Methods for optimizing the topology of cerebral blood vessel segmentation

Abstract

This application discloses a method for optimizing the topology of cerebral blood vessel segmentation. The method includes: performing vascular skeletonization processing on the preliminary cerebral blood vessel segmentation results to extract the vascular centerline representation; performing connectivity analysis based on the vascular centerline representation to locate all topological break regions and obtain the location information of the break regions; generating a break weight map based on the location information of the break regions; constructing a continuous parameterized representation of cerebral blood vessels based on the vascular centerline representation; determining a topology-preserving energy function with the continuous parameterized representation as the optimization variable; iteratively optimizing the continuous parameterized representation based on the topology-preserving energy function to obtain an iteratively optimized continuous parameterized representation; and generating a topologically complete final cerebral blood vessel segmentation result based on the iteratively optimized continuous parameterized representation. The method provided in this application can effectively repair the topological breakage problem in the cerebral blood vessel segmentation results and improve the topological integrity and structural continuity of the cerebral blood vessel segmentation results.

Description

Technical Field

[0001] This application generally relates to the field of image processing technology. More specifically, this application relates to a method for optimizing the topology of cerebral blood vessel segmentation. Background Technology

[0002] Cerebral vascular segmentation is a core foundational task in medical image analysis, with its results widely applicable to quantitative analysis of cerebral vascular structures, numerical simulation of hemodynamics, and 3D visualization modeling. Computed tomography (CT) vascular imaging is the mainstream imaging modality for acquiring 3D structural information of cerebral vessels, and deep learning-based methods can achieve automatic segmentation of cerebral vessels, representing the current mainstream technological approach in this field. However, existing deep learning-based automatic cerebral vascular segmentation methods are prone to topological breakage in the segmentation results of small vessel branches and bifurcation regions, resulting in discontinuous vascular tree structures and missing vessel terminals, directly impacting the subsequent applications of the segmentation results.

[0003] Existing technologies addressing topological breaks in blood vessel segmentation can be broadly categorized into three types. The first type involves post-processing repair methods, including those based on morphological closure operations, spline interpolation, and connected component analysis. These methods connect broken blood vessels using pre-defined fixed rules, relying on manually set empirical thresholds. This approach fails to adapt to the complex topological changes of cerebral blood vessels, easily introducing erroneous vessel connections. Furthermore, these methods can only perform a one-time repair operation and lack a feedback mechanism for dynamically adjusting optimization strategies based on the repair results. The second type involves topology-aware loss function-related methods. These methods introduce topological constraint loss during model training to achieve topology optimization. However, the loss function has high computational complexity and can only indirectly optimize the topology of the segmentation results through training. Their ability to repair existing topological breaks in the generated segmentation results is limited, and they can only be applied to supervised model training scenarios, not directly to optimizing the output of already trained segmentation models. The third type involves two-stage training framework methods. These methods improve segmentation boundary accuracy through distance field pre-training combined with model fine-tuning. However, their direct repair effect on topological breaks in the segmentation results is limited, and they require complete labeled data for model training, thus limiting their application scenarios. The fourth category is post-processing methods based on graph neural networks. These methods convert the segmentation results into a graph structure and then optimize them through graph convolutional networks. They do not design a special fracture detection and iterative repair mechanism for the problem of topological fracture of cerebral blood vessels, and require an additional model training process, so they cannot be seamlessly embedded into the existing cerebral blood vessel segmentation process.

[0004] In summary, existing cerebral vessel segmentation technologies suffer from two main shortcomings. First, they lack the ability to actively detect and accurately locate topological breaks in the segmentation results, often relying on passive, uniform repair rules. Second, they lack a closed-loop iterative optimization mechanism, failing to dynamically adjust repair strategies based on optimization results. Furthermore, they struggle to adapt to base segmentation models of varying precision and do not provide mathematical guarantees for topological integrity through continuously parameterized vessel representations. Therefore, there is an urgent need to provide a scheme for optimizing the topology of cerebral vessel segmentation to effectively repair topological breaks in the segmentation results and improve the topological integrity and structural continuity of the segmentation outcomes. Summary of the Invention

[0005] In order to at least address one or more of the technical problems mentioned above, this application proposes a scheme for optimizing the topology of cerebral blood vessel segmentation in several aspects.

[0006] In a first aspect, this application provides a method for optimizing the topology of cerebral blood vessel segmentation, comprising:

[0007] Obtain preliminary cerebral blood vessel segmentation results to be optimized; The preliminary cerebral blood vessel segmentation results are processed into a vascular skeleton to extract the vascular centerline representation. Based on the vascular centerline representation, connectivity analysis is performed to locate all topological break regions and obtain the location information of the break regions. A fracture weight map is generated based on the location information of the fracture region; in the fracture weight map, the weight value of the fracture region is higher than the weight value of the non-fracture region. Based on the vascular centerline representation, a continuous parameterized representation of the cerebral blood vessels is constructed. This continuous parameterized representation is used to characterize the geometric morphology and topological structure of the cerebral blood vessels in a continuous space. A topology-preserving energy function is determined with the continuous parameterized representation as the optimization variable. The continuous parameterized representation is iteratively optimized based on the topology-preserving energy function to obtain the iteratively optimized continuous parameterized representation. Based on the iteratively optimized continuous parameterized representation, the final cerebral blood vessel segmentation result with topological integrity is generated and output.

