CBCT jaw bone rapid morphing simulation method and system based on arap optimization

Abstract

This invention discloses a rapid deformation simulation method for CBCT jawbone based on ARAP, with the following steps: S1. Obtain the jawbone surface mesh and tooth model, and perform hole closure preprocessing on the cavities in the jawbone surface mesh; S2. Construct an accelerated structure and surface mesh deformation solution object for the closed jawbone mesh; S3. Receive the pose transformation matrix corresponding to the tooth model, apply boundary conditions to the tooth model simultaneously in one solution, and execute ARAP solution to output the deformed jawbone mesh; S4. Perform result verification on the deformed jawbone mesh. If the verification fails, implement a repair or degradation strategy and output the result; if the verification passes, output the deformed jawbone mesh. This scheme has high efficiency, maintains the local rigidity characteristics of the solution while ensuring stability, and improves clinical credibility. This invention also discloses a corresponding ARAP-optimized rapid deformation simulation system for CBCT jawbone.

Description

Technical Field

[0001] This invention relates to the fields of computer graphics and medical image processing technology, specifically to a CBCT jawbone rapid deformation simulation method and system based on ARAP-optimized multi-tooth independent control and closed mesh preprocessing. Background Technology

[0002] Currently, more and more digital technologies are being applied to the field of oral medicine. In clinical scenarios such as dental implants and orthodontics, CBCT technology is often used to obtain anatomical images of the oral and maxillofacial region, and combined with finite element analysis (FEA) or physics-based deformation simulation technology [such as ARAP (As-Rigid-As-Possible) optimization technology] to achieve rapid deformation prediction.

[0003] Existing methods for simulating jawbone deformation often solve on open meshes or approximate single-tooth / global rigid bodies. However, in practical applications, directly performing ARAP or similar geometric energy calculations on open jawbone / gingival surface meshes (with openings) frequently leads to instability and surface breaks. This is because the ARAP method relies on local geometry to maintain the rigidity of deformation. When the mesh contains openings or discontinuous regions, local adjacency relationships become incomplete or inconsistent, resulting in numerical instability or deformation distortion during the optimization process.

[0004] In addition, many systems treat single teeth or the entire dentition as rigid bodies, and control the loss of multiple teeth simultaneously, which makes it difficult to reflect the situation of 14 teeth moving independently and in coordination in real clinical practice.

[0005] Furthermore, many systems suffer from excessively long end-to-end processing times (typically in the range of 10-20 minutes) due to the coupled preprocessing and solution processes, where hole closure, constraint construction, and solution are executed in a mixed manner, hindering interactivity. There are also issues with the repeated construction of data structures, such as AABB trees, sparse decomposition, and deformable objects being generated repeatedly in each solution, wasting computational resources. Therefore, a more efficient simulation method and system that can provide more stable data for clinical use is needed. Summary of the Invention

[0006] To address the issues raised in the background, this solution provides a rapid simulation method and system that supports independent and simultaneous control of 14 teeth under closed mesh conditions, and decouples the preparation phase from the moving solution phase while maintaining reusable data structures, achieving near real-time interactive performance and stability suitable for clinical use.

[0007] The technical solution adopted by this invention to solve its technical problem is as follows: a rapid deformation simulation method for the jawbone based on ARAP optimization in CBCT, the steps of which are as follows: S1. Obtain the surface mesh of the jawbone to be simulated and the tooth model on the same jawbone, and perform hole closure preprocessing on the surface mesh of the jawbone to output a closed jawbone mesh; S2. Construct an acceleration structure for nearest neighbor query or intersection / distance calculation on the closed jawbone mesh, and construct a surface mesh deformation solution object based on ARAP; generate control points and / or constraint regions for each tooth in the tooth model to form a control set; pre-decompose the linear system corresponding to the solution object to obtain reusable decomposition results, and associate and store the closed jawbone mesh, acceleration structure, control set and decomposition results as reusable handles; S3. Receive the pose transformation matrix corresponding to the tooth model, where the unmoved teeth correspond to the identity matrix; update the target constraints of the control set based on the pose transformation matrix of each tooth; apply the boundary conditions of the tooth model and perform ARAP solution in one solution; if the solution fails, execute the repair or degradation strategy; if the solution is successful, output the deformed jawbone mesh. S4. Perform result verification on the deformed jawbone mesh. If the verification fails, execute the repair or downgrade strategy and output the result. If the verification passes, output the deformed jawbone mesh.

