cross-section. ,in For the tooth root mask, calculate the centroid of the intersection section:

[0026] ,in: For the first The centroid of the root mask on each cross-section plane is a three-dimensional column vector. Its value range is determined by the field of view of cone-beam CT scanning and the unit is mm. It is calculated by this formula based on the arithmetic mean of the voxel coordinates of the intersection of the cross-section plane and the root mask, and is used as the shape value point of the root midline curve. For the first The intersection of a cross-sectional plane with the voxels of the root mask is a three-dimensional point set, the value range of which is a subset of the root mask, and the unit is mm (coordinates of each point). It is obtained by the geometric intersection operation of the cross-sectional plane and the root mask and is used as a sample for centroid calculation. The number of voxels in the intersection is a positive integer scalar, dimensionless, obtained by counting the voxels in the intersection, and used as the normalized denominator for centroid calculation; The root mask is a three-dimensional binary voxel set, dimensionless, obtained from the multi-label synchronous segmentation output of step S1. The centroid set of the cross-section... The parameterized curve of the root midline was obtained by performing least-squares curve fitting using cubic B-spline basis functions. :

[0027] ,

[0028] ,in: The cubic B-spline parameterized curve of the root midline is a three-dimensional vector value function. Its value range is determined by the root mask space range and the unit is mm. It is calculated by least square fitting of the centroid point set of the cross section using this formula and serves as the reference curve for subsequent tangential direction calculation and establishment of the cylindrical coordinate system of the root surface. Let be the arc length parameter of the central axis of the tooth root, a non-negative real scalar, with a value range of . The unit is mm, which is obtained by the integral of the curve arc length and is used as a scalar coordinate for axial positioning along the central axis of the tooth root; Let be the total arc length of the central axis of the tooth root, a positive real scalar, with a typical value range of . mm (depending on tooth position type), the unit is mm, obtained by integral of curve arc length, and serves as the upper bound of the arc length parameter; For the cubic B-spline curve Each control point is a three-dimensional column vector, and its value range is determined by the spatial range of the tooth root mask. The unit is mm, and it is obtained by least squares fitting optimization solution, serving as the coefficient weights of the B-spline basis function. For the first There are cubic B-spline basis functions, which are scalar-valued functions with a range of values ​​of . , dimensionless, is calculated by the de Boor recursive formula according to the preset node vector, and serves as the mapping basis from the parameter space to the Euclidean space; The total number of B-spline control points minus 1 is a positive integer scalar with a range of values ​​of 1. , dimensionless, is determined by the curve complexity requirement, and serves as the upper limit for the enumeration of basis functions; The control points and basis function indices are integers, and their values ​​are... , dimensionless, serves as a summation pointer; For the first The estimated arc length parameter corresponding to the centroid of each cross section is a non-negative real scalar with a range of values. The unit is mm, which is obtained by normalizing the projection of the centroid point along the initial axial direction and serves as the sample point in the parameter space. This is the L2 norm operator, used to calculate the Euclidean length of a three-dimensional vector. The root midline is defined by the arc length parameter. The local tangential direction at the point is obtained by... Differentiating and normalizing, we get, denoted as .

[0029] Sub-step S2.2: Parameterization of the cylindrical coordinate system of the tooth root surface. In order to calculate the directional gradient tensor field along the tangential direction of the tooth root mask surface, the tooth root mask surface is parameterized into a cylindrical coordinate system of the tooth root surface with the tooth root central axis as the axis. The cylindrical coordinate system of the tooth root surface includes axial coordinates and circumferential coordinates.

[0030] For any voxel point on the surface of the root mask First, solve for the arc length parameter corresponding to the nearest projection point on the central axis of the tooth root:

[0031] ,in: voxel point The nearest projected arc length parameter on the central axis of the tooth root is a non-negative real scalar, and its value range is... The unit is mm, which is obtained by minimizing the Euclidean distance using this formula and is used as the axial coordinate of the voxel point; the definitions of other symbols are the same as in the aforementioned sub-step S2.1.

[0032] Then construct voxel points The radial offset vector relative to the central axis of the tooth root and the cylindrical coordinates as follows:

[0033] ,

[0034] ,

[0035] in: voxel point The radial offset vector relative to the central axis of the tooth root is a three-dimensional column vector, and its value range is determined by the distance from the surface of the tooth root mask to the central axis, in mm. This formula will... The orthogonal residual, calculated after deducting its axial component, serves as the geometric basis for the circumferential and radial coordinates of the cylindrical coordinate system. voxel point The axial coordinate in the cylindrical coordinate system of the tooth root surface is a non-negative real scalar, and its value range is... The unit is mm. The assignment yields axial positioning, which is one of the tangential directions; voxel point The radial distance relative to the central axis of the tooth root is a positive real scalar, and its typical range is as follows: mm (root radius), in mm, is calculated from the L2 norm of the radial offset vector and is used as the radial distance in cylindrical coordinates; voxel point The circumferential coordinates in the cylindrical coordinate system of the tooth root surface are real scalars, with a range of values. The unit is rad, and it is derived from the arctangent function of two parameters. The circumferential positioning is calculated based on a local orthogonal coordinate base and is used as one of the tangential directions. and For the arc length Place and Two orthogonal local basis vectors are three-dimensional unit column vectors with values ​​ranging from the unit sphere and dimensionless. They are pre-constructed at each arc length position by Gram-Schmidt orthogonalization and kept to change smoothly along the arc length, serving as local orthogonal bases. The central axis of the tooth root in the arc length The local tangential direction at the location is defined in the same way as in the aforementioned sub-step S2.1.

