Catalyst structure form analysis method based on computer vision

Abstract

The invention discloses a catalyst structure form analysis method based on computer vision, particularly relates to the field of computer vision, and is used for solving the problem that the segmentation precision and the pore space communication structure stability are difficult to guarantee at the same time under the complex pore form condition in the existing catalyst three-dimensional structure analysis process. According to the method, a multi-dimensional feature vector is constructed for a three-dimensional grayscale image body of the catalyst, probability segmentation is carried out on a pore phase and an entity phase, topological persistence constraint is introduced in the segmentation process, and a stably existing key pore structure is enhanced and reserved; then performing structure correction on a segmentation result in combination with a morphological processing mode of direction perception, and further improving continuity and consistency of a pore channel; finally, a skeleton network structure of a pore space is extracted through three-dimensional central axis transformation, effective expression of a pore communication relation and a channel form is achieved, and therefore a reliable technical means is provided for analysis and optimization of the structural performance of the catalyst.

Description

Technical Field

[0001] This invention relates to the field of computer image processing technology, and more specifically, to a method for analyzing the structure and morphology of catalysts based on computer vision. Background Technology

[0002] In the process of catalyst development, performance evaluation, and failure mechanism analysis, the spatial morphology and connectivity of the internal pore structure of the catalyst are important factors affecting reactant diffusion efficiency, active site utilization, and overall catalytic performance. With the development of three-dimensional imaging technology, three-dimensional grayscale images with micron and nanometer resolution can more completely reflect the complex pore distribution and structural morphology inside the catalyst, providing a data foundation for refined structural analysis.

[0003] In practical applications, 3D images of catalysts often suffer from uneven grayscale distribution, significant differences in structural scale, blurred pore boundaries, and noise interference. This makes it difficult to accurately distinguish between the porous phase and the solid phase by relying solely on manual experience or simple threshold segmentation methods. This is especially true in regions with long, thin, interwoven pores or weak local connectivity, where structural breaks, misclassification, or false connectivity are prone to occur. Existing methods based on traditional image segmentation or morphological processing often focus on local grayscale or geometric features, lacking the ability to characterize the overall connectivity and stability of the pore space, making it difficult to maintain global structural consistency while ensuring precise local segmentation.

[0004] Furthermore, segmentation results are typically presented in voxel or volume form, which is not conducive to intuitive analysis and quantitative characterization of the connectivity, channel orientation, and topology of pore networks. This limits its practical value in applications such as catalyst structure optimization, performance comparison analysis, and multi-scale transport modeling. Therefore, a catalyst structure morphology analysis method that combines 3D image features, structural stability constraints, and spatial connectivity analysis is needed to achieve reliable identification and effective representation of complex pore structures. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art, embodiments of the present invention provide a catalyst structure morphology analysis method based on computer vision to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A computer vision-based method for analyzing the structural morphology of catalysts includes the following steps: S1. Based on the input three-dimensional grayscale image volume data of the catalyst, generate a multi-dimensional feature vector corresponding to each voxel; S2. Based on multidimensional feature vectors, an energy function minimization problem is constructed through image segmentation to obtain the initial classification probability distribution map of each voxel belonging to the foreground or background phase. S3. Perform sub-layer thresholding on the initial classification probability distribution map to generate a binarized slice image, and perform continuous homology analysis on the slice image to extract the manifestation and disappearance levels of key topological features. S4. Based on the manifestation and disappearance levels of key topological features, construct topological persistence constraints, fuse the constraints with the energy function during image segmentation, and re-solve to obtain the final classification probability distribution map. S5. On the final classification probability distribution map, determine the local principal direction based on the Hessian matrix eigenvector at each voxel position, and construct asymmetric structural elements along the local principal direction. S6. Asymmetric structuring elements are used to perform guided morphological erosion on the final classification probability distribution map. After iterative convergence, the final binary segmentation image is obtained. S7. Apply the three-dimensional median transformation algorithm to the final binary segmented image to extract the skeleton network diagram representing the spatial connectivity structure of the pores.

[0007] As a further aspect of the present invention, in step S1, generating the multidimensional feature vector corresponding to each voxel specifically includes: Acquire three-dimensional grayscale image data of the catalyst and perform voxel extraction; A local neighborhood window is constructed with each voxel as the center, and the mean, variance, and skewness of the gray values ​​of all voxels within the local neighborhood window are calculated as the statistical moments of the local gray distribution. Calculate the second-order Hessian matrix at each voxel location, solve for the eigenvalues ​​of the matrix, and calculate the tubular and sheet-like feature measures based on the relative magnitudes of the eigenvalues. Calculate the gradient magnitude map of the catalyst's three-dimensional grayscale image volume, identify the local maxima in the gradient magnitude map as the image gradient peaks, and calculate the three-dimensional Euclidean distance of each voxel to its nearest image gradient peak. The local gray-level distribution statistical moments, the tubular and sheet-like feature measures, and the three-dimensional Euclidean distance are linearly concatenated to form a multidimensional feature vector corresponding to each voxel.