[0008] In some implementations, all topological break regions are located, and the location information of the break regions is obtained, including: For each voxel represented by the vessel centerline, a neighborhood analysis is performed, and voxels with only one voxel in each of the 26 neighborhoods that belong to the vessel centerline are marked as centerline endpoints, thus obtaining the centerline endpoint set. Connectivity analysis was performed on the representation of the blood vessel centerline to obtain multiple independent centerline connected components; Calculate the Euclidean distance between the endpoints of any two different centerline connected components, mark a pair of endpoints whose Euclidean distance is less than the preset maximum fracture distance as a set of fracture points, record the spatial coordinates and fracture distances of all fracture points, and obtain the location information of the fracture area.

[0009] In some implementations, the fracture weight map is a spatially adaptive fracture weight map that matches the spatial dimension of the preliminary cerebral vessel segmentation result, and is implemented using the following formula:

[0010] in, Spatial location of the preliminary cerebral blood vessel segmentation results The weight value at that point, For the set of break points, Let f be the spatial coordinates of the break point. For preset weighting coefficients, The default Gaussian kernel width is set, and the base weight value for the non-fractured region is 1.

[0011] In some implementations, constructing a continuous parameterized representation of the cerebral blood vessels includes: Extract a set of key points from the representation of the blood vessel centerline, the set of key points including blood vessel bifurcation points, centerline endpoints and extreme points of blood vessel curvature; A vascular topology graph is constructed using the set of key points as vertices, and the edge set of the vascular topology graph corresponds to the connection relationship of vascular segments; The blood vessel segments between adjacent vertices are interpolated using parametric smooth curves to obtain a continuous parametric representation embedded in three-dimensional space. Each vertex of the continuous parametric representation is associated with its corresponding three-dimensional spatial coordinates and blood vessel radius parameter.

[0012] In some implementations, the parameterized smoothing curve is a cubic spline curve. When interpolating blood vessel segments between adjacent vertices, the fitting of the continuous parameterized representation is completed by minimizing the fitting energy function, the expression of which is:

[0013] in, Let i be the three-dimensional coordinates of vertex i. Let i be the initial coordinates of vertex i on the representation of the vessel centerline. For the preset smoothing coefficient, Let be the edge set of the blood vessel topology graph. This is the parametric equation for the cubic spline curve of the blood vessel segment between adjacent vertices. It is the second derivative of the cubic spline curve.

[0014] In some implementations, the expression for the topology-preserving energy function is:

[0015] in, To preserve the energy function for the topology, To represent the corresponding probability measure as a continuous parameterization, For data fidelity items, For geometric regular terms, For topological constraint terms, and This is the preset balance coefficient.

[0016] In some implementations, the data fidelity item The expression used to constrain the spatial consistency between the optimized continuous parameterized representation and the preliminary cerebral vessel segmentation results is as follows:

[0017] in, The voxel probability value corresponding to the preliminary cerebral blood vessel segmentation result. The corresponding voxel probability distribution is represented by continuous parameterization.

[0018] In some implementations, the geometric regularization term The expression used to punish excessive tortuosity and curvature abrupt changes in a vessel segment is:

[0019] in, Let be the edge set of the blood vessel topology graph. This is the parametric equation for the cubic spline curve of the blood vessel segment between adjacent vertices. It is the second derivative of the cubic spline curve.

[0020] In some implementations, the topology constraint term This is used to apply a penalty to the fracture region based on the fracture weight map, driving topological fracture repair. Its expression is:

[0021] in, For fracture weighting, A binary function indicating the fracture region. This is the difference between the current number of connected components in the continuously parameterized representation and the preset target number of connected components. This is a preset penalty coefficient.

[0022] In some implementations, iterative optimization of the continuous parameterized representation based on the topology-preserving energy function includes: The topology-preserving energy function is minimized using Wasserstein gradient flow in the probability measure space, and the vertex parameters of the continuously parameterized representation are iteratively updated, with the iterative update rule being:

[0023] in, Let be the probability measure corresponding to the continuous parameterized representation of the t-th iteration. For the first The probability measure corresponding to the continuous parameterized representation of each iteration. To preserve the energy function in the topology gradient at, To preset the iteration step size, The second-order Wasserstein distance. It is the square of the second-order Wasserstein distance.

[0024] In some implementations, the iterative optimization of the continuous parameterized representation is performed as a multi-round closed-loop iterative optimization, with each round of closed-loop iteration performing the following operations: Based on the continuous parameterized representation obtained from the current round of optimization, an updated blood vessel segmentation result is generated; The updated blood vessel segmentation results are reprocessed into a blood vessel skeleton, the updated blood vessel centerline representation is extracted, the topological break regions are repositioned, and the location information of the break regions is updated. Based on the updated location information of the fracture region, a new fracture weight map is generated. Based on the updated blood vessel centerline representation and fracture weight map, the topology-preserving energy function is updated, and the continuous parameterized representation is further optimized.

