Method for three-dimensional reconstruction of bone based on statistical shape model and laplacian operator

Abstract

The application discloses a three-dimensional reconstruction method of a skeleton based on a statistical shape model and a Laplace operator, and comprises the following steps: obtaining a standard skeleton three-dimensional sample set and a target skeleton two-dimensional contour; solving shape feature principal components and an average model of the standard skeleton three-dimensional sample set, and constructing a linear reconstruction model; performing first 2D / 3D registration, solving shape feature weight parameters of the target skeleton two-dimensional contour, and inputting the linear reconstruction model to obtain a preliminary target skeleton three-dimensional model; performing second 2D / 3D registration, fitting the preliminary target skeleton three-dimensional model with the target skeleton two-dimensional contour based on a Laplace operator, and obtaining a target skeleton three-dimensional model. The application effectively processes feature differences among individual skeletons, realizes a more accurate and natural skeleton three-dimensional model, significantly reduces radiation exposure and cost, makes the application more suitable for routine clinical examination and frequent monitoring, and can provide a model basis for a more personalized medical scheme.

Description

Technical Field

[0001] This invention relates to the field of medical imaging technology, and in particular to a method for three-dimensional bone reconstruction based on statistical shape models and the Laplacian operator. Background Technology

[0002] With the development of medical imaging technology, 3D bone reconstruction plays an increasingly important role in orthopedic surgical planning, prosthesis design, and biomechanical analysis. Traditional 3D reconstruction techniques mainly rely on computed tomography (CT) or magnetic resonance imaging (MRI). However, these methods typically involve high radiation doses, are costly, and time-consuming. Furthermore, they can introduce errors due to changes in patient positioning or movement during the scanning process.

[0003] In recent years, methods for 3D bone reconstruction using 2D images have attracted considerable attention from researchers. This approach reduces the risk of radiation exposure and promises to improve reconstruction speed. However, the 2D-to-3D mapping itself is highly complex, particularly challenging in maintaining reconstruction accuracy and detail.

[0004] Currently, some research focuses on using Statistical Shape Models (SSMs) to improve reconstruction accuracy. SSMs can extract the average shape and major variation patterns of bones from a set of training data, thus providing valuable prior information during the reconstruction process. However, using SSMs alone still has limitations when dealing with inter-individual morphological differences and complex anatomical structures.

[0005] Furthermore, Laplacian surface deformation (LSD) has demonstrated its superiority as an effective geometric manipulation tool in shape analysis and editing. It can perform precise shape transformations while preserving local and global shape properties. However, research on applying the Laplacian operator to 3D skeletal reconstruction, especially in combination with SSM, remains limited. Summary of the Invention

[0006] This invention proposes a novel method for three-dimensional femoral reconstruction based on a statistical shape model and the Laplacian operator. This method aims to overcome the limitations of existing technologies, improve the accuracy and efficiency of reconstruction, and provide more reliable decision support for orthopedic diagnosis and treatment.

[0007] To achieve the above-mentioned objectives, the technical solution provided by this invention includes:

[0008] A 3D skeleton reconstruction method based on statistical shape models and the Laplacian operator includes the following steps:

[0009] S1. Obtain a standard 3D skeleton sample set; obtain the 2D contour of the target skeleton;

[0010] S2. Based on principal component analysis, solve the principal components and average model of the shape features of the standard three-dimensional skeleton sample set, and construct a linear reconstruction model;

[0011] S3. Perform the first 2D / 3D registration on the target bone 2D contour and average model, solve the shape feature weight parameters of the target bone 2D contour, and input them into the linear reconstruction model to obtain the preliminary target bone 3D model.

[0012] S4. Perform a second 2D / 3D registration on the target bone 2D contour and the preliminary target bone 3D model. Fit the preliminary target bone 3D model with the target bone 2D contour based on the Laplacian operator to obtain the target bone 3D model.