[0008] As a further aspect of the present invention, in step S2, based on multi-dimensional feature vectors, an energy function minimization problem is constructed through image segmentation to obtain the initial classification probability distribution map of each voxel belonging to the foreground or background phase. Specifically, this includes: Calculate the single-point potential energy of each voxel belonging to the foreground and background phases based on the multidimensional feature vectors; Construct the edges between all adjacent voxels, and calculate the smoothing term potential energy of each edge based on the difference in the initial multidimensional feature vectors between adjacent voxels; Treat all voxels as nodes, and assign the single-point potential energy and smoothing term potential energy to the corresponding nodes and edges to construct a weighted graph structure. The minimum cut of the energy function is solved by applying the maximum flow minimum cut algorithm on the graph structure. The nodes are marked according to the minimum cut result, and the marking result is converted into the probability value of each voxel belonging to the foreground phase, forming the initial classification probability distribution map.

[0009] As a further embodiment of the present invention, the energy function is a Markov random field energy function constructed based on the graph cut algorithm, which is constructed by linearly superimposing the data terms composed of the single-point potential energy and the smoothing terms composed of the smoothing term potential energy.

[0010] As a further aspect of the present invention, in step S3, the extraction of the manifestation level and disappearance level of key topological features specifically includes: The initial classification probability distribution map is segmented by setting a sub-layer threshold sequence and generating a corresponding binary image sequence. Three-dimensional connected component labeling is performed on each binary image in the binary image sequence to identify all connected pore regions. Along the sequential direction of the sublayer threshold sequence, the appearance, merging, and disappearance of each connected pore region as the threshold changes are traced; When a connected void region first appears, the corresponding threshold is recorded as the manifestation level of the topological feature. When two or more connected void regions merge, it is recorded as a merging event. When a connected void region completely disappears, the corresponding threshold is recorded as the disappearance level of the topological feature. All connected void regions not covered by merged events are aggregated, and the corresponding manifestation and disappearance levels are used as persistent data for the key topological features.

[0011] As a further aspect of the present invention, in step S4, constructing a topological persistence constraint term based on the manifestation and disappearance levels of key topological features, fusing the constraint term with the energy function during image segmentation, and resolving to obtain the final classification probability distribution map specifically includes: Based on the manifestation and disappearance levels of the key topological features, the persistence value of each feature is calculated, and features with persistence values ​​exceeding a preset persistence threshold are selected as key features. Extract the persistent connected regions between the manifestation and disappearance levels of key features, and record the coordinates of all voxels constituting these connected regions as a set of key voxels. A penalty function based on voxel attribution is constructed as a topological persistence constraint term. The penalty function applies a constant penalty value when voxels belonging to the key voxel set are marked as background phase. The topological persistence constraint term is fused with the energy function, and the maximum flow minimum cut algorithm is applied to solve it again. The final classification probability distribution map is generated based on the solution results.

[0012] As a further aspect of the present invention, in step S5, determining the local principal direction based on the Hessian matrix eigenvector at each voxel position on the final classification probability distribution map, and constructing asymmetric structural elements along the local principal direction specifically includes: Calculate the second-order Hessian matrix at each voxel position on the final classification probability distribution map, and perform eigenvalue decomposition on the matrix to obtain eigenvalues. Select the eigenvector with the smallest absolute value of the eigenvalue and determine the direction indicated by the eigenvector as the local principal direction. With the local principal direction as the major axis, an ellipsoid prototype is defined in a three-dimensional orthogonal coordinate system. The ellipsoid prototype is then compressed at a fixed scale on a cross section perpendicular to the local principal direction to construct an asymmetric three-dimensional structural element extending along the principal direction. The center of this asymmetric three-dimensional structural element is aligned with the current voxel position.

[0013] As a further aspect of the present invention, in step S6, the guided morphological erosion operation is performed on the final classification probability distribution map using asymmetric structuring elements, and the final binary segmentation image is obtained after iterative convergence. Specifically, this includes: The final classification probability distribution map is used as the input image, and the asymmetric structural element is used as the operation template. Slide an asymmetric structuring element on the input image, calculate the minimum probability of all voxels in the space covered by the structuring element at each position, and replace the probability value of the central voxel with this minimum value to complete one guided erosion operation. The guided erosion operation is repeated with the image obtained from the erosion operation as a new input image until the change in the probability values ​​of all voxels between two consecutive erosion operations is less than the preset tolerance threshold, which is considered to be iterative convergence. The probability value of each voxel in the image after iterative convergence is binarized to generate the final binary segmentation image.

[0014] As a further aspect of the present invention, in step S7, applying a three-dimensional median transformation algorithm to the final binary segmented image to extract the skeleton network diagram representing the spatial connectivity structure of the pores specifically includes: Calculate the distance from each foreground voxel to the nearest background voxel in the final binary segmented image, generate a three-dimensional distance field, and identify local distance maxima points in the distance field as initial skeleton points; Using the initial skeleton points as nodes, a connection graph is constructed based on spatial adjacency relationships and distance field values. The minimum spanning tree is then solved in the connection graph, and the nodes and edges are output based on the minimum spanning tree to form the skeleton network graph.