[0025] In some implementations, iterative optimization terminates when any one of the following preset convergence conditions is met: The current vessel centerline represents a connected component with a quantity of 1, indicating no topological breaks. The absolute value of the difference between the number of vascular connected components in the current round and the previous round is less than a preset number threshold. The absolute value of the difference between the topology preservation energy function value of the current round and the previous round is less than the preset energy threshold; The number of iterations has reached the preset maximum number of iterations.

[0026] In some implementations, obtaining preliminary cerebral blood vessel segmentation results to be optimized includes: Head CTA medical images are input into a pre-trained blood vessel segmentation network. Through the inference processing of the blood vessel segmentation network, a brain blood vessel segmentation probability map is output. The parameters of the blood vessel segmentation network remain fixed throughout the optimization process. Thresholding is applied to the segmentation probability map to obtain preliminary cerebral blood vessel segmentation results to be optimized.

[0027] In some implementations, the initial brain vessel segmentation results to be optimized are generated by a trainable vessel segmentation network; throughout the optimization process, the gradient of the topology-preserving energy function is backpropagated to the vessel segmentation network via a chain rule, and the parameters of the vessel segmentation network are updated synchronously.

[0028] In some implementations, a hierarchical learning rate strategy is used when synchronously updating the parameters of the blood vessel segmentation network; and the hierarchical learning rate strategy includes: The parameters of the blood vessel segmentation network are divided into shallow feature extraction layer parameters and deep segmentation head layer parameters; The learning rate of the shallow feature extraction layer parameters is set to 0 or a preset minimum value, and the learning rate of the deep segmentation head layer parameters is set to a preset learning rate.

[0029] In a second aspect, this application provides an electronic device, characterized in that it includes a processor; and a memory storing program instructions for optimizing a cerebral blood vessel segmentation topology, wherein when the program instructions are executed by the processor, the method for optimizing a cerebral blood vessel segmentation topology according to any one of the embodiments in the first aspect is implemented.

[0030] In a third aspect, this application provides a computer-readable storage medium having stored thereon program instructions for optimizing the topology of cerebral blood vessel segmentation, which, when executed by a processor, implement the method for optimizing the topology of cerebral blood vessel segmentation as described in any one of the embodiments of the first aspect.

[0031] Using the above-described scheme for optimizing the topology of cerebral blood vessel segmentation, this embodiment of the application extracts the vascular centerline representation by performing vascular skeletonization processing on the preliminary cerebral blood vessel segmentation results, and completes the localization and location information acquisition of topological break regions by combining connectivity analysis. This enables the active identification of topological break regions in the cerebral blood vessel segmentation results, clarifying the target region for the subsequent topology optimization process. By generating a break weight map based on the location information of the break regions, the weight values ​​of the break regions are higher than those of the non-break regions. This allows for differentiated guidance for topology optimization through spatial weight differences, enabling the optimization process to be directionally adjusted for the break regions. By constructing a cerebral blood vessel topology representation based on the vascular centerline representation... The continuous parameterized representation of blood vessels enables a unified representation of the geometric morphology and topology of cerebral blood vessels in a continuous space, providing mathematical support for the coherent optimization of vascular topology. By constructing a topology-preserving energy function with the continuous parameterized representation as the optimization variable, and iteratively optimizing the continuous parameterized representation based on this energy function, a closed-loop topology optimization process can be formed. During the iteration process, the parameterized representation of cerebral blood vessels is continuously adjusted, achieving continuous optimization of the cerebral vascular topology. Finally, based on the optimized continuous parameterized representation, a cerebral blood vessel segmentation result with complete topological structure and continuous vascular structure can be output, improving the structural integrity and topological coherence of the cerebral blood vessel segmentation result. Furthermore, this method can be directly executed based on the generated preliminary cerebral blood vessel segmentation result, without relying on a specific type of base segmentation model. It is adaptable to preliminary segmentation results from different sources, has good process compatibility, and can be flexibly embedded into existing cerebral blood vessel segmentation processing workflows. Attached Figure Description

[0032] The above and other objects, features, and advantages of exemplary embodiments of this application will become readily understood by reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of this application are illustrated by way of example and not limitation, and the same or corresponding reference numerals denote the same or corresponding parts, wherein: Figure 1 An exemplary flowchart of a method for optimizing the topology of cerebral blood vessel segmentation according to an embodiment of this application is shown; Figure 2 Exemplary processes of iterative operations in some embodiments of this application are illustrated; Figure 3 A structural block diagram of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0033] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0034] It should be understood that the terms "comprising" and "including" used in the specification and claims of this application indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0035] It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this specification and claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this specification and claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations.

[0036] As used in this specification and claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."

[0037] The specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0038] Figure 1 An exemplary flowchart of a method 100 for optimizing cerebral blood vessel segmentation topology according to an embodiment of this application is shown. It is understood that the execution entity of method 100 is an electronic device with graphics processing capabilities and deep learning model computation capabilities, including but not limited to medical image post-processing workstations, servers, computer terminals, or embedded medical devices. The electronic device may be equipped with a medical image processing system compliant with the DICOM standard, capable of reading, processing, and storing three-dimensional medical image data; this application does not limit this.