[0013] In some preferred embodiments, the method for obtaining the average model in step S2 includes:

[0014] S201, The standard 3D skeleton sample set [S1,S2,…,S…] is used. N Each sample in the diagram is represented as S. i =(x1,y1,z1,…x m ,y m ,z m ) T Where N represents the number of standard 3D bone samples, and m represents the number of nodes in any standard 3D bone sample;

[0015] S202, Calculation of Average Model Among them, S i This represents standard skeletal point cloud data. denoted as the average model, and p represents the number of standard 3D skeleton samples.

[0016] In some preferred embodiments, the method for obtaining the principal components of the shape features in step S2 includes:

[0017] Solve for the covariance matrix of the standard 3D skeleton sample set, and then solve for the eigenvector P of the covariance matrix. i As principal components of shape features.

[0018] In some preferred embodiments, the linear reconstruction model S′ includes: Where, φ i denoted as the weight parameter for each principal component of the shape feature, and k is the number of principal components of the shape feature.

[0019] In some preferred embodiments, the method for implementing the first 2D / 3D registration in step S3 includes:

[0020] S301. Map the three-dimensional point cloud of the average model from three-dimensional space to the two-dimensional plane containing the two-dimensional contour of the target skeleton, and obtain the 2D / 2D correspondence by iterating the nearest point;

[0021] S302. Map the iterated average model points on the two-dimensional plane to the three-dimensional space, and obtain the 2D / 3D correspondence after calibrating with the original average model three-dimensional point cloud.

[0022] S303. Map the points of the target skeleton's two-dimensional contour to the normal vector direction of the corresponding three-dimensional node of the average model in three-dimensional space to obtain the 3D / 3D correspondence.

[0023] In some preferred embodiments, the method for solving the shape feature weight parameters in step S3 includes:

[0024] The average distance between the point mapped from the 2D contour of the target skeleton to the corresponding point on the linear reconstruction model and the loss function f is used: Where n represents the number of sampling points of the two-dimensional contour of the target skeleton, S′ j This represents the corresponding point mapped from the two-dimensional contour of the target skeleton to three-dimensional space. Indicates the average model with S′ j The corresponding point, P ij P represents the principal component of the i-th shape feature. i The value corresponding to the j-th point; φ i Let be the weight parameters of the principal component of the i-th shape feature.

[0025] In some preferred embodiments, the method for implementing the second 2D / 3D registration in step S4 includes:

[0026] S401. Map the three-dimensional point cloud of the preliminary target skeleton three-dimensional model from three-dimensional space to the two-dimensional plane where the target skeleton two-dimensional contour is located, and obtain the 2D / 2D correspondence by iterating the nearest point;

[0027] S402. Map the points of the preliminary target skeleton 3D model after iteration on the 2D plane to the 3D space, and obtain the 2D / 3D correspondence after calibrating with the original preliminary target skeleton 3D model point cloud.

[0028] S403. Map the points of the two-dimensional contour of the target skeleton to the normal vector direction of the corresponding node of the initial three-dimensional model of the target skeleton in three-dimensional space to obtain the 3D / 3D correspondence.

[0029] In some preferred embodiments, the method for obtaining the target skeleton 3D model in step S4 includes:

[0030] The local nodes of the initial target skeleton 3D model are transformed using Laplacian surface transformation with reference to the corresponding points of the registered target skeleton 2D contour. This extends the coordinate transformation of the local nodes to the 3D deformation of the entire initial target skeleton 3D model. While keeping the Laplacian operator of the model before and after the transformation as invariant as possible, the corresponding nodes are fitted to the target position. This is then used as the loss function E(V′) to solve for the deformed coordinates v′. i ;

[0031] in,

[0032] v i v′ represents the point coordinates of the initial target skeleton 3D model. i For v i The coordinates of the points after the surface transformation, L() is the Laplacian operator, u i For v i The target coordinates of the surface transformation, where m is the number of nodes in any standard 3D bone sample and n is the number of sampling points in the 2D contour of the target bone.

