Fibrous molecule cloud identification and analysis method, medium and equipment

Abstract

The invention provides a fibrous molecular cloud identification and analysis method, a medium and equipment, the first part is an identification method based on synergy, the fibrous molecular cloud in a data cube is identified by using direction and position synergy between adjacent block masses and local filament axes, and meanwhile, the identification method is used for identifying the fibrous molecular cloud in the data cube by using the direction and position synergy between the adjacent block masses and local filament axes; the region of the fibrous molecular cloud can directly inherit the region of the molecular cloud mass. And the second part relates to skeleton analysis, wherein the fibrous molecular cloud is analyzed by adopting a morphology and graph theory-based skeletonization technology. The third part is a sub-structuring method based on the graph theory, allowing a complex filament to be decomposed into simpler sub-filaments. The method is applied to observation data of a Yinhe picture scroll sky tour project, fibrous molecular clouds of different scales can be accurately identified based on the identification method of the synergy, and skeletons and substructures of the fibrous molecular clouds can be effectively analyzed based on the skeletonization and substructuring methods of the graph theory.

Description

Technical Field

[0001] The invention belongs to the field of astronomy, and specifically relates to a fibrous molecular cloud identification and analysis method, medium and equipment. Background Art

[0002] Both the atomic and molecular phases of the interstellar medium have been observed to have filamentary structures. Filamentary molecular clouds are composed of gas and dust, and filamentary structures exist in various environments, ranging from large to small scales. Due to the presence of filamentary structures, the matter within the molecular cloud can gather into filamentary forms, forming high-density regions, which provide a suitable environment for star formation. The condensation of the core from the surrounding cloud gas represents a key step in the star formation process, and its formation plays a key role in determining the mass of the final star. Filamentary molecular clouds are usually not isolated objects, but are observed to form systems with multiple intersections and crossings. Filamentary structures can provide higher column density at the intersections, further promoting the formation of stars. More and more studies have shown that the intersections of filamentary structures are the preferred environments for the formation of massive stars and star clusters. Therefore, understanding the core formation within filamentary molecular clouds has become an urgent task, and studying filamentary molecular clouds is crucial to revealing the formation of interstellar matter, the birth of stars, the circulation of matter in the universe, and the cantilever structure of the Milky Way.

[0003] The definition methods of filamentary molecular clouds can be mainly divided into two categories: visual judgment and definition based on identification algorithms. In addition, the characteristics of filamentary molecular clouds may vary depending on the observation probe used. In general, filamentary molecular clouds are elongated, continuous and high-density structures. The identification algorithms of filamentary molecular clouds mainly include GetFilamems, FilFinder, DisPerSe and MST. GetFilaments identifies filamentary molecular clouds by applying a series of Gaussian smoothing kernels and defines filamentary molecular clouds as structures that persist at multiple scales and have significant anisotropy (extending along one axis). FilFinder uses morphological methods to detect filamentary molecular clouds on binary mask images. GetFilaments and FilFinder are only applicable to two-dimensional data, while identifying filamentary molecular clouds in molecular spectral line data is an inherent three-dimensional problem, and the difficulty of inferring three-dimensional spatial information from position-position-velocity data must be dealt with. DisPerSe is a widely used algorithm for identifying filamentary molecular clouds in two-dimensional and three-dimensional space. DisPerSe defines filamentary molecular clouds as ascending 1-manifolds: a one-dimensional structure that connects overdense regions in the Morse decomposition of data, and a linear structure that connects overdense regions in the image. The region of a filamentary molecular cloud is necessary information for analyzing its mass, characteristic radius and other parameters, while the output of DisPerSe is a one-dimensional skeleton of a filamentary molecular cloud, and additional techniques are required to obtain the region of a filamentary molecular cloud. The MST algorithm automatically identifies filamentary molecular clouds by connecting molecular cloud clusters with velocity coherence. MST is an algorithm that clusters in position-position-velocity space and has been used to identify and characterize a group of large-scale filamentary molecular clouds with consistent velocities. Since the existing molecular cloud cluster catalog lacks regional information, the filamentary molecular clouds identified by MST are not continuous, and discontinuous filamentary molecular clouds are not conducive to subsequent skeleton analysis. Summary of the invention

[0004] The present invention provides a method, medium and device for identifying and analyzing fibrous molecular clouds in order to solve the defects of existing algorithms in the identification of fibrous molecular clouds, including the inability to be applied to observation data in position-position-velocity space, the inability to detect the region of fibrous molecular clouds, the lack of connectivity of the identified fibrous molecular clouds, and the lack of strength skeleton and substructure analysis methods of fibrous molecular clouds. The purpose of the present invention is to develop a set of high-efficiency, high-adaptability and high-accuracy fibrous molecular cloud identification and analysis tools in the face of the current situation of weak adaptability and poor effect of algorithms for detecting and analyzing fibrous molecular clouds in molecular spectral line data.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for identifying and analyzing a fibrous molecular cloud, comprising the following steps:

[0007] Definition A filamentary molecular cloud consisting of molecular cloud clumps;

[0008] Extract molecular cloud clusters from the galaxy scroll data based on the FacetClumps algorithm;

[0009] Evaluate the coherence of molecular cloud clumps and identify filamentary molecular clouds;

[0010] The skeleton is extracted based on morphology and graph theory to obtain the morphological skeleton and intensity skeleton of the fibrous molecular cloud.