[0039] The method described in this embodiment is applicable to the optimization of segmentation results of three-dimensional cerebral vascular images, including but not limited to three-dimensional cerebral vascular images of modalities such as computed tomography angiography and magnetic resonance angiography. The following embodiment uses head CTA images as an application scenario for detailed description.

[0040] like Figure 1 As shown, in step S101, the preliminary cerebral blood vessel segmentation results to be optimized are obtained. This step includes two selectable implementation scenarios: post-processing optimization mode and joint training mode, as detailed below: In post-processing optimization mode, the following operations can be performed to obtain the preliminary cerebral blood vessel segmentation results to be optimized: Head CTA medical images are input into a pre-trained blood vessel segmentation network. Through inference processing by the blood vessel segmentation network, a cerebral blood vessel segmentation probability map is output. The segmentation probability map is then thresholded. A preset segmentation threshold can be set to 0.5, meaning that voxels with a probability value greater than or equal to 0.5 in the segmentation probability map are marked as foreground blood vessels, and voxels with a probability value less than 0.5 are marked as background, resulting in a binarized preliminary cerebral blood vessel segmentation result to be optimized. In this case, the parameters of the blood vessel segmentation network remain fixed throughout the entire optimization process of the cerebral blood vessel segmentation topology. This mode only serves as a post-processing module to perform topology optimization on the generated segmentation results, without requiring retraining of the basic segmentation network, and can be seamlessly embedded into existing cerebral blood vessel segmentation processing workflows.

[0041] In the joint training mode, the preliminary brain vessel segmentation results to be optimized can also be generated by a trainable vessel segmentation network. In this case, during the entire optimization process of the brain vessel segmentation topology, the gradient of the topology-preserving energy function is backpropagated to the vessel segmentation network through the chain rule, and the parameters of the vessel segmentation network are updated synchronously.

[0042] When synchronously updating the parameters of the blood vessel segmentation network, a hierarchical learning rate strategy is adopted. Specifically, this strategy can include: dividing the parameters of the blood vessel segmentation network into shallow feature extraction layer parameters and deep segmentation head layer parameters; setting the learning rate of the shallow feature extraction layer parameters to 0 or a preset minimum value, and setting the learning rate of the deep segmentation head layer parameters to a preset normal learning rate. By fixing the parameters of the shallow feature extraction layer, the general image feature extraction capability learned by the basic segmentation network on large-scale image data can be preserved. Only the deep segmentation head layer parameters are adjusted to adapt to the topology optimization objective, avoiding model overfitting and reducing the computational cost of joint training.

[0043] Next, in step S102, the preliminary cerebral blood vessel segmentation results are processed into a vascular skeleton to extract the representation of the vascular centerline. Based on the representation of the vascular centerline, connectivity analysis is performed to locate all topological break regions and obtain the location information of the break regions.

[0044] Specifically, the vascular skeletonization process can be implemented using a three-dimensional topology refinement algorithm. Specifically, a skeleton extraction algorithm based on distance transformation or an iterative voxel stripping algorithm can be selected to strip the binary foreground region of the preliminary brain blood vessel segmentation result layer by layer, and finally obtain a three-dimensional blood vessel centerline representation with a single pixel width.

[0045] The following steps are performed to locate the fracture region: A 26-neighborhood analysis is conducted on each voxel representing the vessel centerline. Voxels with only one member belonging to the vessel centerline within their 26-neighborhood are marked as centerline endpoints, resulting in a set of centerline endpoints. Then, connected component analysis is performed on the vessel centerline representation, yielding multiple independent centerline connected components. Finally, the Euclidean distance between the centerline endpoints of any two different centerline connected components is calculated. A pair of endpoints with an Euclidean distance less than a preset maximum fracture distance is marked as a set of fracture points. The spatial coordinates and fracture distances of all fracture points are recorded to obtain the location information of the fracture region. Here, the preset maximum fracture distance can be set according to the image voxel resolution; for example, it can be set to 10 voxels to adapt to the standard resolution of clinical head CTA images.

[0046] Next, in step S103, a fracture weight map is generated based on the location information of the fracture region. In this fracture weight map, the weight value of the fracture region is higher than the weight value of the non-fracture region.

[0047] In this embodiment, the fracture weight map is a spatially adaptive fracture weight map that matches the spatial dimension of the preliminary cerebral blood vessel segmentation result. It is a three-dimensional weight matrix, with each voxel position corresponding to a weight value, and can be implemented using the following formula:

[0048] in, Spatial location of preliminary cerebral blood vessel segmentation results The weight value at that point, For the set of break points, Let f be the spatial coordinates of the break point. For preset weighting coefficients, To preset the Gaussian kernel width, the base weight value for non-fracture regions is 1. For example, the preset weight coefficient... It can be set to 5, which is the preset Gaussian kernel width. It can be set to 3 voxels, and the Gaussian kernel function is used to achieve a smooth transition of weights around the breakpoint, avoiding instability in the optimization process caused by sudden weight changes.

