A method for orthodontic path planning based on feasible region projection

Abstract

This invention provides a method for orthodontic path planning based on feasible region projection, comprising: constructing an energy function for generating tooth state parameters at each stage of orthodontic treatment based on the input full-mouth tooth model before and after orthodontic treatment; iteratively optimizing the energy function based on the idea of ​​feasible region projection, correcting the variables and gradients corresponding to the tooth centroid coordinates in the energy function at each iteration, and obtaining the optimized tooth state parameters at each stage; generating and outputting the tooth model at each stage based on the tooth state parameters obtained in the second step of optimization. This invention, by rationally constructing an energy function for the tooth path planning problem and projecting the tooth displacement-related variables and gradients into the geometrically feasible region during each iteration of energy function optimization, naturally ensures that there is no collision between any two teeth, achieving the same constraint effect as explicit constraints more efficiently.

Description

Technical Field

[0001] This invention relates to the field of orthodontic technology, and in particular to an orthodontic path planning method based on feasible region projection. Background Technology

[0002] Orthodontic pathway planning is the core technology for generating invisible orthodontic treatment plans and also has significant clinical value. Automation of orthodontic pathway planning through computer technology can not only quickly help orthodontists predict the final orthodontic outcome and assist in designing orthodontic plans, but also provide patients with a clear view of the entire orthodontic treatment process through generated 3D animation plans.

[0003] In 2009, Li Binjie et al. proposed using genetic algorithms to solve the orthodontic path planning problem in their paper "Research on path planning for tooth movement based on genetic algorithms. International Conference on Artificial Intelligence and Computational Intelligence". However, due to the limitations of genetic algorithms themselves, this method is inefficient and suffers from premature convergence. In 2019, Fu Jingding et al. proposed an improved RRT algorithm for orthodontic path search in their paper "Research on Orthodontic Path Planning in Invisible Orthodontic Technology". This method successfully solved the collision problem in orthodontic paths, but due to the randomness of the method, it could not guarantee the smoothness of the path. In 2020, Xu Xiaoqiang et al.'s paper "Orthodontic Path Planning Method Based on Improved Particle Swarm Optimization Algorithm" and in 2021, Ma Tian et al.'s paper "Orthodontic Path Planning Based on Improved Multi-Particle Swarm Optimization Algorithm" both proposed using improved particle swarm optimization algorithms to solve the orthodontic path planning problem, but both suffer from low efficiency due to excessive dimensionality. In 2023, Du Xiaozhi et al. proposed an improved Gray Wolf algorithm for orthodontic path planning in their paper “An Orthodontic Path Planning Method Based on Improved Gray Wolf Optimization Algorithm”. However, this algorithm requires solving integer planning problems, so both the accuracy and efficiency costs are relatively high.

[0004] The above ideas and methods have solved the problem of orthodontic path planning and avoided collisions during the orthodontic process. However, since their solutions are all global optimization methods, they have a certain degree of randomness or heuristics, which leads to low efficiency or a more tortuous path. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for orthodontic path planning based on feasible region projection, comprising:

[0006] S1. Based on the input full-mouth dental model of the patient before and after orthodontics, construct an energy function to generate the dental state parameters at each stage of the orthodontic process.

[0007] S2. Based on the idea of ​​feasible region projection, the energy function is iteratively optimized, and the variables and gradients corresponding to the tooth centroid coordinates in the energy function are corrected in each iteration to obtain the optimized tooth state parameters at each stage.

[0008] S3. Based on the tooth state parameters of each stage obtained from the second step of optimization, generate and output the tooth model of each stage.

[0009] In an optional embodiment, step S1 includes:

[0010] S11. Divide the orthodontic process into N stages, where the first stage corresponds to the full mouth dental model of the patient before orthodontics, and the Nth stage corresponds to the dental model after orthodontics.

[0011] S12. Construct the energy function E based on the state parameters of the tooth at each stage, as shown in the following formula:

[0012]

[0013] Where M is the number of teeth in the patient, N is the number of stages in the orthodontic process, s is the centroid coordinate of the tooth, r is the quaternion in spherical coordinates corresponding to the current rotational posture of the tooth, and λ is an adjustable parameter.