[0008] Furthermore, the jawbone surface mesh includes a maxillary surface mesh and / or a mandibular surface mesh, and the tooth model consists of N teeth on the same jawbone, where N is a positive integer, preferably N is 14. Steps S1 to S4 are performed on the maxillary surface mesh and the mandibular surface mesh respectively to obtain the deformed jawbone meshes of the maxilla and mandible and their corresponding handles.

[0009] Furthermore, in step S1, the operation steps for the hole closure pretreatment are as follows: a) Extract the boundary ring of the hole; b) Sort the holes in descending order of the perimeter of the boundary rings; c) Generate patch triangles sequentially for the sorted holes to achieve hole closure; d) Smooth / fair the patch triangles to ensure geometric continuity with the original jawbone surface mesh.

[0010] Furthermore, in step S1, a geometric consistency check is performed before outputting the closed jawbone mesh. The geometric consistency check includes at least: boundary edge check, manifold check, duplicate vertex check, degenerate triangle check, and normal consistency check; and requires that there be no boundary edges, no duplicate vertices, no degenerate triangles, and consistent normals.

[0011] Furthermore, step S1 also includes performing an outward expansion process on the tooth model to increase the probability of intersection between the tooth and the jawbone; performing a joint refinement process on the outward-expanded tooth model and the jawbone surface mesh to form a clear intersection line; and using the outward-expanded tooth model to trim the jawbone surface mesh to remove the jawbone mesh located inside the tooth, thereby forming a hole to be closed on the trimmed jawbone mesh.

[0012] Furthermore, step S1 or step S2 also includes performing remeshing on the closed jawbone mesh to improve the quality of the closed jawbone mesh and suppress degenerate elements, thereby improving the stability of ARAP solution.

[0013] Furthermore, the handle includes two or more of the following: closed jawbone mesh data, accelerated structure, ARAP-based surface mesh deformation solution object, control set, linear system pre-decomposition results, vertex-to-tooth mapping relationship, and mesh quality / diagnostic metadata; the handle is uniquely identified and persistently stored through a handle identifier, and the ARAP linear system pre-decomposition results can be reused in subsequent solutions through the handle identifier. Specifically, the ARAP linear system pre-decomposition results are pre-calculated in step S2 for the linear system corresponding to the ARAP-based surface mesh deformation solution object and stored in association with the handle identifier. The "subsequent solution" specifically refers to step S3, after receiving the pose transformation matrix corresponding to the tooth model, performing ARAP linear system solution on the updated target constraints to obtain the deformed jawbone mesh.

[0014] Furthermore, the method for reusing the pre-decomposition results of the ARAP linear system in this scheme includes a preparation call and a solution call: the preparation call is performed in steps S1 and S2 to generate the handle identifier; the solution call is performed in step S3, and the handle identifier and the pose transformation matrix corresponding to the tooth model are input. Each solution call corresponds to one ARAP solution, and the boundary conditions of multiple teeth are applied simultaneously in this ARAP solution, rather than solving for each tooth individually.

[0015] Furthermore, when the topology of the closed jawbone mesh remains unchanged and the topology of the control set remains unchanged, the pre-decomposition results of the linear system are reused in the ARAP solution of subsequent steps S3; when either of the reuse conditions (the topology of the closed jawbone mesh remains unchanged and the topology of the control set remains unchanged) is not met, the handle is invalidated, and step S2 is re-executed to reconstruct the acceleration structure, the solution object, the control set, and the pre-decomposition results of the linear system, and then the ARAP solution of step S3 is executed.

[0016] Furthermore, step S2, generating control points and / or constraint regions per tooth, includes: dividing the vertices of the closed jawbone mesh into control point sets and interest region sets based on their distances to the corresponding tooth models using the acceleration structure; and setting different constraint methods or weights for different sets to achieve independent control and collaborative solution for multiple teeth. Specifically, hard constraints are set for the control point sets, and soft constraints are set for the interest region sets; or, based on the distance from the vertex to the tooth or anatomical partition, regionalized stiffness weights are assigned to the vertices, making the weights near the periodontal region lower than those in the distal bone region.

[0017] Furthermore, the result verification in step S4 also includes local distortion threshold verification, which is used to measure the degree to which local deformation deviates from rigid rotation, and triggers the repair or degradation strategy when the maximum distortion exceeds a preset threshold.

[0018] Furthermore, the repair or downgrade strategy includes at least one of the following: a) Perform reshaping or remeshing on the mesh before solving; b) Output only the closed jawbone mesh after closed preprocessing, without outputting the ARAP deformation results; c) If the current solution fails, output the deformation result that passed the previous verification.

