An automated segmentation method for aneurysm 3D point cloud combined with geometric topology analysis

Abstract

The present invention relates to an automatic segmentation method of aneurysm 3D point cloud combined with geometric topological analysis, which belongs to the field of the combination of artificial intelligence and medical data processing, and aims to improve the segmentation accuracy of aneurysm 3D point cloud. The technical scheme includes: first, data preprocessing is performed on the aneurysm 3D point cloud reconstructed from the MRA image. Then, a dual-branch feature extraction framework is constructed, the first branch is a hierarchical geometric feature learning module, which extracts the local geometric information of the aneurysm point cloud; the second branch is a topological analysis module, which captures the multi-scale topological invariant characteristics of the object by filtering the influence of local noise through persistent coherence. Finally, an attention fusion module is designed to deeply fuse the information from different receptive fields in the dual-branch feature extraction framework. The present invention significantly enhances the processing and feature extraction capabilities of aneurysm 3D point cloud data, thereby realizing the automatic and accurate segmentation of aneurysms.

Description

Technical Field

[0001] The present invention belongs to the field of integration of artificial intelligence and medical data processing, and specifically relates to an automatic segmentation method of aneurysm 3D point cloud combined with geometric topological analysis. Background Art

[0002] Intracranial aneurysms (IA) are abnormal dilations of cerebral arteries. Once an aneurysm ruptures, it can trigger subarachnoid hemorrhage, which is extremely dangerous and carries high morbidity and mortality. However, unruptured IAs are more challenging to manage. With advances in medical imaging, most unruptured aneurysms are discovered incidentally during computed tomography angiography (CTA) or magnetic resonance angiography (MRA) examinations, such as trauma testing after an accident. Detecting aneurysms before they rupture and stratifying their risk are key steps to guide preventive measures.

[0003] However, due to the relatively small size of IA and the complex intracranial vascular structure, IA detection by blindly reviewing CTA or MRA images is a difficult task and requires a lot of medical resources. Especially in resource-poor areas and developing countries, there is a relative shortage of experienced radiologists. In addition, there is a high degree of variability between and within observers, which can lead to missed or misdiagnosed cases. Therefore, the demand for automatic IA detection or segmentation technology is urgent.

[0004] Traditional methods mainly focus on imaging data, using specific features in image data or applying predefined rules to automatically identify aneurysms. With the continuous development of deep learning-based image segmentation methods, three-dimensional (3D) vascular geometry or point clouds derived from vascular data have become easy to obtain, enabling automatic detection of IA. Compared with traditional two-dimensional aneurysm images, reconstructed 3D data can more comprehensively describe the shape of the object, which is crucial for capturing the tiny features and fine details of the aneurysm. More and more researchers have developed advanced point cloud segmentation methods. However, 3D point clouds are disordered and irregular, and a single voxelization or multi-view method will result in high computational complexity. In addition, some deep learning methods that are directly based on point geometric information ignore the overall topological invariance, resulting in low segmentation accuracy.

[0005] In fact, both geometric information and topological information are important clues to understand the shape of fine-grained complex objects. To this end, this study aims to improve IA detection and segmentation by introducing topological data analysis (TDA) and auxiliary geometric information, thereby effectively solving the above problems. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention proposes an automated segmentation method for aneurysm 3D point cloud combined with geometric topological analysis, which integrates topological persistent homology features into the hierarchical geometric learning network of the point cloud, enhancing its ability to capture multi-scale topological features of complex structures in fine-grained 3D objects, thereby improving the accuracy of point cloud segmentation. The method comprises:

[0007] 3D aneurysm point cloud data preprocessing module, used to preprocess the original 3D aneurysm point cloud data set reconstructed from MRA images, effectively improving the quality and input consistency of 3D point cloud data;

[0008] A dual-branch feature extraction framework is used to obtain the geometric information and topological information of the input data respectively; the first branch is a hierarchical geometric feature learning module, which is used to extract the local contextual geometric information of the aneurysm point cloud; the second branch is a topological analysis module, which is used to quantitatively calculate the topological features of the aneurysm and filter out the influence of local noise;

[0009] The attention fusion module is used to integrate the information of different receptive fields obtained by the hierarchical geometric feature learning module and the topological analysis module to obtain the final segmentation result;

[0010] The joint loss function is used to optimize the model using both geometric and topological information. By introducing the topological loss function, the topological structure of the aneurysm can be better preserved, the segmentation error can be further reduced, and thus the segmentation performance can be improved.