[0014] In an optional embodiment, step S2 includes:

[0015] S21, using s 0,j and s N,j r 0,j and r N,j Interpolation yields all s i,j and r i,j The energy function E(s,r) is initialized, and the termination error ε and the closest distance d between the two teeth are set. min Let the number of iterations k:=0;

[0016] S22, Calculate the value of each tooth. and Will Projecting into the feasible region yields like or k>0 and Then stop iterating and output s. k and r k Otherwise, proceed to the next step;

[0017] S23. Perform a one-dimensional search to find t. k The formula is as follows:

[0018]

[0019] S24, Order k:=k+1;

[0020] S25. Correct the teeth that collided due to the one-dimensional search by pulling them outwards along the line connecting their centroids. k ,get

[0021] S26 Return to step S22.

[0022] Furthermore, the aforementioned Projecting into the feasible region yields The following method is used:

[0023] When a tooth model M a Model M with another tooth b The distance between the c-th stages is less than d. min At that time, and To M a M b The formula for correcting the perpendicular direction of the line connecting the centroids of two teeth is as follows:

[0024]

[0025]

[0026] In an optional embodiment, step S3 includes:

[0027] Based on the obtained centroid coordinates s and quaternions r, the vertex coordinates of each tooth at each stage are calculated, and the connection relationship between the original vertices is preserved to obtain the full mouth tooth model of N stages in the orthodontic process.

[0028] By adopting the above technical solution, the present invention has at least the following beneficial effects:

[0029] (1) This invention proposes a new approach to transform a constrained optimization problem into an unconstrained optimization problem, namely, by projecting the variables and gradient of the energy function into the geometrically feasible region, the same constraint effect as the specific constraint condition is achieved, and the iterative process during optimization is given.

[0030] (2) By rationally constructing the energy function of the orthodontic path planning task, this invention effectively avoids the collision between teeth during the orthodontic process and ensures the smoothness and simplicity of the orthodontic path.

[0031] (3) By projecting the variables and gradients corresponding to the centroid coordinates of the teeth in the energy function into the geometrically feasible region, this invention naturally restricts the energy function and its variables to the geometrically feasible region, which greatly improves the solution efficiency. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 A flowchart illustrating a method for orthodontic path planning based on feasible domain projection provided in this disclosure embodiment;

[0034] Figure 2 To be To M a M b A schematic diagram of the projection of the line connecting the centroids of two teeth in the vertical direction.

[0035] Figure 3 This relates the number of stages in the orthodontic process to the average solution time and the average number of iterations.

[0036] Figure 4 This is a schematic diagram of the orthodontic pathway planning results. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0038] Through research, this invention proposes a novel approach to solving constrained optimization problems. Specifically, when optimizing the energy function, the variables and gradient of the energy function are projected into the feasible region to achieve the same constraint effect as the constraints themselves, thus transforming the constrained optimization problem into an unconstrained one. The specific steps for optimizing the energy function f are as follows:

[0039] 1. Select an initial point x0, give a termination error ε>0, and let the number of iterations k:=0;

[0040] 2. Calculation And project it into the feasible region to obtain like or k>0 and Stop iterating and output x k Otherwise, proceed to step 3;

[0041] 3. Perform a one-dimensional search to find t. k , making

[0042]

[0043] 4. Order k:=k+1;

[0044] 5. x k Projecting onto the feasible region yields...

[0045] 6. Return to step 2.

[0046] For orthodontic path planning, the constraint can be considered as ensuring that no two teeth collide during orthodontic treatment. Projecting onto the feasible region can be represented as correcting the variables and gradients in the energy function corresponding to the tooth centroid coordinates in the opposite or perpendicular direction to the line connecting the centroids of two teeth that might collide. This ensures that the teeth do not shift in the direction of collision, thus avoiding collisions between teeth. Figure 1 As shown in the figure, an orthodontic path planning method based on feasible region projection provided in this disclosure includes:

[0047] S1. Based on the input full-mouth dental model of the patient before and after orthodontics, construct an energy function to generate the dental state parameters at each stage of the orthodontic process.

[0048] In this embodiment, the input consists of a pre-orthodontic full-mouth dental model and an ideal post-orthodontic full-mouth dental model. The former can be obtained by modeling the patient's oral cavity through a scan, while the latter can be predicted by the doctor's adjustments or deep learning methods. The output consists of N full-mouth dental models, dividing the orthodontic process into N stages, where N is a freely set positive integer. The first stage corresponds to the pre-orthodontic full-mouth dental model, and the Nth stage corresponds to the post-orthodontic dental model.

[0049] To obtain high-quality target output, an energy function E is constructed based on the state parameters of each tooth at each stage. This function measures the difference between the state of each tooth at each stage and the state of the previous stage. The constraint condition is that "there is no collision between any two teeth in the same stage". The formula is as follows:

[0050]

[0051] Where M is the number of teeth in the patient, N is the number of stages in the orthodontic process, s is the centroid coordinate of the tooth, r is the quaternion in spherical coordinates corresponding to the current rotational posture of the tooth, and λ is an adjustable parameter, which is generally set to λ = 1.

