A method for fitting the basal bone contour of the jawbone in a population and predicting its changes.

Abstract

This invention relates to the fields of medical image analysis and dentistry, specifically to a method for fitting the basal bone contour of a population and predicting its changes. This method addresses the problem of existing technologies lacking automated algorithms for fitting basal bone contours and population variation prediction models. The method includes: acquiring CBCT images, determining the basal bone contour boundaries, and extracting the coordinates of landmark points; applying generalized Protodyakonov analysis for coordinate alignment and morphological normalization; setting a 2mm relative positional offset between the maxillary and mandibular basal bones; performing factor analysis to extract the main factors that explain the cumulative variation ratio exceeding a predetermined threshold; predicting variations in basal bone morphology based on principal component analysis; symmetricizing and smoothing the predicted contour; and generating a clinical reference document. This invention achieves automated fitting of the bimaxillary basal bone contours, extracts the main variation patterns, and ensures that the results conform to biological symmetry and continuity, providing a scientific basis for boundary determination and safety assessment of tooth movement in orthodontic treatment.

Description

Technical Field

[0001] This invention relates to the fields of medical image analysis and dentistry, specifically to a method for fitting and predicting changes in the basal bone contour of the jawbone based on cone-beam computed tomography (CBCT) images. This method can be applied to the determination of tooth movement boundaries and safety assessment in clinical dental treatment, providing personalized scientific reference for orthodontic treatment. Background Technology

[0002] The basal bone arch, as the supporting bone of the dental arch, shapes its shape and serves as the limiting boundary for tooth movement. The alveolar cortex plays a crucial role in orthodontic treatment; its location and thickness directly determine the range of safe tooth movement. In actual clinical practice, to minimize potential damage to the molar roots and alveolar bone, dentists need to clearly understand the morphology of the maxillary and mandibular basal bones, especially the morphology of the transverse region behind the molars.

[0003] Currently, cone-beam computed tomography (CBCT) is commonly used in clinical practice to obtain the morphology of the basal bone. However, this method has the following significant shortcomings: First, there is a lack of effective algorithms to automatically draw and fit the contour of the inner cortical bone of the basal bone, and doctors often need to draw it manually, which is time-consuming and highly subjective. Second, there is no model for predicting the variation of the bimaxillary basal bone contour in a population, which cannot provide a scientific population reference standard for individualized treatment. Finally, existing methods are difficult to standardize the relative position of the maxillary and mandibular basal bones, affecting the comparability of data between different individuals.

[0004] Therefore, there is an urgent need for a new data processing and prediction algorithm that can automatically fit the bimaxillary basal bone contour and extract the main variation patterns through statistical methods, thereby providing a safe and quantitative reference for personalized orthodontic treatment. Summary of the Invention

[0005] The purpose of this invention is to provide a method for fitting the contour of the jawbone basal bone of a population and predicting its changes. This method can automatically fit the average contour of the jawbone basal bone of a population based on the coordinates of key anatomical points in CBCT images, and use statistical methods to extract the main variation factors of the jawbone basal bone morphology, so as to achieve scientific prediction of the variation trend of the basal bone morphology of the population.

[0006] This invention proposes a method for fitting the basal bone contour of a human jaw and predicting its changes, comprising:

[0007] Acquire cone-beam computed tomography (CBCT) images, determine the basal bone contour boundaries, and extract the coordinates of basal bone landmarks;

[0008] Based on the coordinates of the basal bone landmarks, coordinate alignment and morphological normalization are performed using generalized Protodyakonov analysis.

[0009] A relative positional offset is set between the maxillary basal bone and the mandibular basal bone to achieve the fitting of the average bimaxillary contour of the population.

[0010] Factor analysis was performed on the fitting results to extract the main factors that explain the cumulative variance ratio exceeding a predetermined threshold;

[0011] Based on principal component analysis, variation prediction of the basal bone morphology of the jawbone is performed to generate a predicted contour.

[0012] The predicted contour is symmetricized and smoothed; and

[0013] Generate image and data files for clinical diagnosis and treatment planning reference.