[0011] In one embodiment, the 3D aneurysm point cloud data preprocessing module is specifically used to perform farthest point sampling and coordinate normalization processing on the original point cloud data. The farthest point sampling technology effectively reduces the redundant information in the point cloud data while retaining key structural features, thereby improving the data quality and calculation efficiency. Coordinate normalization ensures the consistency of the point cloud data at different scales and ranges, providing reliable and stable input data for subsequent aneurysm detection and segmentation algorithms.

[0012] In one embodiment, the hierarchical geometric feature learning module in the dual-branch feature extraction framework uses a hierarchical neural network to iteratively process the point set sampled in the metric space, and trains and predicts the aneurysm point cloud data set processed by the 3D aneurysm point cloud data preprocessing module. The classification cross entropy loss is used as the loss function during training to gradually capture and learn the higher-level geometric information of the aneurysm from the local to the whole.

[0013] In one embodiment, the topological analysis module of the dual-branch feature extraction framework extracts the topological structure representation of the aneurysm, while filtering the influence of local noise, facilitating further shape analysis from geometric modeling, and introducing topological loss to enhance the segmentation output of the correct topological relationship;

[0014] In one embodiment, the attention fusion module deeply fuses the complementary information from the hierarchical geometric feature learning module and the topology module through an efficient information integration mechanism to achieve fine segmentation of the aneurysm 3D point cloud data;

[0015] In one embodiment, the joint loss function is used to simultaneously optimize geometric features and topological features to improve the segmentation accuracy of the aneurysm 3D point cloud. The joint loss function consists of geometric loss and topological loss, which respectively optimize the geometric information extraction and topological invariance features of the model.

[0016] Compared with the existing technology, the beneficial effects of the above scheme are: first, the original aneurysm point cloud samples are subjected to the farthest point sampling technology through the 3D aneurysm point cloud data preprocessing module, which effectively reduces data redundancy while maintaining the integrity of key information. The coordinate normalization process further improves the consistency and quality of the data; secondly, the preprocessed data is divided into training sets and test sets, and input into the dual-branch feature extraction framework for training. The hierarchical geometric feature learning module can capture and learn the local contextual geometric information in the aneurysm point cloud data through multi-level feature extraction and abstraction. During the training process, the classification cross entropy loss is used as the optimization target to ensure that the model can accurately distinguish aneurysms from other vascular structures and ensure the accuracy of segmentation. The topological analysis module utilizes advanced computational topological methods to quantitatively calculate the topological features in the aneurysm training set, namely the topological persistent homology features, filter out the interference of local noise, and reveal the intrinsic topological structure of the aneurysm. The introduction of topological loss further enhances the model's ability to recognize the correct topological relationship, ensuring that the segmentation results are consistent with the geometric morphology and maintain the correct topological structure. Finally, the attention fusion module is used to integrate the complementary information obtained from the hierarchical geometric feature learning module and the topological analysis module, and dynamically adjusts the information according to its importance and relevance, thereby generating a richer, more comprehensive and accurate aneurysm feature representation. Therefore, this method not only significantly improves the accuracy and robustness of aneurysm segmentation, but also achieves excellent generalization performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention or the description of the prior art:

