A non-rigid point cloud registration method for computer-assisted liver surgery

Abstract

The present invention proposes a non-rigid point cloud registration method for computer-assisted liver surgery, which obtains a source point cloud point set and a target point cloud point set; uses a feature extraction module to extract the source point cloud point set features and the target point cloud point set features respectively; adopts the optimal transmission idea, based on the source point cloud point set features and the target point cloud point set features, calculates the correspondence matrix between the two point sets; obtains the optimal displacement vector according to the correspondence matrix, uses the optimal displacement vector to correct the source point cloud point set, and obtains the corrected source point cloud point set; calculates the reconstruction loss based on the corrected source point cloud point set and the target point cloud point set, and trains the LCNet model for point set registration. The present invention extracts features through a feature extraction module, and uses an optimal transmission module to calculate point correspondences, and finally estimates the displacement by solving the matrix equation involved, thereby achieving robustness to noise and rotation changes.

Description

Technical Field

[0001] The present invention relates to the field of computer-assisted surgery, and in particular to a non-rigid point cloud registration method for computer-assisted liver surgery. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] There are several challenges in accurately registering preoperative and intraoperative liver point sets. First, the intraoperative liver point set obtained by 3D reconstruction usually contains non-negligible noise, which seriously affects the accuracy of registration. Second, the preoperative and intraoperative data points show significant differences in the coordinate reference frames (i.e., CT and navigation frames), that is, there are rigid transformations (i.e., rotations and translations) between the two spaces, which makes non-rigid registration more difficult. In addition, during liver surgery, the liver will undergo significant non-rigid deformation due to factors such as compression by other organs, respiratory movement, heartbeat, pneumoperitoneum, etc. Traditional image-guided surgery relies on the precise alignment of preoperative images with the actual intraoperative situation, but this process is often affected by intraoperative liver deformation.

[0004] To address these challenges, existing techniques mainly rely on traditional point cloud registration algorithms, such as the non-rigid iterative closest point (NICP) algorithm, Gaussian mixture model-based methods (CPD, BCPD), and graph Laplace regularization-based methods. Although these methods can handle point cloud registration problems to a certain extent, they have some limitations, such as dependence on initialization, sensitivity to noise and outliers, and efficiency and accuracy issues when dealing with large-scale deformations.

[0005] In recent years, with the development of deep learning technology, some deep learning-based point cloud registration methods have been proposed, which improve the robustness and accuracy of registration by learning local and global features of point clouds. However, these methods still face challenges in dealing with non-rigid deformations in image-guided surgery, especially when dealing with noise and rotation changes. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a non-rigid point cloud registration method for computer-assisted liver surgery. During the preoperative and intraoperative liver point set registration process, a feature extraction module is used to obtain rotation-invariant features, and an adapted optimal transmission module is used to calculate point correspondences to improve the accuracy and efficiency of non-rigid registration.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a non-rigid point cloud registration method for computer-assisted liver surgery, comprising:

[0009] Get the source point cloud point set and the target point cloud point set;

[0010] The feature extraction module is used to extract the features of the source point cloud point set and the target point cloud point set respectively;

[0011] Adopting the optimal transmission idea, based on the features of the source point cloud point set and the target point cloud point set, the correspondence matrix between the two point sets is calculated;

[0012] The optimal displacement vector is obtained according to the correspondence matrix, and the source point cloud point set is corrected by using the optimal displacement vector to obtain the corrected source point cloud point set;

[0013] The reconstruction loss is calculated based on the corrected source point cloud point set and the target point cloud point set, and the LCNet model is trained for point set registration.

[0014] Preferably, the feature extraction module includes a two-dimensional convolution layer, a feature normalization layer and a maximum pooling layer; the two-dimensional convolution layer is used to extract local geometric features of a point set through dot product calculation; the feature normalization layer is used to normalize the local geometric features; and the maximum pooling layer is used to downsample the output of the feature normalization layer.