[0015] The technical effects and advantages of the catalyst structure morphology analysis method based on computer vision of the present invention are as follows: Compared to traditional methods that rely solely on local grayscale or single geometric features, this invention effectively suppresses noise interference and local misclassification under conditions of complex grayscale distributions and the coexistence of multi-scale pores, significantly improving the continuity and structural integrity of pore segmentation results. By introducing a constraint mechanism based on topological persistence during the segmentation process, this invention can automatically preserve key pore structures that are stable under multi-scale conditions, preventing the destruction of slender channels and important connectivity paths in subsequent processing. Simultaneously, by combining orientation-aware morphological processing, the segmentation results better conform to the actual extension direction of the pores, which is beneficial for maintaining the spatial coherence of the pore network. Furthermore, by performing a three-dimensional mid-axis transformation on the segmentation results, the complex pore structure can be transformed into an intuitive skeleton network representation, providing a reliable data foundation for subsequent pore connectivity analysis, channel orientation evaluation, and transport behavior modeling, thereby enhancing the practical value of this method in catalyst development and performance analysis. This invention achieves stable identification and fine characterization of the three-dimensional pore structure of catalysts by introducing an analysis process that combines multidimensional feature modeling, probability segmentation and topological constraints. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a catalyst structure morphology analysis method based on computer vision according to the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] Example 1 Figure 1 This invention presents a computer vision-based method for analyzing the structural morphology of catalysts, comprising the following steps: S1. Based on the input three-dimensional grayscale image volume data of the catalyst, generate a multi-dimensional feature vector corresponding to each voxel; S2. Based on multidimensional feature vectors, an energy function minimization problem is constructed through image segmentation to obtain the initial classification probability distribution map of each voxel belonging to the foreground or background phase. S3. Perform sub-layer thresholding on the initial classification probability distribution map to generate a binarized slice image, and perform continuous homology analysis on the slice image to extract the manifestation and disappearance levels of key topological features. S4. Based on the manifestation and disappearance levels of key topological features, construct topological persistence constraints, fuse the constraints with the energy function during image segmentation, and re-solve to obtain the final classification probability distribution map. S5. On the final classification probability distribution map, determine the local principal direction based on the Hessian matrix eigenvector at each voxel position, and construct asymmetric structural elements along the local principal direction. S6. Asymmetric structuring elements are used to perform guided morphological erosion on the final classification probability distribution map. After iterative convergence, the final binary segmentation image is obtained. S7. Apply the three-dimensional median transformation algorithm to the final binary segmented image to extract the skeleton network diagram representing the spatial connectivity structure of the pores.

[0019] In step S1, a multidimensional feature vector is generated for each voxel.

[0020] Three-dimensional grayscale image data characterizing the internal structure of the catalyst is acquired. This 3D grayscale image data originates from continuous grayscale volume data obtained after volume imaging of the catalyst sample. The grayscale volume data is spatially composed of regularly arranged voxel units, each voxel corresponding to a fixed spatial location and its grayscale intensity value. After reading the 3D grayscale image data, voxel-level analysis is performed, dividing the overall image volume into independent voxel sets according to a predetermined spatial resolution to ensure that subsequent processing is performed at the voxel scale. Based on this, a local neighborhood window is constructed within the 3D spatial neighborhood of each voxel as the central voxel. The size of the local neighborhood window is set according to the typical spatial scale of the catalyst pores, for example, selecting a cubic window form covering several adjacent voxels to ensure that the neighborhood includes both the central voxel itself and a sufficient number of its surrounding neighboring voxels. Subsequently, within this local neighborhood window, the gray values ​​of all voxels are statistically processed. The gray mean is calculated to reflect the overall brightness level of the area, the gray variance is calculated to characterize the dispersion of the gray distribution, and the gray skewness is calculated to describe the asymmetric characteristics of the gray distribution.

[0021] After calculating the statistical moments of the local grayscale distribution, for each voxel in the three-dimensional grayscale image volume of the catalyst, the second-order Hessian matrix at that voxel is calculated to describe the curvature characteristics of the grayscale change at that location in various spatial directions. Specifically, by performing a second-order differential operation on the three-dimensional grayscale image volume at the voxel scale, the second-order change information of the voxel in three orthogonal spatial directions and their intersection directions is obtained, and the corresponding second-order Hessian matrix is ​​constructed accordingly. After obtaining the Hessian matrix, eigenvalues ​​are obtained through eigenvalue decomposition to reflect the intensity of grayscale changes in different principal directions. Based on the relative magnitudes of the eigenvalues, the geometric shape of the voxel's location is determined: when the eigenvalue in one direction is significantly different from the others, it indicates that the location is more consistent with the geometric characteristics of a slender structure, and the corresponding tubular feature measure is calculated accordingly; when the eigenvalues ​​in two directions are relatively consistent but clearly distinguishable from the third direction, it indicates that the location is more consistent with the characteristics of a sheet-like or layered structure, and the corresponding sheet-like feature measure is calculated accordingly. In a specific implementation, the tubular feature measure and the sheet feature measure are obtained by mapping the proportional relationship of feature values, and the mapping result is subjected to unified numerical standardization processing.