[0018] Figure 1: is a schematic diagram of a framework of an aneurysm 3D point cloud automatic segmentation method combined with geometric topological analysis in an embodiment, the marked numbers are the serial numbers of the modules, and the line segments indicate the execution order of the model, wherein S01 is the first step of data processing, i.e., preprocessing the 3D aneurysm point cloud data reconstructed from the MRA image, S02 constructs a dual-branch feature extraction framework, which uses the data obtained in S01 to be sent to the hierarchical geometric feature learning module S0201 and the topological analysis module S0202 for training, and S03 is to fuse the geometric and topological features obtained in S02 through the attention module, so as to accurately generate the segmentation result of the aneurysm;

[0019] Figure 2 is a flow chart of a 3D aneurysm point cloud data preprocessing module in one embodiment;

[0020] Figure 3 Schematic diagram of the structure of a hierarchical geometric feature learning module in a dual-branch feature extraction framework in one embodiment;

[0021] Figure 4 Schematic diagram of the structure of a topology analysis module in a dual-branch feature extraction framework in one embodiment;

[0022] Figure 5 is a schematic diagram of the structure of an attention fusion module in one embodiment; DETAILED DESCRIPTION

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments; obviously, the drawings described below are only some examples or embodiments of the present invention, and for ordinary technicians in this field, without paying any creative work, the present invention can also be applied to other similar scenarios based on these drawings. Unless it is obvious from the language environment or otherwise explained, the same numbers in the figures represent the same structure or operation.

[0024] like Figure 1As shown, an embodiment of the present invention provides an automatic segmentation method for aneurysm 3D point cloud combined with geometric topological analysis, the method comprising a 3D aneurysm point cloud data preprocessing module S01, for performing data preprocessing such as sampling and normalization on individual aneurysm point cloud samples; a dual-branch feature extraction framework is used to extract features from the data processed by S01, firstly a hierarchical geometric feature learning module S0201 is used to extract local contextual geometric information of the point cloud representing the intracranial blood vessels to obtain a preliminary segmentation result; a topological analysis module S0202 is used to quantitatively calculate the topological features of the aneurysm point cloud data, while filtering the influence of local noise, and further performing shape analysis from geometric modeling; an attention fusion module, which utilizes the attention mechanism to fuse the information of different scales obtained by the hierarchical geometric feature learning module S0201 and the topological analysis module S0202, and introduces a topological loss function during the training process to obtain the final fine segmentation result.

[0025] like Figure 2 As shown, the original aneurysm point cloud samples are first preprocessed. Specifically, the original dataset includes 116 IA aneurysm segments manually annotated by medical experts, each of which is represented by a 3D point cloud, and each point of the data in the point cloud contains a three-dimensional vector consisting of its coordinates.

[0026] The specific preprocessing process includes sampling and data normalization steps:

[0027] Sampling reads the original sample, obtains the point coordinates, segmentation labels, and point cloud quantity And set the target points .Compare , Size, if < , then complete the point cloud data; calculate the number of points required for completion :

[0028]

[0029] From the original point cloud data Random selection Copy the points and complete them to the required number of points .

[0030] Otherwise, the farthest point sampling method is used to sample the inconsistent input sample data, so that the input of the subsequent model remains consistent while maximally maintaining the shape of the original data;

[0031] First, from the input point cloud data Randomly select a point As the initial point, then calculate all unsampled points to The distance between the two points is , and the point with the longest distance is selected as the next sampling point; then, for each newly selected sampling point, all unsampled points are calculated. To the selected sampling point set The minimum distance :

[0032]

[0033] Select so that The maximized point is used as the next sampling point and added to the selected point set. This process is repeated until the specified number of points is sampled. .

[0034] Data normalization calculates the centroid of the sampled input point cloud , then decentralize the point cloud and subtract the centroid from the coordinates of each point to get the new point cloud coordinates , so that the center of the point cloud moves to the origin, eliminating the translation effect of the point cloud. Next, calculate The maximum distance from all points in the point cloud to the origin , which is the scaling factor:

[0035]

[0036] It is the first after decentralization Point The value of the dimension; finally, the final normalized point is obtained :

[0037]

[0038] The coordinates of the normalized data will be in the consistent range of [-1, 1].