[0019] This invention also discloses a CBCT fast deformation simulation system based on ARAP optimization, including a data connection interface unit, a mesh preprocessing unit, a mesh closure unit, a preparation unit, a moving solver unit, a persistent reuse unit, and a verification and degradation unit; The interface unit is used to receive and convert the jawbone surface mesh, tooth model, and tooth pose transformation matrix. The mesh preprocessing unit is used to perform hole closure preprocessing on the jawbone mesh; The preparation unit is used to construct the acceleration structure and ARAP deformation solution object on the closed jawbone mesh, and generate control sets tooth by tooth; The mesh closure unit is used to output a closed jawbone mesh; The persistent reuse unit is used to perform pre-decomposition on the ARAP linear system and associate and store the closed jawbone mesh, acceleration structure, control set and pre-decomposition results as a reusable handle; The moving solver unit is used to receive the pose transformation matrix of multiple teeth and simultaneously apply multi-tooth boundary conditions to perform ARAP solution in one solution to output the deformed jawbone mesh. The verification and degradation unit is used to perform closure and finiteness verification on the solution results, and to execute repair or degradation strategies to output results when the verification fails or the solution fails.

[0020] Furthermore, the interface unit provides a network interface to support separate calls between the preparation phase and the solution phase. The preparation phase outputs a handle identifier, and the solution phase inputs the handle identifier and the pose transformation matrix to reuse the pre-decomposition results.

[0021] Furthermore, the verification and degradation unit is also used to output quality indicators and performance indicators corresponding to the results, and the performance indicators include at least the time consumed in the preprocessing stage and the time consumed in the moving solution stage.

[0022] The beneficial effects of this invention are as follows: This scheme takes closed mesh + multi-tooth synchronous control as its core premise, removes the time-consuming preprocessing from the interactive closed loop, and achieves near real-time in the movement stage; through sparse decomposition reuse and AABB acceleration, redundant construction is reduced; the initial deformation solution time can be reduced to about 16.1 seconds, the number of mesh boundary edges after solution is 0, and the maximum value of the distortion index does not exceed 0.5, maintaining the local rigidity characteristics of the solution while ensuring stability, thus improving clinical reliability. The system structure of this scheme is simple, easy to construct, and can quickly and stably handle jawbone deformation simulation work. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention; Figures 2a-2c This is a schematic diagram of the operation of step S1 in the method of the present invention; Figure 3 This is a schematic diagram of step S2 of the method of the present invention; Figure 4a A schematic diagram of step S3 in method S3 of -4c; Figure 5 This is a system block diagram of the present invention. Detailed Implementation

[0024] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0025] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0026] The jawbone surface mesh described in this solution includes a maxillary surface mesh and / or a mandibular surface mesh. In this embodiment, mandibular manipulation is used as an example to illustrate the specific implementation process of the ARAP-optimized CBCT jawbone mesh rapid deformation simulation method. It should be understood that this embodiment is only for explaining the invention and does not limit the scope of protection; the same method is also applicable to the maxilla.

[0027] A CBCT jawbone rapid deformation simulation system based on ARAP optimization, such as Figure 1 As shown, the steps include: S1. Mesh preprocessing, S2. Preparation stage, S3. Tooth movement stage, S4. Mesh verification.

[0028] Furthermore, step S1 includes the following steps: S1.0. Input Data like Figure 2a As shown, the input data includes: The mandibular surface mesh file Mandible_Fused.stl to be simulated is a triangular mesh obtained after CBCT segmentation, which contains multiple openings and holes; Model files for the 14 teeth on the mandible, from Tooth_31_Fused.stl to Tooth_47_Fused.stl; The pose transformation matrix T

[14] of the 14 tooth model is a 4×4 homogeneous transformation matrix for each tooth; the unmoved teeth use the identity matrix.

[0029] The runtime environment backend of this embodiment is implemented in C++. Geometry processing can use the CGAL library, and sparse linear algebra can use Eigen or SuiteSparse. The interface layer can provide / prepare and / solve via REST, or provide local SDK calls. The libraries here are merely examples and can be replaced with equivalent implementations.

[0030] S1.1. Mesh Preprocessing and Closure like Figure 2b and 2c As shown, a hole-closing preprocessing is performed on the jawbone surface mesh, and a geometric consistency check is conducted to obtain a closed jawbone mesh. The specific operation steps are as follows: S1.1.1. Preparation for hole generation: Considering the often very small gaps between the tooth model and the jawbone mesh obtained from CBCT segmentation, direct cutting can easily result in unclear intersection lines or missed cuts. In this embodiment, each tooth mesh in the tooth model is expanded outwards (e.g., by 0.2 mm) to increase the probability of intersection with the jawbone. This is because the jawbone and tooth models generated by CT scans often fit closely but have some gaps; expanding each tooth by 0.2 mm ensures that the teeth and jawbone intersect. Subsequently, the expanded teeth and mandibular bone meshes are co-refined to form a clear intersection line; then, the co-refined mandibular bone is cut using the expanded teeth to remove the jawbone mesh located inside the teeth. After cutting, at least 14 open holes are formed on the surface of the mandible.

