3D oral point cloud arch curve reconstruction method

Abstract

This invention relates to the field of digital oral healthcare technology and discloses a method for reconstructing dental arch curves from 3D oral point clouds. The method includes: constructing target feature vectors for each key point in each tooth point cloud based on the true 3D coordinates, curvature, and 3D normal vectors of each key point; training and obtaining a target PointTransformer model; inputting the 3D oral point cloud to be reconstructed into the target PointTransformer model to obtain the 3D coordinates and confidence levels of each predicted key point in each tooth; filtering predicted key points with confidence levels higher than a preset confidence threshold and associating them according to the dental arch sequence to form a set of key points for the dental arch; selecting key landmarks from the set of key points for the dental arch and reconstructing the dental arch curve based on these key landmarks; and performing multi-constraint optimization, local adjustment, and segmented blending on the reconstructed dental arch curve to reconstruct a dental arch curve with higher fit.

Description

Technical Field

[0001] This invention relates to the field of digital technology in oral healthcare, and in particular to a method for reconstructing dental arch curves using 3D point cloud data. Background Technology

[0002] The development of human teeth from adolescence to adulthood has been a subject of extensive research for dentists, orthodontists, and other experts. Over the past few decades, the main focus has been on preventing and treating dental diseases, surgically reconstructing dental malformations, and studying the development of teeth and dental arches during growth and development. In recent years, however, significant efforts have been devoted to the mathematical analysis of dental arch curvature, particularly in studies of children from different age groups, ethnicities, and national backgrounds. Proper care of deciduous teeth and their development into permanent teeth is of great importance. Research on dental arch curvature is closely related to the ideal occlusion and the expected achievement of normal permanent teeth, which are of great interest to dentists and orthodontists. However, a precise definition of the shape and form of dental arch curvature has yet to be provided.

[0003] Many researchers have proposed mathematical models to describe the human dental arch curve. Some believe it can be represented as a parabola, ellipse, or conic section, while others consider it a cubic spline curve. Some argue that the beta function best reflects its actual shape. In numerous studies, polynomials from the 2nd to the 6th order have also been mentioned for defining the dental arch. These traditional mathematical models have certain application value. Their core advantages lie in their simple model structure, low computational complexity, and the fact that they do not require complex data preprocessing or high computational power. Core parameters (such as focal length, semi-axis, and polynomial coefficients) are easy to calculate and intuitively adjust. They can quickly achieve a preliminary fit of the overall arch contour using a small number of feature points or two-dimensional images, providing fundamental theoretical support and morphological reference for early oral anatomy research, teaching demonstrations, and simple prosthesis design. They are also suitable for scenarios with limited data acquisition conditions in traditional diagnostic and treatment processes. However, these traditional mathematical models have obvious limitations: on the one hand, most of them are based on two-dimensional data, which makes it difficult to fully reflect the three-dimensional spatial morphological characteristics of the dental arch and to accurately capture the anatomical details of the dental arch in the vertical direction; on the other hand, due to the limitations of data dimensions and the characteristics of the model itself, it is difficult to simultaneously and accurately depict the overall arc shape of the dental arch, the physiological spacing between teeth, and the symmetrical or asymmetrical distribution characteristics of the bilateral dentition in the anatomical structure, which cannot meet the needs of digital diagnosis and treatment for high-precision dental arch curve fitting.

[0004] With the development of digital oral technology, advancements in imaging technology and computer-aided simulation have brought new directions to dental arch curve research, and 3D point cloud technology has gradually become an important data support for dental arch curve fitting. The introduction of deep learning models has further solved the core pain point of traditional feature point extraction—through training with a large amount of labeled 3D point cloud data, the model can automatically learn the correlation of anatomical features of the crown, accurately predict key anatomical points such as the apex of the canine, the mesial and distal margins of the first molar, and the midline of the incisors. End-to-end feature point extraction can be achieved without manual intervention, improving the consistency and accuracy of key point localization and adapting to complex scenarios with different dental arch morphologies (such as missing teeth and crowded teeth), laying a crucial foundation for high-precision fitting of dental arch curves based on 3D point cloud data. 3D point clouds, through devices such as intraoral optical scanners, can directly collect three-dimensional surface information of teeth and jawbones in the oral cavity, completely preserving the anatomical morphology of the dental arch in the X, Y, and Z directions. Combined with the automatic feature point prediction capability of deep learning models, this effectively overcomes the limitations of traditional models, providing a new technical path for achieving high-precision dental arch curve fitting.

[0005] Whether in dental arch morphology research or clinical diagnosis and treatment, precise acquisition of core anatomical parameters of the dental arch has long been essential. These parameters include the overall morphological characteristics of the dental arch, three-dimensional dimensional parameters, occlusal relationship parameters, and physiological gaps in the primary dentition stage. These parameters directly determine the rationality of occlusal function assessment and treatment plans, and the size of the dental arch has been considered more important than the size of the teeth. Although researchers have used terms such as ellipse and parabola to describe the dental arch, and used biometric methods such as perimeter, width, and depth measurements, as well as angles, linear distances, and ratios to define the curvature of the dental arch, these analyses based on two-dimensional data or traditional measurement methods have significant limitations in describing this three-dimensional structure: they cannot fully acquire the three-dimensional spatial information of the dental arch, and are prone to measurement errors and fitting biases due to missing data dimensions, making it difficult to meet the high precision and high adaptability requirements of modern digital dental diagnosis and treatment for dental arch curves.

[0006] The emergence of 3D point cloud technology effectively solves the pain points of traditional modeling methods. Its sampling resolution can reach the 0.01mm level, which can accurately restore key anatomical details such as crown margins, cusps, and crown necks, providing a high-precision, full-dimensional data foundation for dental arch curve fitting. At the same time, 3D point cloud data can be directly imported into dental CAD / CAM systems, seamlessly connecting with subsequent digital diagnosis and treatment processes, significantly improving the practicality and reliability of dental arch curve fitting in clinical applications, and providing a better technical solution for dental arch morphology research and clinical diagnosis and treatment.

[0007] However, existing methods for reconstructing dental arch curves based on 3D point cloud technology still have many unresolved shortcomings: First, the extraction of key anatomical points relies on manual operation, which is inefficient and inconsistent. Most existing methods require physicians to manually mark core anatomical points such as mesial, distal, and cusp points in the 3D point cloud. This is not only cumbersome and time-consuming, but also prone to deviations in key point positioning due to differences in physician experience, thus affecting the accuracy of curve fitting. Furthermore, these methods often rely solely on the three-dimensional coordinate information of the point cloud to construct features, without fully integrating geometric attributes such as curvature and normal vectors. This makes it difficult to accurately capture the anatomical details of the tooth surface through automation, and thus fails to achieve efficient and accurate automatic extraction of key anatomical points. Second, the model adaptability is limited. Existing methods often use a single fitting model (such as a simple polynomial or B-spline curve) to process the data. In scenarios involving dental arches, the model architecture cannot be dynamically adjusted based on the integrity of the dental arch (e.g., the presence of missing teeth or jaw deformities), which can easily lead to distorted curve morphology or insufficient fit. Third, the constraint mechanism is imperfect. Some methods do not fully incorporate oral anatomy into the design and optimization of constraints, or only introduce single morphological constraints, ignoring core requirements such as bilateral dentition symmetry, the correlation of jaw anatomical positions, and functional occlusal fit. This results in reconstructed curves that meet data fitting requirements but do not conform to the anatomical and functional standards of clinical diagnosis and treatment. Fourth, the correlation between feature points and curves is insufficient. Existing methods lack a confidence calibration mechanism for the selection of key points, which can easily include low-reliability key points in the fitting process. At the same time, they do not design differentiated fitting strategies for the differences in anatomical morphology between the anterior and posterior segments of the dental arch, making it difficult to balance the overall continuity of the curve with local accuracy. Summary of the Invention

[0008] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the existing technology cannot accurately extract key points and cannot adapt to dental arches of different integrity, resulting in the distortion of the reconstructed dental arch curve shape.