[0022] After calculating the voxel-level grayscale statistical features and geometric morphological features, a supplementary description of the voxels is provided from the perspective of spatial positional relationships. Gradient operations are performed on the three-dimensional grayscale image volume of the catalyst to obtain the grayscale gradient amplitude at each voxel location, thereby generating a complete gradient amplitude map. Local maxima are identified in the gradient amplitude map. These local maxima correspond to the locations with the most drastic grayscale changes, reflecting the positional characteristics of pore boundaries or structural interfaces, and are uniformly marked as image gradient peaks. After identifying the gradient peaks, for each voxel, the three-dimensional Euclidean distance between its spatial location and the nearest image gradient peak is calculated. This distance is used to characterize the spatial positional relationship of the voxel relative to the structural boundary or central region; for example, voxels with larger distances are more likely to be located in the core region inside the pores. Finally, the local grayscale distribution statistical moments, tubular feature measures, sheet-like feature measures, and three-dimensional Euclidean distances obtained in the preceding steps are linearly concatenated according to a predetermined feature order to form a multidimensional feature vector corresponding to each voxel.

[0023] In step S2, based on multidimensional feature vectors, an energy function minimization problem is constructed through image segmentation, and the initial classification probability distribution map of each voxel belonging to the foreground or background phase is obtained by solving the problem.

[0024] For each voxel with a corresponding multidimensional feature vector, the single-point potential energy of the voxel belonging to the foreground and background phases is calculated. The single-point potential energy is used to characterize the cost incurred when the voxel is assigned a certain category label, and is determined by calculating the degree of matching between the voxel's multidimensional features and the typical feature distributions of the foreground and background phases.

[0025] Specifically, statistical analysis is performed on voxel regions with obvious porosity and solid features in a preset or 3D grayscale image to form feature distribution descriptions of the foreground and background phases. Based on this, the approximation of the current voxel's multidimensional feature vector to these two feature distributions is determined. For voxels whose features better match porosity, the single-point potential energy belonging to the foreground phase is set to a smaller value, while the single-point potential energy belonging to the background phase is set to a larger value; for voxels whose features better match solid structure, the opposite is true. The single-point potential energy is normalized using a uniform numerical scale to ensure comparability of potential energy values ​​between different voxels. After calculating the single-point potential energy, adjacency relationships are further constructed at the voxel level, connecting voxels that are spatially in contact or within a preset adjacency range to form adjacency edges. For each adjacency edge, a smoothing term potential energy is calculated based on the degree of difference between the initial multidimensional feature vectors of adjacent voxels. This degree of difference is obtained by comprehensively evaluating the differences between the components of the multidimensional feature vector. When the feature differences between adjacent voxels are small, it indicates that they are more likely to belong to the same structural region. In this case, a larger smoothing term potential is set to suppress the two from being assigned to different categories. When the feature differences are large, the smoothing term potential is reduced accordingly to allow the existence of structural boundaries.

[0026] After calculating the single-point potential energy and the smoothing term potential energy, all voxels in the catalyst's 3D grayscale image are uniformly considered as nodes in a graph structure. The calculated single-point potential energy is assigned to the foreground and background phase labels corresponding to each node, while the smoothing term potential energy is assigned to the adjacent edges between nodes, constructing a weighted graph structure containing node weights and edge weights. In the graph structure, node weights characterize the cost of assigning a specific category label to a single voxel, while edge weights characterize the constraint strength of maintaining the same category label between adjacent voxels. Based on the above node and edge weight settings, an energy function represented in the form of a Markov random field is constructed. The energy function is composed of the linear superposition of the data terms corresponding to all nodes and the smoothing terms corresponding to all adjacent edges, used to comprehensively measure the overall cost of the current voxel labeling scheme in terms of single-point rationality and spatial consistency. Subsequently, the maximum flow minimum cut algorithm is applied to the graph structure to globally minimize the energy function, dividing the nodes into foreground and background phases by finding the cut set with the minimum cost. The maximum flow minimum cut algorithm ensures the minimum overall cut cost during the solution process, thereby obtaining the most consistent voxel labeling results in a global sense. After obtaining the minimum cut result, each voxel node is labeled according to its connection relationship with the foreground or background. Furthermore, based on the node's affiliation in the cut result, the discrete labeling results are mapped into continuous numerical representations to reflect the relative degree to which the voxel belongs to the foreground phase. Through this mapping method, the final node labeling result is transformed into a foreground phase affiliation probability value for each voxel, thus forming a complete initial classification probability distribution map.

[0027] In S3, the manifestation and disappearance levels of key topological features are extracted.

[0028] For the obtained initial classification probability distribution map, a set of sub-layer threshold sequences is set to segment the probability distribution map. The sub-layer threshold sequences are arranged in ascending order of probability value, and their value range covers the main variation range of voxel probability values ​​in the probability distribution map. For example, a uniformly spaced threshold sequence from near zero to near one is used to ensure that the spatial morphological changes of the pore region under different confidence levels are fully reflected. Subsequently, the sub-layer thresholds are applied sequentially to the initial classification probability distribution map. Voxels with probability values ​​greater than or equal to the current threshold are marked as foreground, and the remaining voxels are marked as background, thereby generating a corresponding 3D binary image at each threshold level. For each generated 3D binary image, a 3D connected component labeling operation is performed. Interconnected foreground voxels are aggregated according to a predetermined 3D adjacency rule, and spatially continuous sets of voxels are identified as independent connected pore regions. Through this connected component labeling process, all existing pore regions can be completely identified at each sub-layer threshold level.