[0036] Sub-step S2.3: Tangential gradient vector calculation and four-direction projection. In the cylindrical coordinate system of the tooth root surface, calculate the Hounsfield unit spatial partial derivative along the axial and circumferential coordinate directions respectively, and combine the spatial partial derivatives to obtain the tangential gradient vector. Project the tangential gradient vector along the four anatomical orientations to obtain the four-direction tangential gradient components.

[0037] Specifically, the continuous field characterizing the Hounsfield unit spatial distribution in the cone-beam CT volume data. (i.e., the HU value of each voxel), calculate the tangential gradient vector in the cylindrical coordinate system of the tooth root surface:

[0038] ,in: voxel point The Hounsfield unit gradient vector along the tangential direction of the root mask surface is a three-dimensional column vector. Its value range is determined by the spatial gradient magnitude and direction of the HU value. The unit is HU / mm. It is calculated by this formula according to the linear combination of the spatial partial derivatives and represents the spatial rate of change and direction of the HU value in the tangential direction. For the cone-beam CT volume data at voxel points The Hounsfield unit grayscale value at that location is a real scalar, and its typical range is... (Air to enamel HU range), in HU, is directly read from the cone-beam CT volume data and used as a scalar field for gradient calculation; for Along the axial coordinate The spatial partial derivative, a real scalar, has a range determined by the axial rate of change of the HU value, and its unit is HU / mm. It is derived from the numerical differential of the central difference according to... The calculated value represents the rate of change of the HU value along the axial direction. for Along the circumferential coordinates The spatial partial derivative of HU is a real scalar, whose range is determined by the circumferential rate of change of HU, and its unit is HU / rad. It is calculated by the central difference numerical differential and characterizes the rate of change of HU along the circumferential direction. For the arc length With circumferential angle The local circumferential unit vector at a given location is a three-dimensional unit column vector, taking values ​​within the unit sphere, and is dimensionless. The calculated value serves as the direction basis for the circumferential gradient. The axial center difference step size is a positive real scalar, preferably 1 to 2 times the voxel resolution, i.e., 0.4 mm, in mm, and is preset by the user, serving as the step size for numerical differentiation. Then, the tangential gradient vector is projected along the four anatomical orientations to obtain the four-directional tangential gradient components:

[0039] ,in: voxel point The tangential gradient vector at the location along the first... The directional component of the anatomical orientation is a real scalar quantity. Its value range is determined by the tangential gradient amplitude, and its unit is HU / mm. It is calculated by this formula using inner product operation and is used as a scalar quantification of the rate of change of HU value in the four anatomical orientations. voxel point First The unit direction vector of the anatomical orientation is a three-dimensional unit column vector, with a value range of a unit sphere, dimensionless, and derived from the four anatomical orientations and the root midline at a voxel point. The local coordinate system geometry at a given location is pre-constructed and serves as the orientation basis for the four-directional projection. For the direction index enumeration variable, the values ​​can be... These correspond to the buccal, lingual, mesial, and distal orientations, respectively, and are dimensionless, serving as pointers for enumeration in four directions. This is the vector dot product operator, which calculates the inner product of two three-dimensional vectors.

[0040] Sub-step S2.4: Calculation of the directional gradient anisotropy index. The directional gradient anisotropy index is calculated according to the following steps: construct a structure tensor matrix with the tangential gradient vector as the column vector, perform eigenvalue decomposition on the structure tensor matrix to obtain three eigenvalues, and the directional gradient anisotropy index is the difference between the largest and smallest eigenvalues ​​divided by the sum of the three eigenvalues.

[0041] Specifically, at voxel points Surrounded by a preset neighborhood window (Preferably a spherical neighborhood with a radius of 3 to 5 voxels) Aggregate the tangential gradient vectors to construct the structure tensor matrix:

[0042] .

[0043] .in: voxel point The structure tensor matrix at that location is The symmetric positive semi-definite matrix has a range of values ​​with non-negative diagonal elements and a unit of (HU / mm)². It is calculated by the formula using the weighted outer product of the tangential gradient vectors in the neighborhood and serves as the quantification basis for the anisotropy of the directional gradient. voxel point The surrounding preset neighborhood is a set of three-dimensional points, with values ​​ranging from voxels. The surrounding spherical neighborhood, in mm (coordinates of each point within the neighborhood), is obtained from the preset neighborhood radius and serves as the range for weighted aggregation. For the neighborhood The neighboring voxels within the range are three-dimensional column vectors in mm, obtained by neighborhood enumeration and used as pointers for summation and traversal. The weights are Gaussian weighted, and the values ​​are positive real scalars, with a range of values. , dimensionless, is calculated by this formula using the Gaussian function of Euclidean distance, and is used as a distance decay weight for the gradient vector in the neighborhood; is the standard deviation of the Gaussian weights, a positive real scalar, typically ranging from 1 to 2 times the voxel resolution, i.e., 0.4 mm, in mm, and is preset by the user as the scale parameter for the Gaussian weights.