[0009] To address the aforementioned technical problems, this invention provides a 3D oral cavity point cloud dental arch curve reconstruction method, comprising: Based on the key points of each tooth in the 3D oral scan data, the tooth point cloud of each tooth is obtained; the real three-dimensional coordinates, curvature and three-dimensional normal vector of each key point in each tooth point cloud are obtained as the target feature vector of each key point in each tooth point cloud. Input the target feature vectors of all key points in the tooth point cloud into the initial PointTransformer model to obtain multiple predicted key points of the tooth point cloud, their predicted 3D coordinates, and prediction confidence scores, including: Based on linear transformation and sinusoidal position coding, the target feature vectors of each key point are mapped to a high-dimensional semantic feature space to obtain the high-dimensional semantic features of each key point. The high-dimensional semantic features of each key point are passed through multiple attention modules that are sequentially connected along the forward propagation direction and have residual connections between layers. The attention features output by the last attention module are obtained as the global features of each key point. The attention module includes local neighborhood sampling, self-attention calculation, feature aggregation and feedforward network sequentially connected along the forward propagation direction. Global average pooling is performed on the global features of all key points to obtain the overall features of the tooth point cloud. The overall features of the tooth point cloud are input into the coordinate regression head to obtain multiple predicted key points of the tooth point cloud and their predicted 3D coordinates. The overall features of the tooth point cloud are input into the confidence prediction head to obtain multiple prediction key points of the tooth point cloud and their prediction confidence. Based on the true and predicted 3D coordinates of each key point, as well as the true and predicted confidence scores, coordinate regression loss and confidence calibration loss are constructed to train the initial PointTransformer model and obtain the target PointTransformer model. The 3D oral cavity point cloud to be reconstructed is input into the target PointTransformer model to obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth. Predicted key points with confidence higher than the preset confidence threshold are filtered out and associated according to the dental arch sequence to form a set of dental arch key points. Key landmarks are selected from the set of dental arch key points, and dental arch curves are reconstructed based on the key landmarks.

[0010] Preferably, the 3D oral cavity point cloud to be reconstructed is input into the target PointTransformer model to obtain the three-dimensional coordinates and confidence scores of each predicted key point in each tooth. Predicted key points with confidence scores higher than a preset confidence threshold are selected and associated according to the dental arch sequence to form a set of dental arch key points. Key landmarks are selected from the set of dental arch key points, and dental arch curves are reconstructed based on the key landmarks, including: The 3D oral cavity point cloud to be reconstructed is input into the target PointTransformer model to obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth. Predicted key points with confidence higher than the preset confidence threshold are selected as high confidence key points. The high-confidence key points are sorted according to the physiological order of the dental arch to form a set of dental arch key points; Based on the type of key point and the location of the tooth to which it belongs, multiple key landmarks are selected from the set of key points in the dental arch; Multiple key landmarks are projected onto the occlusal plane to obtain the initial dental arch morphology: If the initial dental arch morphology is complete, then a quadratic combined with a quartic polynomial model is used as the initial curve. If there are abnormalities in the initial dental arch morphology, a cubic B-spline curve or a NURBS curve shall be used as the initial curve. The target dental arch curve is obtained by fitting the initial curve using the least squares method.

[0011] Preferably, after obtaining the target dental arch curve, the process includes performing multi-constraint optimization on the target dental arch curve to obtain an optimized dental arch curve, including: Anatomical hard constraints are applied to the target dental arch curve, causing it to pass through all key landmarks in the 3D oral cavity point cloud to be reconstructed, thus obtaining the first dental arch curve; A symmetrical soft constraint is applied to the first dental arch curve to ensure that the distance between a pair of key landmarks symmetrical to the first dental arch curve is no greater than a preset physiological difference, and then the second dental arch curve is obtained. Apply a smoothness constraint to the second dental arch curve so that the curvature at each position on the second dental arch curve is not greater than a preset curvature threshold, and then obtain the third dental arch curve. The third dental arch curve is subjected to jawbone energy constraint, so that the third dental arch curve is located in the preset jawbone anatomical center region, and an optimized dental arch curve is obtained.

[0012] Preferably, after obtaining the optimized dental arch curve, the process includes segmenting, mixing, and splicing the optimized dental arch curve to obtain the suitable dental arch curve, including: For the portion of the arch curve corresponding to the anterior segment, circular curve fitting is used, and the radius of the circle is adjusted based on the comprehensive width of the incisors to obtain the anterior segment curve; For the portion of the arch curve corresponding to the posterior segment, a fourth-order polynomial is used for fitting, and the polynomial coefficients are corrected by the distance to the mesial point of the first molar to obtain the posterior curve. At the junction of the front and rear curves, a Bezier curve is used to smoothly splice them together to obtain the appropriate dental arch curve.

[0013] Preferably, after obtaining the matching dental arch curve, the process includes making local adjustments to the matching dental arch curve, including: Calculate the shortest distance between the fitted dental arch curve and each key landmark point of the 3D oral cavity point cloud to be reconstructed, and obtain the mean and standard deviation of the deviation of all shortest distances; The area containing key markers whose shortest distance is greater than the sum of the mean deviation and twice the standard deviation is considered as an area with excessive local deviation. Based on the type of the initial curve used for adapting the dental arch curve, local adjustments are made to the adapting dental arch curve, including: If the initial curve is a quadratic combined with a quartic polynomial model, then a sixth-order term is introduced in the region where the local deviation is too large for piecewise correction. If the initial curve is a cubic B-spline curve or a NURBS curve, then the curve shape control points corresponding to the areas with excessive local deviations will be fine-tuned.

[0014] Preferably, the key points of the tooth include the mesial point, distal point, cusp, inner surface point, outer surface point, and axial point; Key landmarks include the midpoint of the incisal edge of the central incisors on the left and right sides, the cusp of the canines, the buccal cusp of the premolars, the mesiobuccal cusp of the molars, and the distobuccal cusp of the molars.

[0015] Preferably, the true 3D coordinates, curvature, and 3D normal vector of each key point in each tooth point cloud are obtained as the target feature vector of each key point in each tooth point cloud, including: Based on key points True 3D coordinates Obtain key points neighborhood point set ; Calculate key points using the mean curvature formula. curvature : ; Key points The key points are obtained by averaging the true 3D coordinates of the neighboring points in the neighborhood point set. Mean three-dimensional coordinates , represented as: ; Based on key points Calculate key points using the mean 3D coordinates of the given data and the true 3D coordinates of neighboring points in the neighborhood point set. covariance matrix , represented as: ; Key points The covariance matrix is ​​subjected to eigenvalue decomposition to obtain the eigenvector corresponding to the smallest eigenvalue, which is used as the three-dimensional normal vector, represented as: ; Key points Target feature vector , represented as: ; in, Indicate key points neighborhood point set The number of middle neighbor points; and These represent key points. neighborhood point set The Middle The true 3D coordinates and 3D normal vectors of each neighboring point.

[0016] Preferably, the attention module includes a local neighborhood sampling unit, a self-attention calculation unit, a feature aggregation unit, and a feedforward network connected in series along the forward propagation direction, comprising: The local neighborhood sampling unit selects M seed points from the input features using the farthest point sampling, performs ball query on each seed point, and obtains local features; The self-attention computation unit calculates the scoring function between points in the local features using a multi-head attention mechanism, and then constructs the dependency relationship between points in the local features based on a sparse self-attention mechanism. The feature aggregation unit concatenates the dependencies between points in the local features and then performs a linear transformation to obtain aggregated features. The feedforward network activates and normalizes the aggregated features through a multilayer perceptron to obtain attention feature outputs.

[0017] Preferably, based on the true and predicted 3D coordinates of each key point, and the true and predicted confidence levels, coordinate regression loss and confidence calibration loss are constructed, including: Based on the true 3D coordinates of each key point With predicted three-dimensional coordinates Construct coordinate regression loss , represented as: ; True confidence level based on each key point With prediction confidence Construct confidence calibration loss , represented as: ; Based on coordinate regression loss With confidence calibration loss Construct the total loss function , represented as: ; in, Indicates the total number of key point categories. Indicates the preset category weights. Represents Euclidean distance; true confidence level. Represented as , Indicates the preset error threshold; This indicates the preset proportional weight.