[0015] Preferably, the optimal transmission idea is adopted to calculate the correspondence matrix between the two point sets based on the features of the source point cloud point set and the target point cloud point set; the correspondence matrix is ​​expressed as:

[0016]

[0017] C ij =(1-S ij )·W ij

[0018]

[0019] Among them, P * is the correspondence matrix; there are M points in the source point cloud point set and N points in the target point cloud point set; is the transmission cost between the i-th point in the source point cloud and the j-th point in the target point cloud; S ij represents the cosine similarity between the i-th point in the source point cloud and the j-th point in the target point cloud; h(x i ) represents the source point cloud point set features; h(y i ) represents the target point cloud point set features; W ij is the matching threshold; P ij is the quality of transmission between the i-th point in the source point cloud and the j-th point in the target point cloud; Pij (log P ij -1) is the entropy regularization term, It is a hyperparameter that determines the degree of regularization.

[0020] Preferably, the iterative process of the correspondence matrix is:

[0021] S301: Initialize parameter K to e -C / λ , initialize the parameter a to 1 / M1 M , initialize the maximum number of iterations to a constant value, and initialize the hyperparameters λ and μ to constant values, where 1 M is an M-dimensional vector with all elements equal to 1;

[0022] S302: Calculate the intermediate parameter b, which is:

[0023] b=[(1 / N)1 N / (K T a)] μ / λ+μ

[0024] Among them, 1 N is an N-dimensional vector whose elements are all 1;

[0025] S303: Calculate the intermediate parameter a, which is:

[0026] a=[(1 / M)1 M (Kb)] μ / λ+μ ;

[0027] S304: Determine whether the current number of iterations reaches the maximum number of iterations. If not, increase the number of iterations by 1 and return to S302:, otherwise, execute S305;

[0028] S305: Calculate the corresponding relationship matrix P * ,for:

[0029] P * =diag(a)Kdiag(b)

[0030] Where diag(·) means diagonalizing the matrix.

[0031] Preferably, the step of obtaining an optimal displacement vector according to the correspondence matrix and using the optimal displacement vector to correct the source point cloud point set to obtain a corrected source point cloud point set specifically includes:

[0032] S401: Input correspondence matrix P * ;

[0033] S402: Initialize the maximum number of iterations and the value of the initial local noise uncertainty σ 2 ,for:

[0034]

[0035] S403: Initialize the Gaussian kernel matrix Q. Each element of the matrix Q ij for:

[0036] Q ij =exp(-1 / 2β||x i -y i || 2 )

[0037] Among them, β is a parameter that defines the width of the Gaussian filter;

[0038] S404: Calculate the weight matrix V by solving the matrix equation, the solution equation is:

[0039] (Q+2σ 2 d(P1) -1 )V=d(P1) -1 PY-X

[0040] Where d(·) -1 Indicates diagonalization of the inverse of the matrix, 1 indicates the identity matrix;

[0041] S405: Update local noise uncertainty σ 2 ,for:

[0042]

[0043] Where U = 1 T P1,X′=X+QV,tr(·) represents the trace of the matrix;

[0044] S406: Determine whether the current number of iterations reaches the maximum number of iterations. If not, add 1 to the current number of iterations and return to S404. Otherwise, execute S407.

[0045] S407: Calculate the predicted displacement matrix D according to the weight matrix V obtained after iteration pred :

[0046] D pred =QV;

[0047] S408: Calculate the deformed source point set according to the predicted displacement matrix:

[0048] X′=X+D pred .

[0049] Preferably, the step of calculating the reconstruction loss based on the modified source point cloud point set and the target point cloud point set and training the LCNet model for point set registration includes:

[0050] For the LCNet model, the Chamfer loss function is calculated according to the Chamfer distance between the corrected source point cloud point set and the target point cloud point set; when the loss is minimized, the LCNet model training is completed; the Chamfer loss function is:

[0051]

[0052] Among them, M is the number of points in the source point cloud, N is the number of points in the target point cloud; x′ i To correct the points in the source point cloud, y i is a point in the target point cloud.

[0053] Preferably, it also includes:

[0054] For the LCNet-ED model, the Euclidean loss function is calculated based on the average Euclidean distance between the modified source point cloud point set and the target point cloud point set, and the average Euclidean distance is weighted by the corresponding probability; when the loss is minimized, the LCNet-ED model training is completed; the Euclidean loss function is:

[0055]

[0056] Among them, M is the number of points in the source point cloud, N is the number of points in the target point cloud; x′ i To correct the points in the source point cloud, y i is a point in the target point cloud; is the corresponding relationship matrix.