[0014] Preferably, the process of acquiring cone-beam computed tomography (CBCT) images, determining the basal bone contour boundaries, and extracting the coordinates of basal bone landmarks includes:

[0015] Adjust the head position in the CBCT image so that the infraorbital plane is parallel to the ground plane and the mandibular occlusal plane is parallel to the ground plane;

[0016] The posterior basal bone of the mandibular molar is defined by the anterior border of the ramus, with the most distal point being the intersection of the mandibular occlusal plane and the anterior border of the ramus; and

[0017] On the plane passing through the bifurcation of the maxillary first molar root and the mandibular first molar root, mark the landmarks of the maxillary and mandibular basal bones, and obtain the coordinates of the landmarks of the maxillary and mandibular basal bones respectively.

[0018] Preferably, the maxillary basal bone landmarks include 80 points, and the mandibular basal bone landmarks include 72 points; wherein, the landmarks include buccal points in the retromolar region, buccal points for each tooth position, lingual points for each tooth position, and lingual points in the retromolar region.

[0019] Preferably, the coordinate alignment and shape normalization performed through generalized Protodyakonov analysis includes:

[0020] Calculate the initial average configuration for all samples;

[0021] Each sample is transformed by rotation, scaling, and translation to best match the average configuration;

[0022] Recalculate the average configuration of all samples after transformation; and

[0023] Repeat the aforementioned transformation and recalculation steps until the morphological differences no longer decrease significantly.

[0024] Preferably, the relative position offset between the maxillary abdominis and mandibular abdominis is set to 2 mm, and the maxillary abdominis as a whole is moved upward relative to the mandibular abdominis by 2 mm.

[0025] Preferably, the factor analysis of the fitting results includes:

[0026] Calculate the covariance matrix of the standardized coordinates;

[0027] Extract feature values ​​and feature vectors;

[0028] The number of major common factors is determined based on the magnitude of the eigenvalues;

[0029] Perform factor rotation to make the factor structure more interpretable; and

[0030] Calculate the score for each sample on each factor.

[0031] Preferably, the predetermined threshold is 50%, and the top three public factors that explain more than 50% of the cumulative variation are selected.

[0032] Preferably, the method for predicting variations in the basal bone morphology of the jawbone based on principal component analysis includes:

[0033] Principal component analysis was performed based on the factor score matrix to extract principal components;

[0034] Determine the average basal bone morphology of the population;

[0035] Calculate the standard deviation along each principal component direction; and

[0036] The predicted profile is generated by perturbing the average shape along the principal component direction with a multiple of the standard deviation.

[0037] Preferably, the symmetry and smoothing process for the predicted contour includes:

[0038] Construct a set of symmetric points by mirroring the image about the vertical axis;

[0039] The original point set and the mirror point set are spliced ​​together according to anatomical correspondence to form a symmetrical contour; and

[0040] The moving average method is used to calculate the average position of each point within the window range, resulting in a smoothed contour curve.

[0041] Preferably, the generation of image files and data files for clinical diagnosis and treatment planning reference includes:

[0042] Generate an average contour map showing the average basal bone contour of the jawbone in the population, wherein the maxillary basal bone is placed 2 mm above the mandibular basal bone;

[0043] Generate a variance prediction map containing the mean profile and the ±1 standard deviation prediction profile; and

[0044] The output data file contains coordinate points and variation parameters for further analysis and clinical applications.

[0045] The present invention has the following beneficial effects:

[0046] 1. An automated method for fitting the basal bone contour of the bimaxillary bone is provided, which overcomes the inconvenience of relying on manual drawing in existing methods and significantly improves efficiency and accuracy;

[0047] 2. Based on factor analysis and principal component analysis of population statistical characteristics, a scientific prediction model was established, which improved the universality and reliability of the prediction results;

[0048] 3. By setting standardized relative positions between the maxillary and mandibular basal bones, a unified comparison standard for data from different patients was achieved, enhancing the clinical reference value of the analysis results;

[0049] 4. Employing symmetry and smoothing techniques ensures that the predicted contours conform to biological symmetry and continuity, making the results more consistent with anatomical principles;

[0050] 5. It can output the average contour and variation trend of the basal bone morphology, presenting the results intuitively, which facilitates doctors to design personalized treatment plans in clinical practice;

[0051] 6. The method has strong scalability and can be applied to the analysis of basal bone morphology in different age groups, genders, or other populations, with a wide range of applications. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of CBCT image localization in the method of the present invention, wherein: (a) is a sagittal head position calibration diagram; (b) is a right 45° head position calibration diagram; and (c) is a coronal head position calibration diagram.