[0018] Preferably, after acquiring the tooth point cloud of each tooth, the tooth point cloud is preprocessed; before inputting the 3D oral cavity point cloud to be reconstructed into the target PointTransformer model, the 3D oral cavity point cloud to be reconstructed is preprocessed; the point cloud preprocessing includes: Using the midpoint of the mandibular central incisor landmark as the zero coordinate point, a horizontal xy plane is constructed. The z coordinate of the point cloud is normalized, and the point cloud is projected onto a unified coordinate system. And / or, use statistical filtering to remove outliers from the point cloud; And / or, downsample the point cloud so that the point density of the downsampled point cloud is within a preset density range; And / or, randomly flip, translate, scale, or add Gaussian noise to the point cloud.

[0019] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0020] The 3D oral cavity point cloud arch curve reconstruction method of this invention constructs a target feature vector including real 3D coordinates, curvature, and 3D normal vectors when training the PointTransformer model. Curvature is calculated by the difference between neighboring points and the normal vector, and the normal vector is solved by eigenvalue decomposition of the covariance matrix, comprehensively capturing the geometric properties and spatial morphological features of the tooth surface. This multi-dimensional feature combination enables the model to simultaneously perceive macroscopic shape and microscopic details, improving the prediction accuracy of key points. Simultaneously, the PointTransformer model, combined with multi-head self-attention mechanism and positional encoding, accurately models the inter-point dependencies, significantly improving the consistency and accuracy of key point prediction. Based on the difference in 3D coordinates and confidence between the predicted key points and the input key points, the PointTransformer model is trained to obtain the target PointTransformer model, extracting the predicted key points of the 3D oral cavity point cloud to be reconstructed. High-precision predicted key points ensure the accuracy of arch curve fitting. Furthermore, this invention requires no manual intervention throughout the entire process from oral scan data input to arch curve output, with fully automated processing significantly shortening treatment preparation time and reducing reliance on manual intervention.

[0021] This invention selects a corresponding model for curve fitting based on the initial dental arch morphology; if the initial dental arch morphology is complete, a quadratic combined with a quartic polynomial model is used as the initial curve; if the initial dental arch morphology is abnormal, a 3rd-order B-spline curve or a NURBS curve is used as the initial curve; this adaptive fitting model selection mechanism improves the adaptability of this invention to complex dental arch scenarios.

[0022] This invention provides a multi-constraint optimization method based on anatomical hard constraints, symmetry soft constraints, smoothness constraints, and jawbone energy constraints to constrain the acquired target dental arch curve. Anatomical hard constraints force the curve through key anatomical points such as canine apex and dental arch midline point; symmetry soft constraints control bilateral morphological symmetry; smoothness constraints ensure a gentle morphology based on the second derivative of the curve; and jawbone energy constraints adjust the curve position by balancing jawbone point cloud intensity and distance information. Multi-constraint optimization ensures that the reconstructed dental arch curve fits the data and conforms to anatomical rules and functional requirements, improving the fitting accuracy and precision of the dental arch curve.

[0023] This invention provides a segmented hybrid approach for the anterior and posterior segments; the radius of the anterior segment is adjusted based on the comprehensive width of the incisors to make the anterior segment conform to the anatomical features of the arc; the polynomial coefficients of the posterior segment are adjusted based on the mesial distance of the first molar to make the posterior segment adapt to the progressive convergence morphology; and smooth splicing is achieved through Bézier curves, thus achieving a unity of overall continuity and local precision.

[0024] This invention makes local adjustments to the dental arch curve, and while maintaining a reasonable overall shape, it specifically corrects the deviation in areas with excessive local deviation, making the fitted dental arch curve more accurate. Attached Figure Description

[0025] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a flowchart of the steps of the 3D oral point cloud dental arch curve reconstruction method of the present invention; Figure 2 This is a flowchart of the prediction process for the PointTransformer model; Figure 3 This is a schematic diagram of a 4-layer attention module; Figure 4 This is a flowchart illustrating the steps involved in fitting dental arch curves based on predicted key points. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0027] Reference Figure 1 The flowchart shown illustrates the steps of the 3D oral cavity point cloud dental arch curve reconstruction method of the present invention, which specifically include: S101: Based on the key points of each tooth in the 3D oral scan data, the tooth point cloud of each tooth is obtained; the true three-dimensional coordinates, curvature and three-dimensional normal vector of each key point in each tooth point cloud are obtained as the target feature vector of each key point in each tooth point cloud. S102: Input the target feature vectors of all key points in the tooth point cloud into the initial PointTransformer model to obtain multiple predicted key points of the tooth point cloud and their predicted 3D coordinates and prediction confidence, including: S102-1: Based on linear transformation and sinusoidal position coding, the target feature vectors of each key point are mapped to a high-dimensional semantic feature space to obtain the high-dimensional semantic features of each key point. S102-2: Pass the high-dimensional semantic features of each key point through multiple attention modules that are sequentially connected along the forward propagation direction and have residual connections between layers, and obtain the attention features output by the last attention module as the global features of each key point. The attention module comprises a local neighborhood sampling, self-attention computation, feature aggregation, and feedforward network sequentially connected along the forward propagation direction, including: The local neighborhood sampling unit selects M seed points from the input features using the farthest point sampling, performs ball query on each seed point, and obtains local features; The self-attention computation unit calculates the scoring function between points in the local features using a multi-head attention mechanism, and then constructs the dependency relationship between points in the local features based on a sparse self-attention mechanism. The feature aggregation unit concatenates the dependencies between points in the local features and then performs a linear transformation to obtain aggregated features. The feedforward network activates and normalizes the aggregated features through a multilayer perceptron to obtain attention feature outputs. S102-3: Perform global average pooling on the global features of all key points to obtain the overall features of the tooth point cloud; S102-4: Input the overall features of the tooth point cloud into the coordinate regression head to obtain multiple predicted key points of the tooth point cloud and their predicted three-dimensional coordinates; S102-5: Input the overall features of the tooth point cloud into the confidence prediction head to obtain multiple prediction key points of the tooth point cloud and their prediction confidence. S103: Based on the true and predicted 3D coordinates of each key point, as well as the true and predicted confidence, construct coordinate regression loss and confidence calibration loss, train the initial PointTransformer model, and obtain the target PointTransformer model. S103-1: Based on the true 3D coordinates of each key point With predicted three-dimensional coordinates Construct coordinate regression loss , represented as: ; S103-2: True confidence level based on each key point With prediction confidence Construct confidence calibration loss , represented as: ; S103-3: Based on coordinate regression loss With confidence calibration loss Construct the total loss function , represented as: ; in, Indicates the total number of key point categories. Indicates the preset category weights. Represents Euclidean distance; true confidence level. Represented as , Indicates the preset error threshold; Indicates the preset proportional weight; S104: Input the 3D oral cavity point cloud to be reconstructed into the target PointTransformer model, obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth, filter the predicted key points with confidence higher than the preset confidence threshold, and associate them according to the dental arch sequence to form a set of dental arch key points; select key landmarks from the set of dental arch key points, and reconstruct the dental arch curve based on the key landmarks.

[0028] Specifically, the key points of a tooth include the mesial point, distal point, cusp, inner surface point, outer surface point, and axial point; the key landmarks selected in this embodiment include the midpoint of the incisal edge of the central incisor on the left and right sides, the cusp of the canine, the buccal cusp of the premolar, the mesiobuccal cusp of the molar, and the distal buccal cusp of the molar.

[0029] Specifically, in step S101, the acquisition of the target feature vector of each key point in each tooth point cloud includes: S101-1: Based on key points True 3D coordinates Obtain key points neighborhood point set ; S101-2: Calculate key points using the mean curvature formula. curvature : ; S101-3: Key Points The key points are obtained by averaging the true 3D coordinates of the neighboring points in the neighborhood point set. Mean three-dimensional coordinates , represented as: ; S101-4: Based on key points Calculate key points using the mean 3D coordinates of the given data and the true 3D coordinates of neighboring points in the neighborhood point set. covariance matrix , represented as: ; S101-5: Key Points The covariance matrix is ​​subjected to eigenvalue decomposition to obtain the eigenvector corresponding to the smallest eigenvalue, which is used as the three-dimensional normal vector, represented as: ; S101-6: Key Points Target feature vector , represented as: ; in, Indicate key points neighborhood point set The number of middle neighbor points; and These represent key points. neighborhood point set The Middle The true 3D coordinates and 3D normal vectors of each neighboring point.