[0029] After identifying the connected porosity regions corresponding to each sub-layer threshold, the connected porosity regions obtained at each threshold level are continuously tracked and analyzed in ascending order of the sub-layer threshold sequence. Specifically, the correspondence between porosity regions at different threshold levels is determined by comparing the spatial location and voxel composition overlap of connected porosity regions at adjacent threshold levels. When a connected porosity region that did not exist in the previous threshold level first appears at a certain threshold level, that threshold is recorded as the manifestation level of the corresponding topological feature of that porosity region, representing the probability level at which the structure begins to stably manifest. As the threshold changes further, when two or more connected porosity regions that existed independently in the previous level merge into a new connected region at the current threshold level, this phenomenon is recorded as a merging event, and the original porosity regions involved in the merging are marked to reflect the process of topological integration. When a connected porosity region completely disappears as the threshold continues to increase, i.e., it no longer appears in the current and subsequent threshold levels, the corresponding threshold is recorded as the disappearance level of that topological feature. Through the above continuous tracking process, the life cycle changes of each pore region under different probability levels are fully recorded.

[0030] After recording the occurrence, merging, and disappearance processes of all connected pore regions in the sub-layer threshold sequence, the obtained evolution information of all pore regions is summarized and organized. First, all pore regions that experienced merging events are screened; regions absorbed or covered by other pore regions during the merging process are marked as non-independent structures and removed from subsequent key feature statistics. Then, connected pore regions that were not covered by merging events throughout the entire threshold evolution process and can exist independently and continuously within a certain threshold range are prioritized for retention. For each retained connected pore region, its corresponding manifestation and disappearance levels are extracted, and the span between them is used as a quantitative description of the topological stability of the pore region. The manifestation and disappearance level information of all retained regions is uniformly summarized to form a persistent dataset of the key topological features. This persistent data is used to reflect the stable existence range of the pore structure under different probability segmentation conditions.

[0031] In step S4, a topological persistence constraint term is constructed based on the manifestation and disappearance levels of key topological features. The constraint term is then fused with the energy function during image segmentation, and the final classification probability distribution map is obtained by resolving the problem.

[0032] For each key topological feature, its persistence value is calculated based on its corresponding manifestation and disappearance levels. This persistence value characterizes the stable existence of the topological feature within the sub-layer threshold sequence. The calculation method is determined by comparing the span between the manifestation and disappearance levels; a larger span indicates that the feature persists over a wider threshold range, indicating higher structural stability. Subsequently, a persistence threshold is set to screen key features. This threshold is determined based on the overall persistence distribution of topological features; for example, the statistical median level of all persistence values ​​or values ​​above the average level can be selected as the criterion to ensure that the selected features have a significant stability advantage. Topological features with persistence values ​​exceeding the persistence threshold are uniformly marked as key features and processed centrally. For each key feature, the connected void regions corresponding to each sub-layer threshold between the manifestation and disappearance levels are further traced. Spatial regions that consistently exist within this threshold range are extracted and considered as the stable structure corresponding to the key feature. Finally, the spatial coordinates of all voxels constituting the aforementioned stable connected region are recorded and summarized to form a key voxel set, which is used to accurately identify the spatial location range of voxels that need to be given special protection.

[0033] After determining the key voxel set, a penalty function based on voxel attribution is constructed for this set to form the topological persistence constraint term. Specifically, the penalty function operates as follows: when a voxel belonging to the key voxel set is marked as background during segmentation, a constant penalty value is applied to the marking decision; when the voxel is marked as foreground, no additional penalty is applied. The magnitude of the constant penalty value is set based on the numerical range of the single-point potential energy; for example, a fixed value equivalent to the average level of single-point potential energy can be selected to ensure that the penalty intensity is sufficient to affect the segmentation result but does not dominate the overall optimization process. Subsequently, the topological persistence constraint term is incorporated into the original energy function structure, so that the energy function, while maintaining the original data and smoothing constraints, additionally considers the topological stability requirements of the key voxels. After energy function fusion, the maximum flow minimum cut algorithm is applied again to the updated graph structure for global solution. By re-finding the cut set with the minimum cost, the foreground and background phase markings of the voxels are corrected. Based on the solution results, the labeling state of all voxels is updated, and the discrete labeling results are transformed into continuous numerical expressions in the same mapping method as before, thereby generating the final classification probability distribution map. This further enhances the preservation of stable pore structures on the basis of overall spatial consistency in the segmentation results.

[0034] In step S5, on the final classification probability distribution map, the local principal direction is determined based on the Hessian matrix eigenvector at each voxel position, and asymmetric structural elements are constructed along the local principal direction.