[0033] Beneficial effects

[0034] This invention is applicable to the three-dimensional reconstruction of the entire skeletal system and can be widely used in various orthopedic surgeries and treatment planning. While maintaining reconstruction accuracy, it effectively handles the characteristic differences between individual bones, achieving a more accurate and natural three-dimensional skeletal model. Compared with traditional CT or MRI scans, this invention significantly reduces radiation exposure and cost, making it more suitable for routine clinical examinations and frequent monitoring. The high precision and adaptability of this invention enable more personalized medical solutions, providing a model basis for personalized prosthesis design, biomechanical analysis, and surgical planning. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the skeletal 3D reconstruction method based on statistical shape model and Laplacian operator in a preferred embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram illustrating the principle of Laplace surface transformation in a preferred embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram illustrating the extension of the coordinate transformation of local nodes to the three-dimensional deformation of the entire skeleton in a preferred embodiment of the present invention.

[0038] Figure 4 This is a schematic diagram illustrating the reconstruction effects of LSD, SSLM, and SSM under different feature number conditions in an experimental example of the present invention;

[0039] Figure 5This is a schematic diagram of the reconstruction error distribution of LSD, SSLM, and SSM under different feature number conditions in an experimental example of the present invention;

[0040] Figure 6 This is a schematic diagram of the reconstruction error distribution of SSLM and SSM under different information content conditions in an experimental example of the present invention;

[0041] Figure 7 This is a schematic diagram of the interval angle for obtaining a two-dimensional image of the target skeleton in an experimental example of the present invention;

[0042] Figure 8 This is a schematic diagram of the reconstruction error distribution of SSLM and SSM under different target skeleton two-dimensional contour numbers in an experimental example of the present invention; Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings. In the description of this invention, it should be understood that the terms "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not 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 invention.

[0044] Example 1

[0045] like Figure 1 As shown, this embodiment provides a method for 3D bone reconstruction based on a statistical shape model and the Laplacian operator, including the following steps:

[0046] S1. Obtain a standard 3D skeleton sample set; obtain the 2D contour of the target skeleton.

[0047] The construction of the standard 3D skeletal sample set is based on historically acquired standard 3D skeletal samples. In this field, it is generally recognized that directly acquired 3D skeletal models cannot usually be used directly for subsequent processing and analysis because they may contain noise or require adjustment of their point cloud pose to better suit subsequent steps; therefore, preprocessing steps are necessary. Many preprocessing methods exist in this field, and this invention provides a preferred embodiment for reference. It should be understood that this preferred embodiment should not be construed as the sole limitation of the preprocessing steps of this invention.

[0048] First, the acquired 3D skeletal model undergoes detailed preprocessing. This includes converting the skeletal model into a uniformly distributed triangular mesh, with each mesh spaced at 1 mm. This step not only makes the model representation more refined but also facilitates subsequent processing. The processed model is saved as a 3D point cloud and its corresponding triangular facet information for further analysis and manipulation.

[0049] Next, each skeletal point cloud is normalized. Normalization is a necessary step because skeletal models in the original dataset may vary in pose and size. Through linear scaling, all skeletal models are adjusted to a uniform size range, which not only emphasizes the shape features of the bones but also facilitates subsequent fitting of patient-specific models. After decentralization, further pose adjustment is performed using the Iterative Closest Point (ICP) algorithm. This algorithm ensures that the pose of all skeletal point clouds is as consistent as possible with the pose acquired from the patient's 2D images by minimizing the distance from each point to its nearest point. This step is crucial because it eliminates pose differences in the original data, ensuring the accuracy of statistical analysis.

[0050] Ultimately, through this series of preprocessing steps, a standardized and uniformly posed 3D skeletal sample set was established. This sample set will play a crucial role in the subsequent establishment and analysis of statistical shape models, enabling the final 3D skeletal reconstruction method to be effectively applied to the personalized needs of different patients.

[0051] The acquisition of the target skeleton's two-dimensional contour is achieved by extracting the contour and uniformly sampling the input target skeleton's two-dimensional image. This process first involves accurately identifying and extracting the contour lines in the skeleton image, which can be achieved using existing image processing techniques in the field, such as edge detection and contour tracking algorithms, to ensure the integrity and accuracy of the contour.