[0011] Substructure decomposition of fibrous molecular clouds based on graph theory.

[0012] Optionally, the fibrous molecular cloud is defined as follows:

[0013] In position-position space, the fibrous molecular cloud is a structure with an aspect ratio greater than 2.5;

[0014] In the position-position-velocity space, the structure of the fibrous molecular cloud has both spatial continuity and velocity continuity;

[0015] The fibrous molecular cloud is composed of at least two adjacent molecular cloud clusters, and the directions of the adjacent molecular cloud clusters are consistent with the direction of the local axis of the fibrous molecular cloud; if there are molecular cloud clusters in the fibrous molecular cloud that do not show directional coordination, their positions show coordination with the local axis established by the adjacent molecular cloud clusters that show directional coordination.

[0016] Optionally, the FacetClumps algorithm combines the Facet model and the extreme value determination theorem of multivariable functions to automatically locate the center of the molecular cloud clusters in the preprocessed signal area, and then uses a connectivity-based minimum distance clustering method to merge local areas segmented by local gradients to identify the area corresponding to each molecular cloud cluster.

[0017] Optionally, the step of evaluating the coherence of the molecular cloud clusters and identifying the fibrous molecular clouds comprises:

[0018] Starting from any cluster A, search its adjacent cluster set S1; for each adjacent cluster B in set S1, connect the spatial positions of clusters A and B to form a line segment LAB;

[0019] Calculate the angles ΔθA and ΔθB between the main axis directions of cluster A and cluster B relative to the direction of line segment LAB; if both ΔθA and ΔθB are smaller than the specified angle tolerance, it is considered that the two adjacent clusters A and B have directional compatibility;

[0020] Record all clusters that have directional co-ordination with cluster A; when cluster B has directional co-ordination with cluster A, search for cluster B's adjacent cluster set S2 and merge it with set S1 to obtain adjacent cluster set S31;

[0021] For each cluster C1 in the set S31, the intersection of the perpendicular line from cluster C1 to line segment LAB and line segment LAB is calculated; if the distance between the intersection and cluster C1 is less than the specified distance tolerance, cluster C1 is considered to have positional compatibility with clusters A and B; if cluster C1 has positional compatibility and the intersection is outside line segment LAB, the adjacent cluster set S32 of cluster C1 is searched;

[0022] For each cluster C2 in set S32, determine whether C2 has positional compatibility with clusters A and B, record all clusters that have positional compatibility with clusters A and B, form a cluster record list, and merge the lists containing the same clusters to obtain a record list representing a fibrous molecular cloud.

[0023] Optionally, the skeleton extraction is performed based on morphology to obtain the morphological skeleton of the fibrous molecular cloud, as follows:

[0024] The morphological skeletonization method based on morphology extracts the morphological skeleton from the spatial mask of the fibrous molecular cloud, regards each pixel in the morphological skeleton as a node, regards the distance between each pair of nodes as the connecting edge and assigns a weight to construct a weighted undirected graph G1;

[0025] Apply the GMST algorithm to the graph G1 to form a tree T11; in the tree T11, the nodes with degree 1 represent the endpoints of the morphological skeleton, and the endpoints are extended to the boundaries of the mask;

[0026] Merge the extended part into the node information of tree T11 to generate a minimum spanning tree T12;

[0027] Calculate the shortest paths between all pairs of nodes present in the tree T12, and determine the path with the most nodes as the longest shortest path, which corresponds to the longest skeleton in the morphological skeleton;

[0028] The ordered coordinates in the longest skeleton are used as the control points of the B-spline curve, and the control points are fitted using cubic basis functions to generate a smooth and continuous representation; the B-spline curve is uniformly sampled at the pixel interval to generate a series of sampling points, and the first-order derivative of each sampling point is calculated to determine the line segments perpendicular to the sampling points. The parts of these line segments that fall within the mask range of the fibrous molecular cloud correspond to the outline of the fibrous molecular cloud.

[0029] Optionally, the skeleton extraction based on graph theory to obtain the strength skeleton of the fibrous molecular cloud is specifically:

[0030] All points in the fibrous molecular cloud space mask are taken as nodes, each point is connected to its adjacent points through edges, and weights are assigned according to formula 1 to create a weighted undirected graph G2;

[0031] The minimum spanning tree T2 is obtained by using the GMST algorithm on the graph G2. The tree T2 contains all the points in the mask. The weight of the tree T2 is updated according to formula 2:

[0032] Formula 1:

[0033] Formula 2:

[0034] Where WeightSK Gij WeightSK represents the weight of two adjacent coordinates in the fiber region of graph G2 in the position-position space. Tij Represents the update weight of two adjacent coordinates in tree T2; DistLB ij is the Euclidean distance between adjacent coordinates, Ii 和 I j are the integrated intensities at coordinates i and j, respectively;

[0035] Calculate the shortest path between each pair of nodes in tree T2, and select the path with the highest total weight among all the shortest paths to obtain the initial strength skeleton;

[0036] The initial strength skeleton is refined to obtain the final strength skeleton.

