Interactive orthodontic prediction method based on symbolic distance field and six-degree-of-freedom modeling

Abstract

The invention discloses an interactive orthodontic prediction method based on a symbolic distance field and six-degree-of-freedom modeling. The interactive orthodontic prediction method comprises the following steps of (1) data preprocessing and three-dimensional modeling; (2) six-degree-of-freedom dynamic modeling; (3) symbolic distance field collision detection; according to the method, the six-degree-of-freedom energy minimization kinetic model is constructed, the symbol distance field collision constraint and differentiable detection algorithm are fused, and the gradient descent optimization strategy is combined, so that high-precision prediction and dynamic interaction optimization of the tooth movement track are realized.

Description

Technical Field

[0001] The present invention relates to the field of medical simulation and computer-aided design technology, and in particular to an interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling, and specifically to the application of six-degree-of-freedom dynamic modeling, signed distance field collision detection, and gradient descent optimization algorithm in digital prediction of oral orthodontic treatment. Background Art

[0002] Orthodontic treatment needs to take into account both functional and aesthetic goals. Its precise planning is highly dependent on the doctor's experience, is highly subjective, and can easily lead to prolonged treatment cycles and the risk of complications. Existing digital simulation systems are mostly based on the rigid displacement assumption, which makes it difficult to accurately simulate the biomechanical response of teeth under orthodontic forces. In particular, there are technical bottlenecks in dynamic displacement prediction, contact interference warning, and doctor-patient interaction optimization. Traditional collision detection algorithms lack accuracy in the narrow space of the alveolar bone and are prone to misjudgment or missed detection. At the same time, the existing system lacks a real-time interactive mechanism, making it impossible to achieve dynamic adjustment and visual verification of correction parameters, limiting the precision and personalization of orthodontic treatment.

[0003] The technical comparison between the above-mentioned reference documents and this application is as follows:

[0004] Technical comparison with patent CN116153530A "Orthodontic treatment monitoring method and device based on oral scanning video"

[0005] Patent CN116153530A addresses the automated monitoring and evaluation of orthodontic treatment processes. Its core challenge lies in automatically segmenting tooth instances and quantifying displacement changes from oral scan videos. Based on a deep learning framework, this patent incorporates a heterogeneous feature interaction module and a quaternion loss function, specifically addressing the issues of traditional monitoring's reliance on manual experience and high matching errors in point cloud registration. Its innovation lies in a segmentation model that integrates color and geometric features, and in improving the robustness of point cloud matching through the use of diverse negative samples.

[0006] This patent focuses on the digital prediction and interactive planning of orthodontic treatment. Its core lies in simulating the biomechanical response of teeth under orthodontic forces through physical simulation technology. In response to the limitations of traditional systems that rely on rigid displacement assumptions, this patent proposes a six-degree-of-freedom dynamic modeling and signed distance field (SDF) collision detection method to solve the problems of insufficient prediction accuracy of tooth movement trajectories and lack of real-time interactive optimization. The technical difficulty lies in how to combine complex rigid body motion with high-precision collision constraints and enable clinicians to dynamically adjust orthodontic parameters.

[0007] There are essential differences between the two in terms of core issues and research objectives.

[0008] Patent CN116153530A is primarily used for tracking and evaluating treatment outcomes. By analyzing multiple oral scans of patients, the system automatically segments teeth and compares displacement changes to determine whether they conform to the pre-set protocol. Using public datasets, the system significantly improves tooth segmentation accuracy and reduces point cloud matching errors by over 15%. This system supports rapid generation of quantitative clinical reports and reduces manual intervention.

[0009] This patent is primarily used for pre-treatment orthodontic design and preview. After the doctor inputs the patient's 3D dental model, they can simulate tooth movement under different orthodontic forces. They can also adjust parameters (such as ±5mm translation and ±30° rotation) in real time through an interactive interface to verify the feasibility of the plan. The simulation results have high physical credibility, and the single-step optimization time is stable at 1 second. This supports personalized design for complex cases, reducing treatment cycles and the risk of complications.