[0057] In a second aspect, the present invention provides a non-rigid point cloud registration system for computer-assisted liver surgery, comprising:

[0058] A data acquisition module is used to acquire a source point cloud point set and a target point cloud point set;

[0059] A feature extraction module, used to respectively extract source point cloud point set features and target point cloud point set features using the feature extraction module;

[0060] The optimal transmission module is used to calculate the correspondence matrix between the two point sets based on the features of the source point cloud point set and the target point cloud point set using the optimal transmission idea;

[0061] A transformation calculation module is used to obtain an optimal displacement vector according to a corresponding relationship matrix, and to modify a source point cloud point set using the optimal displacement vector to obtain a modified source point cloud point set;

[0062] The model training module is used to calculate the reconstruction loss based on the corrected source point cloud point set and the target point cloud point set, and train the LCNet model for point set registration.

[0063] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a non-rigid point cloud registration method for computer-assisted liver surgery described in the first aspect.

[0064] In a fourth aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the non-rigid point cloud registration method for computer-assisted liver surgery described in the first aspect are implemented.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] 1. Through the feature extraction module (FEM), the present invention can perform deep feature learning on the source point cloud and the target point cloud, and extract robust point cloud features using convolutional layers and maximum pooling operations. This deep feature learning not only enhances the model's understanding of point cloud data, but also improves the robustness to noise and rotation that may occur during surgery.

[0067] 2. The present invention uses optimal transmission to use the original point set and the learned features to establish a reliable correspondence between the two point sets. This correspondence is very robust to rigid transformations due to the combination of optimal transmission theory, and can reduce the erroneous correspondence caused by rigid transformations between point sets, thereby improving the accuracy of registration.

[0068] 3. The transformation calculation module of the present invention does not directly regress the displacement vector, but calculates the displacement by solving the matrix equation. This method has good robustness to outliers and noise, and can more accurately estimate the relative position changes between point sets. At the same time, the module explicitly considers local noise, reduces the impact of noise on the registration results through iterative optimization, and further improves the accuracy and reliability of registration.

[0069] 4. The present invention uses three different LCNet variants, each of which is trained using a different loss function. The diverse loss function design allows the model to be optimized according to different registration requirements and scenarios, thereby improving the applicability and flexibility of the model.

[0070] 5. Experimental results show that the present invention has significant improvements over the existing state-of-the-art non-rigid registration methods when dealing with three challenging scenarios (i.e., scenarios with large deformation, noise, and rotation differences), which provides strong support for its potential application in image-guided liver surgery.

[0071] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their description are used to explain the present invention but do not constitute a limitation of the present invention.

[0073] Figure 1 A main flow chart of a non-rigid point cloud registration method for computer-assisted liver surgery provided by an embodiment of the present invention;

[0074] Figure 2 A detailed flow chart of a non-rigid point cloud registration method for computer-assisted liver surgery provided by an embodiment of the present invention;

[0075] Figure 3 A schematic diagram of a feature extraction module provided in an embodiment of the present invention;

[0076] Figure 4 A flow chart of corresponding relationship matrix calculation provided by an embodiment of the present invention;

[0077] Figure 5 A flow chart of correcting a source point cloud point set provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0078] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0079] Embodiment 1

[0080] like Figure 1 As shown, this embodiment discloses a non-rigid point cloud registration method for computer-assisted liver surgery, comprising the following steps:

[0081] S1: Get the source point cloud point set and the target point cloud point set;

[0082] S2: Use the feature extraction module to extract the source point cloud point set features and the target point cloud point set features respectively;

[0083] S3: Adopting the optimal transmission idea, based on the features of the source point cloud point set and the target point cloud point set, the correspondence matrix between the two point sets is calculated;

[0084] S4: Obtain an optimal displacement vector according to the correspondence matrix, and use the optimal displacement vector to correct the source point cloud point set to obtain a corrected source point cloud point set;

[0085] S5: Calculate the reconstruction loss based on the corrected source point cloud point set and the target point cloud point set, and train the LCNet model for point set registration.