[0030] The 3D oral cavity point cloud arch curve reconstruction method of this invention constructs a target feature vector including real 3D coordinates, curvature, and 3D normal vectors when training the PointTransformer model. Curvature is calculated by the difference between neighboring points and the normal vector, and the normal vector is solved by eigenvalue decomposition of the covariance matrix, comprehensively capturing the geometric properties and spatial morphological features of the tooth surface. This multi-dimensional feature combination enables the model to simultaneously perceive macroscopic shape and microscopic details, improving the prediction accuracy of key points. Simultaneously, the PointTransformer model, combined with multi-head self-attention mechanism and positional encoding, accurately models the inter-point dependencies, significantly improving the consistency and accuracy of key point prediction. Based on the difference in 3D coordinates and confidence between the predicted key points and the input key points, the PointTransformer model is trained to obtain the target PointTransformer model, extracting the predicted key points of the 3D oral cavity point cloud to be reconstructed. High-precision predicted key points ensure the accuracy of arch curve fitting. Furthermore, this invention requires no manual intervention throughout the entire process from oral scan data input to arch curve output, with fully automated processing significantly shortening treatment preparation time and reducing reliance on manual intervention.

[0031] Specifically, in step S104, the present invention includes the following when performing dental arch reconstruction: S104-1: Input the 3D oral cavity point cloud to be reconstructed into the target PointTransformer model, obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth, and filter the predicted key points with confidence higher than the preset confidence threshold as high confidence key points; S104-2: Sort the high-confidence key points according to the physiological order of the dental arch to form a set of dental arch key points; S104-3: Select multiple key landmarks from the set of key arch landmarks based on the type of key points and the location of the teeth to which they belong; S104-4: Project multiple key landmarks onto the occlusal plane to obtain the initial dental arch morphology: S104-5: If the initial dental arch morphology is complete, then a quadratic combined with a quartic polynomial model is used as the initial curve. S104-6: If there are abnormalities in the initial dental arch morphology, a cubic B-spline curve or a NURBS curve shall be used as the initial curve. S104-7: The initial curve is fitted using the least squares method to obtain the target dental arch curve.

[0032] This invention selects a corresponding model for curve fitting based on the initial dental arch morphology; if the initial dental arch morphology is complete, a quadratic combined with a quartic polynomial model is used as the initial curve; if the initial dental arch morphology is abnormal, a 3rd-order B-spline curve or a NURBS curve is used as the initial curve; this adaptive fitting model selection mechanism improves the adaptability of this invention to complex dental arch scenarios.

[0033] Based on the above embodiments, after obtaining the target dental arch curve, the present invention includes performing multi-constraint optimization on the target dental arch curve to obtain an optimized dental arch curve, including: Anatomical hard constraints are applied to the target dental arch curve, causing it to pass through all key landmarks in the 3D oral cavity point cloud to be reconstructed, thus obtaining the first dental arch curve; A symmetrical soft constraint is applied to the first dental arch curve to ensure that the distance between a pair of key landmarks symmetrical to the first dental arch curve is no greater than a preset physiological difference, and then the second dental arch curve is obtained. Apply a smoothness constraint to the second dental arch curve so that the curvature at each position on the second dental arch curve is not greater than a preset curvature threshold, and then obtain the third dental arch curve. The third dental arch curve is subjected to jawbone energy constraint, so that the third dental arch curve is located in the preset jawbone anatomical center region, and an optimized dental arch curve is obtained.

[0034] This invention provides a multi-constraint optimization method based on anatomical hard constraints, symmetry soft constraints, smoothness constraints, and jawbone energy constraints to constrain the acquired target dental arch curve. Anatomical hard constraints force the curve through key anatomical points such as canine apex and dental arch midline point; symmetry soft constraints control bilateral morphological symmetry; smoothness constraints ensure a gentle morphology based on the second derivative of the curve; and jawbone energy constraints adjust the curve position by balancing jawbone point cloud intensity and distance information. Multi-constraint optimization ensures that the reconstructed dental arch curve fits the data and conforms to anatomical rules and functional requirements, improving the fitting accuracy and precision of the dental arch curve.

[0035] Based on the above embodiments, after obtaining the optimized dental arch curve, the present invention includes segmenting, mixing, and splicing the optimized dental arch curve to obtain a suitable dental arch curve, including: For the portion of the arch curve corresponding to the anterior segment, circular curve fitting is used, and the radius of the circle is adjusted based on the comprehensive width of the incisors to obtain the anterior segment curve; For the portion of the arch curve corresponding to the posterior segment, a fourth-order polynomial is used for fitting, and the polynomial coefficients are corrected by the distance to the mesial point of the first molar to obtain the posterior curve. At the junction of the front and rear curves, a Bezier curve is used to smoothly splice them together to obtain the appropriate dental arch curve.

[0036] This invention provides a segmented hybrid approach for the anterior and posterior segments; the radius of the anterior segment is adjusted based on the comprehensive width of the incisors to make the anterior segment conform to the anatomical features of the arc; the polynomial coefficients of the posterior segment are adjusted based on the mesial distance of the first molar to make the posterior segment adapt to the progressive convergence morphology; and smooth splicing is achieved through Bézier curves, thus achieving a unity of overall continuity and local precision.

[0037] Based on the above embodiments, after obtaining the matching dental arch curve, the present invention includes making local adjustments to the matching dental arch curve, including: Calculate the shortest distance between the fitted dental arch curve and each key landmark point of the 3D oral cavity point cloud to be reconstructed, and obtain the mean and standard deviation of the deviation of all shortest distances; The area containing key markers whose shortest distance is greater than the sum of the mean deviation and twice the standard deviation is considered as an area with excessive local deviation. Based on the type of the initial curve used for adapting the dental arch curve, local adjustments are made to the adapting dental arch curve, including: If the initial curve is a quadratic combined with a quartic polynomial model, then a sixth-order term is introduced in the region where the local deviation is too large for piecewise correction. If the initial curve is a cubic B-spline curve or a NURBS curve, then the curve shape control points corresponding to the areas with excessive local deviations will be fine-tuned.

[0038] This invention makes local adjustments to the dental arch curve, and while maintaining a reasonable overall shape, it specifically corrects the deviation in areas with excessive local deviation, making the fitted dental arch curve more accurate.

[0039] Specifically, in this embodiment, after acquiring the tooth point cloud of each tooth, the tooth point cloud is preprocessed; in this embodiment, before inputting the 3D oral cavity point cloud to be reconstructed into the target PointTransformer model, the 3D oral cavity point cloud to be reconstructed is preprocessed; wherein, the point cloud preprocessing includes: using the midpoint of the mandibular central incisor landmark as the zero coordinate point to construct a horizontal xy plane, normalizing the z coordinate of the point cloud, so that the point cloud is projected to a unified coordinate system; and / or, using statistical filtering to remove outliers in the point cloud; and / or, downsampling the point cloud so that the point density of the downsampled point cloud is within a preset density range; and / or, randomly flipping, translating, scaling, or adding Gaussian noise to the point cloud.