[0037] Optionally, the substructure decomposition of the fibrous molecular cloud based on graph theory is specifically:

[0038] The positions of molecular cloud clusters in the fibrous molecular cloud are taken as nodes of the graph, and the weights between any two adjacent molecular cloud clusters are calculated according to Formula 3. The weights are used to establish connections and construct a weighted undirected graph G3.

[0039] Applying the GMST algorithm to the graph G3, we obtain the minimum spanning tree T31 that contains all the molecular cloud clusters that constitute the fibrous molecular cloud; the weight of the tree T31 is updated according to the following formula:

[0040] Formula 3:

[0041] Formula 4:

[0042] In the formula, WeightST Gij WeightST represents the weights of two adjacent molecular cloud clusters i and j in graph G3. Tij Represents the updated weights of two adjacent molecular cloud clusters in tree T31; DistLBij is the Euclidean distance between adjacent molecular cloud clusters in the spatial direction, DistV ij is the difference in speed channel, I k is the intensity at coordinate k in the position-position-velocity space along the line segment between the center coordinates of molecular cloud clusters i and j, and N represents the number of voxels in the line segment;

[0043] Based on the tree T31, the decomposition of the fibrous molecular cloud is performed according to a recursive function.

[0044] Optionally, the decomposition of the fibrous molecular cloud is performed according to a recursive function, specifically:

[0045] S1: Calculate the shortest path between each pair of nodes in the tree T31, and select the shortest path with the highest total weight among all the shortest paths as the longest shortest path;

[0046] S2: Remove the edges on the longest shortest path in tree T31 and check the corresponding nodes; if the degree of a node becomes 0, remove it as well;

[0047] S3: If there are still nodes left, use the remaining nodes and edges to generate subtree T3i. The edge weights are determined using Formula 3.

[0048] S4: Replace tree T31 with subtree T3i and update the weight using formula 4; recursively perform operations S1-S3 until there are no nodes in tree T31, and the recursion terminates. The nodes on the different longest shortest paths obtained correspond to molecular cloud clusters in different sub-fibrous molecular clouds.

[0049] In a second aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the method for identifying and analyzing fibrous molecular clouds as described in the first aspect.

[0050] In a third aspect, the present invention provides an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the fibrous molecular cloud identification and analysis method as described in the first aspect is implemented.

[0051] The beneficial effects of the present invention are as follows: each process of the identification and analysis method of the present invention has a strong theoretical basis, a high degree of automation, a small number of parameters, and a small dependence on parameters. The identification method of the present invention can be applied to observational data in position-position space and position-position-velocity space, and can directly detect the region of fibrous molecular clouds, and the identified fibrous molecular clouds have connectivity. The analysis method of the present invention can extract the strength skeleton and substructure of fibrous molecular clouds, filling the gap in related research. The identification and analysis method of the present invention can adapt to unknown and complex astronomical measured data and can be easily extended to other application fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the process of a fibrous molecular cloud identification and analysis method of the present invention.

[0053] Figure 2 It is the 13CO spectral line data of the Milky Way.

[0054] Figure 3 is the direction and position of the molecular cloud cluster in PP space. There are a total of 127 molecular cloud clusters, 89 of which do not touch the edge. The asterisks indicate the spatial position of the molecular cloud clusters, and the different colors of the asterisks indicate different speed positions. The red line indicates the main axis direction of the molecular cloud clusters that do not touch the edge.

[0055] Figure 4 This is an example of the detection process. The background is from Figure 2 The velocity integrated intensity map of a fibrous molecular cloud detected in . The red circles indicate the positions of the molecular cloud clumps, which are numbered in sequence. The red line indicates the main axis direction of the molecular cloud clump, the cyan line indicates the line connecting the positions of adjacent molecular cloud clumps, the blue arc indicates the angle between the direction of the molecular cloud clump and the cyan line, and the green line is the perpendicular line between the position of the molecular cloud clump and the cyan line.

[0056] Figure 5 The integrated intensity diagram of the filamentary molecular cloud structure in different directions. Left panel: velocity integrated intensity diagram. Middle panel: latitude integrated intensity diagram. Right panel: longitude integrated intensity diagram. The red star indicates the center position of the filamentary molecular cloud, the green line indicates its direction, and the yellow contour line is the boundary of the filamentary molecular cloud region.

[0057] Figure 6 is the morphological skeleton analysis. (a) The morphological skeleton extracted using the morphology-based skeletonization method; (b) The extended longest morphological skeleton; (c) The fitted morphological skeleton and contour. The thicker red curve represents the smoothed morphological skeleton obtained by B-spline fitting, while the thinner red straight line represents the contour. The blue scattered points represent the peak intensity pixels on the contour. The aspect ratio is 5.15.