[0035] For the obtained final classification probability distribution map, it is treated as a continuous three-dimensional scalar field, and a second-order spatial variation analysis is performed on each voxel location. Second-order difference calculations are performed on the probability distribution map at the voxel scale to obtain the variation information of the voxel in three orthogonal spatial directions and their combinations, thereby constructing the second-order Hessian matrix corresponding to the voxel. The Hessian matrix describes the curvature and trend of the probability value in a local spatial region, reflecting the extension characteristics of the surrounding structure in different directions. After obtaining the second-order Hessian matrix, eigenvalue decomposition is performed on the matrix to obtain a set of eigenvalues ​​and eigenvectors corresponding to spatial directions. Subsequently, the eigenvalues ​​are compared, and the eigenvector corresponding to the eigenvalue with the smallest absolute value is selected. The spatial direction indicated by this eigenvector is determined as the local principal direction at the current voxel location. The direction with the smallest absolute value is selected because it corresponds to the direction with the most gradual change in probability distribution, and can stably reflect the main extension direction of the pore channel or structure in space. Throughout the entire process, Hessian matrix calculation and eigenvalue decomposition are performed on all voxels according to the same rules.

[0036] After determining the local principal direction for each voxel, an asymmetric three-dimensional structural element for morphological processing is constructed based on this direction. A standard ellipsoid is defined as the prototype of the structural element in a three-dimensional orthogonal coordinate system. This ellipsoid prototype has different scale parameters in three spatial directions, with one axis representing the main extension direction of the structural element. Subsequently, the major axis of the ellipsoid prototype is aligned with the local principal direction corresponding to the current voxel, ensuring that the principal axis of the ellipsoid is consistent with the actual extension direction of the pore structure. After alignment, a fixed-proportion scale compression is performed on the ellipsoid prototype in a cross-section perpendicular to the local principal direction. That is, the lateral dimensions of the ellipsoid are reduced in two directions orthogonal to the principal direction, while the length along the principal direction remains unchanged, thus forming an asymmetric three-dimensional structural element with a clear spatial directionality. The scale compression ratio is set according to the slenderness of the pore structure; for example, a ratio where the lateral scale is significantly smaller than the longitudinal scale can be selected to ensure that the structural element mainly functions along the principal direction during morphological operations. Finally, the center position of the constructed asymmetric 3D structural element is aligned with the spatial coordinates of the current voxel, so that when the structural element is applied to the probability distribution map, it can perform local operations with the current voxel as the reference point.

[0037] In step S6, an asymmetric structuring element is used to perform a guided morphological erosion operation on the final classification probability distribution map, and the final binary segmentation image is obtained after iterative convergence.

[0038] The final classification probability distribution map is used as input for morphological processing. This probability distribution map is stored in the form of three-dimensional voxels, with each voxel position corresponding to a probability value representing its degree of belonging to the foreground phase. Subsequently, an asymmetric three-dimensional structural element, constructed for each voxel, is used as a morphological operation template. This asymmetric structural element is spatially aligned with the local principal direction corresponding to the voxel, exhibiting significant directional extension characteristics. During guided erosion, the asymmetric structural element is slid voxel by voxel to various spatial positions in the input image, ensuring that the center of the structural element always coincides with the position of the currently processed voxel. At each sliding position, the set of voxels covered by the asymmetric structural element in the current pose is determined, and the probability values ​​corresponding to all voxels within this coverage area are read. Then, the minimum probability value is selected from this covered voxel set and assigned as the new probability value to the voxel corresponding to the center position of the structural element, thus completing one guided erosion update for the current voxel position. In this method, probability updates are strictly propagated along the principal direction of the asymmetric structuring element, ensuring the continuity of the probability distribution in the principal direction while subjecting stronger contraction constraints in the lateral space perpendicular to the principal direction. After processing all voxels in the input image according to the above rules, a probability distribution image after a complete guided erosion operation is obtained. This image effectively suppresses isolated noise and lateral pseudo-connected regions while maintaining the consistency of the pore channel direction.

[0039] After completing one guided erosion operation, the resulting probability distribution image is used as the new input image, and the guided erosion process described above is repeated to gradually stabilize the probability values ​​over multiple iterations. After each iteration, the probability distribution image obtained in the current iteration is compared with the result of the previous iteration on a voxel-by-voxel basis, and the change in probability value at the corresponding voxel position is calculated. To determine whether the iterative process has reached a stable state, a tolerance threshold is pre-set to represent the degree of convergence. This tolerance threshold is uniformly determined based on the range of probability values; for example, a fixed value much smaller than the overall change in probability can be selected to indicate that the probability distribution no longer changes significantly at the numerical level. When the probability distribution images obtained from two consecutive guided erosion operations show that the change in probability for all voxels is less than the tolerance threshold, the current iterative process is considered to have converged, and subsequent erosion iterations are terminated. After completing the iterative convergence determination, the final stable probability distribution image is subjected to binarization determination processing. According to the pre-defined probability determination rules, voxels with probability values ​​higher than the determination benchmark are marked as foreground phase, and the remaining voxels are marked as background phase, thereby generating the final 3D binary segmentation image. Through this iterative guided erosion and convergence determination process, the final binary segmentation result is ensured to be stable and consistent in spatial structure.