[0052] Next, uniform sampling is performed. During sampling, points on the contour line are selected evenly, and their two-dimensional coordinates are recorded. This uniform sampling method ensures that key features on the contour are fully captured, while avoiding data redundancy caused by oversampling. The sampling accuracy can be adjusted according to specific application requirements and computing resources to achieve the optimal balance.

[0053] S2. Based on principal component analysis, solve the principal components and average model of the shape features of the standard 3D skeleton sample set, and construct a linear reconstruction model.

[0054] The linear reconstruction model is constructed based on the concept of statistical shape model (SSM), and uses principal component analysis (PCA) to parameterize the shape features of the preprocessed standard 3D skeleton sample set. The core of this process is to extract common shape features from a large number of standard skeleton point cloud models and use them as the basis for reconstruction.

[0055] Inspired by existing technologies, the steps generally include: First, based on a pre-processed skeletal point cloud model with known point correspondences, the PCA method is applied to extract the main shape variations of standard bones. This method yields a set of shape feature parameters that capture the main patterns of bone shape change. Next, a linear model is constructed, representing any bone as a linear combination of an average model and these shape feature parameters and their corresponding weight coefficients. The advantage of this representation method is that even without updating the standard 3D bone sample set, diverse 3D skeletal models can be reconstructed by adjusting the weight parameters of different shape features.

[0056] S3. Perform the first 2D / 3D registration on the target skeleton's two-dimensional contour and average model, solve for the shape feature weight parameters of the target skeleton's two-dimensional contour, and input them into the linear reconstruction model to obtain a preliminary three-dimensional model of the target skeleton. Considering the properties of point cloud models, planar two-dimensional points and three-dimensional point clouds can be mutually mapped. This means that the correspondence between the two-dimensional image and the three-dimensional model can be clearly defined, and then the two-dimensional contour of the target skeleton can be mapped onto the three-dimensional linear reconstruction model to complete the preliminary three-dimensional reconstruction.

[0057] In some preferred embodiments, a preferred method for solving the shape feature weight parameters is provided, including:

[0058] The average distance between the point mapped from the 2D contour of the target skeleton to the corresponding point on the linear reconstruction model and the loss function f is used: Where n represents the number of sampling points of the two-dimensional contour of the target skeleton, S′ j This represents the corresponding point mapped from the two-dimensional contour of the target skeleton to three-dimensional space. Indicates the average model with S′ j The corresponding point, P ij P represents the principal component of the i-th shape feature. i The value corresponding to the j-th point; φ i Let be the weight parameters of the principal component of the i-th shape feature.

[0059] It should be noted that the principal component of the shape feature P i A 3*m×1 vector, with the same size as the node coordinate vector of each linear reconstruction model, and corresponding one-to-one with it. When taking the point on the average model corresponding to the two-dimensional sampling point, P ijThis represents the value at the position corresponding to the j-th point in the principal component vector of the shape features and the coordinate vector of the average model node.

[0060] Preferably, the loss function f can be solved using the least squares method.

[0061] S4. Perform a second 2D / 3D registration on the target bone 2D contour and the preliminary target bone 3D model. Fit the preliminary target bone 3D model with the target bone 2D contour based on the Laplacian operator to obtain the target bone 3D model.

[0062] Given the limitations of the Statistical Shape Model (SSM), the initially generated 3D model of the target skeleton may not perfectly fit the extracted 2D contour of the target skeleton. Although this model has captured the basic shape features of the skeleton, there is still room for improvement in matching fine local structures and complex surfaces. Therefore, the key in this step is to fine-tune the initially reconstructed model in 3D space to fully fit the 2D contour information and improve the overall accuracy of the reconstruction.

[0063] The Laplacian surface deformation (LSD) is based on the Laplacian operator, which can effectively express the local surface shape features of each node in the model. Its principle is as follows: Figure 2 As shown, the Laplacian operator is implemented by calculating the difference vector between the centroids of each node and all its adjacent nodes in the model. The magnitude of this vector reflects the buckling degree of the surface at that point, while its direction corresponds to the surface normal vector at that point. Therefore, the Laplacian operator not only describes the local surface features of any node in the 3D mesh model but also influences the shape of the entire model through the topological transitivity between nodes. When the Laplacian operator of a node changes, the local shape features of its adjacent nodes also change accordingly. This change is then propagated to all interconnected nodes, achieving a global adjustment of the entire model.