[0031] S1.1.2. Batch hole closure: (1) Extracting the hole boundary rings: Extract all hole boundary rings from the mandibular mesh; (2) Sort in descending order by the perimeter of the hole boundary ring; (3) Generate patch triangles for each hole: Use triangulation and refinement hole-filling strategies to generate patches; (4) Perform smoothing / fairing processing on the patch area: make the patch transition smoothly with the original mesh, and avoid sharp wrinkles affecting the stability of subsequent ARAP solutions.

[0032] S1.1.3. Geometric consistency check: a. Boundary edge check: holes == 0 (no boundary edges) b. Manifold check: manifold == true (2-manifold), no mesh self-intersection. c. Vertex deduplication: Tolerance 1e-6, no duplicate vertices. d. Degenerate triangular inspection: Area > 1e-10, no degenerate surfaces; S1.2. After successful verification, output the closed mandibular grid: For example, Mandible_trimmed.stl (fills holes and is optimized to 259,621 vertices via isotropic remeshing).

[0033] Preferably, isotropic remeshing can be further performed on the closed mandibular mesh to improve mesh quality and suppress degenerate elements, thereby improving ARAP solution stability.

[0034] Furthermore, the preparation phase of step S2 includes: constructing the deformable object, controlling the set, and pre-decomposing the cache. For example... Figure 3 As shown, a one-time preparation process is performed on a closed mesh, allowing the computation results to be reused in subsequent interactive moves. The specific steps are as follows: S2.1. Constructing the accelerated structure and ARAP deformation solution object: Acceleration structures (e.g., AABB trees or BVH) are constructed on closed mandibular meshes for: (1) Assign the apex of the jawbone to the nearest tooth; (2) Calculate the minimum distance from the vertex to the tooth surface; (3) Accelerate ROI generation and control point location.

[0035] Simultaneously, construct a surface mesh deformation solution object (such as an ARAP deformer) and establish the adjacency, Laplacian weights, and energy terms required for subsequent solutions.

[0036] S2.2. Generate control points / constraint regions one tooth at a time to form a control set: like Figure 4a As shown, control sets are established tooth by tooth, with each tooth constituting a unit of 14 teeth. Example rules are as follows: Control point set: Select the jawbone apex as control points from the area near the tooth attachment region (e.g., less than control_dist from the tooth surface); ROI set: Select jaw vertices as ROIs within a larger neighborhood (e.g., less than roi_dist from the tooth surface); Vertex-to-teeth mapping table: Records the nearest tooth number for each jawbone vertex, used to merge the constraint objectives of all teeth in a single solution.

[0037] Optional enhancements: Different stiffness weights can be assigned to different anatomical regions (e.g., lower weights for the periodontal ligament region and higher weights for the distal bone region) to improve clinical credibility.

[0038] S2.3. Pre-decompose ARAP linear systems and generate handle caches: In step S2, the linear system corresponding to the ARAP-based surface mesh deformation solution object is pre-decomposed. This pre-decomposition is used for the ARAP solution in the subsequent step S3. The pre-decomposition itself is a pre-calculation operation in the preparation stage and is not a solution step for outputting the deformed jawbone mesh.

[0039] Pre-decomposition can be implemented using LDLT, Cholesky, or other sparse decomposition methods, and at least two of the following should be associated and stored as handles: closed mandibular mesh data, accelerated structure, ARAP-based surface mesh deformation solution object, control set (14 tooth control points and ROIs and their weights / types), linear system pre-decomposition results, vertex-to-tooth mapping relationships, and quality diagnostic metadata. These handles are identified by handle_id and persistently stored. The ARAP linear system pre-decomposition results can be reused in subsequent solutions using this handle identifier.

[0040] In subsequent calls, if the topology of the closed mandibular mesh remains unchanged and the topological relationship of the control set remains unchanged, the linear system pre-decomposition results can be directly reused in each ARAP solution in step S3, and only the target constraints need to be updated; if the mesh topology changes or the control set changes, the handle becomes invalid, and step S2 needs to be re-executed to reconstruct the linear system pre-decomposition results before step S3 is executed.