[0040] In step S7, a three-dimensional median transformation algorithm is applied to the final binary segmented image to extract a skeleton network diagram representing the spatial connectivity structure of the pores.

[0041] For the obtained final 3D binary segmentation image, voxels marked as foreground phase are processed voxels one by one, and these foreground voxels are used as effective constituent units of the pore space. Subsequently, within the 3D space, the spatial distance between each foreground voxel and its nearest background voxel is calculated. The background voxels are those marked as non-pore regions in the binary segmentation image. A uniform 3D spatial distance metric is used for distance calculation, so that each foreground voxel corresponds to a value reflecting its nearest distance to the pore boundary. By performing the above distance calculation on all foreground voxels, a complete 3D distance field is formed. This distance field is continuously distributed in space, with distance values ​​being larger in the pore center region and gradually decreasing near the pore boundary. After generating the 3D distance field, the distance field is scanned voxel by one, and the distance values ​​are compared within the local neighborhood. The voxel positions with the maximum distance values ​​in their neighborhoods are identified, and these voxels are marked as local distance maxima. These local distance maxima are usually located in the central region of the pore cross section and can stably reflect the central orientation of the pore space; therefore, they are uniformly selected as the initial skeleton points.

[0042] All initial skeleton points are treated as nodes in a graph structure. Then, based on the relative positions of these skeleton points in 3D space, spatial adjacency relationships are established between nodes, specifically by determining whether skeleton points are within a predetermined spatial proximity range. Based on this, the connection relationships between nodes are weighted by combining the distance values ​​corresponding to each skeleton point in the 3D distance field, giving higher priority to skeleton points with larger distance values ​​and continuous spatial positions. This process constructs a connection graph structure containing the connections between nodes. After obtaining the connection graph, a minimum spanning tree solution is performed. By traversing all nodes and selecting the connection path with the minimum overall connection cost, all skeleton nodes are connected into an acyclic, connected tree structure. The minimum spanning tree effectively avoids redundant connections and unnecessary loops while ensuring all skeleton points are connected, resulting in a concise and coherent skeleton representation. Finally, based on the minimum spanning tree result, the node information and connection information between nodes in the skeleton network are output, forming a complete 3D skeleton network graph. The skeleton network diagram uses nodes to represent key locations of pore channels and lines to represent the connection relationships between pore channels, which can intuitively reflect the overall connectivity structure and channel orientation of the pore space.

[0043] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0044] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0045] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0046] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0047] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0048] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0049] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0051] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the structural morphology of catalysts based on computer vision, characterized in that, Includes the following steps: S1. Based on the input three-dimensional grayscale image volume data of the catalyst, generate a multi-dimensional feature vector corresponding to each voxel; S2. Based on multidimensional feature vectors, an energy function minimization problem is constructed through image segmentation to obtain the initial classification probability distribution map of each voxel belonging to the foreground or background phase. S3. Perform sub-layer thresholding on the initial classification probability distribution map to generate a binarized slice image, and perform continuous homology analysis on the slice image to extract the manifestation and disappearance levels of key topological features. S4. Based on the manifestation and disappearance levels of key topological features, construct topological persistence constraints, fuse the constraints with the energy function during image segmentation, and re-solve to obtain the final classification probability distribution map. S5. On the final classification probability distribution map, determine the local principal direction based on the Hessian matrix eigenvector at each voxel position, and construct asymmetric structural elements along the local principal direction. S6. Asymmetric structuring elements are used to perform guided morphological erosion on the final classification probability distribution map. After iterative convergence, the final binary segmentation image is obtained. S7. Apply the three-dimensional median transformation algorithm to the final binary segmented image to extract the skeleton network diagram representing the spatial connectivity structure of the pores.

2. The method for analyzing the structure and morphology of a catalyst based on computer vision according to claim 1, characterized in that, In step S1, generating the multidimensional feature vector corresponding to each voxel specifically includes: Acquire three-dimensional grayscale image data of the catalyst and perform voxel extraction; A local neighborhood window is constructed with each voxel as the center, and the mean, variance, and skewness of the gray values ​​of all voxels within the local neighborhood window are calculated as the statistical moments of the local gray distribution. Calculate the second-order Hessian matrix at each voxel location, solve for the eigenvalues ​​of the matrix, and calculate the tubular and sheet-like feature measures based on the relative magnitudes of the eigenvalues. Calculate the gradient magnitude map of the catalyst's three-dimensional grayscale image volume, identify the local maxima in the gradient magnitude map as the image gradient peaks, and calculate the three-dimensional Euclidean distance of each voxel to its nearest image gradient peak. The local gray-level distribution statistical moments, the tubular and sheet-like feature measures, and the three-dimensional Euclidean distance are linearly concatenated to form a multidimensional feature vector corresponding to each voxel.