[0053] Figure 2 This is a schematic diagram of the basal bone boundary of the retromolar region in the method of the present invention, wherein: (a) is the bilateral boundary of the retromolar space in the coronal plane; (b) is the retromolar space in the sagittal plane.

[0054] Figure 3 This is a schematic diagram of the basal bone contour marking in the method of the present invention, wherein: (a) is a maxillary basal bone contour image marking point (80 points); (b) is a mandibular basal bone contour image marking point (72 points); (c) is an enlarged image of the white rectangular frame in (b); and (d) is an enlarged image of the space behind the right molars of the mandible.

[0055] Figure 4 Here is an example of the basal bone contour output by the method of the present invention, wherein: (a) is the average maxillary basal bone contour of males and females; and (b) is the average mandibular basal bone contour of males and females.

[0056] Figure 5 This is an example of the basal bone variation prediction map and its principal component analysis results output by the method of the present invention. Detailed Implementation

[0057] Please refer to Figure 1 - Figure 5 The present invention will now be described in detail with reference to the accompanying drawings and embodiments, but the scope of protection of the present invention is not limited thereto.

[0058] This invention provides a method for fitting the basal contour of the jawbone in a population and predicting its changes. This method involves standardizing CBCT images, extracting key anatomical landmarks, applying statistical methods to analyze basal bone morphological variations, and making scientific predictions to provide a reference for clinical treatment.

[0059] The method of the present invention includes seven main steps: acquiring CBCT images and extracting landmark coordinates, performing generalized Protodyakonov analysis, setting the relative positions of the maxilla and mandible, performing factor analysis, performing principal component analysis prediction, optimizing the predicted contour, and generating a clinical reference file.

[0060] First, cone-beam computed tomography (CBCT) images are acquired to determine the basal bone contour and extract the coordinates of basal bone landmarks. In clinical practice, physicians need to perform CBCT scans on patients to obtain three-dimensional image data of the jawbone. To ensure the accuracy and comparability of the data, the CBCT images need to be standardized, including head position adjustment and basal bone boundary determination. Afterward, key anatomical landmarks are marked on a specific plane, and their coordinate data are extracted.

[0061] Secondly, based on the extracted basal bone landmark coordinates, the Generalized Procrustes Analysis (GPA) method was applied for coordinate alignment and morphological normalization. This step aims to eliminate non-morphological variations between individuals caused by differences in location, orientation, and scale, so that subsequent morphological analysis can focus on true morphological variations.

[0062] Third, a relative positional offset is set between the maxillary and mandibular basal bones to fit the average bimaxillary contour of the population. This step establishes a standardized spatial relationship between the maxillary and mandibular basal bones, providing a unified reference framework for bimaxillary analysis.

[0063] Fourth, factor analysis is performed on the fitting results to extract the main factors that explain the cumulative variance exceeding a predetermined threshold. Factor analysis can identify key variable factors from numerous variables, reduce data dimensionality, and lay the foundation for subsequent analysis.

[0064] Fifth, based on Principal Component Analysis (PCA), variation prediction of the jawbone basal morphology is performed to generate a predicted profile. PCA further refines the variation patterns, extracts the most significant variation directions, and performs morphological prediction accordingly.

[0065] Sixth, the predicted contours are symmetricized and smoothed. This step ensures that the prediction results conform to biological symmetry and continuity, enhancing the clinical usability of the results.

[0066] Finally, image and data files are generated for clinical diagnosis and treatment planning reference. These outputs visually present the analysis results, making them easy for doctors to use in clinical practice.