[0049] In step S104, a continuous parameterized representation of cerebral blood vessels is constructed based on the vascular centerline representation. This continuous parameterized representation is used to characterize the geometric morphology and topology of cerebral blood vessels in continuous space. In this step, the cerebral vascular network is modeled as a one-dimensional manifold embedded in three-dimensional space, and the construction of the continuous parameterized representation is completed using Adaptive Vessel Axes (AVA).

[0050] Specifically, a set of key points is first extracted from the representation of the vessel centerline. This set of key points includes vessel bifurcation points, centerline endpoints, and extreme points of vessel curvature. The extraction of key points can be achieved using the distance transform ridge method, extracting key points at equal intervals along the vessel centerline. The number of control points for a single vessel segment can be set to four, achieving a balance between capturing local curvature changes in the vessel and maintaining the convexity of the optimization process.

[0051] Then, a vascular topology graph is constructed using the set of key points as vertices, and the edge set of the vascular topology graph corresponds to the connection relationships of vascular segments. Specifically, the structure of the vascular topology graph is defined as follows: vertex set For the key points extracted above, the edge set Represents the connection relationships of blood vessel segments; each vertex All are associated with corresponding three-dimensional spatial coordinates and blood vessel radius parameters It fully represents the spatial location and diameter information of blood vessels.

[0052] Next, parametric smoothing curves are used to interpolate the blood vessel segments between adjacent vertices to obtain a continuous parametric representation embedded in three-dimensional space. Each vertex in the continuous parametric representation is associated with its corresponding three-dimensional space coordinates and blood vessel radius parameter.

[0053] In practice, the parameterized smooth curve is a cubic spline curve. When interpolating the blood vessel segments between adjacent vertices, the fitting of the continuous parameterized representation is completed by minimizing the fitting energy function. The expression of the fitting energy function is:

[0054] in, Let i be the three-dimensional coordinates of vertex i. Let i be the initial coordinates of vertex i on the representation of the vessel centerline. For the preset smoothing coefficient, Let be the edge set of the blood vessel topology graph. This is the parametric equation for the cubic spline curve of the blood vessel segment between adjacent vertices. It is the second derivative of the cubic spline curve.

[0055] It is understandable that the first term in formula (1) is a data fitting term, used to constrain the spatial position deviation between the fitted curve and the original vessel centerline, ensuring that the fitting result does not deviate from the original segmented vessel position; the second term is a smoothing regularization term, used to constrain the curvature change of the vessel segment, avoiding excessive bending of the fitted vessel, and ensuring the rationality of the vessel morphology. For example, a preset smoothing coefficient is used. It can be set to 0.1.

[0056] In step S105, a topology-preserving energy function with continuous parameterized representation as the optimization variable is determined, and the continuous parameterized representation is iteratively optimized based on the topology-preserving energy function to obtain the iteratively optimized continuous parameterized representation.

[0057] In this embodiment, the expression for the topology-preserving energy function is:

[0058] in, To preserve the energy function for the topology, To represent the corresponding probability measure as a continuous parameterization, For data fidelity items, For geometric regular terms, For topological constraint terms, and This is a preset balance coefficient. For example, a preset balance coefficient... It can be set to 0.1. It can be set to 0.5, and the above coefficients can be optimized and adjusted through grid search of the validation set.

[0059] Data fidelity item The expression used to constrain the spatial consistency between the optimized continuous parameterized representation and the preliminary cerebral vessel segmentation results is as follows:

[0060] in, These are the voxel probability values ​​corresponding to the preliminary cerebral blood vessel segmentation results. The corresponding voxel probability distribution is represented by continuous parameterization.

[0061] Geometric regularization term The expression used to punish excessive tortuosity and curvature abrupt changes in a vessel segment is:

[0062] in, Let be the edge set of the blood vessel topology graph. This is the parametric equation for the cubic spline curve of the blood vessel segment between adjacent vertices. It is the second derivative of the cubic spline curve.

[0063] Topology constraint terms This is used to apply a penalty to the fracture region based on the fracture weight map, driving topological fracture repair. Its expression is:

[0064] in, For fracture weighting, A binary function indicating the fracture region. This is the difference between the current number of connected components in the continuously parameterized representation and the preset target number of connected components. This is a preset penalty coefficient. For example, the preset target connected component count is 1, and the preset penalty coefficient is... It can be set to 1.

[0065] Therefore, based on the iterative optimization of the continuous parameterized representation using the topology-preserving energy function, the topology-preserving energy function can be minimized in the probability measure space using the Wasserstein gradient flow, iteratively updating the vertex parameters of the continuous parameterized representation. The iterative update rule is as follows:

[0066] in, Let be the probability measure corresponding to the continuous parameterized representation of the t-th iteration. For the first The probability measure corresponding to the continuous parameterized representation of each iteration. To preserve the energy function in the topology gradient at, To preset the iteration step size, The second-order Wasserstein distance. It is the square of the second-order Wasserstein distance.