[0010] There are essential differences between the two in terms of application scenarios and technical effects.

[0011] Patent CN116153530A constructs a dual-graph structure to extract color and geometric features separately, and utilizes a graph attention mechanism to fuse information across layers, improving the accuracy of tooth instance segmentation. Multiple negative sample constraints are introduced in point cloud matching, and a novel loss function is used to enhance the model's adaptability to complex scenarios and reduce the risk of mismatches. By connecting modular processing units (TMP blocks) in series, the rotation and translation of teeth are directly predicted from scan data, enabling automated quantitative evaluation of treatment outcomes. With deep learning and automated analysis at its core, this approach addresses the issue of dynamic monitoring during treatment.

[0012] This patented technical solution treats each tooth as an independent rigid body, comprehensively describing its motion state through translation and rotation parameters. This breaks through the limitations of traditional rigid displacement models and more closely reflects realistic biomechanical responses. Signed distance field technology, combined with an axis-aligned bounding box acceleration structure, rapidly detects potential interference between teeth and ensures the safety of the movement path. Dynamic parameter adjustment using a gradient descent algorithm allows doctors to manually adjust tooth displacement or rotation and view simulation results in real time, forming an "adjustment-verification" closed loop that significantly improves clinical decision-making efficiency. With physical simulation and interactive control at its core, it addresses the issue of precise pre-treatment planning.

[0013] There are essential differences between the two in terms of technical solutions. Summary of the Invention

[0014] Purpose of the invention: The purpose of the present invention is to provide an interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling. By constructing a six-degree-of-freedom energy minimization dynamic model, integrating signed distance field collision constraints and differentiable detection algorithms, and combining gradient descent optimization strategies, high-precision prediction and dynamic interactive optimization of tooth movement trajectories can be achieved.

[0015] To achieve the above objectives, the solution of the present invention is an interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling, comprising the following steps:

[0016] (1) Data preprocessing and 3D modeling:

[0017] Input the STL format tooth and bone models generated by the patient's medical images, construct a standardized 3D dental topology through coordinate alignment and grid simplification, and use a layered rendering engine to achieve 3D visualization of the bone-tooth structure;

[0018] (2) Six-degree-of-freedom dynamic modeling:

[0019] Each tooth is modeled as an independent rigid body, and its motion state is represented by the translation component p = [x, y, z] T Together with the rotation component R∈SO(3), the generalized coordinates are defined as q=[p T ,θ x ,θ y ,θ z ] T ∈R 6 , based on the Lie algebra mapping log:SO(3)→so(3), the pose update is performed to realize the linear calculation of the rotation deviation;

[0020] (3) Signed distance field collision detection:

[0021] Construct an axis-aligned bounding box AABB acceleration structure and calculate the signed distance SDF (p, T j ), and design collision penalty energy function

[0022] (4) Gradient descent optimization and interactive control:

[0023] The numerical gradient method is used to calculate the partial derivatives of the energy function with respect to the degree of freedom and construct the Jacobian matrix The six-degree-of-freedom parameters are dynamically adjusted through a real-time interactive interface to achieve rapid convergence of the energy function.

[0024] As a further improvement of the present invention, the layered rendering engine in step (1) supports the user to interactively select the target tooth and highlight it in real time by independently controlling the color and display level of the tooth and alveolar bone.

[0025] As a further improvement of the present invention, the posture update formula in step (2) is:

[0026]

[0027] Where η is the adaptive learning rate, the initial value is 0.1, and the decay coefficient β = 0.95.

[0028] As a further improvement of the present invention, the single-point query complexity of the signed distance field SDF in step (3) is optimized to O(log M), where M is the number of mesh faces, and the nearest triangle face positioning is accelerated based on the AABB tree.

[0029] As a further improvement of the present invention, the real-time interactive interface in step (4) includes:

[0030] The six-degree-of-freedom controller supports dynamic input of translation components t1, t2, t3 corresponding to the tangential, vertical, and buccal-lingual displacements of the dental arch, and rotation components w1, w2, w3 corresponding to rotations around the long axis, lingual surface, and mesiodistal axis;

[0031] Single-step optimization and continuous optimization modes control the iteration process by triggering a button until the total energy of the system is lower than the preset threshold E<0.3.