3. The method for catalyst structure and morphology analysis based on computer vision according to claim 1, characterized in that, In step S2, based on multidimensional feature vectors, an energy function minimization problem is constructed through image segmentation to obtain the initial classification probability distribution map of each voxel belonging to the foreground or background phase. Specifically, this includes: Calculate the single-point potential energy of each voxel belonging to the foreground and background phases based on the multidimensional feature vectors; Construct the edges between all adjacent voxels, and calculate the smoothing term potential energy of each edge based on the difference in the initial multidimensional feature vectors between adjacent voxels; Treat all voxels as nodes, and assign the single-point potential energy and smoothing term potential energy to the corresponding nodes and edges to construct a weighted graph structure. The minimum cut of the energy function is solved by applying the maximum flow minimum cut algorithm on the graph structure. The nodes are marked according to the minimum cut result, and the marking result is converted into the probability value of each voxel belonging to the foreground phase, forming the initial classification probability distribution map.

4. The method for catalyst structure and morphology analysis based on computer vision according to claim 3, characterized in that, The energy function is a Markov random field energy function constructed based on the graph cut algorithm, which is constructed by linearly superimposing the data terms composed of the single-point potential energy and the smoothing terms composed of the smoothing term potential energy.

5. The method for catalyst structure and morphology analysis based on computer vision according to claim 1, characterized in that, In step S3, the specific manifestation and disappearance levels for extracting key topological features include: The initial classification probability distribution map is segmented by setting a sub-layer threshold sequence and generating a corresponding binary image sequence. Three-dimensional connected component labeling is performed on each binary image in the binary image sequence to identify all connected pore regions. Along the sequential direction of the sublayer threshold sequence, the appearance, merging, and disappearance of each connected pore region as the threshold changes are traced; When a connected void region first appears, the corresponding threshold is recorded as the manifestation level of the topological feature. When two or more connected void regions merge, it is recorded as a merging event. When a connected void region completely disappears, the corresponding threshold is recorded as the disappearance level of the topological feature. All connected void regions not covered by merged events are aggregated, and the corresponding manifestation and disappearance levels are used as persistent data for the key topological features.

6. The method for catalyst structure and morphology analysis based on computer vision according to claim 1, characterized in that, In step S4, based on the manifestation and disappearance levels of key topological features, a topological persistence constraint term is constructed. This constraint term is then fused with the energy function used in image segmentation to re-solve and obtain the final classification probability distribution map. Specifically, this includes: Based on the manifestation and disappearance levels of the key topological features, the persistence value of each feature is calculated, and features with persistence values ​​exceeding a preset persistence threshold are selected as key features. Extract the persistent connected regions between the manifestation and disappearance levels of key features, and record the coordinates of all voxels constituting these connected regions as a set of key voxels. A penalty function based on voxel attribution is constructed as a topological persistence constraint term. The penalty function applies a constant penalty value when voxels belonging to the key voxel set are marked as background phase. The topological persistence constraint term is fused with the energy function, and the maximum flow minimum cut algorithm is applied to solve it again. The final classification probability distribution map is generated based on the solution results.

7. The method for catalyst structure and morphology analysis based on computer vision according to claim 1, characterized in that, In step S5, on the final classification probability distribution map, the local principal direction is determined based on the Hessian matrix eigenvector at each voxel location, and the asymmetric structural element is constructed along the local principal direction, specifically including: Calculate the second-order Hessian matrix at each voxel position on the final classification probability distribution map, and perform eigenvalue decomposition on the matrix to obtain eigenvalues. Select the eigenvector with the smallest absolute value of the eigenvalue and determine the direction indicated by the eigenvector as the local principal direction. With the local principal direction as the major axis, an ellipsoid prototype is defined in a three-dimensional orthogonal coordinate system. The ellipsoid prototype is then compressed at a fixed scale on a cross section perpendicular to the local principal direction to construct an asymmetric three-dimensional structural element extending along the principal direction. The center of this asymmetric three-dimensional structural element is aligned with the current voxel position.

8. The method for analyzing the structure and morphology of a catalyst based on computer vision according to claim 1, characterized in that, In step S6, a guided morphological erosion operation is performed on the final classification probability distribution map using an asymmetric structuring element. After iterative convergence, the final binary segmentation image is obtained, specifically including: The final classification probability distribution map is used as the input image, and the asymmetric structural element is used as the operation template. Slide an asymmetric structuring element on the input image, calculate the minimum probability of all voxels in the space covered by the structuring element at each position, and replace the probability value of the central voxel with this minimum value to complete one guided erosion operation. The guided erosion operation is repeated with the image obtained from the erosion operation as a new input image until the change in the probability values ​​of all voxels between two consecutive erosion operations is less than the preset tolerance threshold, which is considered to be iterative convergence. The probability value of each voxel in the image after iterative convergence is binarized to generate the final binary segmentation image.

9. The method for analyzing the structure and morphology of a catalyst based on computer vision according to claim 1, characterized in that, In step S7, applying a three-dimensional median transformation algorithm to the final binary segmented image to extract the skeleton network graph representing the spatial connectivity structure of the pores specifically includes: Calculate the distance from each foreground voxel to the nearest background voxel in the final binary segmented image to generate a 3D distance field. Identify local distance maxima in the distance field as initial skeleton points. Using the initial skeleton points as nodes, construct a connection graph based on spatial adjacency relationships and distance field values. Solve for the minimum spanning tree in the connection graph. Output nodes and edges based on the minimum spanning tree to form a skeleton network graph.

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