[0041] Furthermore, step S3 includes tooth movement and a one-time solution of multi-tooth boundary conditions, receiving the pose transformation matrices of 14 teeth and performing a one-time solution. For example... Figures 4b-4c As shown, the specific steps are as follows: S3.1. Receive the pose matrix and construct target constraints Input T

[14] receives the pose matrix corresponding to the tooth model, and the identity matrix for the unmoved teeth. For each tooth: a. Using the initial position of the control point of the tooth as a reference, the coordinates of the control point are transformed using the pose matrix to obtain the target position; b. Write the target location of the control point of the tooth together with the ROI soft constraint into a unified set of boundary conditions.

[0042] S3.2. Simultaneous application of multi-tooth boundary conditions in a single solution Boundary conditions for all 14 teeth are applied and solved simultaneously in the same ARAP linear system to obtain the deformed mandibular mesh. If the solution fails, a repair or degradation strategy is implemented. By reusing the pre-decomposition results of S2, subsequent interactive adjustments only update the target constraints and solve quickly.

[0043] During this period, to facilitate engineering optimization and regression, two types of time consumption, tp and tm, were recorded. The purpose of recording tp and tm is to track performance optimization. tp (mesh preprocessing time): Measures the one-time setup cost and identifies preprocessing bottlenecks. tm (Total time spent in the movement phase): Measures the final interaction performance.

[0044] To address the issue of long processing times in existing problems, optimizations can be achieved by separating the execution of the TP / TM stages and using persistent caching of data structures.

[0045] tp phase (one-time): includes mesh closure processing, AABB construction, matrix decomposition, and control point generation; tm stage (repeatable): Only update the control objective, solve quickly.

[0046] Persistent caching First call: Build and cache (included in tp) Subsequent calls: direct reuse (only tm is counted) Actual measurement evidence (based on actual execution logs): Use case: Interactive tooth movement planning (14 teeth) Initial setup (tp): The system performs a preparation phase (20.0 seconds). Initial Deformation (tm): With 14 teeth initially moved, the system completed ARAP calculation in 16.1 seconds. Interactive adjustment (TM reuse): Subsequent adjustments to tooth movement are updated by the system within less than 50ms (reuse decomposition). Total time comparison (assuming 20 adjustments): No TP / TM separation: 20 adjustments × 36.1 seconds = 722 seconds (12 minutes) With TP / TM separation: 1 × 20.0 seconds (TP) + 1 × 16.1 seconds (initial TM) + 19 × 0.033 seconds (subsequent TM reuse) = 36.7 seconds.

[0047] In a set of interactive tooth movement planning examples: the initial preparation phase takes about 20.0 seconds; the initial deformation solution takes about 16.1 seconds; and subsequent multi-round interactive adjustments can be completed in less than 50ms under the condition of reusing pre-decomposition, thus significantly reducing end-to-end interaction latency.

[0048] S3.3. Output the deformed jawbone mesh.

[0049] Furthermore, the mesh verification described in step S4 includes result verification and a degradation strategy. Specifically: Perform at least the following checks on the deformed jawbone mesh: 1. Closure check: The number of mesh boundary edges should be 0 after deformation; 2. Finiteness check: All vertex coordinates must satisfy finiteness (no NaN / Inf) and be within a reasonable range (e.g., absolute coordinate value less than 1000mm). 3. Local distortion threshold verification (optional but preferred): Calculate the deformation gradient and the degree of deviation from the most recent rotation for the triangular face, and the maximum distortion does not exceed the threshold ε (e.g., default 0.5).

[0050] If the verification fails or the solution fails, a repair or degradation strategy is executed, which includes at least one of the following methods: a. Perform mesh reshaping or remeshing and then retry the solution; the mesh reshaping may include: remeshing, normal reconstruction, self-intersection removal, local smoothing and other processing methods; b. Output only the closed mesh after preprocessing and do not output the ARAP deformation results; c. If the solution fails, output the deformation result that passed the last verification and return an error / warning message.

[0051] Specifically, the following embodiment further details the verification standards and algorithms.

[0052] Verification 1: Closure check Standard: The mesh must have no boundary edges (a fully closed 2-manifold). Threshold: Precisely zero boundary edges (hard requirement) algorithm:

[0053]

[0054] Verification 2: Finiteness check Standard: All vertex coordinates must be finite (no NaN, no Inf) and within a reasonable range. Threshold: All coordinates satisfy isfinite() and |coord| < 1000mm algorithm:

[0055]

[0056] Verification 3: Distortion Threshold Check Standard: Local deformation should maintain rigidity (ARAP principle); measure the degree of deviation from pure rotation. Specific threshold requirements: Strict mode: ε = 0.2 (20% distortion) - for high-quality clinical applications Normal mode: ε = 0.5 (50% distortion) - Default setting Relaxed mode: ε = 1.0 (100% distortion) - for extreme deformations Mathematical definition:

[0057] algorithm:

[0058]

[0059] This embodiment uses the mandibular deformation scenario as a specific example, but the solution is also applicable to the mandible. In another embodiment, the S1 to S4 processes of embodiment 1 are executed on the maxillary and mandibular meshes respectively to generate handle_id_maxilla and handle_id_mandible for the maxilla and mandible respectively; when the input tooth pose matrix is ​​applied to the 14 maxillary teeth and 14 mandibular teeth respectively, the maxillary / mandibular deformed mesh can be solved and output once on the corresponding handle, and finally synthesized and presented in the display layer.