[0067] The CBCT image processing and landmark extraction in the method of this invention specifically include the following steps:

[0068] First, the head position in the CBCT images was adjusted so that the infraorbital plane was parallel to the ground plane, and the mandibular occlusal plane was also parallel to the ground plane. This standardized three-dimensional localization ensured that all samples were in the same spatial reference frame, enhancing data comparability. Figure 1 As shown, precise three-dimensional positioning was achieved by adjusting the head position in the sagittal plane (a), 45° lateral plane (b), and coronal plane (c). Preferably, three-dimensional reconstruction software can be used to adjust the head position, and the key planes can be brought to the predetermined positions through rotation and translation operations.

[0069] Secondly, the posterior basal bone of the mandibular molar is determined by the anterior border of the ramus, with the most distal point being the intersection of the mandibular occlusal plane and the anterior border of the ramus. For example... Figure 2 As shown, the anatomical boundaries of the retromolar region are clearly defined in the coronal (a) and sagittal (b) planes. This clear boundary definition is crucial for the precise placement of subsequent landmarks, especially since the retromolar region is a key boundary area for tooth movement, and its accurate description is of great clinical significance.

[0070] Finally, on the plane passing through the bifurcation of the maxillary and mandibular first molar roots, landmarks of the maxillary and mandibular basal bones were marked, and the coordinates of the maxillary and mandibular basal bone landmarks were obtained respectively. The plane of the first molar root bifurcation was chosen as the marking plane because it is relatively stable in anatomical position, facilitating standardized comparisons between different individuals.

[0071] The design of the marker system in the method of this invention has a clear anatomical basis:

[0072] The maxillary basal bone landmarks include 80 points, and the mandibular basal bone landmarks include 72 points. These landmarks include buccal points in the retromolar region, buccal points for each tooth position, lingual points for each tooth position, and lingual points in the retromolar region, comprehensively covering all key areas of the basal bone contour. For example... Figure 3 As shown, the distribution of the markers follows the characteristics of the anatomical structure, ensuring the accuracy and completeness of the contour description.

[0073] Specifically, the maxillary basal bone landmarks are distributed as follows: the most distal point on the right side (L1), the buccal points of the right retromolar region (L2-L5), the buccal points from the right second molar to the central incisor (L6-L20), the most anterior point of the maxilla (L21), the buccal points from the left central incisor to the second molar (L22-L36), the buccal points of the left retromolar region (L37-L40), the most distal point on the left side (L41), and the corresponding lingual points (L42-L80).

[0074] The mandibular basal bone landmarks include: the most distal point on the right side (L1), the buccal points of the right retromolar region (L2-L3), the buccal points from the right second molar to the central incisor (L4-L18), the most anterior point of the mandible (L19), the buccal points from the left central incisor to the second molar (L20-L34), the buccal points of the left retromolar region (L35-L36), the most distal point on the left side (L37), and the corresponding lingual points (L38-L72).

[0075] This comprehensive and systematic marker setup ensures accurate capture of the basal bone contour, providing high-quality input data for subsequent analysis. In clinical practice, experienced physicians can mark the markers based on anatomical features, or specialized medical image marking software can be used to assist in the process.

[0076] The generalized Prototype analysis (GPA) alignment step in the method of this invention specifically includes:

[0077] Calculate the initial average placement for all samples. Assuming there are n samples, each with p markers, first calculate the average position of each marker to form the initial average placement. This step can be represented as:

[0078] ,

[0079] in: For the average configuration, representing the average position of all sample marker points, is a p×2 dimensional matrix; Let n be the set of markers for the i-th sample, which is a p×2 matrix containing the two-dimensional coordinates of p markers; n is the total number of samples. This indicates that the summation operation is performed on all n samples.

[0080] Each sample is transformed by rotation, scaling, and translation to best match the average configuration. This process can be represented as an optimization problem:

[0081] ,

[0082] in: The rotation matrix is ​​a 2×2 orthogonal matrix used to adjust the orientation of the samples; The scaling factor is a positive scalar used to adjust the sample size. The translation vector is a 2D vector used to adjust the position of the sample. Let represent the sum of squares of the Euclidean distances. The optimization problem aims to find the optimal transformation parameters that minimize the difference between the transformed samples and the average configuration.