[0067] For example, a preset iteration step size It can be set to 0.01. In the actual optimization process, the particle approximation method can be used, treating each vertex in the continuous parameterized representation as a particle, and achieving near-end mapping by solving the linear assignment problem. In the joint training mode, the differentiable Sinkhorn algorithm can be used to solve the optimal transport problem, expanding the gradient flow iteration process into a differentiable computational graph, ensuring that the gradient of the topology-preserving energy function can be backpropagated completely through the chain rule. During the joint training process, the number of iterations in the inner loop of the Wasserstein gradient flow can be set to 5, balancing computational overhead and gradient stability while ensuring optimization performance.

[0068] In the joint training mode, to ensure end-to-end gradient backpropagation, all operations in this step and the aforementioned steps S102 to S104 are implemented using differentiable operators: centerline extraction can be achieved using a differentiable soft skeleton extraction algorithm, fracture detection and weight graph generation can be achieved using differentiable distance transformation and Gaussian kernel function, and spline curve fitting uses a differentiable interpolation operator to ensure that the gradient of the entire topology optimization process can be completely backpropagated to the input of the basic segmentation network.

[0069] Finally, in step S106, based on the iteratively optimized continuous parameterized representation, the topologically complete final cerebral blood vessel segmentation result is generated and output.

[0070] Specifically, based on the optimized continuous parameterized representation, the continuous curve can be reconstructed in three dimensions using the blood vessel radius parameter associated with each vertex, generating a binary segmentation mask with the same spatial dimension as the original image, which is the final brain blood vessel segmentation result. The final segmentation result can be stored according to the DICOM standard or a three-dimensional visualization model can be generated for subsequent image analysis and processing.

[0071] In practice, iterative optimization of continuous parameterized representations is performed as a multi-round closed-loop iterative optimization, and each round of closed-loop iteration executes as follows: Figure 2 The iterative operation 200 shown forms a closed-loop feedback optimization mechanism.

[0072] like Figure 2 As shown, in step S201, an updated blood vessel segmentation result is generated based on the continuous parameterized representation obtained from the current round of optimization.

[0073] In step S202, the updated blood vessel segmentation results are reprocessed into a blood vessel skeleton, the updated blood vessel centerline representation is extracted, the topological break region is repositioned, and the location information of the break region is updated.

[0074] In step S203, a fracture weight map is regenerated based on the updated location information of the fracture region.

[0075] At step S204, based on the updated blood vessel centerline representation and fracture weight map, the topology preservation energy function is updated, and the continuous parameterized representation is further optimized.

[0076] Each round completed Figure 2After each closed-loop iterative operation, a convergence condition check must be performed. Iterative optimization terminates when any of the following preset convergence conditions are met: the number of connected components represented by the current vessel centerline is 1, with no topological breaks; the absolute value of the difference between the number of connected components in the current iteration and the previous iteration is less than a preset number threshold; the absolute value of the difference between the topology preservation energy function value in the current iteration and the previous iteration is less than a preset energy threshold; or the number of iterations reaches a preset maximum number of iterations. For example, the preset number threshold can be set to 0, and the preset energy threshold can be set to... The maximum number of iterations can be set to 50.

[0077] The following specific implementation example further illustrates the multi-round closed-loop iteration process: Assuming that in the initial state, the vascular centerline of the preliminary brain vascular segmentation result contains 2 connected components, there is 1 set of breakpoints, and the initial distance between the two endpoints is 8 voxels.

[0078] First iteration: The updated continuous parameterized representation is obtained through Wasserstein gradient flow optimization, and the distance between the two fracture endpoints is reduced from 8 voxels to 7 voxels; the centerline is re-extracted and the fracture is detected. The fracture is confirmed to still exist. The fracture weight map is updated, and the high weight setting around the two endpoints is maintained. The next iteration begins.

[0079] 8th iteration: In the optimized continuous parameterized representation, the two fracture endpoints are completely connected with a distance of 0 voxels; the centerline is re-extracted and connected component analysis is performed to confirm that the number of connected components is 1, the fracture disappears, and the fracture weight map is updated to the basic weight value of 1 for the entire region; at this time, the topological constraint penalty value of the topology-preserving energy function is 0, the energy function value no longer decreases, the convergence condition is met, the iteration is terminated, and the final cerebral blood vessel segmentation result is output.

[0080] The above combination Figure 1 and Figure 2This application describes a method for optimizing the topology of cerebral blood vessel segmentation. This method extracts the vascular centerline representation by performing vascular skeletonization processing on the preliminary cerebral blood vessel segmentation results, and combines connectivity analysis to locate and obtain the positional information of topological break regions. This enables proactive identification of topological break regions in the cerebral blood vessel segmentation results, clarifying the target region for subsequent topology optimization. By generating a break weight map based on the positional information of the break regions, the method provides differentiated guidance for topology optimization through spatial weight differences, allowing the optimization process to be directionally adjusted for break regions. Furthermore, it constructs a cerebral blood vessel network based on the vascular centerline representation. The continuous parameterized representation enables a unified representation of the geometric morphology and topology of cerebral blood vessels in a continuous space, providing mathematical support for the coherent optimization of vascular topology. By constructing a topology-preserving energy function with the continuous parameterized representation as the optimization variable, and iteratively optimizing the continuous parameterized representation based on this energy function, a closed-loop topology optimization process can be formed. During the iteration process, the parameterized representation of cerebral blood vessels is continuously adjusted, achieving continuous optimization of the cerebral vascular topology. Finally, based on the optimized continuous parameterized representation, a cerebral blood vessel segmentation result with complete topological structure and continuous vascular structure can be output, improving the structural integrity and topological coherence of the cerebral blood vessel segmentation result. Furthermore, this method can be directly executed based on the generated preliminary cerebral blood vessel segmentation result, without relying on a specific type of base segmentation model. It can adapt to preliminary segmentation results from different sources, has good process compatibility, and can be flexibly embedded into existing cerebral blood vessel segmentation processing workflows.