[0052] S2. Based on the idea of ​​feasible region projection, the energy function is iteratively optimized, and the variables and gradients corresponding to the centroid coordinates of the teeth in the energy function are corrected in each iteration to avoid collisions between teeth, and the tooth correction state parameters of each stage are obtained after optimization.

[0053] S21, using s 0,j and s N,j r 0,j and r N,j Interpolation yields all s i,j and r i,j The energy function E(s,r) is initialized, and the termination error ε = 10 is set. -5 The closest distance d between two teeth min =10 -2 mm, let the iteration number k:=0;

[0054] S22, Calculate the value of each tooth. and Will Projecting into the feasible region yields That is, when a model M of a tooth a Model M with another tooth b The distance between the c-th stages is less than d. min At that time, and To M a M b The vertical direction of the line connecting the centroids of the two teeth is corrected to avoid collisions caused by the teeth continuing to move in the original direction; the original gradient... Subtract itself in direction The projection onto the original gradient. In the perpendicular direction The projection on is The formula is as follows: like Figure 2 As shown, if or k>0 and Then stop iterating and output s. k and r k Otherwise, proceed to the next step;

[0055] S23. Perform a one-dimensional search to find t. k The formula is as follows:

[0056]

[0057] S24, Order k:=k+1;

[0058] S25. Correct the teeth that collided due to the one-dimensional search by pulling them outwards along the line connecting their centroids. k ,get

[0059] S26 Return to step S22.

[0060] In this embodiment, by projecting the variables and gradients corresponding to the tooth centroid coordinates in the energy function into the geometrically feasible region, the energy function and its variables are naturally confined within the geometrically feasible region, greatly improving the solution efficiency. Figure 3 As shown.

[0061] S3. Based on the tooth state parameters of each stage obtained from the second step of optimization, generate and output the tooth model of each stage.

[0062] In this embodiment, based on the obtained centroid coordinates s and quaternions r, the vertex coordinates corresponding to each tooth at each stage are calculated, and the original connection relationships between vertices are preserved, resulting in a full-mouth tooth model for N stages in the orthodontic process, thus realizing orthodontic path planning. Figure 4 As shown.

[0063] Although the present invention has been disclosed above with reference to embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications and refinements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for orthodontic path planning based on feasible region projection, characterized in that, include: S1. Based on the input full-mouth dental model of the patient before and after orthodontics, construct an energy function to generate the dental state parameters at each stage of the orthodontic process. S2. Based on the idea of ​​feasible region projection, the energy function is iteratively optimized, and the variables and gradients corresponding to the tooth centroid coordinates in the energy function are corrected in each iteration to obtain the optimized tooth state parameters at each stage. S3. Based on the tooth state parameters of each stage obtained from the second step of optimization, generate and output the tooth model of each stage. Step S1 includes: S11. Divide the orthodontic process into N stages, where the first stage corresponds to the full mouth dental model of the patient before orthodontics, and the Nth stage corresponds to the dental model after orthodontics. S12. Construct the energy function E based on the state parameters of the tooth at each stage, as shown in the following formula: Where M is the number of teeth in the patient, N is the number of stages in the orthodontic process, s is the centroid coordinate of the tooth, r is the quaternion in spherical coordinates corresponding to the current rotational posture of the tooth, and λ is an adjustable parameter. Step S2 includes: S21, Utilization and , and Interpolation gets all and and the energy function Perform initialization and set the termination error. The closest distance between two teeth Let the number of iterations be... ; S22, Calculate the value of each tooth. and ,Will Projecting into the feasible region yields ,like or Then stop iterating and outputting. and Otherwise, proceed to the next step; S23. Perform a one-dimensional search to find... The formula is as follows: S24, Order , , ; S25. Correct the teeth that collided due to the one-dimensional search by pulling them outwards along the line connecting their centroids. ,get ; S26 Return to step S22; The Projecting into the feasible region yields The following method is used: When a tooth model Model with another tooth In the The distance between each stage is less than At that time, and Towards , The formula for correcting the perpendicular direction of the line connecting the centroids of two teeth is as follows: ， 。 2. The orthodontic path planning method based on feasible region projection according to claim 1, characterized in that, Step S3 includes: Based on the obtained centroid coordinates Calculate the vertex coordinates of each tooth at each stage, and preserve the original connections between vertices to obtain the orthodontic process. A complete set of dental models for each stage.

Images