[0083] Recalculate the average configuration of all samples after the transformation. Apply the transformation to all samples and recalculate the average configuration:

[0084] ,

[0085] in: This is the new average configuration; other symbols have the same meaning as before. This step calculates the average of all transformed samples as the reference configuration for the next iteration.

[0086] Repeat the aforementioned transformation and recalculation steps until the morphological differences no longer decrease significantly. A convergence criterion is typically that the average change in configuration between two consecutive iterations is less than a preset threshold (e.g., 0.001). This threshold is chosen based on empirical values, small enough to ensure accurate morphological alignment without leading to excessive unnecessary computational iterations.

[0087] In clinical applications, GPA alignment is typically performed using specialized morphometric software. The key value of this step lies in eliminating non-morphological differences between individuals, allowing subsequent analyses to focus on true morphological variations.

[0088] The method of the present invention sets a relative position offset of 2mm between the maxillary abdominis and the mandibular abdominis, and moves the entire maxillary abdominis upward relative to the mandibular abdominis by 2mm.

[0089] The selection of this specific offset value is based on extensive clinical observation and anatomical studies. A 2mm gap roughly reflects the average relative position between the maxillary and mandibular basal bones under normal occlusion, and also facilitates visualization and comparison in clinical applications. In practice, after completing the generalized Protodyakonov analysis, this standardized offset can be achieved by uniformly adding 2mm to the Y-coordinate of all landmark points on the maxillary basal bones.

[0090] This standardized approach provides a unified reference framework for analyzing bimaxillary relationships, significantly enhancing the comparability of data between different individuals. In clinical practice, doctors can use this standardized model to make personalized adjustments based on the patient's specific situation, improving the accuracy of treatment plans.

[0091] The factor analysis step in the method of this invention specifically includes:

[0092] Calculate the covariance matrix of the standardized coordinates. First, organize the standardized coordinate data into a matrix form, and then calculate its covariance matrix:

[0093] ,

[0094] in: Let p be the covariance matrix with dimensions (2p) × (2p), where p is the number of markers for each sample; The matrix contains the standardized coordinates of all samples, with dimensions n×(2p), where n is the number of samples, and each sample contains the x and y coordinates of p marker points; for The average value of each column of the matrix is ​​a 1×(2p) row vector; This means subtracting the average value from the coordinates of each sample to obtain a centered data matrix; express The transpose of the matrix; These are unbiased estimation coefficients.

[0095] Extract eigenvalues ​​and eigenvectors. For the covariance matrix... Perform eigenvalue decomposition:

[0096] ,

[0097] in: It is a diagonal matrix with dimensions (2p) × (2p), and the diagonal elements are eigenvalues. (Arranged in descending order), representing the variation of each principal component decomposition; The corresponding eigenvector matrix has a dimension of (2p) × (2p), with each column being an eigenvector representing the direction of each principal component; express The transpose of .

[0098] The number of major common factors is determined based on the magnitude of the eigenvalues. In practical applications, the top few eigenvectors with eigenvalues ​​greater than 1 or whose cumulative explained variance reaches a predetermined threshold (e.g., 50%) can be selected as factors. The cumulative explained variance is calculated as follows:

[0099] ,

[0100] in: The number of feature vectors selected; Let j be the j-th eigenvalue; This represents the sum of the first k eigenvalues; This represents the sum of all eigenvalues. This proportion indicates the percentage of total variation that the first k principal components can explain, and is used to determine how many principal components to retain.

[0101] Factor rotations can be performed to make the factor structure more interpretable. Common rotation methods include orthogonal rotations (such as Varimax) and oblique rotations (such as Promax). Taking Varimax rotation as an example, its goal is to maximize the variance of the factor loadings:

[0102] ,

[0103] in: The rotation matrix has dimensions k×k; Let i be the loading of the i-th variable on the j-th factor after rotation; This represents a double summation over all variables and factors; These are the standardized coefficients. The optimization objective is to maximize the variance of the loadings on each factor, making the factor structure more explicit.