[0064] In this invention, Laplacian Surface Deformation (LSD) is combined with 3D skeletal reconstruction results based on Statistical Shape Models (SSM) to form a novel method, namely SSLM (Statistical Shape And Laplacian Models). The core of this method lies in minimizing the changes in the Laplacian operator before and after the transformation while achieving accurate transformation of the skeletal shape to the target position, thereby ensuring the consistency of the overall shape features. Figure 3As shown, the key to the SSLM method lies in extending the coordinate transformation of local nodes to the 3D deformation of the entire skeleton. This local-to-global transformation not only preserves the prior shape features in the SSM reconstruction results but also allows the bone surface to adapt to new features, thereby more accurately fitting the 2D contour of the target bone. In this process, SSLM finely adjusts the position of each node to ensure that the entire skeleton model retains its original structural features and shape details while adapting to the 2D contour.

[0065] SSLM not only improves the accuracy of 3D reconstruction but also enhances the adaptability of the model, enabling it to better meet the needs of complex and unique bone shapes. By combining the robustness of SSM with the flexibility of LSD, SSLM provides an efficient and accurate new approach to 3D bone reconstruction. This method is particularly suitable for orthopedic medical applications requiring high personalization, such as surgical planning and prosthesis design, and can significantly improve the accuracy and effectiveness of clinical procedures. In some preferred embodiments, a preferred method for obtaining a target skeleton 3D model is provided, which includes: performing a Laplacian surface transformation on the local nodes of the preliminary target skeleton 3D model with reference to the corresponding points of the registered target skeleton 2D contour, thereby extending the coordinate transformation of the local nodes to the 3D deformation of the entire preliminary target skeleton 3D model; while keeping the Laplacian operator of the model before and after the transformation as unchanged as possible, fitting the corresponding nodes to the target position, and using this as the loss function E(V′) to solve for the deformed coordinates v′. i ;

[0066] in,

[0067] Among them, v i v′ represents the point coordinates of the initial target skeleton 3D model. i For v i The coordinates of the point after surface transformation, u i For v i The target coordinates of the surface transformation are the 3D mapping points of the 2D contour of the target skeleton; m is the number of nodes in any standard 3D skeleton sample, and n is the number of sampling points in the 2D contour of the target skeleton; L() is the Laplacian operator. Where v ij For v i 1-Points within the domain, d i For v i The number of adjacent nodes.

[0068] Example 2

[0069] This embodiment is based on the above embodiment 1, and provides a preferred example of a linear reconstruction model construction method.

[0070] In some preferred embodiments, the method for obtaining the average model includes:

[0071] S201, The standard 3D skeleton sample set [S1,S2,…,S…] is used. N Each sample in the diagram is represented as S. i =(x1,y1,z1,…x m ,y m ,z m ) T Where N represents the number of standard 3D bone samples, and m represents the number of nodes in any standard 3D bone sample;

[0072] S202, Calculation of Average Model Among them, S i This represents standard skeletal point cloud data. denoted as the average model, and p represents the number of standard 3D skeleton samples.

[0073] Based on the above embodiments, the method for obtaining the principal components of the shape features includes:

[0074] Solve for the covariance matrix of the standard 3D skeleton sample set. Then, the eigenvector P of the covariance matrix Cov is solved. i As principal components of shape features. Furthermore, due to the eigenvector P i The number of features is relatively large, and their contributions to bone shape features vary, while an excessive number of feature vectors P i Selecting certain parameters will increase the computational resource consumption of the reconstruction model; therefore, the number of principal components of shape features can be further limited. In some preferred embodiments, this is mainly done through principal component analysis, as shown below:

[0075] Solve for the eigenvalues ​​λ of the covariance matrix Cov. i and eigenvector P i According to λ i The magnitude of the feature vector P i When sorting, it should be understood that each feature vector represents a major shape feature of the skeleton. The feature vectors corresponding to the feature values ​​with a ratio of 0.9 to 0.99 are selected as the principal components of the shape features in this standard 3D skeleton sample set.