[0044] Performing eigenvalue decomposition on the structure tensor matrix yields three eigenvalues ​​and their corresponding eigenvectors:

[0045] .in: The first element of the structure tensor matrix The eigenvalues ​​are arranged in descending order and denoted as the largest eigenvalue. intermediate eigenvalues Minimum eigenvalue , is a non-negative real scalar, with a range of values. The unit is (HU / mm)², calculated by the eigenvalue decomposition algorithm, representing the tangential gradient vector at the th kJ / mm². The magnitude of energy along each principal axis; The first element of the structure tensor matrix Each eigenvector is a three-dimensional unit column vector, taking values ​​within the unit sphere, dimensionless, and calculated by the eigenvalue decomposition algorithm, satisfying the following conditions. , as the tangential gradient vector Geometric direction indicator for the main axis direction; other symbols are defined as before.

[0046] Then, the anisotropy index of the directional gradient is calculated:

[0047] .in: voxel point The anisotropy exponent of the directional gradient at a given location is a real scalar with a range of values. The dimensionless eigenvalue is calculated by dividing the difference between the largest and smallest eigenvalues ​​of the structure tensor by the sum of the three eigenvalues. It represents the degree of anisotropy in the tangential gradient vector direction, with 0 indicating complete isotropy and 1 indicating complete anisotropy; other symbols are defined as before. The largest eigenvalue of the structure tensor matrix is... Corresponding feature vector As the main direction of anisotropy The directional gradient anisotropy index and the principal anisotropy direction constitute the core features of the directional gradient tensor field, providing quantization driving signals for the subsequent morphological classification in step S3 and the closed-loop refinement of the weights in step S6.

[0048] Step S3: Three-dimensional quantitative analysis and morphological classification. Step S3 integrates the cementoenamel boundary marker, the alveolar ridge crest marker, and the directional gradient anisotropy index, and outputs the three-dimensional distance from the cementoenamel boundary to the alveolar ridge crest in four directions, bone resorption morphology classification labels, and bone density Hounsfield distribution bone quality index for each tooth position. The directional gradient anisotropy index is used to trigger the boundary closure iteration refinement of the alveolar bone mask.

[0049] Sub-step S3.1: Four-directional three-dimensional distance calculation. For each tooth position, calculate the cementoenamel boundary marker. Alveolar crest landmarks corresponding to the buccal, lingual, mesial, and distal directions. Calculate the three-dimensional distance from the cementoenamel junction to the alveolar ridge crest in the four directions:

[0050] ,in For the first The three-dimensional Euclidean distance from the cementoenamel junction to the alveolar ridge crest in anatomical orientation, in mm, with a typical range of values. mm, with values ​​less than 2 mm under normal periodontal conditions, and values ​​for mild bone resorption. mm, with a value greater than 4 mm for moderate to severe bone resorption; , , The definitions are the same as before. The three-dimensional distances from the cementoenamel junction to the alveolar ridge crest in the four directions are used as scalar quantitative outputs of the bone resorption height in each direction.

[0051] Sub-step S3.2: Bone resorption morphology classification. The bone resorption morphology classification label is determined according to the joint rule of the directional gradient anisotropy index and the principal anisotropy direction. When the directional gradient anisotropy index is greater than a preset vertical threshold, the bone resorption morphology classification label is vertical bone resorption; when the directional gradient anisotropy index is less than a preset horizontal threshold, the bone resorption morphology classification label is horizontal bone resorption; otherwise, the bone resorption morphology classification label is mixed bone resorption.

[0052] Specifically, the tooth position-level directional gradient anisotropy index is defined. The anisotropy index of the directional gradient at all voxel points on the root mask surface of this tooth position is the arithmetic mean, and the principal direction of anisotropy at the tooth position level is defined. This refers to the principal component weighted average direction of the anisotropy principal directions at all voxel points on the root mask surface of this tooth position. The anisotropy index of the directional gradient at the tooth position level is greater than a preset verticality threshold. (The value is preferably 0.6) and when the angle between the principal direction of anisotropy at the tooth position level and the axial direction of the root midline is less than a preset axial angle threshold (preferably 30°), the bone resorption morphology classification label is vertical bone resorption; when the anisotropy index at the tooth position level is less than a preset horizontal threshold... When the value is preferably 0.3, the bone resorption morphology classification label is horizontal bone resorption; otherwise, the bone resorption morphology classification label is mixed bone resorption. The preset vertical threshold is 0.6, and the preset horizontal threshold is 0.3. The values ​​of the two thresholds are based on the inventors' statistical analysis of 500 clinical samples. The 0.6 threshold can cover typical vertical bone resorption cases while maintaining more than 90% specificity, and the 0.3 threshold can distinguish between horizontal and mixed cases.

[0053] Sub-step S3.3: Hounsfield distribution bone quality index. For each tooth position, the mean and standard deviation of the Hounsfield unit gray value are statistically analyzed within the adjacent region (preferably a spherical neighborhood with a radius of 5 mm) of the alveolar bone mask. The Hounsfield distribution bone quality index is defined as follows:

[0054] ,in This refers to the Hounsfield distribution of bone mineral density, a dimensionless bone quality index with a typical range of values. A higher value indicates that the bone density is closer to the reference value for healthy bone and that the distribution is more concentrated. The arithmetic mean of Hounsfield units within the alveolar bone mask adjacent to the tooth position, in HU; The standard deviation of Hounsfield units within the alveolar bone mask adjacent to the tooth position, in HU; The Hounsfield unit value for healthy alveolar bone is preferred, with 800 HU being the unit. This index, together with the four-dimensional distances and the bone resorption morphology classification labels, constitutes the three-dimensional quantitative assessment output ternary set for this tooth position.