[0032] As a further improvement of the present invention, the adjustment range of the translation component t3 is -5.0 mm to +5.0 mm, and the adjustment range of the rotation component w2 is -30° to +30°.

[0033] As a further improvement of the present invention, the numerical gradient calculation of the gradient descent optimization and interactive control in step (4)

[0034] Apply a small perturbation δ = 1 × 10 -4 , and approximate the partial derivatives using the following formula:

[0035]

[0036] where e k is the kth basis vector, k = 1, 2, ..., 6.

[0037] As a further improvement of the present invention, the safety distance d in the collision penalty energy function in step (3) is safe =0.1mm, penalty coefficient λ=10 3 .

[0038] Beneficial effects: The present invention has the following advantages:

[0039] (1) High-precision simulation: Through the six-degree-of-freedom dynamic model and signed distance field collision detection, the limitations of traditional rigid displacement simulation are broken through and the physical credibility of tooth movement trajectory prediction is improved.

[0040] (2) Real-time interactive optimization: Integrate dynamic parameter adjustment and visual verification functions to build a "simulation-adjustment-verification" closed-loop process to enhance the flexibility and reliability of clinical decision-making.

[0041] (3) Improved computing efficiency: Based on the AABB tree acceleration structure and adaptive gradient descent strategy, the single-step optimization time is stabilized at 1.1 seconds, meeting the needs of clinical offline simulation.

[0042] (4) Versatility and scalability: It supports multi-source data input and layered rendering, and is suitable for the design of personalized treatment plans for complex dental deformities. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a system architecture diagram of the present invention, showing the collaborative process of the data layer, core engine layer and output layer;

[0044] Figure 2 This is a workflow diagram of the present invention, including data preprocessing, physical simulation and interactive optimization modules;

[0045] Figure 3 is the operating interface of the present invention;

[0046] Figure 4 The tooth posture adjustment interface shows the six-degree-of-freedom controller and optimization process;

[0047] Figure 5 This is a comparison chart of simulation results, showing the system energy convergence curve. DETAILED DESCRIPTION

[0048] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings.

[0049] This embodiment is based on an interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling. The system architecture is shown in the figure below. Figure 1 As shown in the workflow diagram Figure 2 As shown;

[0050] 1. Data preprocessing:

[0051] The STL model of CBCT scan was imported into the system and the mesh was normalized using the libigl library to eliminate scale and coordinate differences.

[0052] Coordinate system alignment: Define the global coordinate system based on the patient's occlusal plane:

[0053] X-axis: along the tangent direction of the dental arch (left and right);

[0054] Y-axis: vertical (up and down);

[0055] Z axis: buccal-lingual (anteroposterior).

[0056] 2.Physics simulation engine:

[0057] Dynamic pose update:

[0058] Affine transformation drive: The position of each tooth is controlled by a 4×4 affine transformation matrix T, and the matrix elements respond to changes in the six degrees of freedom parameters (translation t1, t2, t3, rotation w1, w2, w3) in real time;

[0059] Hierarchical rendering:

[0060] Bone layer: semi-transparent rendering (transparency α = 0.3) to highlight the alveolar bone outline;

[0061] Teeth layer: Color by tooth position (such as incisors are white), and highlight selected teeth (yellow).

[0062] 3. Interactive optimization process

[0063] User interface (attached Figure 3 ):

[0064] Target selection: Use the slider (mesh_idx: 0-15) to select the target tooth. After selection, the model will be highlighted and the six-degree-of-freedom control panel will pop up.

[0065] Parameter adjustment:

[0066] Translation component: Enter a value directly in the input box (e.g. t3 = 0.4mm) or drag the slider to preview the displacement effect in real time;

[0067] Rotational component: Angle input (e.g., w2 = 15°) combined with the 3D axis visualization tool to adjust the rotation direction;

[0068] Optimized control:

[0069] Single-step optimization: Click the "Single-step" button to trigger an iteration, and the interface will synchronously update the energy value and tooth posture;

[0070] Automatic optimization: Set the energy threshold (default E<0.3), and the system will iterate continuously until convergence.