[0086] Next, combine Figure 2, a non-rigid point cloud registration method for computer-assisted liver surgery disclosed in this embodiment is described in detail.

[0087] First, technicians in this field can choose laser scanners, depth cameras, etc. to obtain source point cloud points and target point cloud points before and during surgery.

[0088] In S2, the feature extraction module is used to extract the source point cloud point set features and the target point cloud point set features, such as Figure 3 As shown, specifically including:

[0089] S201: input the source point cloud point set X and the target point cloud point set Y, and send them to the FEM module respectively;

[0090] S202: The FEM module includes two parts: a two-dimensional convolution module and a feature normalization module, wherein the convolution kernel of the two-dimensional convolution module slides in a local neighborhood of the point cloud, and extracts local geometric features through dot product calculation; the feature normalization module normalizes the output of the convolution layer to ensure that the network is robust to features of different scales;

[0091] S203: Perform feature downsampling through the maximum pooling layer to reduce the spatial dimension of the feature map while retaining the most important feature information;

[0092] S204: The outputs of the feature encoding layer and the maximum pooling layer are used as feature representations of the source point cloud point set and the target point cloud point set, i.e., the source point cloud point set features h(X) and the target point cloud point set features h(Y), to provide input for the subsequent optimal transmission module.

[0093] This embodiment uses a feature extraction module (FEM). The two-dimensional convolution module can effectively extract the local geometric features of the point cloud by sliding the convolution kernel in the local neighborhood of the point cloud and calculating the dot product, which helps to capture the detailed information in the point cloud, which is particularly important for complex structures that need to be accurately aligned in surgical point cloud registration. Compared with global features, local features can better reflect the subtle changes in the point cloud, thereby providing richer information for the subsequent registration process.

[0094] The feature normalization module normalizes the output of the convolutional layer to ensure that the network is robust to features of different scales. In liver surgery point cloud registration, due to differences in scanning equipment, scanning angles, and scanning distances, point cloud data may have scale differences. Feature normalization can reduce the impact of such scale differences on the registration results and improve the stability and accuracy of the registration.

[0095] The outputs of the feature encoding layer and the maximum pooling layer are feature representations of the source point cloud and the target point cloud. These features contain rich local geometric information and have been normalized and downsampled, with high quality and robustness. These high-quality feature representations provide a solid foundation for the subsequent optimal transfer module, which helps to achieve more accurate surgical point cloud registration.

[0096] In S3, the optimal transmission idea is adopted to calculate the correspondence matrix between the two point sets based on the features of the source point cloud point set and the target point cloud point set.

[0097] like Figure 4 As shown, as a specific implementation method, this embodiment uses the Sinkhorn algorithm to calculate the corresponding relationship matrix The correspondence estimation task in point cloud registration is transformed into an optimal transmission problem. The goal is to find an optimal transmission plan to distribute the source point set X Transformed into the distribution of target point set Y At the same time, transmission costs are minimized.

[0098] Assume that there are M points in the source point set and N points in the target point set. The mass of each point in the source point set is The quality received by each point in the target point set is And there is no quality loss during the transmission process. The optimal transmission problem can be expressed as:

[0099]

[0100] Among them, P * is the optimal transportation matrix, that is, the corresponding relationship matrix, is the transmission cost between the i-th point in the source point cloud and the j-th point in the target point cloud, P ij is the quality of the transmission between the i-th point in the source point cloud and the j-th point in the target point cloud, P ij (logP ij -1) is the entropy regularization term used to reduce the complexity of solving the optimal transport problem, is a hyperparameter that determines the degree of regularization.

[0101] By considering the cost factor, the Sinkhorn algorithm in this embodiment can further improve the accuracy and efficiency of the registration and meet the high requirements of users. At the same time, by adjusting the parameters in the cost function or introducing new constraints, the user can flexibly control the calculation process of the correspondence matrix to meet different application scenarios and requirements. Therefore, considering the cost factor in the correspondence matrix can improve accuracy, efficiency, robustness and flexibility.