[0076] Thus, any skeleton can be represented by a linear combination of an average model and shape features and their weight coefficients. To keep the deformed skeleton model within a reasonable range, the weight coefficients corresponding to each shape feature are preferably limited to... Inside.

[0077] Based on the above embodiments, the linear reconstruction model S′ includes: Where, φ i denoted as the weight parameter for each principal component of the shape feature, and k is the number of principal components of the shape feature.

[0078] Example 2

[0079] This embodiment is based on the above embodiment 1, and provides a better method for 2D / 3D registration.

[0080] In this embodiment, the registration method aims to achieve accurate registration between a two-dimensional image and a three-dimensional model by using a point cloud in three-dimensional space as an intermediary. The core of this method lies in using spatial point clouds as a bridge to connect the correspondence between the two-dimensional image and the three-dimensional model.

[0081] The specific process is as follows:

[0082] First, the point cloud of the 3D model is projected onto a 2D plane. This step ensures that the 2D mapping reflects the shape features of the 3D model as accurately as possible.

[0083] Next, calibration is performed using the two-dimensional contour of the target skeleton. In this step, the difference between the two-dimensional mapped point cloud and the actual two-dimensional contour is compared and adjusted to achieve accurate registration of the three-dimensional model on the two-dimensional plane.

[0084] The calibrated 2D contour is mapped back to 3D space, corresponding to the point cloud of the 3D model. This step ensures that the 3D point cloud correctly reflects the calibration results of the 2D contour.

[0085] Through the above steps, a correspondence is finally established from 2D / 2D, 2D / 3D to 3D / 3D. This series of registration processes ensures an accurate correspondence between the two-dimensional image and the three-dimensional model, providing a solid foundation for subsequent 3D reconstruction.

[0086] Furthermore, although the object names are different in the two registrations in this invention, the methods are the same, and the specific process is as follows:

[0087] The method for implementing the first 2D / 3D registration in step S3 includes:

[0088] S301. Map the three-dimensional point cloud of the average model from three-dimensional space to the two-dimensional plane containing the two-dimensional contour of the target skeleton, and obtain the 2D / 2D correspondence by iterating the nearest point;

[0089] S302. Map the iterated average model points on the two-dimensional plane to the three-dimensional space, and obtain the 2D / 3D correspondence after calibrating with the original average model three-dimensional point cloud.

[0090] S303. Map the points of the target skeleton's two-dimensional contour to the normal vector direction of the corresponding three-dimensional node of the average model in three-dimensional space to obtain the 3D / 3D correspondence.

[0091] The method for implementing the second 2D / 3D registration in step S4 includes:

[0092] S401. Map the three-dimensional point cloud of the preliminary target skeleton three-dimensional model from three-dimensional space to the two-dimensional plane where the target skeleton two-dimensional contour is located, and obtain the 2D / 2D correspondence by iterating the nearest point;

[0093] S402. Map the points of the preliminary target skeleton 3D model after iteration on the 2D plane to the 3D space, and obtain the 2D / 3D correspondence after calibrating with the original preliminary target skeleton 3D model point cloud.

[0094] S403. Map the points of the two-dimensional contour of the target skeleton to the normal vector direction of the corresponding node of the initial three-dimensional model of the target skeleton in three-dimensional space to obtain the 3D / 3D correspondence.

[0095] Experimental Example 1

[0096] This experimental case focuses on femoral reconstruction, using different feature numbers as variables to examine the reconstruction effects of LSD, SSLM, and SSM.