[0058] Figure 7 is the intensity skeleton analysis. (a) Intensity skeleton extracted using graph-based skeletonization method; (b) Intensity skeleton after refinement; (c) Fitted intensity skeleton and contour. The thicker red curve represents the smoothed intensity skeleton obtained by B-spline fitting, while the thinner red straight line represents the contour. The blue scattered points represent the peak intensity pixels on the contour. The aspect ratio is 4.67.

[0059] Figure 8 are substructures of the filamentary molecular cloud. The numbered blue and red circles connected by a blue line indicate the locations of clumps in the first subfilamentary molecular cloud, while the blue outline indicates the boundary of this substructure. Similarly, the numbered green and red circles connected by a green line indicate the locations of clumps in the second subfilamentary molecular cloud, while the green outline indicates the boundary of this substructure. The red clumps correspond to nodes shared between the two subfilamentary molecular clouds, whose boundaries are outlined by the red outline.

[0060] Fig. 9 are all the fibrous molecular clouds identified from the experimental data. The background is the velocity-integrated intensity map. Curves of different colors represent the B-spline curves of the intensity skeletons of different fibrous molecular clouds, while numbered circles of different colors represent the positions of different fibers. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0062] In one embodiment, the present invention provides a method for identifying and analyzing fibrous molecular clouds, such as Figure 1 As shown, the specific steps include the following steps.

[0063] Step 1: Fibrous molecular cloud definition.

[0064] Although the fibrous molecular clouds identified in the position-position-velocity space are not closely related to those identified in the position-position-position space, their projected morphologies in the position-position space are roughly similar. It is observed that dense molecular cloud clumps can indeed form along the fibrous molecular cloud axis. In addition, MHD and hydrodynamic simulations show that there is a certain tendency for the fibrous molecular cloud axis to align with the stretching direction. The connecting line between the positions of adjacent molecular cloud clumps can represent the local axis of the fibrous molecular cloud, and the direction of the molecular cloud clump can indicate the direction of local stretching.

[0065] Taking the above factors into consideration, the definition of fibrous molecular cloud is as follows:

[0066] 1. In position-position space, a filamentary molecular cloud is a structure characterized by being elongated.

[0067] 2. In the position-position-velocity space, the fibrous molecular cloud is a structure that has both spatial continuity and velocity continuity.

[0068] 3. A filamentary molecular cloud consists of at least two adjacent molecular cloud clumps, the orientations of which are consistent with the local axis of the filamentary molecular cloud. If the molecular cloud clumps within a filamentary molecular cloud do not exhibit directional coordination, their positions will exhibit coordination with the local axis established by the adjacent molecular cloud clumps that exhibit directional coordination.

[0069] Step 2: Molecular cloud cluster detection based on FacetClumps.

[0070] The Milky Way Picture Scroll Project (MWISP) is an extensive CO survey of the Milky Way plane conducted by Purple Mountain Observatory (PMO). The survey has advantages such as wide sky coverage, multiple spectral lines and high sensitivity. FacetClumps is an innovative algorithm for extracting and analyzing molecular cloud clumps proposed by Jiang et al. in 2023. The algorithm combines the Facet model and the extreme value determination theorem of multivariate functions to automatically locate the centers of molecular cloud clumps in the preprocessed signal region. Subsequently, it uses a connectivity-based minimum distance clustering method to merge local regions segmented by local gradients to identify the region corresponding to each molecular cloud clump.

[0071] The filamentary molecular cloud detection algorithm is based on the position, direction and area information of molecular cloud clumps. FacetClumps has been successfully applied to extract molecular cloud clumps from the Milky Way scroll data. Compared with other molecular cloud cluster detection algorithms, it shows superior performance, especially in terms of the positioning accuracy and regional segmentation accuracy of molecular cloud clumps, which is crucial for the subsequent identification of filamentary molecular clouds. In addition, by comparing the molecular cloud cluster detection algorithms FellWalker, ConBased and FacetClumps, it is found that the molecular cloud clumps obtained by FacetClumps significantly improve the performance of the filamentary molecular cloud detection algorithm. Therefore, this embodiment chooses to use the FacetClumps algorithm to detect molecular cloud clumps. The Milky Way scroll data is as follows: Figure 2 As shown, applying the FacetClumps algorithm, we get Figure 3 The molecular cloud cluster detection results are shown.

[0072] Step 3: Identification of fibrous molecular clouds based on coordination.