[0102] The corresponding relationship matrix P is obtained by iteration *, the specific steps are:

[0103] S301: Initialize parameter K to e -C / λ , initialize the parameter a to 1 / M1 M , initialize the maximum number of iterations to a constant value, and initialize the hyperparameters λ and μ to constant values, where 1 M is an M-dimensional vector with all elements equal to 1;

[0104] S302: Calculate the intermediate parameter b, which is:

[0105] b=[(1 / N)1 N / (K T a)] μ / λ+μ

[0106] Among them, 1 N is an N-dimensional vector whose elements are all 1;

[0107] S303: Calculate the intermediate parameter a, which is:

[0108] a=[(1 / M)1 M (Kb)] μ / λ+μ ;

[0109] S304: Determine whether the current number of iterations reaches the maximum number of iterations. If not, increase the number of iterations by 1 and return to S302:, otherwise, execute S305;

[0110] S305: Calculate the corresponding relationship matrix P * ,for:

[0111] P * =diag(a)Kdiag(b)

[0112] Where diag(·) means diagonalizing the matrix.

[0113] The influence of noise on the registration results is reduced through iterative optimization, which further improves the accuracy and reliability of the registration.

[0114] It should be understood that is the definition of the corresponding relationship matrix, P * =diag(a)Kdiag(b) is the corresponding relationship matrix expression actually obtained after the parameter iteration is completed.

[0115] In S4, the optimal displacement vector is obtained according to the corresponding relationship matrix, and the source point cloud point set is corrected using the optimal displacement vector to obtain the corrected source point cloud point set; Figure 5 As shown, the specific steps are:

[0116] S401: Input correspondence matrix P * ;

[0117] S402: Initialize the maximum number of iterations and the value of the initial local noise uncertainty σ 2 ,for:

[0118]

[0119] S403: Initialize the Gaussian kernel matrix Q. Each element of the matrix Q ij for:

[0120] Q ij =exp(-1 / 2β||x i -y i || 2 )

[0121] Among them, β is a parameter that defines the width of the Gaussian filter;

[0122] S404: Calculate the weight matrix V by solving the matrix equation, the solution equation is:

[0123] (Q+2σ 2 d(P1) -1 )V=d(P1) -1 PY-X

[0124] Where d(·) -1 Indicates diagonalization of the inverse of the matrix, 1 indicates the identity matrix;

[0125] S405: Update local noise uncertainty σ 2 ,for:

[0126]

[0127] Where U = 1 T P1,X′=X+QV,tr(·) represents the trace of the matrix;

[0128] S406: Determine whether the current number of iterations reaches the maximum number of iterations. If not, add 1 to the current number of iterations and return to S404. Otherwise, execute S407.

[0129] S407: Calculate the predicted displacement matrix D according to the weight matrix V obtained after iteration pred :

[0130] D pred =QV;

[0131] S408: Calculate the deformed source point set according to the predicted displacement matrix:

[0132] X′=X+D qred .

[0133] In order to verify the performance of the registration method proposed in the present invention, this embodiment selects two traditional registration methods CPD and BCPD and six deep learning-based algorithms Pointpwc, FLOT, SPFlowNet, FPT, Lepard and Livermatch for comparison with the method proposed in this embodiment. The performance of each model is evaluated based on the evaluation indicators, and the experimental results are shown in Table 1.

[0134] The experiment uses a data set with a rotation angle of [-45°, 45°], a maximum noise amplitude of 2mm, and an average deformation amplitude of 12mm. Three evaluation indicators, namely the mean absolute error (MAE), the root mean square error (RMSE), and the chamfer distance (CD), are used to judge the quality of the registration results. The three indicators are expressed as:

[0135]

[0136] in, Represents the true value of the displacement vector. Since the three indicators are measured by the error distance of the registration, the smaller the value of the three indicators, the better.

[0137] Three different unsupervised loss functions in this embodiment are used to train the LCNet model and its variants LCNet-ED and LCNet-WD. These loss functions are:

[0138] 1. Chamfer distance: used in LCNet to calculate the Chamfer distance between the deformed source point set X' and the target point set Y, that is, the sum of the average distance between each point in the deformed source point set and its corresponding point in the target point set and the average distance between each point in the target point set and its corresponding point in the deformed source point set, which is:

[0139]

[0140] 2. Weighted Euclidean distance: used in LCNet-ED, it calculates the average Euclidean distance between X' and Y, which is weighted by the corresponding probability:

[0141]

[0142] 3. Combined loss function: used in LCNet-WD, it is a combination of Chamfer distance and weighted Euclidean distance, which is:

[0143]

[0144] Among them, 0<α<1.