[0097] Standard 3D skeletal sample sets were established using 50 femurs and 49 femurs respectively, representing cases with sufficiency of feature counts. When using only LSD for reconstruction, the mean absolute error of the reconstructed model was 2.432 mm, and the standard deviation was 1.855 mm. The error was mainly concentrated on the non-projective surface, but due to the surface fitting properties of LSD, the error on the projective surface was very small, and the reconstruction effect was as follows. Figure 4 As shown in (a), when the standard 3D bone sample set has few features or does not contain features of the target femur, the mean absolute error of SSM reconstruction is 2.342 mm with a standard deviation of 1.237 mm, and the mean absolute error of SSLM is 1.736 mm with a standard deviation of 0.987 mm. The reconstruction results are as follows: Figure 4 As shown in (b) and (c), the error distribution is as follows: Figure 5 As shown in (b), SSLM improves reconstruction accuracy by 25.9% compared to SSM, and the error distribution is more concentrated. When the standard 3D skeleton sample set has sufficient features or contains features of the target image's 3D model, SSM alone can achieve a reconstruction accuracy of 0.449mm, while SSLM's accuracy improvement is smaller, and the reconstruction effect is as follows. Figure 4 As shown in (d) and (e), the error distribution is as follows: Figure 5 As shown in (a). In summary, SSLM can effectively improve the accuracy problem caused by insufficient features in SSM and improve the quality of the reconstructed model.

[0098] Experiment Example 2

[0099] This experimental case focuses on femoral reconstruction, using different information levels as variables to examine the reconstruction effects of SSLM and SSM.

[0100] Under the condition of a standard 3D skeletal sample set with a limited number of features, SSM and SSLM models were established. The errors in the 3D femoral reconstruction results using different numbers of principal components, i.e., different information contents, were as follows: Figure 6 As shown, the reconstruction error gradually decreases with increasing principal components, but the rate of error reduction slows down after using more than 10 principal components. The mean absolute error of SSM reconstruction using more than 10 principal components is between 2.1 mm and 2.5 mm, while the mean absolute error of SSLM reconstruction is between 1.7 mm and 1.9 mm. With decreasing principal components, the improvement in reconstruction accuracy by LSD gradually increases. When using 40 principal components, the information content is 98.2%, and the reconstruction accuracies of SSM and SSLM are 2.058 mm and 1.712 mm, respectively, with SSLM improving accuracy by 16.8%. When using 5 principal components, the information content is 85.8%, and the reconstruction accuracies of SSM and SSLM are 2.596 mm and 2.018 mm, respectively, with SSLM improving accuracy by 22.2%. In conclusion, SSLM can effectively optimize the accuracy problem caused by information loss in SSM and reduce the reconstruction error of the model.

[0101] Experimental Example 3

[0102] This experimental case focuses on femoral reconstruction, using the number of two-dimensional contours of different target bones as variables to examine the reconstruction effects of SSLM and SSM.

[0103] This experimental example was taken starting from the anteroposterior and lateral views, such as... Figure 7 As shown, a two-dimensional image is taken at every 22.5° interval. To verify the rationality and continuity of the method, 20 principal components are used, and two different methods are used to perform three-dimensional reconstruction by sequentially accumulating images 1 to 8.

[0104] The results of 3D reconstruction from 1 to 8 2D images are as follows Figure 8 As shown, when using only one image, the reconstruction errors of both SSM and SSLM are above 2.5mm; after using a second orthogonal image, the reconstruction accuracy of SSLM improves to 1.736mm. However, when adding two-dimensional images from other perspectives, the accuracy of the reconstruction results of either SSM or SSLM does not improve significantly. Therefore, it can be concluded that the present invention's use of two orthogonal two-dimensional images for three-dimensional skeleton reconstruction and model verification is reasonable and meets the accuracy requirements.