[0104] Calculate the score for each sample on each factor. Factor scores can be calculated using the following formula:

[0105] ,

[0106] in: This is a factor score matrix with dimensions n×k, representing the scores of n samples on k factors; The original data matrix (after centering); The matrix is ​​composed of the first k eigenvectors, with dimensions (2p) × k; Let be a rotation matrix with dimensions k×k. Factor scores reflect the performance of each sample in each major direction of variation.

[0107] In practical applications of this invention, factor analysis can extract key variation factors from complex coordinate variations, providing a scientific basis for understanding the main patterns of basal bone morphological variations. Preferably, professional statistical software (such as SPSS, R, etc.) can be used to perform factor analysis to improve analytical efficiency and accuracy.

[0108] In the method of this invention, the top three common factors that explain more than 50% of the cumulative variation are selected.

[0109] This threshold is set based on a comprehensive consideration of statistical principles and clinical experience. In morphological analysis, the first few principal factors are usually sufficient to capture most of the meaningful variations, while subsequent factors may mainly reflect noise or minor variations. A cumulative explanation ratio of 50% is a balance point that retains information on major variations while effectively reducing data dimensionality.

[0110] In practical applications, this threshold may need to be adjusted depending on the characteristics of different population groups. For example, for abnormal populations with large morphological variations, the threshold may need to be increased to 60% or higher to capture more variation information; while for homogeneous populations with relatively consistent morphology, a threshold of 45% may be sufficient.

[0111] Furthermore, the first three common factors usually have clear anatomical interpretations. For example, in the analysis of the jawbone basal bone, the first factor often reflects overall size variation (size factor), the second factor may reflect variation in anteroposterior diameter (length factor), and the third factor may reflect variation in width (width factor). This factor structure, corresponding to anatomy, facilitates clinical interpretation.

[0112] The principal component analysis and variation prediction steps in the method of this invention specifically include:

[0113] Principal component analysis is performed based on the factor score matrix to extract principal components. Using the factor score matrix obtained in the previous step as input, its covariance matrix is ​​calculated, and eigenvalue decomposition is performed.

[0114] ,

[0115] in: Let be the kth principal component, representing the projection of the data along the kth principal variation direction; The score for the j-th factor represents the sample's performance on the j-th factor; is the coefficient (an element of the eigenvector), representing the contribution weight of the j-th factor to the k-th principal component; k is the index of the principal component, and this method takes the first three principal components (k=1,2,3); p is the total number of factors.

[0116] Determine the average basal morphology of the population. Calculate the average morphology of all samples in the standardized space:

[0117] ,

[0118] in: In its average form, it is a p×2 matrix representing the average coordinates of p marker points; Let be the standardized coordinates of the i-th sample, which is also a p×2 dimensional matrix; n is the total number of samples. This indicates a summation operation performed on all samples.

[0119] Calculate the standard deviation along each principal component direction. For each principal component, calculate the standard deviation of the sample distribution along that direction:

[0120] ,

[0121] in: Let be the standard deviation of the k-th principal component, representing the degree of dispersion of the sample along that principal component direction; The score of the i-th sample on the k-th principal component; The average score of the k-th principal component; n is the number of samples; These are unbiased estimated coefficients; This represents the square root operation.

[0122] The predicted profile is generated by perturbing the average shape along the principal component direction with a multiple of the standard deviation. The predicted profile can be represented as:

[0123] ,

[0124] in: For predicting the profile, it represents the basal bone morphology with a variation of ±1 standard deviation in the direction of the kth principal component; It is an average shape; This is the adjustment factor, usually set to 1, representing the range of variation within ±1 standard deviation; Let $\frac{k}{k}$ be the standard deviation of the $k$-th principal component. Let p be the eigenvector corresponding to the k-th principal component (its representation in the original coordinate space), with a dimension of p×2, representing the direction of variation. The symbol "±" indicates that prediction can be made along the positive or negative direction, yielding predicted profiles with +1 standard deviation and -1 standard deviation, respectively.