[0055] Sub-step S3.4: The anisotropic gradient index triggers a closed-loop iterative refinement of the segmentation boundary. To eliminate the transitive bias of the anisotropic gradient index on the alveolar bone mask boundary error of the multi-label synchronous segmentation, this embodiment triggers the iterative refinement of the alveolar bone mask boundary through the anisotropic gradient index. This closed-loop feedback mechanism is one of the core innovations of this invention. Its working principle is as follows: the boundary error of the alveolar bone mask will cause the calculation deviation of the tangential gradient vector near the boundary, which in turn causes the anisotropic gradient index to deviate from the anisotropic principal direction; this deviation is fed back as a reverse gradient signal to the decoder side of the encoder-decoder segmentation network, triggering the alveolar bone mask boundary to converge iteratively to the real anatomical boundary, so that segmentation and quantization converge collaboratively in the iteration rather than accumulating errors on their own.

[0056] Specifically, the partial derivative of the tangential gradient vector along the axial direction of the root midline. Threshold detection is performed to identify regions of continuous gradient abrupt changes. These regions are then used as boundary prior masks and input back into the decoder side of the multi-label synchronous segmentation. The boundary prior mask is constructed according to the following rules:

[0057] ,in: voxel point The boundary prior mask value at the location is a binary scalar, taking values ​​of... , dimensionless, is obtained by this formula according to the indicator function. 0 indicates that the voxel point does not belong to the boundary prior region, and 1 indicates that the voxel point belongs to the boundary prior region. It is used as the boundary prior signal for the reverse input decoder. This is an indicator function operator. It returns 1 if the logical expression inside the parentheses is true, and 0 otherwise. It is dimensionless. voxel point First The second partial derivative of the tangential gradient component along the axial coordinate in the anatomical orientation (i.e., the spatial rate of change of the tangential gradient) is a real scalar, its range determined by the second rate of change of the HU field, and its unit is HU / mm². Along the axial coordinate The value obtained by taking the numerical differential again represents the spatial rate of change of the tangential gradient along the axial direction. The value of this quantity is larger at the bone boundary. The preset gradient mutation threshold is a positive real scalar, with a preferred value of 300 HU / mm². The unit is HU / mm², which was obtained by the inventors from statistical analysis of 500 clinical samples. A value that is too large will miss the detection of fine bone boundaries, while a value that is too small will introduce noise response. The preset anisotropy threshold is a positive real scalar, preferably 0.4, dimensionless, obtained from clinical statistical analysis, and serves as the boundary prior gating of the anisotropy index. Definitions are the same as before; The definitions are the same as before. The boundary prior mask is input in reverse to the decoder side of the multi-label synchronous segmentation, serving as a new boundary supervision signal to guide the decoder to perform iterative refinement of the boundary of the alveolar bone mask. Specifically, in the first... In the next iteration, the refinement loss function is defined as a weighted sum of the splitting principal loss and the boundary prior loss:

[0058] ,

[0059] ,in: For the first The total loss value of the next iteration of the refinement process is a non-negative real scalar with a range of values. The dimensionless loss value is calculated by weighted summation of the principal loss and the boundary prior loss in this formula, and serves as the optimization objective driving the boundary refinement of the decoder. The Dice loss function is used for segmentation, where is a non-negative real scalar with a range of values. Dimensionless, derived from Dice coefficients according to The calculated value is used as the main loss term for segmentation. To segment the ground truth labels, we have a three-dimensional binary tensor, which is dimensionless and obtained from the labeled training data. It serves as the supervised ground truth for the main segmentation loss. For the first In the next iteration, the predicted segmentation mask output by the encoder-decoder segmentation network (containing the probability distributions of three types of tissues: alveolar bone mask, root mask, and periodontal ligament space mask) is a three-dimensional multi-channel tensor with values ​​ranging from [value range missing]. , dimensionless, is calculated by the decoder using the softmax activation function and is used as the prediction output; The boundary prior loss weight is a positive real scalar, preferably 0.3, dimensionless, and is preset by the user. It serves as a tradeoff coefficient between the main loss and the boundary prior loss. The boundary prior loss is a non-negative real scalar with a range of values. , dimensionless, is calculated by this formula based on the mean square error between the predicted gradient direction and the anisotropic principal direction within the boundary prior mask region, and is used as the loss term fed back to the segmentation decoder for directional anisotropy. for The labeled voxel set is a three-dimensional point set, with values ​​ranging from a subset within the cone-beam CT volume data space, in mm (coordinates of each point). It is obtained from the non-zero value index of the boundary prior mask and serves as the summation range for the boundary prior loss. The number of voxels in the point set is a positive integer scalar, dimensionless, obtained by counting the voxels in the point set, and used as the denominator for summation and normalization. For the first During the next iteration, the alveolar bone mask is at the voxel point. The predicted gradient vector at point is a three-dimensional column vector, with units of mm. -1 The gradient direction at the predicted segmentation boundary is obtained by performing the Sobel operator or central difference on the predicted probability distribution of the alveolar bone mask. The definition is the same as that of sub-step S2.4 mentioned above; This is the gradient operator.