[0039] like Figure 3 As shown in Figure 1, the hierarchical geometric feature learning module in the dual-branch feature extraction framework is used to extract the local contextual geometric information of the intracranial vascular point cloud. The entire network consists of multiple abstract modules (two in the example in the figure), each of which includes sampling, grouping, and feature extraction layers:

[0040] In order to effectively reduce the redundancy of point clouds, Points, Dimensions (default is 3D) included Point cloud data with a number of features, the input of the network is a tensor on the spatial scale , after passing the sampling layer, the feature output size becomes ;

[0041] For the point cloud data processed by the sampling layer, a group of local regions are constructed through the grouping layer. point as the center of the sphere, within the specified radius Search for the closest centroid points, divide the input point set into local neighbors of a single scale; if the number of points in the query ball is greater than or equal to , take the front points as a sub-region; if the number of points is less than , then the point set is resampled; in this way, the input point set is divided into multiple spatially overlapping spherical neighborhoods, each of which is a local subset of these points. After the grouping layer is processed, the network output becomes ;

[0042] After the sampling layer processing, the point cloud data representing the intracranial blood vessels are divided into The feature extraction layer uses Pointnet as the backbone network to extract local features from each neighborhood. The coordinates of each point are first mapped to a high-dimensional space through a shared multi-layer perceptron (MLP) network. Subsequently, a maximum pooling layer is introduced to merge the feature vectors of each point into a global feature vector. In this layer, the input is a set of local neighborhood points, of size ; The output of each local neighborhood is extracted from its center and local features (i.e., the local neighborhood features of the encoding center), and the output size is . Given an unordered set of points ,in , and Represents a shared MLP network, and the feature extraction layer is defined as:

[0043]

[0044] In one embodiment, the hierarchical geometric feature learning module in the dual-branch feature extraction framework is specifically used to train and predict the data set processed by the 3D aneurysm point cloud preprocessing module. The module extracts and fuses the local and global geometric features in the point cloud data layer by layer through a multi-layer geometric feature extraction mechanism, and finally provides rich and accurate feature information for subsequent 3D aneurysm segmentation. samples, there are The number of categories, Representation sample Is it The true label of the class, For sample belong The predicted probability of the class, the classification cross entropy loss is used when training the model As a loss function:

[0045] .

[0046] like Figure 4 As shown, the topological analysis module in the dual-branch feature extraction framework will be specifically used to train and predict the data set processed by the 3D aneurysm point cloud preprocessing module. By using Ripser++ for topological feature extraction and GPU-accelerated calculation of persistent barcodes and homology analysis, the topological structure of the aneurysm can be effectively identified, while filtering out the influence of local noise, which is helpful for further shape analysis from geometric modeling.

[0047] The first step is filtering, which is a key step in inferring the topological structure of the sampled data shape. The input point cloud of points is considered as a finite metric space ,exist The filter structure is applied in the paper to capture the evolution of objects by increasing the multi-scale topological space parameters under the data points; the Vietoris-Rips complex filtering method is used here to include the data after preprocessing. Point set , place a closed sphere at each sampling point and gradually increase the radius parameter , if there are intersecting spheres, connect the sphere centers to construct a simplicial complex; by setting different thresholds (radius parameters ), the simple complex formed is used to capture the multi-scale topological information in the data; A subset of , yes The maximum distance between two points in , if , then the complex contains a simplicial complex, the Vietoris-Rips complex It is expressed as:

[0048]

[0049] Then the complex Perform feature mapping. The duration of topological features is directly related to the geometric properties of the object. When the diameter of the closed sphere exceeds the set threshold When the diameter of the closed sphere is smaller than the set threshold, there are some stable topological features in the complex. , the generated transient features are regarded as noise; therefore, in order to track the evolution of topological features during filtering, the composite The features in the multiscale topological feature map are mapped onto the persistence map (PD) to quantitatively calculate the persistence of topological features. First, the life cycle of each multiscale topological feature is recorded as a persistence barcode. Then, the persistence barcode is converted into the specific numerical time of the appearance and disappearance of each topological feature and plotted on the PD. In the PD, each point represents a persistent topological homology class whose diameter is The first occurrence under the threshold disappears when