[0060] The advantages of this embodiment are: 1. Closed mesh prerequisite + forced verification: Hole closure and geometric consistency are made hard prerequisites for ARAP, and an automatic degradation path is built in.

[0061] 2.14 Tooth Independent and Simultaneous Control: Each tooth independently constructs a control set and inputs it as a matrix. The solution is applied simultaneously in one go, avoiding the cumulative error and performance loss caused by sequential tooth control.

[0062] 3. Preparation / Move Decoupling and Result Reuse: The construction and caching of AABB, deformed objects and sparse decomposition are completed in the preparation phase, and can be directly reused in subsequent multiple rounds of movement, significantly reducing interaction latency.

[0063] 4. Dual guarantee of quality and stability: Pre- and post-assertions (closure / finite / distortion thresholds) + anomaly degradation ensure availability in medical scenarios.

[0064] 5. Service-oriented and handle-oriented design: Prepare results for cross-call reuse through handle_id, supporting engineering integration and cluster deployment.

[0065] The service types in this embodiment include: 1. Dual service: / prepare and / solve are separate; 2. Single service baseline: / prepare_solve is executed once for performance benchmarking and rollback.

[0066] The data structure in this embodiment includes: Handle: {mesh_path, AABB, arap_object, factorization, control_set(C14), meta} Control: tooth-by-tooth control points / regions, weights, fixed / soft constraint markers.

[0067] The typical pseudocode for this embodiment is as follows:

[0068] The service-oriented interface call in this embodiment is as follows: POST / prepare: Input open mesh, tooth model, and control rules; Output handle_id, tp, and geometric diagnosis. POST / solve: Input handle_id and T

[14] and threshold parameters, output deformed mesh, tm and quality index (holes, max_distortion, etc.); POST / prepare_solve: A unified rollback call used for baseline or exception rollback.

[0069] This service-oriented approach decouples the preparation phase from the interactive solution phase, facilitating near real-time updates in clinical interactive software.

[0070] Performance and test cases in this embodiment: T1 single-tooth 1mm translational regression; T2 14 teeth independent random displacement of 1mm simultaneously; T3 timing breakdown: tp (preparation) and tm (movement); T4 Anomalies and Degeneracy: Repeated / Degenerate triangles, inconsistent normals, open inputs, etc.

[0071] Quality control in this embodiment:

[0072] The operating environment and dependencies of this embodiment are as follows: C++ backend (can be combined with libraries such as CGAL), REST interface layer (Rust / other), GPU / CPU are all acceptable; Multithreading is used for closure, normal reconstruction, and control set generation; Sparse linear algebra libraries (such as Eigen / SuiteSparse).

[0073] Preferred solutions and optional features of this embodiment: Regionalized stiffness weights (periodontal ligament area / cortical bone differentiation weights); Integrating weight allocation during the S2 preparation phase: Step S2.3 Extension: Generate a 14-tooth control set C14 (including regional weights) Algorithm details:

[0074]

[0075] Anatomical region classification algorithm:

[0076]

[0077] The impact of weights on ARAP energy:

[0078] Switching between soft and hard constraints, and combined rotation / translation / scale control; The switching between soft and hard constraints is implemented during the S2 preparation phase:

[0079] Rotation / translation / scale composite control is achieved in the S3 movement phase:

[0080] If the control topology remains unchanged, reuse and decompose; if the topology changes, automatic failure and reconstruction will occur (as detailed in the S4 verification and degradation section). On the UI side, the translation vector is collected by "pressing down, dragging, and lifting up" → the homogeneous matrix is ​​used to unify the input parameters.

[0081] UI event handler implementation:

[0082]

[0083] Possible variations and equivalent implementations of this embodiment: ARAP can be replaced or integrated into a hybrid solution of deformation map / multi-resolution energy / FEM, but the core idea of ​​"closed-loop pre-processing + multi-tooth synchronization + preparation for reuse" is maintained. The acceleration structure can be replaced by BVH / KD-Tree instead of AABB; The service model can be changed to an embedded SDK or a local library call.