[0040] The 3D oral cavity point cloud arch curve reconstruction method provided by this invention can be summarized into several major steps: data preprocessing, key point extraction, adaptive curve fitting, multi-constraint optimization, hybrid model stitching, and parameter calibration. Data preprocessing involves acquiring 3D oral cavity scan data from the Teeth3DS+ dataset, converting it to point cloud format using the Open3D library while preserving 3D coordinates and normal vector information. Statistical filtering for noise reduction, voxel mesh downsampling, and coordinate normalization are used to unify data standards and eliminate the influence of differences in scanning posture and point density. Key point extraction is used to construct 7-dimensional input features containing 3D coordinates, curvature, and normal vectors. A 4-layer PointTransformer model is used to aggregate local and global features, predicting the 3D coordinates and confidence levels of 6 core anatomical key points, including mesial, distal, and cusp points. High-confidence key points are selected and associated according to the dental arch sequence, resulting in 18 core landmarks directly related to the dental arch morphology. Adaptive curve fitting is used to select the appropriate model based on the integrity of the dental arch. When the dental arch morphology is complete, a quadratic + quartic polynomial model is used. When there are missing teeth or malformations, a tertiary B-spline curve or NURBS curve is used (the morphology is adjusted by controlling the poles and weighting coefficients). The initial fitting is completed based on the least squares method. Multi-constraint optimization introduces anatomical hard constraints (forcing the curve to pass through the canine apex and the midline of the dental arch), symmetry soft constraints (allowing ±5% physiological differences), and smoothness constraints (ensuring smooth curvature changes). If the point cloud contains jawbone information, the curve position is optimized through an energy function to ensure that the curve conforms to the oral anatomy. Hybrid model splicing and parameter calibration adopt a hybrid model of circular curves and quartic polynomials. The radius of the circle in the anterior segment is corrected based on the comprehensive width of the incisors, and the polynomial coefficients in the posterior segment are corrected based on the mesial distance of the first molar. The two segments are smoothly spliced ​​using Bézier curves. Cross-validation is performed by combining functional occlusion annotations and comprehensive tooth width parameters to ensure that the average fitting distance error is ≤0.8mm.

[0041] Based on this, the embodiments of the present invention train the model on the Teeth3DS+ dataset, obtain the target model for keypoint prediction, and then perform dental arch curve fitting based on the predicted keypoints. The specific steps include:

[0042] S201: Data acquisition and point cloud format conversion; Input 3D oral cavity scan data from the Teeth3DS+ dataset, covering maxillary and mandibular mesh data, containing 23,999 labeled teeth and corresponding key point annotations, including mesial points, distal points, cusps, internal points, external points, and axial points; The Open3D library is used to convert mesh data into point cloud format, preserving the 3D coordinates xyz and their normal vector information, while extracting the vertex information of the mesh as a supplementary feature source.

[0043] S202: Statistical filtering (standard deviation threshold set to 2.0) is used to remove outliers, redundant vertices, degenerate mesh surfaces and background noise. Then, voxel mesh sampling is used to downsample the points and unify the point density to 30-80 pts / mm². Subsequently, a horizontal xy plane is constructed with the midpoint of the mandibular central incisor landmark as the zero coordinate point, and the z coordinate of all point clouds is normalized. S202-1: Remove redundant vertices, degenerate mesh surfaces, and background noise from the point cloud, such as irrelevant points in the gingival region and scanning artifacts. Use statistical filtering to remove outliers and set the standard deviation threshold to 2.0. S202-2: The cleaned point cloud is downsampled and the point density is uniformly set to 30-80 pts / mm² by voxel grid sampling to match the scanning accuracy of the Teeth3DS+ dataset and balance computational efficiency with feature preservation. S202-3: Using the midpoint of the lower central incisor landmark as the zero coordinate point, construct a horizontal xy plane (occlusal plane), normalize the z coordinates of all point clouds, and project the point clouds onto a unified coordinate system to eliminate the influence of scanning posture differences;

[0044] S203: Construct the training and test sets; We used 340 IOS scan data with keypoint annotations from the Teeth3DS+ dataset, of which 240 were used as the training set (including segmentation / annotation information) and 100 were used as the test set. The key points marked include six types of core anatomical points: mesial, distal, cusp, inner, outer, and facial axis, and are associated with individual tooth instances according to the FDI tooth numbering system; Random rotation (±10° around the x / y axis), translation (±2mm), scaling (0.9-1.1 times), and Gaussian noise addition (σ=0.01) are applied to the training set point cloud to improve the model's generalization ability.

[0045] S204: Train the PointTransformer model; Reference Figure 2 The diagram shows the prediction flowchart of the PointTransformer model. The PointTransformer model structure is as follows: the input dimension is 3 (xyz coordinates), local and global features are aggregated through a hierarchical attention module, a 4-layer Transformer encoder is set (each layer has 8 attention heads), and the output layer is a keypoint coordinate regression head (predicting the xyz coordinates of 6 types of keypoints). S204-1: Construction of 7-dimensional input features: Input the 3D coordinates of the point cloud of a single tooth ,in This refers to the number of points in a point cloud, including the coordinate information of each point. ; The mean curvature formula is used to calculate the neighborhood of each point using Open3D, and the number of neighborhood points is calculated. curvature Defined as: ; in, Point The set of neighborhood points, ; Point The normal vector is obtained by eigenvalue decomposition of the covariance matrix of the neighborhood points; covariance matrix Represented as: , ; right Eigenvalue decomposition yields the eigenvector corresponding to the smallest eigenvalue, which is also the normal vector, expressed as: ; The final input feature dimension for each point is 7, containing 3-dimensional coordinates, 1-dimensional curvature, and 3-dimensional normal vector. The final input features are represented as follows: ; S204-2: Mapping the 7-dimensional input features to a high-dimensional semantic feature space using a linear transformation: ; in, This indicates a fully connected layer with an output dimension of 256, i.e. ; The sine position code is represented as: , Feature Dimension ; In this embodiment, when the 7-dimensional input features are mapped to the high-dimensional semantic feature space, the feature dimensions are converted to 256 dimensions through a fully connected layer. At the same time, sinusoidal position encoding is added to enhance spatial position information and improve the model's ability to capture spatial relationships.

[0046] S204-3: The attention module has four layers. Each encoder layer contains four sub-modules: local neighborhood sampling, self-attention computation, feature aggregation, and feedforward network. Features are transferred between layers through residual connections and layer normalization; see reference. Figure 3 The diagram shows the structure of the 4-layer attention module. Local neighborhood sampling uses FPS (farthest point sampling) to select seed points. The number of seed points in each layer is 512, 256, 128, and 64, respectively. A ball query (radius 0.5mm) is used to select neighborhood points for each seed point to construct a local feature map. Self-attention calculation uses the sparse self-attention mechanism of PointTransformer. Multi-head attention (8 heads) is used to model the dependencies between points, and relative position encoding is introduced to capture spatial distance information.

[0047] ① Local neighborhood sampling uses FPS (farthest point sampling) to select points in the point cloud. Seed points, layer 1 , second floor , third floor , 4th floor For each seed point, a ball query is used to select neighboring points with a radius of r=0.5mm to construct a local feature map; ② The sparse self-attention mechanism of PointTransformer is used to model the dependencies between points, represented as: ; Scoring function Multi-head attention (H=8 heads) is used to split the features into 8 heads for parallel computation, with each head having a feature dimension of 32; the scoring function is expressed as: ; Among them, query vector key vector , For each head dimension, The weight matrix is ​​a learnable weight matrix; Relative position encoding captures spatial distance information between points; value vector calculation. , Value weight matrix; ③ Multi-head attention fusion: The outputs of the eight heads are concatenated and a linear transformation is used to obtain the layer attention output. ; To output the weight matrix; ④ Residual connectivity and layer normalization, the formulas are as follows: ; ⑤ Feedforward Network (FFN), employing a two-layer MLP with GELU activation function, enhances the nonlinear representation of features: ; in, , , For bias terms; ⑥ The 4-layer encoder outputs global features (256-dimensional features from 64 seed points) The overall features of a single tooth are obtained through global average pooling. : ; S204-4: Keypoint Coordinate Regression Head: Predicts the 3D coordinates of 6 types of keypoints, with an output dimension of [missing information]. , represented as: ; in, , , , For the first Predicted coordinates of key points; S204-5: Confidence Prediction Header: Outputs the confidence score (0-1 range) for each keypoint, with a dimension of 6, represented as follows: ; in, , For the Sigmoid function, The confidence level is for 6 types of key points.

[0048] In this embodiment, the key point coordinate regression head outputs the three-dimensional coordinates of six types of key points, and the confidence prediction head outputs a confidence score in the 0-1 range through the Sigmoid function. In the coordinate regression loss, the weight of the tooth cusp is set to 2.0, the weight of the near / far midpoint is set to 1.5, and the weight of the inner / outer surface point and the surface axis point is set to 1.0. The true confidence label is based on the coordinate prediction error definition, and the smaller the error, the closer the label value is to 1.