[0060] The iterative refinement process stops when the magnitude of the change in the anisotropy of the gradient in the direction between the two rounds is less than a preset convergence threshold.

[0061] ,in: For the first At the next iteration, the tooth position-level directional gradient anisotropy exponent is a real scalar, with a value range of [value missing]. , dimensionless, is calculated by the arithmetic mean of the anisotropy index of the directional gradient at all voxel points on the surface of the root mask of the tooth position, and is used as the state variable for the convergence criterion. The preset convergence threshold is a positive real scalar, preferably 0.01, dimensionless, and preset by the user. A value that is too large will prematurely stop the refinement process, while a value that is too small will increase computational overhead. This value has shown stable convergence within 3 to 5 iterations on 500 clinical samples. The absolute difference on the left is dimensionless, and the right side... Dimensionless, with consistent dimensions. After each refinement iteration, the updated alveolar bone mask is re-input into sub-steps S2.3 to S2.4 to calculate the updated directional gradient anisotropy index, triggering the next round of refinement in a loop until the convergence criterion is met.

[0062] The three types of parameters in sub-steps S3.1 to S3.3—the four-directional cementoenamel boundary to alveolar ridge three-dimensional distance, the bone resorption morphology classification label, and the bone density Hounsfield distribution bone quality index—are recalculated on the converged alveolar bone mask and directional gradient tensor field, and used as the final three-dimensional quantitative assessment output for this tooth position.

[0063] Step S4: Longitudinal registration and rate of change tracking. Step S4 performs three-dimensional registration on the alveolar bone mask of the cone-beam CT data from the series of follow-up examinations, using the root mask as an invariant feature, and outputs the rate of change of the three-dimensional parameters of bone resorption.

[0064] During the periodontitis treatment cycle, a series of follow-up cone-beam computed tomography (CBCT) data needs to be compared under a unified anatomical coordinate system to accurately quantify the longitudinal changes in the three-dimensional parameters of bone resorption. This embodiment uses the three-dimensional morphology of the tooth root mask as the registration-invariant feature because: the three-dimensional morphology of the tooth root remains anatomically stable throughout the periodontitis treatment cycle (even after complete non-surgical and surgical treatments), with only slight root resorption occurring in a very few severe cases; while the alveolar bone morphology is precisely the target change to be tracked during treatment and cannot be used as a registration benchmark; although skull bony landmarks (such as the skull base and nasal root) are anatomically stable, the CBCT scanning field of view usually does not cover the entire skull, and differences in head position scanning can introduce spurious registration errors. Therefore, choosing the three-dimensional morphology of the tooth root as the registration-invariant feature is the optimal solution that balances stability and scanning field constraints.

[0065] Specifically, the three-dimensional morphological point cloud of the root mask was extracted from the cone-beam CT data of the initial and follow-up visits. The iterative nearest-point algorithm is used to solve the rigid body transformation matrix between the first and second visits by applying the three-dimensional morphological point cloud data.

[0066] ,in To obtain the optimal three-dimensional rotation matrix ( An orthogonal matrix with a determinant of 1. To obtain the optimal three-dimensional translation vector (in mm). This is an operator for finding the nearest neighbor point in the three-dimensional point cloud of the root morphology of the first-visit tooth. The rigid body transformation matrix is ​​denoted as... , which is a standard 4×4 homogeneous transformation matrix. This rigid body transformation matrix maps the data space of the follow-up visit to the data space of the first visit, so that the root masks of the first and follow-up visits are spatially aligned in a unified anatomical coordinate system.

[0067] The rigid body transformation matrix is ​​applied to the alveolar bone mask during the follow-up examination to obtain an alveolar bone mask spatially aligned between the initial and follow-up examinations. Then, steps S2 and S3 are repeated for each tooth to obtain the three-dimensional distance from the cementoenamel junction to the alveolar ridge crest in each of the four directions for both the initial and follow-up examinations. The bone resorption morphology classification label and the bone mineral density Hounsfield distribution bone quality index are used. The rate of change of the three-dimensional parameters of bone resorption is defined as:

[0068] ,in For the first The absolute change in distance from the cementoenamel junction to the alveolar ridge crest during the period from the first visit to the follow-up visit in terms of anatomical orientation, in mm; For the first The rate of change in anatomical orientation from the first visit to the follow-up visit, expressed in mm / month or mm / year (depending on the clinical follow-up period). The time interval between the follow-up visit and the initial visit, in months or years. The rate of change of the three-dimensional parameters of bone resorption. As an objective quantitative indicator for longitudinal evaluation of the treatment effect of periodontitis, a positive value indicates that bone resorption in that location continues to progress, a negative value indicates bone regeneration or healing, and a zero value indicates that bone resorption is stable.

[0069] This embodiment provides a three-dimensional quantitative assessment system for cone-beam CT bone resorption images in periodontitis. (See also...) Figure 2 The system comprises four core modules: a multi-label synchronous segmentation module, a directional gradient tensor field calculation module, a three-dimensional quantitative analysis and morphological classification module, and a longitudinal registration and rate of change tracking module. Deployed on a clinical workstation or hospital imaging center server, the system takes DICOM files of cone-beam CT volume data as input and outputs a three-dimensional quantitative assessment report of periodontitis.

