CN111341392B - Multi-domain substance body data internal structure characteristic expression method - Google Patents
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Abstract
The invention discloses a multi-domain substance body data internal structure characteristic expression method, which is implemented according to the following steps: step 1, acquiring a volume data sub-interface, analyzing the interrelation between the volume data sub-interfaces, and constructing a directed skeleton tree; step 2, skeleton shape characteristic representation of the volume data; step 3, ridge-valley shape characteristic representation of the volume data; and 4, constructing a tree structure topological graph and carrying out vector representation on the tree structure topological graph to realize comprehensive and effective representation of three-dimensional space characteristics of the internal structure of the volume data. The method for expressing the internal structural characteristics of the multi-domain substance body data realizes the complete description of the shape characteristics of the interface of the body data.
Description
Technical Field
The invention belongs to the technical field of three-dimensional visualization, and relates to a multi-domain substance body data internal structure characteristic expression method.
Background
The internal structure feature expression of the multi-domain substance body data has important functions in the aspects of identification, understanding, retrieval and the like of the body data, and the research on the internal structure of the multi-domain substance body data only focuses on the identification and extraction of boundary surfaces and interface point sets of various materials of the multi-domain substance, but ignores the effective expression of bisection interfaces. Because of the variety among the materials of the volume data and the complexity of the internal structure of the volume data, if a plurality of interfaces among the materials are to be extracted and observed at the same time, the expression of the topological relation of the split interfaces is not separated; in addition, the internal feature analysis of the volume data is independent of the establishment of a topological structure, which is a significant defect of the current interface extraction method, so that the expression of the internal feature of the volume data by using topological relations is one of focuses of current researchers. However, the existing method is reviewed below, since the method for expressing the internal structure of the volume data based on the topological relation is rarely studied.
The research results S.S.Huang, H.Fu, L.Y.Wei of the teaching task group of the university of Qinghua Hu Shimin, et al, support substructure, support-reduced part-level structural representation [ J ]. IEEE Transactions on Visualization and Computer Graphics,2016,22 (8): 2024-2036. And the research results I.Alhashim, K.Xu, Y.Zhuang of the teaching task group of the university of Simmondsin Frazier, et al, development-driven 3d shape correspondence[J ]. ACM Transactions on Graphics,2015,34 (6): artefact No.236. Develop the topology around the interior of the object, propose the skeleton tree-based internal structure representation method and obtain certain results, but the method mainly expresses the support structure of the artificial object with certain rules, mainly solves the shape editing and operation problems of the artificial object, can not be directly applied to the topology expression of the internal structure of the body data, and the skeleton tree can only reflect the characteristics of the interface of the internal structure of the body data, and can not express the characteristics of the interface.
Based on the expression method of skeleton characteristics, the skeleton is taken as a special expression form of the shape, can intuitively reflect the topological connectivity of the model, and can effectively describe the internal shape characteristics of the sub-interfaces of the volume data. J.M.Reddy, G.M.Turkiyyah.Computation of 3D skeletons using a generalized Delaunay triangulation technique[J Computer-Aided Design,1995,27 (9): 677-694. The method for extracting three-dimensional skeleton of object by utilizing dual and triangulation of Voronoi diagram has the advantages of no need of voonizing for processing grid model based on Voronoi diagram skeleton extraction method, good topology expression, but high computational complexity. The method is characterized in that a continuous function is constructed, then the function value of each vertex of the model is calculated, the vertices with the same function value are clustered, finally, the framework structure diagram of the object is obtained by aggregating the vertices with the same class according to the clustering result, and the framework obtaining method based on topology and geometric analysis is from Y.Shinagawa, T.L.Kunii.Constructing a Reeb graph automatically from cross sections [ J ]. IEEE Computer Graphics and Applications,2002,11 (6): 44-51.
The ridge-valley characteristics can well characterize local convex-concave changes of the surface of an object, effectively describe local shape characteristics of a model curved surface, characterize characteristics of a sub-interface of volume data by using the ridge-valley characteristics, and can well display external convex-concave local shape characteristics of the interface; the existing ridge-valley feature extraction method is mainly used for realizing ridge-valley extraction based on curvature calculation and feature point construction ideas and mainly comprises a method based on surface fitting and a method based on principal component analysis. Pang Xufang, pang Mingyong, shouchunxia, point cloud model valley feature extraction and enhancement algorithm [ J ]. Automation journal 2010,36 (8): 1073-1083, implementing ridge valley feature extraction by multi-step approximation method, firstly calculating curvature of each point according to local least squares fitting surface polynomial of each point, and selecting curvature mark with larger absolute value as potential ridge valley feature point; then projecting the marked feature points onto the nearest potential feature line to obtain enhanced feature points; finally, the enhanced characteristic points are smoothed to obtain ridge valley points, and ridge valley lines are generated by selecting proper smooth points; and correcting and optimizing the ridge lines and the valley lines to obtain smooth ridge lines and valley lines. T.Judd, F.Durand, E.Adelson.Apparent ridges for line drawing [ J ]. ACM Transactions on Graphics,2007,26 (3): arc No.19. The ridge valley lines are extracted for shadow models using higher derivatives using principal component analysis (PCA: principal Components Analysis), which better extracts the ridge valley features of the model. The ridge-valley characteristics of the curved surface can well represent the convex-concave degree of the curved surface, the shape characteristics of the model can be well described, the existing ridge-valley extraction method is mostly based on a grid model, but in practical application, the method is easier to obtain based on a point set model, and the research of extracting the local characteristics of the curved surface based on the point set is less. Although the point set can be gridded and then the local feature extraction of the ridges and the valleys of the curved surface can be carried out, the calculation complexity is greatly increased, in addition, the interface for acquiring the volume data is a scattered point set, and the ridge and valley feature extraction method based on the grid method cannot be directly applied, so that further research is needed.