[0125] In clinical applications, these predicted profiles visually illustrate the main variation patterns of basal bone morphology in a population, providing a reference framework for physicians to assess individual characteristics. For example, if a patient's basal bone morphology is close to the predicted profile of the first principal component +1 standard deviation, it indicates that their basal bone is larger in that direction of variation; if it is close to the profile of -1 standard deviation, it indicates that it is smaller in that direction.

[0126] The symmetry and smoothing steps in the method of this invention specifically include:

[0127] By mirroring the point set about the vertical axis, a symmetric point set is constructed. Let the original contour point set be... Then, a set of symmetric points is constructed through mirroring operations:

[0128] ,

[0129] in: The original contour point set contains m points, each represented by x and y coordinates; It is a mirror set of points, also containing m points; Represents the coordinates of the j-th point in the original point set; This represents the mirror image coordinates obtained by inverting the x-coordinates while keeping the y-coordinates unchanged. This operation mirrors the original contour about the y-axis (vertical axis).

[0130] The original point set and its mirror image are then joined according to anatomical correspondences to form a symmetrical contour. This step requires consideration of the correspondences in anatomical structures to ensure a natural transition at the joining points.

[0131] ,

[0132] in: The set of points after symmetry transformation; This represents the union of the original set of points and its mirror image set. This represents a symmetry operation, including the rearrangement and adjustment of points to ensure that the point sets on both sides remain symmetrical along the vertical axis. In practice, this step may require manually adjusting the correspondence of points based on anatomical knowledge to ensure that the symmetry result conforms to anatomical rules.

[0133] The moving average method is used to calculate the average position of each point within the window range, resulting in a smoothed contour curve.

[0134] ,

[0135] in: This represents the j-th point after smoothing. Let be the (j+k)th original point; r is the radius of the smoothing window, which determines the smoothing intensity, and is usually a value between 2 and 5. Window size (total number of pixels); This indicates the operation of averaging within a window. This formula calculates the average value around each point. The average position of each point is used to replace the original point position, thereby reducing local abrupt changes and noise on the contour.

[0136] These processing steps ensure that the predicted contours conform to biological symmetry and continuity, improving the clinical reference value of the results. In practical applications, smoothing parameters can be adjusted according to specific needs to balance detail preservation and smoothing effect. For example, for areas that need to retain more detail (such as the alveolar ridge), a smaller window radius (such as r=2) can be used; while for areas that need a smoother transition (such as the retromolar region), a larger window radius (such as r=5) can be used.

[0137] The final output file of the method of this invention includes:

[0138] Generate an average contour map showing the average basal bone contour of the jawbone in the population, where the maxillary basal bone is positioned 2 mm above the mandibular basal bone. For example... Figure 4 As shown, the average contours of different genders can be compared separately, visually presenting the morphological differences. In the figure, one grid represents 1 mm, which is convenient for clinical measurement reference.

[0139] Generate a variance prediction plot containing the mean profile and the ±1 standard deviation prediction profile. For example... Figure 5 As shown, the red curve represents the mean profile, while the green and blue curves represent the prediction results at -1 and +1 standard deviations, respectively. These variance prediction plots correspond to the main variance patterns, with plots A, B, and C in the figure corresponding to the variance in the three main principal component directions, respectively.

[0140] The output includes a data file containing coordinate points and variation parameters for further analysis and clinical applications. These data files typically contain standardized coordinates, principal component scores, coefficients of variation, and other information, and can be used for personalized analysis or secondary development.

[0141] These outputs provide clinicians with intuitive and comprehensive reference information. In practice, doctors can design the optimal treatment plan based on the patient's basal bone characteristics, combined with these reference images and data. For example, for patients whose basal bone morphology is close to a certain extreme of a variation, it may be necessary to pay special attention to the safety boundaries of tooth movement; while for patients whose basal bone morphology is close to the mean, a more standardized treatment plan may be applicable.

[0142] Furthermore, these outputs can be applied to medical education and patient communication. Doctors can use these intuitive images to explain the characteristics of the patient's basal bones and the rationale behind the treatment plan, improving treatment transparency and patient compliance.