[0073] Figure 4 A detection example is shown. First, start from any cluster A (e.g. Figure 4 For each adjacent cluster B in S1 (e.g. Figure 4 2 in the figure), connect the spatial positions of clusters A and B to form a line segment LAB (e.g. Figure 4 ). Next, calculate the angles ΔθA and ΔθB between cluster A and cluster B relative to the direction of this line segment. If both ΔθA and ΔθB are less than the specified angle tolerance, the two adjacent clusters are considered to have directional compatibility. Record all clusters that have directional compatibility with cluster A. When cluster B has directional compatibility with cluster A, search for cluster B's adjacent cluster set S2 and merge it with S1 to obtain the adjacent cluster set S31 of the structure composed of clusters A and B. For each cluster C1 in S31 (e.g. Figure 4 3), calculate the intersection of the perpendicular line from cluster C1 to line segment LAB and line segment LAB. If the distance between the intersection and cluster C1 is less than the specified distance tolerance, cluster C1 is considered to have positional compatibility with clusters A and B. If cluster C1 has positional compatibility and the intersection is outside line segment LAB, search for the adjacent cluster set S32 of cluster C1. For each cluster C2 in S32 (e.g. Figure 4 5), determine whether C2 has positional compatibility with clusters A and B, and record all clusters that have positional compatibility with clusters A and B. After performing the above compatibility evaluation on all clusters, update the cluster record list, and merge the lists containing the same clusters to obtain a new record list representing the fibrous molecular cloud.

[0074] The regional detection task of filamentary molecular clouds is challenging, and different regional divisions can significantly affect the characteristic radius and other physical properties of filamentary molecular clouds. Figure 5 The integral plots of the filamentary molecular cloud identified using the associativity-based method in different integration directions are shown. The yellow contours indicate the region of the filamentary molecular cloud, which is obtained by using the region information of the associated clumps. Due to the relatively accurate segmentation of the clump regions, the filamentary molecular cloud region obtained by this method has higher accuracy than other commonly used methods (such as extracting the region within a specific range along the axis of the filamentary molecular cloud).

[0075] Step 4: Skeleton extraction based on morphology and graph theory.

[0076] Mathematical morphological methods, such as medial axis-based skeletonization methods, are widely used in identifying various fibrous skeletons. Morphological skeleton extraction mainly revolves around processing binary images to extract their medial axes, ignoring the intensity information present in the image. However, fibrous molecular clouds inherently contain intensity information and exhibit partial asymmetry. Therefore, in addition to using a morphological-based skeletonization method to extract the morphological skeleton, this embodiment also develops a graph-based skeletonization method to extract the intensity skeleton of a fibrous molecular cloud. In order to generate the contour of a fibrous molecular cloud, spline interpolation is used to fit the skeleton and obtain its B-spline curve. Subsequently, the contour of the fibrous molecular cloud can be constructed by utilizing the first-order derivatives of the nodes on the B-spline curve.

[0077] Step 4 includes the following sub-steps:

[0078] S4.1: Morphology-based skeleton extraction algorithm.

[0079] A morphological skeleton is extracted from the spatial mask of Filament using a morphological skeletonization method. This process produces Figure 6 (a) shows the morphological skeleton. However, it is worth mentioning that the thinning operation involved in the morphological skeletonization method may lead to the loss of some edge information, thus preventing the skeleton from reaching the boundary of the mask.

[0080] To solve this problem, this embodiment regards all points in the skeleton as nodes, and assigns the distance between each pair of points as the weight of the connecting edge, constructing a weighted undirected graph called G1. Subsequently, this embodiment applies the minimum spanning tree (GMST) algorithm to G1 to form a tree called T11. In T11, the leaf nodes with a degree of 1 represent the endpoints of the skeleton. In order to enhance the integrity of the skeleton, this embodiment extends the endpoints to the boundaries of the mask.

[0081] In order to separate the longest skeleton, this embodiment merges the extended part of the skeleton into the node information of tree T11 and generates a minimum spanning tree, called T12. Subsequently, the shortest paths between all leaf node pairs existing in T12 are calculated, and the path with the most nodes is determined as the longest shortest path. This path corresponds to the longest skeleton, such as Figure 6 (b) shows the main skeleton of the morphological skeleton.

[0082] The coordinate sets of the main skeleton are ordered, arranged from one end to the other, ensuring that points that are adjacent in space are also adjacent in the coordinate set. This ordered arrangement allows these coordinates to be used as control points for B-spline curves. By using cubic basis functions, the control points can be fitted to produce a smooth and continuous representation, such as Figure 6The thicker red curve in (c). To obtain the contour of the Filament, the B-spline curve can be uniformly sampled at pixel intervals to generate a series of sampling points. Subsequently, by calculating the first-order derivative of each sampling point, a line perpendicular to that specific point can be determined. The part of these line segments that falls within the Filament mask corresponds to the contour, as shown in Figure 6 This is shown as the thinner red line in (c).

[0083] The aspect ratio of a filament is determined by its length divided by its width. The length is calculated based on the number of coordinates on the main skeleton, while the width is calculated based on the median length of the contours.

[0084] S4.2: Skeleton extraction algorithm based on graph theory.

[0085] Due to the asymmetry of the structural strength of fibrous molecular clouds, the strength skeleton is crucial in analyzing the properties of fibrous molecular clouds such as length, characteristic radius and line quality. In order to obtain the strength skeleton of fibrous molecular clouds, this embodiment proposes a graph-based skeletonization method. All points within the spatial mask of the fibrous molecular cloud are regarded as nodes in the graph. Each point is connected to its adjacent points only by edges, and the weight of each edge is determined by a specific formula (1). This process creates a weighted undirected graph, represented as G2. The GMST algorithm is then used on G2 to obtain the minimum spanning tree T2, which contains all the points within the mask. Next, the weight of tree T2 is updated using formula (2). Leaf nodes located on the boundary of the mask in T2 are searched. Next, this embodiment calculates the shortest path between each pair of these leaf nodes and selects the path with the highest total weight among all shortest paths.