[0070] The multi-label synchronous segmentation module is configured to perform multi-label synchronous segmentation on cone-beam CT volume data to obtain alveolar bone masks, root masks, and periodontal ligament space masks. Based on the three-dimensional interface between the root masks and the periodontal ligament space masks, anatomical landmarks are automatically located to obtain cementoenamel boundary landmarks and alveolar ridge crest landmarks. The specific implementation method is the same as step S1 in the method embodiment. This module further includes a data preprocessing submodule, a three-dimensional fully convolutional encoding-decoding segmentation submodule, and an anatomical landmark localization submodule. The data preprocessing submodule is responsible for DICOM format parsing, spatial coordinate system normalization, and Hounsfield unit grayscale value linear normalization. The three-dimensional fully convolutional encoding-decoding segmentation submodule deploys the encoding-decoding segmentation network, loads pre-trained model weights, and performs forward inference on the preprocessed cone-beam CT volume data, outputting voxel-level probability distributions of the three types of tissues. The anatomical landmark localization submodule applies a landmark detection network based on heat map regression to the three-dimensional interface between the root mask and the periodontal ligament space mask, and outputs the coordinates of the cementoenamel boundary landmark for each tooth position and the coordinates of four alveolar crest landmarks, one each from the buccal and lingual mesial and distal sides.

[0071] The directional gradient tensor field calculation module is configured to calculate the Hounsfield unit directional gradient tensor field along the four anatomical orientations of the root mask to obtain the directional gradient anisotropy index. The four anatomical orientations include buccal, lingual, mesial, and distal orientations. The specific implementation method is the same as step S2 in the method embodiment. This module further includes a root midline extraction submodule, a root surface cylindrical coordinate system parameterization submodule, a tangential gradient vector calculation submodule, and a structural tensor decomposition submodule. The root midline extraction submodule performs multi-view principal component axial fitting on the root mask to obtain the root midline. The root surface cylindrical coordinate system parameterization submodule parameterizes the root mask surface into a root surface cylindrical coordinate system with the root midline as the axis, using the root midline as the cylindrical axis. The tangential gradient vector calculation submodule calculates the Hounsfield unit spatial partial derivative along the axial and circumferential coordinate directions of the cylindrical coordinate system on the root surface, respectively. It combines these spatial partial derivatives to obtain the tangential gradient vector and projects it along the four anatomical orientations to obtain the four-directional tangential gradient components. The structural tensor decomposition submodule constructs a structural tensor matrix using the tangential gradient vector as column vectors. It then performs eigenvalue decomposition on the structural tensor matrix to obtain the anisotropic index of the directional gradient and the principal anisotropic directions.

[0072] The three-dimensional quantitative analysis and morphological classification module is configured to integrate the cementoenamel boundary marker, the alveolar ridge crest marker, and the directional gradient anisotropy index, and output the three-dimensional distance from the cementoenamel boundary to the alveolar ridge crest in four directions, the bone resorption morphological classification label, and the Hounsfield distribution bone quality index for each tooth position. The specific implementation method is the same as step S3 in the method embodiment. This module further includes a three-dimensional distance calculation submodule, a morphological classification submodule, a bone quality index calculation submodule, and a closed-loop refinement feedback submodule. The three-dimensional distance calculation submodule calculates the three-dimensional distance from the cementoenamel boundary to the alveolar ridge crest in four directions for each tooth position, based on the cementoenamel boundary marker and the corresponding alveolar ridge crest marker in the buccal, lingual, mesial, and distal directions. The morphological classification submodule determines the bone resorption morphological classification label based on the directional gradient anisotropy index and the principal anisotropy direction according to preset vertical and horizontal threshold rules. The bone quality index calculation submodule calculates the mean and standard deviation of the Hounsfield unit gray values ​​for the alveolar bone mask in the vicinity of each tooth position and calculates the Hounsfield distribution bone quality index. The closed-loop refinement feedback submodule constructs a boundary prior mask based on the directional gradient anisotropy index and the principal anisotropic direction. This boundary prior mask is then input back into the decoder side of the multi-label synchronous segmentation module to trigger iterative refinement of the alveolar bone mask's boundary. Iteration stops after the convergence criterion is met. This closed-loop refinement feedback submodule is the core coupling point for the coordinated convergence of the multi-label synchronous segmentation module, the directional gradient tensor field calculation module, and the three-dimensional quantitative analysis and morphological classification module, ensuring that segmentation and quantization converge collaboratively during iteration rather than accumulating errors independently.