In summary, based on the characteristic information of the topological relation between the number of the materials of the volume data and the interfaces, based on the characteristic of the trend of the internal trend of the subinterfaces, based on the characteristic of the ridges and valleys, and based on the characteristic of the external convex-concave local characteristics of the subinterfaces, any one of the three can not fully and in detail express the structural characteristics of the volume data.
Disclosure of Invention
The invention aims to provide a multi-domain substance body data internal structure characteristic expression method, which realizes complete description of the shape characteristics of a body data interface.
The technical scheme adopted by the invention is that the method for expressing the internal structural characteristics of the multi-domain substance body data is implemented according to the following steps:
step 3, ridge-valley shape characteristic representation of the volume data;
and 4, constructing a tree structure topological graph and carrying out vector representation on the tree structure topological graph to realize comprehensive and effective representation of three-dimensional space characteristics of the internal structure of the volume data.
The present invention is also characterized in that,
in the step 1, the interrelationship among the sub-interfaces of the volume data is analyzed, and the construction of the directed skeleton tree is specifically as follows:
step 1.1, determining the number of sub-interfaces based on acquired volume data sub-interfaces, wherein the relation among all the sub-interfaces comprises inclusion, adjacency and separation;
step 1.2, mapping the inclusion relation between child interfaces into a directed skeleton tree, converting the inclusion relation into a parent-child relation, and using a solid line of a unidirectional arrow to indicate that if the child interface A contains the child interface B, the parent node B is a child node, and the parent-child relation is indicated as A-B;
mapping adjacent relations between sub-interfaces into directed skeleton trees to be converted into brother relations, wherein the brother relations are represented by dotted lines of double-headed arrows, if the sub-interface A is adjacent to the interface B, the A and the B are the brother relations, and the brother relations are represented as A≡ … - & gt B;
the separation relation between the sub-interfaces is not represented by edges;
step 1.3, constructing a directed skeleton tree, wherein the directed skeleton tree is expressed as G=<P,E,A P ,A E >Wherein P is a directed backboneA set of nodes in the tree representing sub-interfaces; e is an edge set in the directed skeleton tree and represents the topological relation between the sub-interfaces of the volume data; a is that P Is a node attribute feature and represents the number of representing sub-interfaces; a is that E Is an edge attribute feature, namely A E ＝{E ne ，E in ，E dis E, where E ne Is the adjacent relation of the sub-interface, and is represented by the representation method of the adjacent relation edge in the step 1.2; e (E) in The sub-interfaces contain relations, and the relation is represented by a representation method containing relation edges in the step 1.2; e (E) dis Representing the sub-interface separation relationship, no edge representation is performed.
The step 2 is specifically as follows:
step 2.1: analyzing the obtained skeleton characteristics of each sub-interface, and determining the number of skeleton endpoints, the number of skeleton bifurcation nodes and the total number of skeleton branches of each sub-interface;
step 2.2: and (3) according to the number of skeleton endpoints, the number of skeleton bifurcation nodes and the total number of skeleton branches determined in the step (2.1), carrying out skeleton shape feature vector representation of the volume data, wherein the skeleton shape feature vector of the volume data is as follows: t= [ T ] 1 T 2 T 3 ...T n ]，T i The skeleton characteristics representing the ith sub-interface, i=1.2.3..n, T i ＝[B F N]B represents the number of skeleton end points corresponding to the ith sub-interface, F represents the number of skeleton bifurcation nodes corresponding to the ith sub-interface, and N represents the total number of skeleton branches corresponding to the ith sub-interface.