[0049] This application constructs a 7-dimensional comprehensive feature based on 3D coordinates, 1D curvature, and 3D normal vectors. Curvature is calculated by the difference between neighboring points and normal vectors, and normal vectors are solved by eigenvalue decomposition of the covariance matrix. This comprehensively captures the geometric properties and spatial morphological features of the tooth surface. At the same time, a 4-layer PointTransformer module is used to construct a local feature map through FPS farthest point sampling and ball query. Combined with multi-head self-attention mechanism and relative position encoding, the dependency relationship between points is accurately modeled, which greatly improves the consistency and accuracy of key anatomical point prediction and solves the problems of single feature dimension and insufficient capture of spatial relationship in existing methods.

[0050] S205: The loss function design uses weighted MSE loss, while simultaneously constraining coordinate prediction error and confidence calibration, resulting in a total loss. , Weights for confidence loss; S205-1: Coordinate Regression Loss To calculate the average of the squared Euclidean distances between the predicted and actual labeled coordinates, loss weights are applied to highlight key points (cusps, near / far midpoints) in high-curvature regions: ; in, For the first The true coordinates of the key points As weight, tooth cusp Near / far midpoint Inner / outer surface points, surface axis points , The distance is Euclidean.

[0051] S205-2: Confidence calibration loss Cross-entropy loss is used to make the prediction confidence negatively correlated with the coordinate prediction error: ; in, The true label for confidence level is defined as follows: , This is the error threshold; the smaller the error, the better. The closer it is to 1.

[0052] S205-3: The training configuration uses the AdamW optimizer (learning rate 1e-4, weight decay 1e-5), batch size 8, 100 training epochs, and adopts an early stopping strategy, stopping if the validation set loss does not decrease after 5 epochs.

[0053] S206: The PointTransformer model is used to predict feature points in the preprocessed dental arch point cloud and output the three-dimensional coordinates of key anatomical feature points of the dental arch, including the apex of the bilateral canines, the mesial and distal margins of the first molars, the midline of the incisors, and the cervical inflection point of the crown.

[0054] The model performs inference on the preprocessed test set or new patient point cloud data, outputting the three-dimensional coordinates of six key points for each tooth, and also outputting the confidence score of the key points; the threshold is set to 0.7 to filter high-confidence key points.

[0055] The key points of individual teeth are associated according to the order of the dental arch (from left to right, front teeth to back teeth) to form a complete set of key points for the dental arch. Each tooth has 6 key points, and the entire dental arch has a total of 6×14=84 key points, which is adapted to the mainstream distribution of 14 teeth in the Teeth3DS+ dataset.

[0056] From 84 key points, core points directly related to dental arch morphology were selected: midpoint of the incisal edge of the central incisor (derived from the axial point), cusp of the canine, buccal cusp of the premolar (cusp), mesobacterial / disbuccal cusp of the molar (merging of mesobacterial point and cusp), and finally 18 key landmarks were retained (matching the anatomical annotation standards of previous studies).

[0057] Key points and outliers with a confidence level below 0.7 were removed (by fitting the initial curve using the RANSAC algorithm and removing points that are more than 1.5 mm away from the curve).

[0058] The 18 selected key points were projected onto a unified xy plane (the z coordinate was retained for subsequent verification) and sorted in the front-to-back order of the dental arch (left second molar → left first molar → premolar → canine → anterior tooth → right canine → premolar → right first molar → right second molar).

[0059] The coordinates of the sorted key points are normalized by scaling the x / y coordinates to the range of [-10, 10] to eliminate the influence of individual differences in dental arch size on the fitting.

[0060] S207: Based on the dental arch morphology, select the corresponding curve type for preliminary fitting; S207-1: If the dental arch morphology is complete (no missing teeth, no obvious malformations), a quadratic combined with a quartic polynomial model is used as the initial curve. The model expression is: ;in, , For plane coordinates in the normalized coordinate system ( Along the line connecting the first molars on both sides, Along the midline of the dental arch); , These are the initial polynomial coefficients, with initial values ​​referenced from the Welander standard dental arch parameters. , .

[0061] S207-2: If there are missing teeth, local malformations, or jawbone developmental abnormalities in the dental arch, a cubic B-spline curve or NURBS curve should be used as the initial model. The expression for a cubic B-spline curve is: ;in, Let be the three-dimensional coordinates of any point on the curve; For control points (number) (Evenly covering the incisor, canine, and molar regions of the dental arch). The basis functions are cubic B-spline functions, derived from uniformly distributed node vectors. Definition (node ​​vectors satisfy) , (Intermediate nodes are distributed at equal intervals). The NURBS curve expression is: ;in, Control points Weighting coefficients for densely packed tooth areas This enhances the influence of the region on the curve morphology; areas with missing teeth. This reduces interference in the area and avoids distortion of the curve shape.

[0062] S207-3: Curve fitting based on constraint optimization uses least squares preliminary fitting: extracting... dental arch feature points The error function is defined as the sum of squared distances from the feature points to the initial curve, and the optimal model parameters are solved by the least squares method.

[0063] For a polynomial model, the error function is: ; right , Taking the partial derivatives and setting them to zero, we can transform the problem into a linear matrix equation. ,in: ; ; For B-spline NURBS curves, the error function is the sum of squared shortest distances from feature points to the curve, expressed as: ; Iterative optimization method: First fix the control points Each feature point is solved using the bisection method. Corresponding optimal parameters To minimize the distance; then fix Transform the error function into a function of... The linear function is updated using the least squares method. Repeat the iteration until the error is reached. Convergence (convergence threshold set to) );

[0064] In this embodiment, during the initial fitting of the polynomial model, the optimal coefficients are solved using the least squares method to minimize the sum of squared distances from feature points to the curve. The cubic B-spline curve has 8-12 control points, and the basis function is defined using uniformly distributed node vectors. The NURBS curve assigns weight coefficients to the control points, with a weight of 1.2-1.5 for densely toothed areas and 0.5-0.8 for areas with missing teeth. The initial fitting of the B-spline and NURBS curves employs an iterative optimization method, alternately updating the optimal parameters and control point positions until the error converges.

[0065] S208: Perform multi-constraint optimization and local correction on the fitted dental arch curve;

[0066] Anatomical constraint optimization: introduce hard and soft constraints to ensure that the fitted curve conforms to the anatomical rules of the oral cavity; S208-1: Hard constraints force the curve to pass through key anatomical feature points (bilateral canine apexes, dental arch midline points). For the polynomial model, the Lagrange multiplier method is used to substitute the constraints into the matrix equation to construct the augmented objective function: ;in, , For Lagrange multipliers, ( ) represents the coordinates of the vertex of the canine. () represents the coordinates of the centerline point; for B-spline curves, the positions of the corresponding control points are directly fixed to ensure that the curve passes through the feature points; S208-2: Soft constraint, controlling bilateral morphological symmetry of the dental arch (allowing ±5% physiological difference), defining the symmetry error function: ;in, Parameter points for unilateral dental arches ( (Number, evenly distributed) , For the curve at the symmetrical position coordinate; Incorporate the symmetry error into the total error function: ;in, These are weighting coefficients to balance data fit and symmetry. S208-3: Energy function optimization. If the point cloud contains jawbone surface information, define an energy function based on point cloud intensity and distance to ensure the curve lies in the anatomical center region of the jawbone. ; in, , The points on the jawbone above and below the curve are respectively clustered; For point The intensity value, reflecting the density of the jawbone, is output by the scanning equipment; Distance weights Points closer to the curve have greater weight; , Add cloud dots to the jawbone The extreme value of the direction. By minimizing the energy integral. Adjust the curve along The orientation and position are adjusted to fit the center of the jawbone.

[0067] S208-4: Fitting result optimization and correction, deviation analysis, calculation of the shortest distance between the fitted curve and the original point cloud. Statistical deviation mean with standard deviation ,Will The region was identified as an area with excessive local deviation (usually caused by tilted teeth or localized dense point clouds).