[0050] Finally, the features are vectorized, that is, the PD is converted into a spatial structure that can be used for machine learning analysis as the input of the downstream segmentation task; feature vectorization requires converting the original topological data into a matrix with a spatial structure in three steps:

[0051] Creating a persistent surface , which is a weighted sum of normalized symmetric Gaussian functions centered at each point in the persistence map. is the first The coordinates of the points, is the corresponding weight, is the standard deviation of the Gaussian function, mapping each point in the persistence graph to an integrable function :

[0052]

[0053] Discrete The surface is divided into discrete subdomains, each of which consists of small grid cells. In each grid cell, the persistent surface function is calculated. The integral value is used to represent the weight of the corresponding grid cell and quantify the topological information within the grid cell. Row and Column Grid In , the integral of the persistent surface function within the grid is calculated as:

[0054]

[0055] Calculate the persistence image PI; compile the integral value obtained in the above step b into a matrix to form PI, each matrix element corresponds to a grid, and its value represents the intensity or density of the topological structure information in the area. The grid Row and The persistence image PI is expressed as:

[0056]

[0057] Through the above steps, the constructed topological analysis module can effectively extract the topological information in the point cloud data and convert it into feature vectors, providing rich feature representation for further aneurysm segmentation tasks. Therefore, a new topological loss is also added to the loss function. To enhance the segmentation output of correct topological relationships; The topological error between the predicted and true PDs is measured using the first-order Wasserstein distance. Finding the persistence graph of the prediction results Persistence plot with true results The best match between , Used to measure the similarity between two persistence graphs:

[0058]

[0059] for and The set of matches between , where each matching point correspond ; For each pair of matching points ,That The norm distance is the Wasserstein distance; then, for each category (c = 1, 2), the topological loss is calculated :

[0060]

[0061] For all categories, the total It is expressed as:

[0062]

[0063] Finally, the joint loss function By hyperparameters and The losses are weighted and expressed as:

[0064] .

[0065] like Figure 5 As shown, Figure 3 and Figure 4 The geometric features and topological features obtained by the hierarchical geometric feature learning module and the topological analysis module are spliced ​​as the input of the attention fusion module. First, the spliced ​​features are passed through three linear transformation layers to generate query vectors ( ), key vector ( ), and the value vector ( ), these vectors are used to calculate the correlation between features;

[0066] These vectors are then fed into a multi-head scaled dot-product attention mechanism where the multi-head attention ( The scaled dot product attention is calculated by and The dot product of A head of attention, , , The corresponding weight matrix is, is the dimension of the key, and the softmax function is used to normalize the attention weight. The calculation formula of the attention score is as follows:

[0067]

[0068] The attention score is used to The weighted sum is performed to generate the aggregated feature representation, which can capture the most important information in the geometric and topological features. The output of an attention head is:

[0069]

[0070] Finally, the fused features are integrated through a splicing operation and fed into a classifier to perform tasks such as automated segmentation of aneurysm 3D point clouds. In this way, the model can more effectively utilize geometric structure and topological information to improve the recognition and classification performance of complex data structures.

[0071] In summary, compared with the prior art, the method for automatic segmentation of 3D point clouds of aneurysms by combining geometric topological analysis disclosed in the present invention has the following beneficial effects: (1) The automatic segmentation model of 3D point clouds of aneurysms by combining geometric topological analysis established in the present invention can preprocess the 3D point cloud data reconstructed by MRA, and construct a dual-branch feature extraction framework to extract features from the data. First, a hierarchical geometric feature learning module is used to iteratively extract spatial geometric information for rough segmentation. Then, the topological analysis module is used to capture the overall topological invariance of the disordered 3D point cloud and enrich the multi-scale structural representation of the features. Finally, the information of different scales obtained by the two modules in the dual-branch feature extraction framework is integrated to better capture the complex structural relationship between point clouds. At the same time, a joint loss function is constructed during training to optimize the model by using geometric and topological information. By introducing a topological loss function, the topological structure of the aneurysm can be better preserved, the segmentation error can be further reduced, and the segmentation performance can be improved; (2) Verification using the public 3D data of aneurysms shows that the model constructed by the present invention has competitive segmentation performance for fine-grained point cloud segmentation problems and has wide applicability.