[0143] In summary, the method provided by this invention integrates multiple advanced technologies to realize a complete process from CBCT images to clinical applications, providing a scientific and accurate reference for orthodontic treatment, and has significant clinical value and application prospects.

[0144] 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 fitting the basal contour of the jawbone in a population and predicting its changes, characterized in that, include: Acquire cone-beam computed tomography (CBCT) images, determine the basal bone contour boundaries, and extract the coordinates of basal bone landmarks; Based on the coordinates of the basal bone landmarks, coordinate alignment and morphological normalization are performed using generalized Protodyakonov analysis. A relative positional offset is set between the maxillary basal bone and the mandibular basal bone to achieve the fitting of the average bimaxillary contour of the population; Factor analysis was performed on the fitting results to extract the main factors that explain the cumulative variance ratio exceeding a predetermined threshold; Factor analysis is performed on the fitting results, including: calculating the covariance matrix of standardized coordinates; extracting eigenvalues ​​and eigenvectors; determining the number of major common factors based on the magnitude of the eigenvalues; performing factor rotation to make the factor structure more interpretable; and calculating the score of each sample on each factor; the predetermined threshold is 50%, and the top three common factors that explain more than 50% of the cumulative variance are selected. Based on principal component analysis, variation prediction of the basal bone morphology of the jawbone is performed to generate a predicted profile; the variation prediction of the basal bone morphology of the jawbone based on principal component analysis includes: performing principal component analysis based on the factor score matrix to extract principal components; determining the average basal bone morphology of the population; calculating the standard deviation in each principal component direction; and perturbing the average morphology along the principal component direction by a multiple of the standard deviation to generate a predicted profile. The predicted contour is symmetricized and smoothed; and Generate image and data files for clinical diagnosis and treatment planning reference.

2. The method according to claim 1, characterized in that, The process of acquiring cone-beam computed tomography (CBCT) images, determining the basal bone contour boundaries, and extracting the coordinates of basal bone landmarks includes: Adjust the head position in the CBCT image so that the infraorbital plane is parallel to the ground plane and the mandibular occlusal plane is parallel to the ground plane; The posterior basal bone of the mandibular molar is defined by the anterior border of the ramus, with its most distal point being the intersection of the mandibular occlusal plane and the anterior border of the ramus; and On the plane passing through the bifurcation of the maxillary first molar root and the mandibular first molar root, mark the landmarks of the maxillary and mandibular basal bones, and obtain the coordinates of the landmarks of the maxillary and mandibular basal bones respectively.

3. The method according to claim 2, characterized in that, The maxillary basal bone landmarks include 80 points, and the mandibular basal bone landmarks include 72 points; wherein, the landmarks include buccal points in the retromolar region, buccal points for each tooth position, lingual points for each tooth position, and lingual points in the retromolar region.

4. The method according to claim 1, characterized in that, The coordinate alignment and shape normalization performed through generalized Protodyakonov analysis includes: Calculate the initial average configuration for all samples; Each sample is transformed by rotation, scaling, and translation to best match the average configuration; Recalculate the average configuration of all samples after transformation; and Repeat the aforementioned transformation and recalculation steps until the morphological differences no longer decrease significantly.

5. The method according to claim 1, characterized in that, The relative position offset between the maxillary and mandibular basiles is set at 2mm, and the maxillary basiles are moved upward by 2mm relative to the mandibular basiles.

6. The method according to claim 1, characterized in that, The predicted contour is symmetricized and smoothed, including: Construct a set of symmetric points by mirroring the image about the vertical axis; The original point set and the mirror point set are spliced ​​together according to anatomical correspondence to form a symmetrical contour; and The moving average method is used to calculate the average position of each point within the window range, resulting in a smoothed contour curve.

7. The method according to claim 1, characterized in that, The generated image and data files for clinical diagnosis and treatment planning reference include: Generate an average contour map showing the average basal bone contour of the jawbone in the population, wherein the maxillary basal bone is placed 2 mm above the mandibular basal bone; Generate a variance prediction map containing the mean profile and the ±1 standard deviation prediction profile; and The output data file contains coordinate points and variation parameters for further analysis and clinical applications.

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