[0105] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A skeletal 3D reconstruction method based on statistical shape models and the Laplacian operator, characterized in that, Including the following steps: S1. Obtain a standard 3D skeleton sample set; obtain the 2D contour of the target skeleton; S2. Based on principal component analysis, solve the principal components and average model of the shape features of the standard three-dimensional skeleton sample set, and construct a linear reconstruction model; S3. Perform the first 2D / 3D registration on the target bone 2D contour and average model, solve the shape feature weight parameters of the target bone 2D contour, and input them into the linear reconstruction model to obtain the preliminary target bone 3D model. S4. Perform a second 2D / 3D registration on the target bone 2D contour and the preliminary target bone 3D model. Fit the preliminary target bone 3D model with the target bone 2D contour based on the Laplacian operator to obtain the target bone 3D model. The method for solving the shape feature weight parameters in step S3 includes: The average distance between the points mapped from the 2D contour of the target skeleton to the corresponding points on the linear reconstruction model and the loss function is used. : ;in, This represents the number of sampling points on the two-dimensional contour of the target skeleton. This represents the corresponding point mapped from the two-dimensional contour of the target skeleton to three-dimensional space. Indicates the average model and Corresponding points Indicates the first Principal components of shape features Above and below The value corresponding to each point; For the first Principal component weight parameters for each shape feature; The method for obtaining the target skeleton 3D model in step S4 includes: The local nodes of the initial target skeleton 3D model are transformed using Laplacian surface transformation with reference to the corresponding points of the registered target skeleton 2D contour. This extends the coordinate transformation of the local nodes to the 3D deformation of the entire initial target skeleton 3D model. While preserving the Laplacian operator of the model before and after the transformation as much as possible, the corresponding nodes are fitted to the target position, which is then used as the loss function. Solve for the coordinates after deformation ; in, ; The coordinates of points in the initial target skeleton 3D model. for The coordinates of the points after surface transformation For the Laplace operator, for The target coordinates of the surface transformation, where m is the number of nodes in any standard 3D bone sample and n is the number of sampling points in the 2D contour of the target bone.

2. The skeletal 3D reconstruction method based on statistical shape model and Laplacian operator as described in claim 1, characterized in that, The method for obtaining the average model in step S2 includes: S201, The standard 3D skeleton sample set [ The samples in ] are represented as Where N represents the number of standard 3D bone samples, and m represents the number of nodes in any standard 3D bone sample; S202, Calculation of Average Model ;in, This represents standard skeletal point cloud data. Indicates the average model, This indicates the number of standard 3D bone samples.

3. The skeletal 3D reconstruction method based on statistical shape model and Laplacian operator as described in claim 2, characterized in that, The method for obtaining the principal components of shape features in step S2 includes: Solve for the covariance matrix of the standard 3D skeleton sample set, and then solve for the eigenvectors of the covariance matrix. As principal components of shape features.

4. The skeletal 3D reconstruction method based on statistical shape model and Laplacian operator as described in claim 3, characterized in that, The linear reconstruction model include: ;in, These are the weight parameters for the principal components of each shape feature. The number of principal components representing shape features.

5. The skeletal 3D reconstruction method based on statistical shape model and Laplacian operator as described in claim 1, characterized in that, The method for implementing the first 2D / 3D registration in step S3 includes: S301. Map the three-dimensional point cloud of the average model from three-dimensional space to the two-dimensional plane containing the two-dimensional contour of the target skeleton, and obtain the 2D / 2D correspondence by iterating the nearest point; S302. Map the iterated average model points on the two-dimensional plane to the three-dimensional space, and obtain the 2D / 3D correspondence after calibrating with the original average model three-dimensional point cloud. S303. Map the points of the target skeleton's two-dimensional contour to the normal vector direction of the corresponding three-dimensional node of the average model in three-dimensional space to obtain the 3D / 3D correspondence.

6. The skeletal 3D reconstruction method based on statistical shape model and Laplacian operator as described in claim 1, characterized in that, The method for implementing the second 2D / 3D registration in step S4 includes: S401. Map the three-dimensional point cloud of the preliminary target skeleton three-dimensional model from three-dimensional space to the two-dimensional plane where the target skeleton two-dimensional contour is located, and obtain the 2D / 2D correspondence by iterating the nearest point; S402. Map the points of the preliminary target skeleton 3D model after iteration on the 2D plane to the 3D space, and obtain the 2D / 3D correspondence after calibrating with the original preliminary target skeleton 3D model point cloud. S403. Map the points of the two-dimensional contour of the target skeleton to the normal vector direction of the corresponding node of the initial three-dimensional model of the target skeleton in three-dimensional space to obtain the 3D / 3D correspondence.

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