[0145] As can be seen from Table 1, the method of the present invention is superior to other comparison methods in terms of evaluation indicators MAE, RMSE and CD. In terms of evaluation indicators MAE, RMSE and CD, the experimental results of the best result LCNet of the three methods implemented by the present invention are 51.3%, 68.6% and 55.1% ahead of the best results of other methods, respectively. The comparison results in the above table show that the method proposed by the present invention reduces the erroneous correspondence caused by rigid transformation between point sets by introducing FEM feature extraction module, optimal transmission (OT) and transformation calculation, improves the robustness to noise and rotation that may occur during surgery, and improves the accuracy of non-rigid registration.

[0146] Table 1 Model performance evaluation

[0147]

[0148] This specific embodiment extracts features through a feature extraction module (FEM), calculates point correspondence using the optimal transmission (OT) concept, and finally estimates displacement by solving the matrix equation involved, thereby achieving robustness to noise and rotation changes. This method can significantly improve the accuracy of point cloud registration in image-guided liver surgery and provide more reliable support for surgical navigation.

[0149] Embodiment 2

[0150] This embodiment provides a non-rigid point cloud registration system for computer-assisted liver surgery, including:

[0151] A data acquisition module is used to acquire a source point cloud point set and a target point cloud point set;

[0152] A feature extraction module, used to respectively extract source point cloud point set features and target point cloud point set features using the feature extraction module;

[0153] The optimal transmission module is used to calculate the correspondence matrix between the two point sets based on the features of the source point cloud point set and the target point cloud point set using the optimal transmission idea;

[0154] A transformation calculation module is used to obtain an optimal displacement vector according to a corresponding relationship matrix, and to modify a source point cloud point set using the optimal displacement vector to obtain a modified source point cloud point set;

[0155] The model training module is used to calculate the reconstruction loss based on the corrected source point cloud point set and the target point cloud point set, and train the LCNet model for point set registration.

[0156] Embodiment 3

[0157] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps in the non-rigid point cloud registration method for computer-assisted liver surgery as described in the first embodiment above are implemented.

[0158] Embodiment 4

[0159] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the non-rigid point cloud registration method for computer-assisted liver surgery as described in the first embodiment above are implemented.

[0160] The steps or modules involved in the above embodiments 2 to 4 correspond to those in embodiment 1. For the specific implementation, please refer to the relevant description of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0161] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A non-rigid point cloud registration method for computer-assisted liver surgery, characterized in that: include: Get the source point cloud point set and the target point cloud point set; The feature extraction module is used to extract the features of the source point cloud point set and the target point cloud point set respectively; Adopting the optimal transmission idea, based on the features of the source point cloud point set and the target point cloud point set, the correspondence matrix between the two point sets is calculated; The optimal displacement vector is obtained according to the correspondence matrix, and the source point cloud point set is corrected by using the optimal displacement vector to obtain the corrected source point cloud point set; The reconstruction loss is calculated based on the corrected source point cloud point set and the target point cloud point set, and the LCNet model is trained for point set registration.

2. The non-rigid point cloud registration method for computer-assisted liver surgery according to claim 1, characterized in that: The feature extraction module includes a two-dimensional convolution layer, a feature normalization layer and a maximum pooling layer; the two-dimensional convolution layer is used to extract local geometric features of a point set by dot product calculation; the feature normalization layer is used to normalize local geometric features; and the maximum pooling layer is used to downsample the output of the feature normalization layer.

3. The non-rigid point cloud registration method for computer-assisted liver surgery according to claim 1, characterized in that: The optimal transmission idea is adopted to calculate the correspondence matrix between the two point sets based on the features of the source point cloud point set and the target point cloud point set; the correspondence matrix is ​​expressed as: in, is the correspondence matrix; there are M points in the source point cloud point set and N points in the target point cloud point set; is the transmission cost between the i-th point in the source point cloud and the j-th point in the target point cloud; Represents the cosine similarity between the i-th point in the source point cloud and the j-th point in the target point cloud; Represents the features of the source point cloud point set; Represents the point cloud point set features of the target; is the matching threshold; It is the quality of transmission between the i-th point in the source point cloud and the j-th point in the target point cloud; is the entropy regularization term, is a hyperparameter that determines the degree of regularization.