[0086] This results in an initial version of the desired strength skeleton, such as Figure 7 (a) shown.

[0087]

[0088] Among them, WeightSK Gij WeightSK represents the weight of two adjacent coordinates in the fiber region in the position-position space in graph G2. Tij DistLB represents the update weight of two adjacent coordinates in tree T2. ij is the Euclidean distance between these adjacent coordinates. DistLB ij The value can be 1 or I i and I j are the integrated intensities at coordinate i and coordinate j, respectively.

[0089] The designed weight WeightSK encourages the desired path to mainly follow the neighboring points with a distance of 1, thus promoting a more straight skeleton structure. However, this design also sacrifices the slenderness of the skeleton, resulting in inaccurate length calculation. In order to optimize the strength skeleton, this embodiment refines the initial skeleton. This ensures that there are only 3 skeleton points in the 3×3 neighborhood. The final strength skeleton after refinement is as follows Figure 7 (b) as shown.

[0090] The B-spline curves and contours obtained from the intensity skeleton are shown in Figure 7 (c) By comparison Figure 6 (b) and Figure 7 The skeleton points in (b), and Figure 6 (c) and Figure 7 From the fitted skeleton in (c), it is clear that the intensity skeleton is in close agreement with the visual perception of the fiber-like molecular cloud skeleton in this example. Therefore, the aspect ratio derived from the intensity skeleton is generally more reliable. Structures with a smaller aspect ratio (parameter LWRatio) are considered non-fibrous structures and will be filtered.

[0091] Step 5: Substructure decomposition based on graph theory.

[0092] The formation and splitting of filamentary molecular cloud structures is a complex process characterized by entangled, interconnected substructures at different scales and complex kinematics. Analyzing the substructures within complex filamentary molecular cloud systems and studying the connections and interactions between individual sub-filamentary molecular clouds can provide valuable insights into the formation and splitting processes of filamentary molecular clouds, thereby promoting the understanding of these phenomena. The physical intersections between filamentary molecular clouds often have multiple velocity components that track the individual velocities of each merging filamentary molecular cloud. The filamentary structure can provide higher column density at the intersection, further promoting the formation of stars. An increasing number of studies have shown that the intersections of filamentary structures are preferred environments for the formation of massive stars and star clusters.

[0093] In order to obtain the substructure of the fibrous molecular cloud, this embodiment regards the position of the molecular cloud clusters in the fiber as nodes in the graph. According to formula (3), the weights between any two adjacent molecular cloud clusters are calculated. Then these weights are used to establish connections and construct a weighted undirected graph G3. The GMST algorithm is applied to graph G3 to obtain a minimum spanning tree T31 containing all molecular cloud clusters that constitute the fiber. Then, the weight of tree T31 is updated according to formula (4).

[0094]

[0095] Among them, WeightST Gijrepresents the weights of two adjacent molecular cloud clusters i and j in graph G3, while WeightST Tij Represents the updated weights of two adjacent molecular cloud clusters in tree T31. DistLB ij is the Euclidean distance between adjacent molecular cloud clusters in the spatial direction, and DistV ij is the difference in speed channel. k is the intensity at coordinate k in the position-position-velocity space along the line segment between the center coordinates of molecular cloud cluster i and , where N represents the number of voxels in the line segment.

[0096] When adjacent molecular cloud clusters are close in distance, the minimum spanning tree should preferentially connect molecular cloud clusters with higher strength, while larger substructures need to have longer lengths and higher strengths. WeightST can achieve these goals efficiently. This embodiment designs the following recursive function to decompose any complex fiber:

[0097] Operation 1: Retrieve and record the longest shortest path in T31. “Longest” here is defined as having the largest sum of weights.

[0098] Operation 2: Remove the edges on the longest shortest path in T31 and check the corresponding nodes. If the degree of a node becomes 0, remove it as well.

[0099] Operation 3: If there are still remaining nodes, use the remaining nodes and edges to generate all subtrees T3i. The weights of the edges are determined using formula (3).

[0100] Operation 4: Replace T31 with each subtree T3i and update the weight using formula (4). Then, recursively perform operations 1-3.

[0101] When there is no node in T31, the recursion terminates. The nodes on different longest shortest paths correspond to the clusters in different sub-fiber molecular clouds. Figure 8 As shown, the filamentary molecular cloud can be decomposed into two daughter filamentary molecular clouds, one of which contains 2 clumps and the other contains 5 clumps.

[0102] These sub-sub-filaments share a common intersection clump, and each sub-filament includes at least one additional clump beyond the shared clump. Each sub-filament has a unique local high-density structure, which allows better study of star formation on the primary and secondary filaments, as well as possible differences in stellar activity at the intersection point.

[0103] Next, the effectiveness of the method of this embodiment is illustrated by combining a verification example.