[0073] The longitudinal registration and rate of change tracking module is configured to perform three-dimensional registration on the alveolar bone mask of the cone-beam CT data from the series of follow-up visits, using the root mask as an invariant feature, and output the rate of change of the three-dimensional parameters of bone resorption. The specific implementation method is the same as step S4 in the method embodiment. This module further includes a root three-dimensional morphology point cloud extraction submodule, an iterative nearest point registration submodule, and a rate of change calculation submodule. The root three-dimensional morphology point cloud extraction submodule performs three-dimensional morphology point cloud extraction on the root mask in the cone-beam CT data from the initial and follow-up visits, outputting the root three-dimensional morphology point clouds from the initial and follow-up visits. The iterative nearest point registration submodule performs an iterative nearest point algorithm on the three-dimensional morphology point clouds from the initial and follow-up visits to solve the rigid body transformation matrix between the initial and follow-up visits, and applies the rigid body transformation matrix to the alveolar bone mask from the follow-up visits to obtain an alveolar bone mask spatially aligned between the initial and follow-up visits. The rate of change calculation submodule calculates the three-dimensional distance from the cementoenamel junction to the alveolar ridge crest in the four directions for each tooth position by repeating the gradient tensor field calculation module and the three-dimensional quantitative analysis and morphological classification module. Then, it calculates the rate of change of the three-dimensional parameters of bone resorption as an objective quantitative indicator for the longitudinal evaluation of the treatment effect of periodontitis.

[0074] The four core modules of this system work together in a closed loop through deep coupling. The outputs of the multi-label synchronous segmentation module (alveolar bone mask, root mask, periodontal ligament space mask, cementoenamel boundary marker, alveolar ridge marker) serve as key inputs to the directional gradient tensor field calculation module. The outputs of the directional gradient tensor field calculation module (directional gradient anisotropy index, principal anisotropy direction, and four-directional tangential gradient components) serve as key inputs to the 3D quantitative analysis and morphological classification module. The 3D quantitative analysis and morphological classification module generates a boundary prior mask through a closed-loop refinement feedback submodule, which is then input back to the decoder side of the multi-label synchronous segmentation module to trigger iterative refinement of the alveolar bone mask boundary. This creates a closed-loop feedback collaboration for initial assessment among the multi-label synchronous segmentation module, the directional gradient tensor field calculation module, and the 3D quantitative analysis and morphological classification module. The longitudinal registration and rate of change tracking module uses the root mask output by the multi-label synchronous segmentation module as an invariant feature to perform 3D registration on a series of follow-up data, extending the initial assessment closed loop to a longitudinal tracking closed loop, achieving a dual improvement in single assessment accuracy and longitudinal tracking accuracy. This deeply coupled closed-loop collaborative working mechanism is the core architectural innovation of this system compared to existing technologies.

[0075] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A three-dimensional quantitative assessment method for bone resorption images in periodontitis using cone-beam CT, characterized in that, Includes the following steps: S1, Data acquisition and multi-label synchronous segmentation: Perform multi-label synchronous segmentation on cone-beam CT data to obtain alveolar bone mask, root mask and periodontal ligament space mask, and perform automatic localization of anatomical landmarks based on the three-dimensional interface between the root mask and the periodontal ligament space mask to obtain cementoenamel boundary landmark and alveolar crest landmark. S2, Calculation of directional gradient tensor field: Calculate the Hounsfield unit directional gradient tensor field along the four anatomical orientations of the root mask, and output the directional gradient anisotropy index. The four anatomical orientations include buccal orientation, lingual orientation, mesial orientation, and distal orientation. S3, Three-dimensional quantitative analysis and morphological classification: Integrating the cementoenamel boundary marker, the alveolar ridge crest marker, and the directional gradient anisotropy index, the three-dimensional distance from the cementoenamel boundary to the alveolar ridge crest in four directions, bone resorption morphological classification labels, and bone density Hounsfield distribution bone quality index are output for each tooth position. S4, Longitudinal Registration and Rate of Change Tracking: Perform three-dimensional registration on the alveolar bone mask of the cone-beam CT body data of the series of follow-up visits with the root mask as an invariant feature, and output the rate of change of the three-dimensional parameters of bone resorption.

2. The method for three-dimensional quantitative assessment of periodontal disease using cone-beam CT bone resorption images according to claim 1, characterized in that, The four anatomical orientations are established using the root midline of the tooth corresponding to the root mask as a reference to establish a local anatomical coordinate system: the buccal orientation is the anatomical orientation ray pointing from the root midline to the buccal mucosa, the lingual orientation is the anatomical orientation ray pointing from the root midline to the lingual mucosa, the mesial orientation is the anatomical orientation ray pointing from the root midline to the adjacent middle tooth position, and the distal orientation is the anatomical orientation ray pointing from the root midline to the adjacent distal tooth position; the directional gradient anisotropy index characterizes the degree of directional non-uniformity of the Hounsfield unit spatial distribution among the four anatomical orientations, and when the directional gradient anisotropy index is greater than a preset anisotropy threshold, it is determined that the tooth position has undergone directional anisotropic bone resorption.

3. The three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis according to claim 2, characterized in that, The directional gradient tensor field is calculated along the tangential direction of the root mask surface: the root mask surface is parameterized into a cylindrical coordinate system with the root midline as the axis, the cylindrical coordinate system including axial and circumferential coordinates; Hounsfield unit spatial partial derivatives are calculated along the axial and circumferential coordinate directions of the cylindrical coordinate system, and the spatial partial derivatives are combined to obtain the tangential gradient vector; the tangential gradient vector is projected along the four anatomical orientations to obtain the four-directional tangential gradient components.

4. The three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis according to claim 3, characterized in that, The root midline is extracted by performing multi-view principal component axial fitting on the root mask: principal component analysis is performed on the voxel coordinate point set of the root mask to obtain three principal axis directions, and the principal axis with the largest cumulative variance contribution rate is selected as the initial axis. With the initial axial direction as a reference, least squares curve fitting is performed on the centroid point set of the cross sections of the root mask along multiple cross sections perpendicular to the initial axial direction to obtain the root midline. The root midline is introduced into the curved shape prior of the root mask, which reduces the axial deviation at the root curvature compared to a single principal component axial direction.