[0084] Risks and mitigation measures for implementing this embodiment: Risks: Closure failure or ill-conditioned meshes may lead to unstable solutions; Mitigation: Reshaping and remeshing; Ill-conditioned meshes include at least one of the following defects: self-intersection, non-manifold, degenerate triangle ratio exceeding the threshold, minimum angle too small, local flipping, etc. Risk: Inconsistent type / data structure; Mitigation: Unified type header, CI validation; Risk: Performance regression; Mitigation: Cache hit rate monitoring and automatic rebuilding strategy.

[0085] The expected results of this embodiment are: the preparation phase time and the movement phase time are separated, and the movement phase aims for near real-time (<~ hundreds of milliseconds to seconds, depending on the model size); the mesh closure rate is 100% after deformation, and the anomaly return rate is significantly reduced; compared with tooth-by-tooth serial solution, the overall latency is significantly reduced.

[0086] This embodiment illustrates the construction of a 14-tooth control system (including example data):

[0087]

[0088] This embodiment presents a dual-service / single-service architecture (including example data):

[0089] This embodiment illustrates the decomposition and data structure reuse:

[0090] This embodiment of the downgrade processing flow (including example data) is as follows:

[0091]

[0092] This invention also discloses a CBCT jawbone rapid deformation simulation system based on ARAP optimization, such as... Figure 5 As shown, the system includes an interface unit for data connection, a mesh preprocessing unit, a mesh closure unit, a preparation unit, a moving solver unit, a persistent reuse unit, and a verification and degradation unit. The interface unit receives and converts the jawbone surface mesh, tooth model, and tooth pose transformation matrix. The mesh preprocessing unit performs hole closure preprocessing on the jawbone mesh. The preparation unit constructs an acceleration structure and ARAP deformation solver object on the closed jawbone mesh and generates a control set for each tooth. The mesh closure unit outputs the closed jawbone mesh. The persistent reuse unit performs pre-decomposition on the ARAP linear system and associates and stores the closed jawbone mesh, acceleration structure, control set, and pre-decomposition results as reusable handles. The moving solver unit receives the pose transformation matrix of multiple teeth and simultaneously applies multi-tooth boundary conditions to perform ARAP solving in a single solution to output the deformed jawbone mesh. The verification and degradation unit performs closure and finiteness checks on the solution results and executes repair or degradation strategies to output the results when the checks fail or the solution fails.

[0093] Furthermore, the interface unit provides a network interface to support separate calls between the preparation and solution phases. The preparation phase outputs a handle identifier, and the solution phase inputs the handle identifier and the pose transformation matrix to reuse the pre-decomposition results. The verification and degradation unit is also used to output quality and performance indicators corresponding to the results. The performance indicators include at least the time consumed in the preprocessing phase and the time consumed in the moving solution phase. The system is configured to process maxillary and mandibular data in parallel or serially, generating independent handle identifiers respectively to support full-mouth tooth movement simulation.

[0094] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the present invention. Any simple equivalent changes and modifications made in accordance with the scope of the patent application and the description of the invention shall still fall within the scope of the patent of the present invention.

Claims

1. A rapid deformation simulation method for the jawbone based on ARAP optimization in CBCT, characterized in that, The steps are as follows: S1. Obtain the surface mesh of the jawbone to be simulated and the tooth model on the same jawbone, and perform hole closure preprocessing on the surface mesh of the jawbone to output a closed jawbone mesh; S2. Construct an accelerated structure for nearest neighbor query or intersection / distance calculation on the closed jawbone mesh, and construct a surface mesh deformation solution object based on ARAP; generate control points and / or constraint regions for each tooth in the tooth model to form a control set; The linear system corresponding to the solution object is pre-decomposed to obtain reusable decomposition results, and the closed jawbone mesh, acceleration structure, control set and decomposition results are associated and stored as reusable handles. S3. Receive the pose transformation matrix corresponding to the tooth model, where the unmoved teeth correspond to the identity matrix; update the target constraints of the control set based on the pose transformation matrix of each tooth; apply the boundary conditions of the tooth model and perform ARAP solution in one solution; if the solution fails, execute the repair or degradation strategy; if the solution is successful, output the deformed jawbone mesh. S4. Perform result verification on the deformed jawbone mesh. If the verification fails, execute the repair or downgrade strategy and output the result. If the verification passes, output the deformed jawbone mesh.

2. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, The jawbone surface mesh includes a maxillary surface mesh and / or a mandibular surface mesh, and the tooth model consists of N teeth on the same jawbone, where N is a positive integer. Steps S1 to S4 are performed on the maxillary surface mesh and the mandibular surface mesh respectively to obtain the deformed jawbone mesh and the corresponding handle of the maxilla and mandible respectively.

3. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, In step S1, the operation steps for the hole closure pretreatment are as follows: a) Extract the boundary ring of the hole; b) Sort the holes in descending order of the perimeter of the boundary rings; c) Generate patch triangles sequentially for the sorted holes to achieve hole closure; d) Smooth or equalize the patch triangles to ensure geometric continuity with the original jawbone surface mesh.

4. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, Before outputting the closed jawbone mesh, a geometric consistency check is performed, which includes: boundary edge check, manifold check, duplicate vertex check, degenerate triangle check, and normal consistency check; and requires that there be no boundary edges, no duplicate vertices, no degenerate triangles, and consistent normals.

5. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, Step S1 also includes performing an expansion process on the tooth model; and performing a joint refinement process based on the expanded tooth model and the jawbone surface mesh. The jawbone surface mesh was then trimmed using the expanded tooth model to remove the jawbone mesh located inside the teeth, thereby creating a hole to be closed on the trimmed jawbone mesh.

6. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1 or 5, characterized in that, Step S1 or step S2 further includes performing remeshing processing on the closed jawbone mesh to improve the quality of the closed jawbone mesh and suppress degenerate units.

7. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, The handle includes two or more of the following: closed jawbone mesh data, acceleration structure, solver object, control set, decomposition results, vertex-to-tooth mapping relationship, and mesh quality / diagnostic metadata; The ARAP linear system pre-decomposition results are then reused in subsequent solutions by using handle identifiers.

8. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 7, characterized in that, When the topology of the closed jawbone mesh remains unchanged and the topology of the control set remains unchanged, the linear system pre-decomposition results are reused in the ARAP solution of subsequent steps S3; when the topology of the closed jawbone mesh or the topology of the control set changes, the handle is invalidated, and step S2 is re-executed to reconstruct the acceleration structure, the solution object, the control set and the linear system pre-decomposition results, and then the ARAP solution of step S3 is executed.

9. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, Step S2, generating control points and / or constraint regions per tooth, includes: dividing the vertices of the closed jawbone mesh into a set of control points and a set of regions of interest based on their distances to the corresponding tooth models according to the acceleration structure; setting hard constraints on the set of control points and soft constraints on the set of regions of interest.

10. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, Step S2, generating control points and / or constraint regions per tooth, includes: assigning regionalized stiffness weights to the vertices of the closed jawbone mesh based on their distance from the corresponding tooth model or anatomical partitions, such that the weights near the periodontal region are lower than the weights of the far-field bone region.

11. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, The result verification in step S4 includes local distortion threshold verification, which is used to measure the degree to which local deformation deviates from rigid rotation, and triggers the repair or degradation strategy when the maximum distortion exceeds a preset threshold.

12. The ARAP-optimized CBCT jawbone rapid deformation simulation method according to claim 1, characterized in that, The repair or downgrade strategy includes at least one of the following strategies: a) Perform reshaping or remeshing on the mesh before solving; b) Output only the closed jawbone mesh after closed preprocessing, without outputting the ARAP deformation results; c) If the current solution fails, output the deformation result that passed the previous verification.

13. A CBCT jawbone rapid deformation simulation system based on ARAP optimization, characterized in that, It includes interface units for data connection, mesh preprocessing units, mesh closure units, preparation units, moving solver units, persistent reuse units, and verification and degradation units; The interface unit is used to receive and convert the jawbone surface mesh, tooth model, and tooth pose transformation matrix. The mesh preprocessing unit is used to perform hole closure preprocessing on the jawbone mesh; The preparation unit is used to construct the acceleration structure and ARAP deformation solution object on the closed jawbone mesh, and generate control sets tooth by tooth; The mesh closure unit is used to output a closed jawbone mesh; The persistent reuse unit is used to perform pre-decomposition on the ARAP linear system and associate and store the closed jawbone mesh, acceleration structure, control set and pre-decomposition results as a reusable handle; The moving solver unit is used to receive the pose transformation matrix of multiple teeth and simultaneously apply multi-tooth boundary conditions to perform ARAP solution in one solution to output the deformed jawbone mesh. The verification and degradation unit is used to perform closure and finiteness verification on the solution results, and to execute repair or degradation strategies to output results when the verification fails or the solution fails. The interface unit provides a network interface to support separate calls for the preparation phase and the solution phase. The preparation phase outputs a handle identifier, and the solution phase inputs the handle identifier and the pose transformation matrix to reuse the pre-decomposition results.

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