[0081] Next, combine Figure 3 An electronic device 300 provided in an embodiment of this application will be described by way of example. Figure 3 As shown, the electronic device 300 in this application embodiment may include a processor 301, a memory 302, and a communication bus 303.

[0082] In specific embodiments, the processor 301 described above can be at least one of the following: Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), CPU, controller, microcontroller, and microprocessor. It is understood that for different devices, the electronic device used to implement the above processor function can also be other types, and this embodiment does not specifically limit it.

[0083] The memory 302 is used to store computer program instructions that can run on the processor 301, including but not limited to cerebral vascular image reading programs, vascular segmentation network inference programs, program instructions corresponding to the cerebral vascular segmentation topology optimization method described in this application, segmentation result storage and visualization programs, etc.; the memory 302 can be a high-speed random access memory or a non-volatile memory, such as at least one disk storage device.

[0084] The communication bus 303 is used to realize the connection and communication between the processor 301 and the memory 302, and to complete the interaction of data and control instructions.

[0085] Optionally, the electronic device 300 of this embodiment may further include a communication interface, an input / output unit, and a display unit; the communication interface is used to receive externally transmitted medical image data, the input / output unit is used to receive user operation control commands, and the display unit is used to display cerebral blood vessel segmentation results and a three-dimensional visualization model.

[0086] This application also provides a computer-readable storage medium. This computer-readable storage medium stores program instructions for optimizing the topology of cerebral blood vessel segmentation, which can be used to implement the method for optimizing the topology of cerebral blood vessel segmentation described in the embodiments of this application.

[0087] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0088] While numerous embodiments of this application have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will arise for those skilled in the art without departing from the spirit and intent of this application. It should be understood that various alternatives to the embodiments of this application described herein may be employed in the practice of this application. The appended claims are intended to define the scope of protection of this application and therefore cover equivalents or alternatives within the scope of these claims.

Claims

1. A method for optimizing the topology of cerebral blood vessel segmentation, characterized in that, include: Obtain preliminary cerebral blood vessel segmentation results to be optimized; The preliminary cerebral blood vessel segmentation results are processed into a vascular skeleton to extract the vascular centerline representation. Based on the vascular centerline representation, connectivity analysis is performed to locate all topological break regions and obtain the location information of the break regions. A fracture weight map is generated based on the location information of the fracture region; in the fracture weight map, the weight value of the fracture region is higher than the weight value of the non-fracture region. Based on the vascular centerline representation, a continuous parameterized representation of the cerebral blood vessels is constructed. This continuous parameterized representation is used to characterize the geometric morphology and topological structure of the cerebral blood vessels in a continuous space. A topology-preserving energy function is determined with the continuous parameterized representation as the optimization variable. The continuous parameterized representation is iteratively optimized based on the topology-preserving energy function to obtain the iteratively optimized continuous parameterized representation. Based on the iteratively optimized continuous parameterized representation, the final cerebral blood vessel segmentation result with topological integrity is generated and output.

2. The method according to claim 1, characterized in that, Locate all topological break regions and obtain their location information, including: For each voxel represented by the vessel centerline, a neighborhood analysis is performed, and voxels with only one voxel in each of the 26 neighborhoods that belong to the vessel centerline are marked as centerline endpoints, thus obtaining the centerline endpoint set. Connectivity analysis was performed on the representation of the blood vessel centerline to obtain multiple independent centerline connected components; Calculate the Euclidean distance between the endpoints of any two different centerline connected components, mark a pair of endpoints whose Euclidean distance is less than the preset maximum fracture distance as a set of fracture points, record the spatial coordinates and fracture distances of all fracture points, and obtain the location information of the fracture area.

3. The method according to claim 2, characterized in that, The fracture weight map is a spatially adaptive fracture weight map that matches the spatial dimension of the preliminary cerebral blood vessel segmentation result, and is implemented using the following formula: in, Spatial location of the preliminary cerebral blood vessel segmentation results The weight value at that point, For the set of break points, Let f be the spatial coordinates of the break point. For preset weighting coefficients, The default Gaussian kernel width is set, and the base weight value for the non-fractured region is 1.

4. The method according to claim 1, characterized in that, Constructing a continuous parameterized representation of the cerebral blood vessels includes: Extract a set of key points from the representation of the blood vessel centerline, the set of key points including blood vessel bifurcation points, centerline endpoints and extreme points of blood vessel curvature; A vascular topology graph is constructed using the set of key points as vertices, and the edge set of the vascular topology graph corresponds to the connection relationship of vascular segments; The blood vessel segments between adjacent vertices are interpolated using parametric smooth curves to obtain a continuous parametric representation embedded in three-dimensional space. Each vertex of the continuous parametric representation is associated with its corresponding three-dimensional spatial coordinates and blood vessel radius parameter.