[0068] S208-5: Local adjustment of dental arch curve; for polynomial models, introduce a sixth-order term in the deviation region. After segmented correction, the corrected model is as follows: ; in, For the deviation area Coordinate range The solution is obtained by local least squares method; for B-spline NURBS curves, only 2 to 3 adjacent control points corresponding to the deviation area are adjusted to avoid changes in the overall curve shape by utilizing the local support of B-spline. S208-6: Smoothness constraint, ensuring that the curve curvature changes smoothly, conforming to the "continuous arc" anatomical characteristics of the dental arch, defining the smoothness error function: ; in, It is the second derivative of the curve (reflecting the rate of change of curvature).

[0069] Incorporating the smoothness error into the total error function, it can be expressed as: ; in To smooth the weights, minimize To achieve the triple goals of data fit, symmetry and rationality, and smooth shape.

[0070] In this embodiment, the anatomical hard constraints optimize the polynomial model using the Lagrange multiplier method, while the corresponding control point positions are directly fixed for the B-spline curves. The symmetry soft constraints construct an error function by calculating the coordinate differences of the symmetrical positions of the dental arches on one side, with weighting coefficients set to 0.3-0.5. The energy function adjusts the curve to the anatomical center region of the jawbone by balancing the intensity and distance information of the jawbone point clouds above and below the curve. The smoothness constraints construct an error function based on the second derivative of the curve, with weighting coefficients set to 0.1-0.2, which together with other error terms constitute the total error function.

[0071] S209: Segmented blending and splicing of dental arch curves;

[0072] A hybrid model combining circular curves and quartic polynomials was employed to accommodate the morphological differences between the anterior and posterior segments of the dental arch: the anterior segment (left first premolar → right first premolar) was fitted with circular curves (the anterior teeth arrangement exhibits an arc-like characteristic), while the posterior segment (distal to the first premolar → second molar) was fitted with a quartic polynomial (AX). 4 +BX²) fitting (the posterior segment shows a gradual convergence trend).

[0073] S209-1: Six key points were extracted from the anterior segment (buccal cusp of the left first premolar, midpoint of the incisal edge of the central incisor, and buccal cusp of the right first premolar). The circle equation (xa)² + (yb)² = R² was solved using the least squares method, where the center (a, b) and radius R were obtained through iterative optimization of the key point coordinates. Based on the correlation of key points in the Teeth3DS+ dataset, a regression equation was used to correct the radius and improve the fitting accuracy. S209-2: Extract 12 key points from the posterior tooth segment (left second molar, distal left first premolar, distal right first premolar, and right second molar), and substitute them into the quartic polynomial equation y=AX. 4 +BX²; S209-3: Achieve a smooth splicing of circular curve and fourth-order polynomial at the key point of the first premolar, ensuring that the slope of the tangent at the splicing point is consistent, forming a complete 3D dental arch curve (retaining xyz coordinates, with the z coordinate reflecting the vertical height distribution of the teeth). S209-4: Calculate the mean distance error (MAE) between the fitted curve and the original keypoints. If MAE > 0.8 mm, iteratively adjust the circle radius and polynomial coefficient B until MAE ≤ 0.8 mm. The standard settings refer to the annotation accuracy standard of the Teeth3DS+ dataset. S209-5: Use Bézier curves to smooth the splice area, eliminate abrupt changes between the two curves, and ensure the overall continuity of the dental arch curve (smoothing factor set to 0.3). S209-6: Based on the functional occlusion annotations of the Teeth3DS+ dataset, the parameters of the posterior tooth segment curves were adjusted to ensure that the fitted dental arch curves met the following requirements: stable vertical support for posterior teeth in centric occlusion (ICP) and minimal load on anterior teeth; and no interference with canine guidance during lateral movements. S209-7: Based on the tilt information of the face axis point, correct the lateral tilt angle of the dental arch curve so that the curve is consistent with the actual tooth arrangement angle; S209-8: Introduce comprehensive tooth width parameters (Σ2-2, Σ3-3, Σ4-4) for cross-validation. Calculate the width of the entire anterior region using the regression equation Σ5-5=2.0948×Σ2-2+18.6, calibrate the radius of the circular curve and the polynomial coefficients, and ensure that the fitting results are strongly correlated with individual tooth dimensions, with a correlation coefficient r≥0.85. S210: Output 3D dental arch curve data: including the three-dimensional coordinate point set of the curve (one sampling point every 1mm), circular curve parameters (center, radius), and fourth-order polynomial coefficients (A, B). S211: Outputs visualization results, plotting a superimposed image of the 3D dental arch curve and the original point cloud using Matplotlib / Mayavi, annotating the key point positions and fitting errors; outputs .obj format files, supporting import into CAD software for orthodontic appliance design.

[0074] Reference Figure 4The diagram shows the steps for fitting the dental arch curve based on predicted key points. This application designs an adaptive model selection mechanism that dynamically switches between three initial models—a quadratic-quartic polynomial combined with a 3rd-order B-spline curve and a NURBS curve—based on the integrity of the dental arch. The NURBS curve reduces interference from missing areas by setting differentiated weights for control points (1.2-1.5 for densely packed teeth and 0.5-0.8 for missing teeth), addressing the limitation of single models in adapting to complex dental arch scenarios. At the constraint optimization level, this application constructs a multi-dimensional constraint system including anatomical hard constraints, symmetry soft constraints, smoothness constraints, and jawbone energy constraints. Hard constraints force the curve through key anatomical points such as canine apexes and the midline of the dental arch; soft constraints control bilateral morphological symmetry (allowing ±5% physiological difference); energy constraints adjust the curve position by balancing jawbone point cloud intensity and distance information; and smoothness constraints ensure a gentle morphology based on the second derivative of the curve. This ensures that the reconstructed curve both fits the data and conforms to oral anatomy, overcoming the shortcomings of existing methods in terms of constraint mechanisms. At the curve fitting level, a hybrid model combining circular curves and fourth-order polynomials is adopted. The radius of the circle in the anterior segment is corrected based on the comprehensive width of the incisors, and the polynomial coefficients in the posterior segment are corrected based on the mesial distance of the first molar. Smooth splicing is achieved through Bézier curves. At the same time, confidence screening (threshold 0.7) is introduced to remove key points with low reliability. Cross-validation is combined with the comprehensive tooth width parameter (correlation coefficient ≥ 0.85) to ensure the overall continuity of the curve and local accuracy. This solves the problems of insufficient difference in fitting between the anterior and posterior segments and inconsistent reliability of key points in existing methods.

[0075] This invention significantly improves fitting accuracy, reduces prediction errors for key anatomical points, and achieves an average curve distance error of ≤0.8mm, far exceeding the accuracy of existing 3D reconstruction methods. Simultaneously, it offers enhanced scenario adaptability, flexibly addressing various clinical scenarios such as complete dental arches, missing teeth, and jaw deformities, without requiring manual adjustment of model parameters. Furthermore, it boasts higher clinical applicability, as the reconstructed curves conform to oral anatomy and meet functional occlusion requirements. The output .obj format file can be directly imported into CAD software for orthodontic appliance design, seamlessly integrating with digital treatment processes and significantly improving clinical efficiency and the rationality of treatment plans.

[0076] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0077] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0078] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0079] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0080] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for reconstructing dental arch curves from 3D oral point cloud data, characterized in that, include: Based on the key points of each tooth in the 3D oral scan data, the tooth point cloud of each tooth is obtained by conversion; Obtain the true 3D coordinates, curvature, and 3D normal vector of each key point in each tooth point cloud, and use them as the target feature vector of each key point in each tooth point cloud. Input the target feature vectors of all key points in the tooth point cloud into the initial PointTransformer model to obtain multiple predicted key points of the tooth point cloud, their predicted 3D coordinates, and prediction confidence scores, including: Based on linear transformation and sinusoidal position coding, the target feature vectors of each key point are mapped to a high-dimensional semantic feature space to obtain the high-dimensional semantic features of each key point. The high-dimensional semantic features of each key point are passed through multiple attention modules that are sequentially connected along the forward propagation direction and have residual connections between layers. The attention features output by the last attention module are obtained as the global features of each key point. The attention module includes local neighborhood sampling, self-attention calculation, feature aggregation and feedforward network sequentially connected along the forward propagation direction. Global average pooling is performed on the global features of all key points to obtain the overall features of the tooth point cloud. The overall features of the tooth point cloud are input into the coordinate regression head to obtain multiple predicted key points of the tooth point cloud and their predicted 3D coordinates. The overall features of the tooth point cloud are input into the confidence prediction head to obtain multiple prediction key points of the tooth point cloud and their prediction confidence. Based on the true and predicted 3D coordinates of each key point, as well as the true and predicted confidence scores, coordinate regression loss and confidence calibration loss are constructed to train the initial PointTransformer model and obtain the target PointTransformer model. The 3D oral cavity point cloud to be reconstructed is input into the target PointTransformer model to obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth. Predicted key points with confidence higher than the preset confidence threshold are filtered out and associated according to the dental arch sequence to form a set of dental arch key points. Key landmarks are selected from the set of dental arch key points, and dental arch curves are reconstructed based on the key landmarks.

2. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 1, characterized in that, The 3D oral cavity point cloud to be reconstructed is input into the target PointTransformer model to obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth. Predicted key points with confidence higher than the preset confidence threshold are filtered out and associated according to the dental arch order to form a set of dental arch key points. Key landmarks are selected from the set of key points in the dental arch, and dental arch curves are reconstructed based on these key landmarks, including: The 3D oral cavity point cloud to be reconstructed is input into the target PointTransformer model to obtain the three-dimensional coordinates and confidence of each predicted key point in each tooth. Predicted key points with confidence higher than the preset confidence threshold are selected as high confidence key points. The high-confidence key points are sorted according to the physiological order of the dental arch to form a set of dental arch key points; Based on the type of key point and the location of the tooth to which it belongs, multiple key landmarks are selected from the set of key points in the dental arch; Multiple key landmarks are projected onto the occlusal plane to obtain the initial dental arch morphology: If the initial dental arch morphology is complete, then a quadratic combined with a quartic polynomial model is used as the initial curve. If there are abnormalities in the initial dental arch morphology, a cubic B-spline curve or a NURBS curve shall be used as the initial curve. The target dental arch curve is obtained by fitting the initial curve using the least squares method.

3. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 2, characterized in that, After obtaining the target dental arch curve, the process includes performing multi-constraint optimization on the target dental arch curve to obtain the optimized dental arch curve, including: Anatomical hard constraints are applied to the target dental arch curve, causing it to pass through all key landmarks in the 3D oral cavity point cloud to be reconstructed, thus obtaining the first dental arch curve; A symmetrical soft constraint is applied to the first dental arch curve to ensure that the distance between a pair of key landmarks symmetrical to the first dental arch curve is no greater than a preset physiological difference, and then the second dental arch curve is obtained. Apply a smoothness constraint to the second dental arch curve so that the curvature at each position on the second dental arch curve is not greater than a preset curvature threshold, and then obtain the third dental arch curve. The third dental arch curve is subjected to jawbone energy constraint, so that the third dental arch curve is located in the preset jawbone anatomical center region, and an optimized dental arch curve is obtained.

4. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 3, characterized in that, After obtaining the optimized dental arch curve, the process includes segmenting, blending, and splicing the optimized dental arch curve to obtain the suitable dental arch curve, including: For the portion of the arch curve corresponding to the anterior segment, circular curve fitting is used, and the radius of the circle is adjusted based on the comprehensive width of the incisors to obtain the anterior segment curve; For the portion of the arch curve corresponding to the posterior segment, a fourth-order polynomial is used for fitting, and the polynomial coefficients are corrected by the distance to the mesial point of the first molar to obtain the posterior curve. At the junction of the front and rear curves, a Bezier curve is used to smoothly splice them together to obtain the appropriate dental arch curve.

5. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 4, characterized in that, After obtaining the appropriate dental arch curve, local adjustments are made to the appropriate dental arch curve, including: Calculate the shortest distance between the fitted dental arch curve and each key landmark point of the 3D oral cavity point cloud to be reconstructed, and obtain the mean and standard deviation of the deviation of all shortest distances; The area containing key landmarks whose shortest distance is greater than the sum of the mean deviation and twice the standard deviation is considered as an area with excessive local deviation. Based on the type of the initial curve used for adapting the dental arch curve, local adjustments are made to the adapting dental arch curve, including: If the initial curve is a quadratic combined with a quartic polynomial model, then a sixth-order term is introduced in the region where the local deviation is too large for piecewise correction. If the initial curve is a cubic B-spline curve or a NURBS curve, then the curve shape control points corresponding to the areas with excessive local deviations will be fine-tuned.

6. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 1, characterized in that, Key points of a tooth include the mesial point, distal point, cusp, inner surface point, outer surface point, and axial point. Key landmarks include the midpoint of the incisal edge of the central incisors on the left and right sides, the cusp of the canines, the buccal cusp of the premolars, the mesiobuccal cusp of the molars, and the distobuccal cusp of the molars.

7. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 1, characterized in that, Obtain the true 3D coordinates, curvature, and 3D normal vector of each key point in each tooth point cloud, and use them as the target feature vectors of each key point in each tooth point cloud, including: Based on key points True 3D coordinates Obtain key points neighborhood point set ; Calculate key points using the mean curvature formula. curvature : ; Key points The key points are obtained by averaging the true 3D coordinates of the neighboring points in the neighborhood point set. Mean three-dimensional coordinates , is represented as: ; Based on key points Calculate key points using the mean 3D coordinates of the given data and the true 3D coordinates of neighboring points in the neighborhood point set. covariance matrix , is represented as: ; Key points The covariance matrix is ​​subjected to eigenvalue decomposition to obtain the eigenvector corresponding to the smallest eigenvalue, which is used as the three-dimensional normal vector, represented as: ; Key points Target feature vector , is represented as: ; in, Indicate key points neighborhood point set The number of middle neighbor points; and They represent key points respectively. neighborhood point set The Middle The true 3D coordinates and 3D normal vectors of each neighboring point.

8. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 1, characterized in that, The attention module comprises a local neighborhood sampling unit, a self-attention calculation unit, a feature aggregation unit, and a feedforward network, sequentially connected in the forward propagation direction, including: The local neighborhood sampling unit selects M seed points from the input features using the farthest point sampling, performs ball query on each seed point, and obtains local features; The self-attention computation unit calculates the scoring function between points in the local features using a multi-head attention mechanism, and then constructs the dependency relationship between points in the local features based on a sparse self-attention mechanism. The feature aggregation unit concatenates the dependencies between points in the local features and then performs a linear transformation to obtain aggregated features. The feedforward network activates and normalizes the aggregated features through a multilayer perceptron to obtain attention feature outputs.

9. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 1, characterized in that, Based on the true and predicted 3D coordinates of each key point, as well as the true and predicted confidence scores, coordinate regression loss and confidence calibration loss are constructed, including: Based on the true 3D coordinates of each key point With predicted three-dimensional coordinates Construct coordinate regression loss , is represented as: ； True confidence level based on each key point With prediction confidence Construct confidence calibration loss , is represented as: ； Based on coordinate regression loss With confidence calibration loss Construct the total loss function , is represented as: ; in, Indicates the total number of key point categories. Indicates the preset category weights. Represents Euclidean distance; true confidence level. Represented as , Indicates the preset error threshold; This indicates the preset proportional weight.

10. The 3D oral cavity point cloud dental arch curve reconstruction method according to claim 1, characterized in that, After obtaining the point cloud of each tooth, the point cloud of the tooth is preprocessed; before inputting the 3D oral cavity point cloud to be reconstructed into the target PointTransformer model, the 3D oral cavity point cloud to be reconstructed is preprocessed. Point cloud preprocessing includes: Using the midpoint of the mandibular central incisor landmark as the zero coordinate point, a horizontal xy plane is constructed. The z coordinate of the point cloud is normalized, and the point cloud is projected onto a unified coordinate system. And / or, use statistical filtering to remove outliers from the point cloud; And / or, downsample the point cloud so that the point density of the downsampled point cloud is within a preset density range; And / or, randomly flip, translate, scale, or add Gaussian noise to the point cloud.

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