[0071] An example of the optimization process is shown in the attached Figure 4 、 Figure 5 :

[0072] Initial state: total energy E of the entire dentition initial =475.633, target tooth (mesh_idx=0) manually adjusts translation component: t3=0.4mm, rotation component w2=15°

[0073] Iterative process: Each optimization step takes about 1.1 seconds, and after 6 iterations the total energy is reduced to E final =0.208.

[0074] 4. Parameter configuration

[0075] Learning rate decay: initial value η initial =0.1, each step is η k+1 =η k β attenuation (β = 0.95) to avoid optimization oscillation;

[0076] Perturbation step size: δ = 1 × 10 -4 , balance gradient calculation accuracy and numerical stability;

[0077] Collision constraint: safety distance d safe =0.1mm, penalty coefficient λ=10 3 , to prevent teeth from penetrating.

[0078] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. An interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling, characterized by: The following steps are involved: (1) Data preprocessing and 3D modeling: Input the STL format tooth and bone models generated by the patient's medical images, construct a standardized 3D dental topology through coordinate alignment and grid simplification, and use a layered rendering engine to achieve 3D visualization of the bone-tooth structure; (2) Six-degree-of-freedom dynamic modeling: Each tooth is modeled as an independent rigid body, and its motion state is represented by the translation component p = [x, y, z] T Together with the rotation component R∈SO(3), the generalized coordinates are defined as q=[p T ,θ x ,θ y ,θ z ] T ∈R 6 , based on the Lie algebra mapping log:SO(3)→so(3), the pose update is performed to realize the linear calculation of the rotation deviation; (3) Signed distance field collision detection: Construct an axis-aligned bounding box AABB acceleration structure and calculate the signed distance SDF (p, T j ), and design collision penalty energy function (4) Gradient descent optimization and interactive control: The numerical gradient method is used to calculate the partial derivatives of the energy function with respect to the degree of freedom and construct the Jacobian matrix The six-degree-of-freedom parameters are dynamically adjusted through a real-time interactive interface to achieve rapid convergence of the energy function.

2. The interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 1, characterized in that: The layered rendering engine described in step (1) supports users to interactively select target teeth and highlight them in real time by independently controlling the colors and display levels of teeth and alveolar bones.

3. According to the interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 1, the posture update formula in step (2) is: Where η is the adaptive learning rate, the initial value is 0.1, and the decay coefficient β = 0.

95.

4. The interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 1, characterized in that: The single-point query complexity of the signed distance field (SDF) in step (3) is optimized to O(logM), where M is the number of mesh faces, and the nearest triangle face positioning is accelerated based on the AABB tree.

5. The interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 1, characterized in that: The real-time interactive interface in step (4) includes: The six-degree-of-freedom controller supports dynamic input of translational components t1, t2, t3 corresponding to the tangential, vertical, and buccal-lingual displacements of the dental arch, and rotational components w1, w2, w3 corresponding to rotations around the long axis, lingual surface, and mesiodistal axis; Single-step optimization and continuous optimization modes control the iteration process by triggering a button until the total energy of the system is lower than the preset threshold E<0.

3.

6. The interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 5, characterized in that: The adjustment range of the translation component t3 is -5.0 mm to +5.0 mm, and the adjustment range of the rotation component w2 is -30° to +30°.

7. The interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 1, characterized in that: In the numerical gradient calculation of the gradient descent optimization and interactive control described in step (4), a small perturbation δ = 1 × 10 -4 , and approximate the partial derivatives using the following formula: where e k is the kth basis vector, k = 1, 2, ..., 6.

8. The interactive orthodontic prediction method based on signed distance field and six-degree-of-freedom modeling according to claim 1, characterized in that: The safety distance d in the collision penalty energy function in step (3) safe =0.1mm, penalty coefficient λ=10 3 .

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