4. The non-rigid point cloud registration method for computer-assisted liver surgery according to claim 3, characterized in that: The iterative process of the correspondence matrix is: S301: Set the parameters Initialize to , the parameters Initialize to , initialize the maximum number of iterations to a constant value, initialize the hyperparameters and is a constant value, where is an M-dimensional vector with all elements equal to 1; S302: Calculate intermediate parameters ,for: in, is an N-dimensional vector whose elements are all 1; S303: Calculate intermediate parameters ,for: ； S304: Determine whether the current number of iterations reaches the maximum number of iterations. If not, increase the number of iterations by 1 and return to S302:, otherwise, execute S305; S305: Calculate the correspondence matrix ,for: in, Denotes diagonalization of the matrix.

5. The non-rigid point cloud registration method for computer-assisted liver surgery according to claim 3, characterized in that: The optimal displacement vector is obtained according to the correspondence matrix, and the source point cloud point set is corrected by using the optimal displacement vector to obtain the corrected source point cloud point set. The specific steps include: S401: Input correspondence matrix ; S402: Initialize the maximum number of iterations and the value of the initial local noise uncertainty ,for: ； S403: Initialize Gaussian kernel matrix , each element of the matrix for: in, is the parameter that defines the width of the Gaussian filter; S404: Calculate the weight matrix by solving the matrix equation , the solution equation is: in represents the diagonalization of the inverse of the matrix, represents the identity matrix; S405: Update local noise uncertainty ,for: in , , represents the trace of a matrix; S406: Determine whether the current number of iterations reaches the maximum number of iterations. If not, add 1 to the current number of iterations and return to S404. Otherwise, execute S407. S407: The weight matrix obtained after iteration , calculate the predicted displacement matrix : ； S408: Calculate the deformed source point set according to the predicted displacement matrix: 。 6. The non-rigid point cloud registration method for computer-assisted liver surgery according to claim 1, characterized in that: The method of calculating the reconstruction loss based on the modified source point cloud point set and the target point cloud point set and training the LCNet model for point set registration includes: For the LCNet model, the Chamfer loss function is calculated according to the Chamfer distance between the corrected source point cloud point set and the target point cloud point set; when the loss is minimized, the LCNet model training is completed; the Chamfer loss function is: Among them, M is the number of points in the source point cloud point set, and N is the number of points in the target point cloud point set; To correct the points in the source point cloud, It is a point in the target point cloud.

7. The non-rigid point cloud registration method for computer-assisted liver surgery according to claim 6, characterized in that: Also includes: For the LCNet-ED model, the Euclidean loss function is calculated based on the average Euclidean distance between the modified source point cloud point set and the target point cloud point set, and the average Euclidean distance is weighted by the corresponding probability; when the loss is minimized, the LCNet-ED model training is completed; the Euclidean loss function is: Among them, M is the number of points in the source point cloud point set, and N is the number of points in the target point cloud point set; To correct the points in the source point cloud, is a point in the target point cloud; is the corresponding relationship matrix.

8. A non-rigid point cloud registration system for computer-assisted liver surgery, characterized in that: include: A data acquisition module is used to acquire a source point cloud point set and a target point cloud point set; A feature extraction module, used to respectively extract source point cloud point set features and target point cloud point set features using the feature extraction module; The optimal transmission module is used to calculate the correspondence matrix between the two point sets based on the features of the source point cloud point set and the target point cloud point set using the optimal transmission idea; A transformation calculation module is used to obtain an optimal displacement vector according to a corresponding relationship matrix, and to modify a source point cloud point set using the optimal displacement vector to obtain a modified source point cloud point set; The model training module is used to calculate the reconstruction loss based on the corrected source point cloud point set and the target point cloud point set, and train the LCNet model for point set registration.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in a non-rigid point cloud registration method for computer-assisted liver surgery as described in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the non-rigid point cloud registration method for computer-assisted liver surgery as described in any one of claims 1-7 are implemented.

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