[0104] 1. The experimental data comes from the 13CO molecular spectrum line data block of the Milky Way, which has a range of 17.7°≤1≤18.5°, 0°≤b≤0.8°, and 5kmm / s≤v≤30km / s. The molecular cloud cluster detection algorithm is used to detect the data block and obtain the molecular cloud cluster information.

[0105] 2. The initial parameters are set to {TolAngle = 30, TolDistance = 4, LWRatio = 2.5}. TolAngle is the angle tolerance for the orientation coherence between two adjacent clusters, in degrees; TolDistance is the distance tolerance for the position coherence between the cluster and the local fiber axis, in pixels; LWRatio is the minimum aspect ratio of the fibrous molecular cloud.

[0106] 3. By identifying the fibrous molecular cloud in the experimental data based on the identification method in step 3 and obtaining the regional information of the fibrous molecular cloud, the fibrous molecular cloud catalog of the experimental data can be calculated by applying the analysis methods in steps 4 and 5. The catalog includes the position, length, area, aspect ratio, direction, symmetry, fitting width, number of clusters and number of substructures of the fibrous molecular cloud.

[0107] 4. The identified fibrous molecular clouds are as follows: Fig. 9 The edited catalog of fibrous molecular clouds is shown in Table 1. The associative identification method can identify all visually possible fibrous molecular clouds, and the extracted intensity skeleton is consistent with the understanding of the skeleton of fibrous molecular clouds.

[0108] Table 1 Catalogue of fibrous molecular clouds

[0109]

[0110] In Table 1, column (1): ID of the filamentary molecular cloud. Columns (2)-(4): Flow-weighted longitude, latitude and local standard velocity (LSR velocity). Column (5): Angular length. Column (6): Projected angular area in spatial direction. Column (7): Ratio of length to width. Column (8): Angle. Column (9): Velocity gradient. Column (10): Symmetry of the profile. Column (11): Full width at half maximum (FWHM) of the Gaussian fit. Column (12): Number of clumps within the filamentary molecular cloud. Column (13): Number of sub-filamentary molecular clouds.

[0111] In another embodiment, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the fibrous molecular cloud identification and analysis method as described in the aforementioned embodiment.

[0112] In another embodiment, the present invention proposes an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the fibrous molecular cloud identification and analysis method as described in the aforementioned embodiment is implemented.

[0113] In the embodiments disclosed in the present application, the computer storage medium can be a tangible medium that can contain or store a program for use by or in combination with an instruction execution system, device or equipment. The computer storage medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or equipment, or any suitable combination of the above. More specific examples of computer storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CDgROM), optical storage devices, magnetic storage devices, or any suitable combination of the above.

[0114] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0115] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for identifying and analyzing fibrous molecular clouds, characterized in that: The steps include: Definition A filamentary molecular cloud consisting of molecular cloud clumps; Extract molecular cloud clusters from the galaxy scroll data based on the FacetClumps algorithm; Evaluate the coherence of molecular cloud clumps and identify filamentary molecular clouds; The skeleton is extracted based on morphology and graph theory to obtain the morphological skeleton and intensity skeleton of the fibrous molecular cloud. Substructure decomposition of fibrous molecular clouds based on graph theory.

2. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 1, characterized in that: The definition of the fibrous molecular cloud is as follows: In position-position space, the fibrous molecular cloud is a structure with an aspect ratio greater than 2.5; In the position-position-velocity space, the structure of the fibrous molecular cloud has both spatial continuity and velocity continuity; The fibrous molecular cloud is composed of at least two adjacent molecular cloud clusters, and the directions of the adjacent molecular cloud clusters are consistent with the direction of the local axis of the fibrous molecular cloud; if there are molecular cloud clusters in the fibrous molecular cloud that do not show directional coordination, their positions show coordination with the local axis established by the adjacent molecular cloud clusters that show directional coordination.

3. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 1, characterized in that: The FacetClumps algorithm combines the Facet model with the extreme value determination theorem of multivariate functions to automatically locate the center of the molecular cloud clusters in the preprocessed signal area, and then uses the minimum distance clustering method based on connectivity to merge the local areas segmented by local gradients, thereby identifying the area corresponding to each molecular cloud cluster.

4. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 1, characterized in that: The coherence evaluation of the molecular cloud clusters and identification of fibrous molecular clouds are specifically as follows: Starting from any cluster A, search its adjacent cluster set S1; for each adjacent cluster B in set S1, connect the spatial positions of clusters A and B to form a line segment LAB; Calculate the angles ΔθA and ΔθB between the main axis directions of cluster A and cluster B relative to the direction of line segment LAB; if both ΔθA and ΔθB are smaller than the specified angle tolerance, it is considered that the two adjacent clusters A and B have directional compatibility; Record all clusters that have directional co-ordination with cluster A; when cluster B has directional co-ordination with cluster A, search for cluster B's adjacent cluster set S2 and merge it with set S1 to obtain adjacent cluster set S31; For each clumping block C1 in the set S31, the intersection point of the perpendicular line from the clumping block C1 to the line segment LAB and the line segment LAB is calculated; If the distance between the intersection point and cluster C1 is less than the specified distance tolerance, cluster C1 is considered to have positional compatibility with clusters A and B; if cluster C1 has positional compatibility and the intersection point is outside the line segment LAB, the adjacent cluster set S32 of cluster C1 is searched; For each cluster C2 in set S32, determine whether C2 has positional compatibility with clusters A and B, record all clusters that have positional compatibility with clusters A and B, form a cluster record list, and merge the lists containing the same clusters to obtain a record list representing a fibrous molecular cloud.

5. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 1, characterized in that: The skeleton extraction based on morphology obtains the morphological skeleton of the fibrous molecular cloud, which is as follows: The morphological skeletonization method based on morphology extracts the morphological skeleton from the spatial mask of the fibrous molecular cloud, regards each pixel in the morphological skeleton as a node, regards the distance between each pair of nodes as the connecting edge and assigns a weight to construct a weighted undirected graph G1; Apply the GMST algorithm to the graph G1 to form a tree T11; in the tree T11, the nodes with degree 1 represent the endpoints of the morphological skeleton, and the endpoints are extended to the boundaries of the mask; Merge the extended part into the node information of tree T11 to generate a minimum spanning tree T12; Calculate the shortest paths between all pairs of nodes present in the tree T12, and determine the path with the most nodes as the longest shortest path, which corresponds to the longest skeleton in the morphological skeleton; The ordered coordinates in the longest skeleton are used as the control points of the B-spline curve, and the control points are fitted using cubic basis functions to generate a smooth and continuous representation; the B-spline curve is uniformly sampled at the pixel interval to generate a series of sampling points, and the first-order derivative of each sampling point is calculated to determine the line segments perpendicular to the sampling points. The parts of these line segments that fall within the mask range of the fibrous molecular cloud correspond to the outline of the fibrous molecular cloud.

6. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 1, characterized in that: The skeleton extraction based on graph theory is used to obtain the strength skeleton of the fibrous molecular cloud, which is specifically: All points in the fibrous molecular cloud space mask are taken as nodes, each point is connected to its adjacent points through edges, and weights are assigned according to formula 1 to create a weighted undirected graph G2; The minimum spanning tree T2 is obtained by using the GMST algorithm on the graph G2. The tree T2 contains all the points in the mask. The weight of the tree T2 is updated according to formula 2: Where WeightSK Gij WeightSK represents the weight of two adjacent coordinates in the fiber region of graph G2 in the position-position space. Tij Represents the update weight of two adjacent coordinates in tree T2; DistLB ij is the Euclidean distance between adjacent coordinates, I i and I j are the integrated intensities at coordinates i and j, respectively; Calculate the shortest path between each pair of nodes in tree T2, and select the path with the highest total weight among all the shortest paths to obtain the initial strength skeleton; The initial strength skeleton is refined to obtain the final strength skeleton.

7. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 1, characterized in that: The substructure decomposition of the fibrous molecular cloud based on graph theory is specifically as follows: The positions of molecular cloud clusters in the fibrous molecular cloud are taken as nodes of the graph, and the weights between any two adjacent molecular cloud clusters are calculated according to Formula 3. The weights are used to establish connections and construct a weighted undirected graph G3. Applying the GMST algorithm to the graph G3, we obtain the minimum spanning tree T31 that contains all the molecular cloud clusters that constitute the fibrous molecular cloud; the weight of the tree T31 is updated according to the following formula: In the formula, WeightST Gij WeightST represents the weights of two adjacent molecular cloud clusters i and j in graph G3. Tij Represents the updated weights of two adjacent molecular cloud clusters in tree T31; DistLB ij is the Euclidean distance between adjacent molecular cloud clusters in the spatial direction, DistV ij is the difference in speed channel, I k is the intensity at coordinate k in the position-position-velocity space along the line segment between the center coordinates of molecular cloud clusters i and j, and N represents the number of voxels in the line segment; Based on the tree T31, the decomposition of the fibrous molecular cloud is performed according to a recursive function.

8. A method for identifying and analyzing fibrous molecular clouds as claimed in claim 7, characterized in that: The decomposition of the fibrous molecular cloud is performed according to the recursive function, specifically: S1: Calculate the shortest path between each pair of nodes in the tree T31, and select the shortest path with the highest total weight among all the shortest paths as the longest shortest path; S2: Remove the edges on the longest shortest path in tree T31 and check the corresponding nodes; if the degree of a node becomes 0, remove it as well; S3: If there are still nodes left, use the remaining nodes and edges to generate subtree T3i. The edge weights are determined using Formula 3. S4: Replace tree T31 with subtree T3i and update the weight using formula 4; recursively perform operations S1-S3 until there are no nodes in tree T31, and the recursion terminates. The nodes on the different longest shortest paths obtained correspond to molecular cloud clusters in different sub-fibrous molecular clouds.

9. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables a computer to execute the fibrous molecular cloud identification and analysis method according to any one of claims 1 to 8.

10. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the fibrous molecular cloud identification and analysis method as described in any one of claims 1 to 8 is implemented.

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