[0072] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of this application shall be based on the attached claims.

Claims

1. A method for automatic segmentation of aneurysm 3D point cloud combined with geometric topological analysis, characterized in that: It includes the following steps: A 3D aneurysm point cloud data preprocessing module, which is used to preprocess the original 3D aneurysm point cloud data set reconstructed from MRA images, effectively improving the quality and input consistency of the 3D point cloud data; the 3D aneurysm point cloud data preprocessing module includes two main steps: sampling and data normalization: Sampling preprocesses the input sample. First, read the original sample, obtain the coordinates of the points, the segmentation label, the number of points N in the point cloud, and set the target number of points M; then compare the sizes of M and N. If N < M, supplement the point cloud sample data; otherwise, use the farthest point sampling method to sample the input sample to make the input of the model consistent and maximize the preservation of the original data shape; Data normalization normalizes the point cloud data to unify the coordinate scale of each point within the same range, so as to adapt to the input of the network model; A dual-branch feature extraction framework, which is used to obtain the geometric information and topological information of the input data respectively; the first branch is a hierarchical geometric feature learning module, which uses a hierarchical neural network to process the point set sampled in the metric space and is used to extract the local context geometric information of the aneurysm point cloud; For the hierarchical neural network, first, use the distance metric to divide the point set into overlapping local regions; then, at different spatial scales, extract local geometric features from the adjacent points of each local region; finally, aggregate the extracted local geometric features into larger units to generate higher-level feature representations; repeat this process until all features in the point set are completely extracted; the entire network consists of multiple abstraction modules, and each module contains sampling, grouping, and feature extraction layers: To effectively reduce the redundancy of the point cloud, for a point cloud data with N points, d dimensions, and C feature quantities, the input of the network is a tensor N*(d + C) on the spatial scale. After passing through the sampling layer, the feature output size becomes N1*(d + C); After the sampling layer processing, the point cloud data is used to construct a set of local regions through the grouping layer; using the N1 points in the point set as the centers of the spheres, retrieve the K closest points to the centroid within the specified radius r, and divide the input point set into single-scale local neighbors; if the number of points in the sphere is greater than or equal to K, take the first K points as the sub-region; if the number of points is less than K, resample the point set; in this way, the input point set is divided into multiple spatially overlapping spherical neighborhoods, and each neighborhood is a local subset of these points. After passing through the grouping layer processing, the network output becomes N1*K*(d + C); After the grouping layer processing, the point cloud data representing the intracranial blood vessels is divided into N1 spatial spherical neighborhoods; the feature extraction layer uses an affine transformation network T-Net and takes PointNet as the backbone network to extract local features from each neighborhood; The second The branch is a topological analysis module, which is used to quantitatively calculate the topological features of the aneurysm and filter the influence of local noise. It uses persistent homology analysis to identify persistent features, thereby extracting the topological structure representation of the aneurysm, including using Ripser++ to extract topological features and GPU-accelerated calculation of persistent barcodes and homology analysis, which can effectively identify the topological structure of the aneurysm. It includes the following steps: The first step is filtering, which is a key step to infer the topological structure of the sampled data shape. The input point cloud with N points is considered to be a finite metric space x N , in x N The filter structure is applied in the paper to capture the evolution of objects by increasing the multi-scale topological space parameters under the data points. The Vietoris-Rips complex filtering method is used here to filter the point set X containing n points after data preprocessing. n }, place a closed sphere at each sampling point and gradually increase the radius parameter ∈. If there are intersecting spheres, connect the sphere centers to construct a simplicial complex. By setting different thresholds (radius parameter ∈), the simplicial complex formed is used to capture multiple scale topological information in the data. For a subset σ belonging to X, diam(σ) is the maximum distance between two points in σ. If diam(σ)≤∈, a simplicial