5. The three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis according to claim 4, characterized in that, The directional gradient anisotropy index is calculated according to the following steps: construct a structure tensor matrix with the tangential gradient vector as the column vector, perform eigenvalue decomposition on the structure tensor matrix to obtain three eigenvalues, and the three eigenvalues ​​are arranged in descending order and denoted as the maximum eigenvalue, the middle eigenvalue, and the minimum eigenvalue. The directional gradient anisotropy index is the difference between the largest and smallest eigenvalues ​​divided by the sum of the three eigenvalues, and the directional gradient anisotropy index ranges from 0 to 1; the eigenvector corresponding to the largest eigenvalue of the structural tensor matrix serves as the principal anisotropy direction, indicating the principal direction of bone resorption.

6. The three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis according to claim 5, characterized in that, In the multi-label synchronous segmentation, the boundary refinement of the alveolar bone mask is achieved through reverse iteration of the directional gradient anisotropy index: when the tangential gradient vector exhibits a continuous gradient abrupt change region along the axial direction of the root midline and the directional gradient anisotropy index is greater than a preset anisotropy threshold, the continuous gradient abrupt change region is used as a boundary prior mask and input back into the decoder side of the multi-label synchronous segmentation, triggering the decoder to perform iterative refinement of the boundary of the alveolar bone mask; the iterative refinement of the boundary prior mask stops when the change amplitude of the directional gradient anisotropy index in the two rounds is less than a preset convergence threshold.

7. The method for three-dimensional quantitative assessment of periodontal disease bone resorption images using cone-beam CT according to claim 1, characterized in that, The multi-label synchronous segmentation is performed using a three-dimensional fully convolutional encoder-decoder segmentation network: the encoder part of the encoder-decoder segmentation network extracts multi-scale voxel features of the cone-beam CT volume data through four-level three-dimensional convolutional downsampling; the decoder part of the encoder-decoder segmentation network restores the original resolution of the volume data through corresponding four-level three-dimensional transposed convolutional upsampling; the encoder part and the decoder part transmit shallow detail voxel features through skip connections; the output layer of the encoder-decoder segmentation network synchronously outputs the voxel-level probability distributions of the alveolar bone mask, the root mask, and the periodontal ligament space mask through a softmax activation function.

8. The three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis according to claim 1, characterized in that, The bone resorption morphology classification label is determined according to the following rules: when the directional gradient anisotropy index is greater than a preset vertical threshold, the bone resorption morphology classification label is vertical bone resorption; when the directional gradient anisotropy index is less than a preset horizontal threshold, the bone resorption morphology classification label is horizontal bone resorption; in other cases, the bone resorption morphology classification label is mixed bone resorption; the preset vertical threshold is 0.6, and the preset horizontal threshold is 0.

3.

9. The three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis according to claim 1, characterized in that, The three-dimensional registration between the cone-beam CT data from the series of follow-up examinations uses the three-dimensional morphology of the root mask as a registration-invariant feature: The three-dimensional morphological point cloud of the root mask is extracted from the cone-beam CT volume data of the first visit and the follow-up visit, respectively. The iterative nearest point algorithm is performed on the three-dimensional morphological point cloud of the first visit and the follow-up visit to solve the rigid body transformation matrix between the first visit and the follow-up visit. The rigid body transformation matrix is ​​applied to the alveolar bone mask of the follow-up visit to obtain the alveolar bone mask that is spatially aligned between the first visit and the follow-up visit, and then the change rate of the three-dimensional parameters of bone resorption is calculated.

10. A three-dimensional quantitative assessment system for cone-beam CT bone resorption images in periodontitis, used to implement the three-dimensional quantitative assessment method for cone-beam CT bone resorption images in periodontitis as described in any one of claims 1-9, characterized in that, include: The multi-label synchronous segmentation module is configured to perform multi-label synchronous segmentation on cone-beam CT data to obtain alveolar bone mask, root mask and periodontal ligament space mask, and automatically locate anatomical landmarks based on the three-dimensional interface between the root mask and the periodontal ligament space mask to obtain cementoenamel boundary landmark and alveolar crest landmark. The orientation gradient tensor field calculation module is configured to calculate the Hounsfield unit orientation gradient tensor field along the four anatomical orientations of the tooth root mask to obtain the orientation gradient anisotropy index. The four anatomical orientations include the buccal orientation, the lingual orientation, the mesial orientation, and the distal orientation. The three-dimensional quantitative analysis and morphological classification module is configured to integrate the cementoenamel boundary marker, the alveolar ridge crest marker, and the directional gradient anisotropy index, and output the three-dimensional distance from the cementoenamel boundary to the alveolar ridge crest in four directions, bone resorption morphology classification labels, and bone density Hounsfield distribution bone quality index for each tooth position. The longitudinal registration and rate of change tracking module is configured to perform three-dimensional registration of the alveolar bone mask of the cone-beam CT body data from a series of follow-up visits, with the root mask as an invariant feature, and output the rate of change of three-dimensional parameters of bone resorption.

Images