5. The method according to claim 4, characterized in that, The parameterized smoothing curve is a cubic spline curve. When interpolating the blood vessel segments between adjacent vertices, the fitting of the continuous parameterized representation is completed by minimizing the fitting energy function. The expression of the fitting energy function is: in, Let i be the three-dimensional coordinates of vertex i. Let i be the initial coordinates of vertex i on the representation of the vessel centerline. For the preset smoothing coefficient, Let be the edge set of the blood vessel topology graph. This is the parametric equation for the cubic spline curve of the blood vessel segment between adjacent vertices. It is the second derivative of the cubic spline curve.

6. The method according to claim 1, characterized in that, The expression for the topology-preserving energy function is: in, To preserve the energy function for the topology, To represent the corresponding probability measure as a continuous parameterization, For data fidelity items, For geometric regular terms, For topological constraint terms, and This is the preset balance coefficient.

7. The method according to claim 6, characterized in that, The data fidelity item The expression used to constrain the spatial consistency between the optimized continuous parameterized representation and the preliminary cerebral vessel segmentation results is as follows: in, The voxel probability value corresponding to the preliminary cerebral blood vessel segmentation result. The corresponding voxel probability distribution is represented by continuous parameterization.

8. The method according to claim 6, characterized in that, The geometric regularization term The expression used to punish excessive tortuosity and curvature abrupt changes in a vessel segment is: in, Let be the edge set of the blood vessel topology graph. This is the parametric equation for the cubic spline curve of the blood vessel segment between adjacent vertices. It is the second derivative of the cubic spline curve.

9. The method according to claim 6, characterized in that, The topology constraint terms This is used to apply a penalty to the fracture region based on the fracture weight map, driving topological fracture repair. Its expression is: in, For fracture weighting, A binary function indicating the fracture region. This is the difference between the current number of connected components in the continuously parameterized representation and the preset target number of connected components. This is a preset penalty coefficient.

10. The method according to claim 6, characterized in that, Iterative optimization of the continuous parameterized representation based on the topology-preserving energy function includes: The topology-preserving energy function is minimized using Wasserstein gradient flow in the probability measure space, and the vertex parameters of the continuously parameterized representation are iteratively updated, with the iterative update rule being: in, Let be the probability measure corresponding to the continuous parameterized representation of the t-th iteration. For the first The probability measure corresponding to the continuous parameterized representation of each iteration. To preserve the energy function in the topology gradient at, To preset the iteration step size, The second-order Wasserstein distance. It is the square of the second-order Wasserstein distance.

11. The method according to claim 1, characterized in that, The continuous parameterized representation is iteratively optimized as a multi-round closed-loop iterative optimization, and each round of closed-loop iteration performs the following operations: Based on the continuous parameterized representation obtained from the current round of optimization, an updated blood vessel segmentation result is generated; The updated blood vessel segmentation results are reprocessed into a blood vessel skeleton, the updated blood vessel centerline representation is extracted, the topological break regions are repositioned, and the location information of the break regions is updated. Based on the updated location information of the fracture region, a new fracture weight map is generated. Based on the updated blood vessel centerline representation and fracture weight map, the topology-preserving energy function is updated, and the continuous parameterized representation is further optimized.

12. The method according to claim 11, characterized in that, Iterative optimization terminates when any of the following preset convergence conditions are met: The current vessel centerline represents a connected component with a quantity of 1, indicating no topological breaks. The absolute value of the difference between the number of vascular connected components in the current round and the previous round is less than a preset number threshold. The absolute value of the difference between the topology preservation energy function value of the current round and the previous round is less than the preset energy threshold; The number of iterations has reached the preset maximum number of iterations.

13. The method according to claim 1, characterized in that, Obtain preliminary cerebral blood vessel segmentation results to be optimized, including: Head CTA medical images are input into a pre-trained blood vessel segmentation network. Through the inference processing of the blood vessel segmentation network, a brain blood vessel segmentation probability map is output. The parameters of the blood vessel segmentation network remain fixed throughout the optimization process. Thresholding is applied to the segmentation probability map to obtain preliminary cerebral blood vessel segmentation results to be optimized.

14. The method according to claim 1, characterized in that, The preliminary brain vessel segmentation results to be optimized are generated by a trainable vessel segmentation network. Throughout the optimization process, the gradient of the topology-preserving energy function is backpropagated to the vessel segmentation network via the chain rule, and the parameters of the vessel segmentation network are updated synchronously.

15. The method according to claim 14, characterized in that, A hierarchical learning rate strategy is used when synchronously updating the parameters of the blood vessel segmentation network; and the hierarchical learning rate strategy includes: The parameters of the blood vessel segmentation network are divided into shallow feature extraction layer parameters and deep segmentation head layer parameters; The learning rate of the shallow feature extraction layer parameters is set to 0 or a preset minimum value, and the learning rate of the deep segmentation head layer parameters is set to a preset learning rate.

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