complex is contained in the complex, the Vietoris-Rips complex V ∈ (X) is represented by: Then, the complex V ∈ (X) performs feature mapping. The duration of topological features is directly related to the geometric properties of the object. When the diameter of the closed sphere exceeds the set threshold R1, there are some stable topological features in the complex. When the diameter of the closed sphere is less than the set threshold R2, the generated short-term features are regarded as noise. Therefore, in order to track the evolution of topological features during the filtering process, the complex V ∈ The features in (X) are mapped to the persistence map (PD) to quantitatively calculate the persistence of topological features. First, the life cycle of each multi-scale topological feature is recorded as a persistence barcode. Then, the persistence barcode is converted into the specific numerical time of the appearance and disappearance of each topological feature and plotted on the PD. In the PD, each point (x, y) represents a persistent topological homology class, which is on a closed sphere with a diameter R. birth The first occurrence is at a larger threshold R death disappears when Finally, the features are vectorized, that is, the PD is converted into a spatial structure that can be used for machine learning analysis as the input of the downstream segmentation task; feature vectorization requires converting the original topological data into a matrix with a spatial structure in three steps: a. Create a persistent surface Map each point on PD to an integrable function ρ PD , and sum up all functions to form a smooth surface; b. Discrete ρ B subdomain; divide the surface into discrete subdomains, each of which consists of small grid cells; in each grid cell, calculate the persistent surface function ρ PD The integral value is used to represent the weight of the corresponding grid cell and quantify the topological information in the grid cell; the grid in the i-th row and j-th column i,j In this grid, the integral of the persistent surface function is calculated as: c. Calculate the persistence image PI; compile the integral of the persistent surface function obtained in b above into a matrix to form PI, where each matrix element corresponds to a grid and its value represents the strength or density of the topological structure information in the grid; I ij is the integral of the persistent surface in the i-th row and j-th column of the grid, then PI is expressed as: The topological analysis module represents one-dimensional and two-dimensional topological homology features as persistent images, and then converts them into feature vectors for splicing operations; the dimensions of the topological feature vectors are expanded to merge with the geometric local features obtained by the hierarchical geometric feature learning module in the dual-branch feature extraction framework; An attention fusion module is used to integrate the information of different receptive fields obtained by the hierarchical geometric feature learning module and the topological analysis module to obtain the final segmentation result; the attention fusion module specifically concatenates the vectors obtained by the hierarchical geometric feature learning module and the topological analysis module in the dual-branch feature extraction framework, and performs linear transformation through the attention head with an independent weight matrix; for each attention head, a scaled dot product attention mechanism is used, the inner product of the query and the key after linear transformation is used as the attention score, and it is normalized by the softmax function, and finally the value is weighted by the attention score to obtain the output of each attention head; The joint loss function is used to optimize the model by using both geometric and topological information. By introducing the topological loss function, the topological structure of the aneurysm can be better preserved, the segmentation error can be further reduced, and the segmentation performance can be improved. First, the cross entropy loss function is used The supervised model generates a rough classification result based on spatial position coordinates and geometric information, and at the same time, introduces topological loss Measuring the difference between two PDs to achieve optimal segmentation; It measures the topological error between the PD of the predicted result and the true result, and uses the first-order Wasserstein distance W1 to find the persistence graph dgm of the predicted result. PL Persistence plot dgm with true results GT The best match between * , m * Used to measure the similarity between two persistence graphs: m is dgm PL and dgm GT The matching set between them, where each matching point u∈dgm PL Corresponding to v∈dgm GT ; For each pair of matching points (u,v)∈m, The norm distance is the Wasserstein distance; then, for each category (c = 1, 2), the topological loss is calculated For all categories, the total It is expressed as: Finally, the joint loss function Each loss is weighted by the hyperparameters λ1 and λ2, expressed as:

Images