The step 3 is specifically as follows:
step 3.1, all coordinates of the ridge point and the valley point of each sub-interface are extracted respectively, and eight vertex coordinates of the minimum direction bounding box are obtained, namely (X) min ,Y min ,Z min )、(X max ,Y min ,Z min )、(X min ,Y max ,Z min )、(X max ,Y max ,Z min )、(X min ,Y min ,Z max )、(X max ,Y min ,Z max )、(X min ,Y max ,Z max )、(X max ,Y max ,Z max ) Wherein X is min ，X max ，Y min ，Y max ，Z min ，Z max Respectively representing the minimum coordinate, the maximum coordinate, the minimum coordinate, the maximum coordinate and the minimum coordinate of the minimum bounding box in the X axis, the minimum coordinate and the maximum coordinate in the Y axis and the minimum coordinate and the maximum coordinate in the Z axis of the point set;
step 3.2, equally dividing the whole bounding box to obtain grids, numbering the grids, and respectively realizing three-dimensional rasterization of ridge points and valley points of the sub-interfaces;
step 3.3, determining a space density histogram according to the number of ridge points and valley points in each grid and the number of total ridge points and valley points of the sub-interfaces, wherein the density histogram is a one-dimensional discrete function, and the calculation is shown in a formula (2):
wherein f is the total number of ridge points or valley points of the sub-interface, N i The number of the ridge points or the valley points in the ith grid;
step 3.4, calculating the average distance in each grid by respectively calculating the distances from all the ridge points and the valley points in each grid after three-dimensional rasterization to the center of mass of the sub-interface point set, and respectively generating a distance characteristic histogram of the ridge points and the valley points;
step 3.5, representing ridge-valley shape feature vectors of the volume data: the ridge-valley shape feature vector of the volume data is: h= [ H ] 1r H 1v ；H 2r H 2v ；...；H nr H nv ]，H nr ＝[ρ r d r ]Ridge point density histogram and distance histogram features representing a sub-interface ρ r Representing the density of the ridge points corresponding to the sub-interfaces, d r Represents the distance of the ridge point corresponding to the sub-interface, H nv ＝[ρ v d v ]Density histogram and distance histogram features, ρ, representing a subinterface dip v Represents the density of the valley point corresponding to the sub-interface, d v Representation ofThe distance of the ridge point corresponding to the sub-interface.
The step 4 is specifically as follows:
step 4.1, determining characteristic expressions of directional skeleton trees, skeletons of sub-interfaces and ridges and valleys of the sub-interfaces in the volume data on the basis of the step 1-3, and constructing a tree topology graph of the volume data;
and 4.2, the feature vector of the whole tree structure topological graph is M= [ TrT H ], wherein Tr is the feature vector of the directed skeleton tree of the volume data, T is the skeleton shape feature vector of the volume data, and H is the ridge-valley vector of the volume data.
Feature vector tr= [ N ] of volumetric data directed skeletal tree P N Ene N Ein N Edis ]Wherein N is p Representing the number of sub-interfaces; n (N) Ene Representing the number, N, of sub-interface adjacency relations Ein Representing the number, N, of sub-interface inclusion relationships Edis The number of separation relations between sub-interfaces is shown.
Feature vector tr= [ N ] of volumetric data directed skeletal tree P N Ene N Ein N Edis ]The method is obtained by inquiring and reading the spatial incidence matrix of the directed skeleton tree, wherein the spatial incidence matrix of the directed skeleton tree is as follows:
wherein P is i And P j The i-th sub-interface and the j-th sub-interface are respectively represented, and when the sub-interface interfaces are containing relations, psi (i, j) = 2 and psi (i, j) = -2 are in one-to-one correspondence in the spatial relation matrix, and only one sub-interface is taken when a vector is acquired.
The beneficial effects of the invention are as follows:
the invention discloses a multi-domain substance body data internal structure feature expression method, which is characterized in that based on the acquired sub-interfaces of the body data, the number and the interrelationship of the sub-interfaces are analyzed to construct a directed skeleton tree, and then based on the acquired sub-interface skeleton shape features and the ridge-valley shape features thereof, a body data tree structure topological graph with three-dimensional features is constructed, so that the complete description of the body data interface shape features is realized, and three-dimensional shape feature information is provided for body data identification, understanding and retrieval.
Drawings
FIG. 1 is a schematic diagram showing the relationship between neutron interfaces in the method for expressing internal structural features of multi-domain material volume data according to the present invention
FIG. 2 is a diagram showing a directed skeleton tree and its matrix representation in the method for expressing internal structural features of multi-domain material body data according to the present invention
FIG. 3 is a schematic diagram of the neutron interface ridge valley point rasterization in the internal structural feature expression method of the multi-domain substance body data according to the present invention;
fig. 4 is a topological schematic diagram of a tree structure in the method for expressing internal structural features of multi-domain substance body data according to the present invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a multi-domain substance body data internal structure feature expression method, which is implemented according to the following steps:
step 1.1, determining the number of sub-interfaces based on acquired volume data sub-interfaces, wherein the relation among the sub-interfaces comprises inclusion, adjacent and separation, as shown in figure 1;
step 1.2, mapping the inclusion relation between child interfaces into a directed skeleton tree, converting the inclusion relation into a parent-child relation, and using a solid line of a unidirectional arrow to indicate that if the child interface A contains the child interface B, the parent node B is a child node, and the parent-child relation is indicated as A-B;
mapping the adjacent relation between the sub-interfaces into a brother relation in the directed skeleton tree, and using a dotted line of a bidirectional arrow to indicate that if the sub-interface A is adjacent to the interface B, the A and the B are the brother relation, and the brother relation is expressed as A≡ … - & gt B;
the separation relation between the sub-interfaces is not represented by edges;
step 1.3, constructing a directed skeleton tree, wherein the directed skeleton tree is expressed as G=<P,E,A P ,A E >Wherein P is a set of nodes in the directed skeletal tree representing sub-interfaces; e is an edge set in the directed skeleton tree and represents the topological relation between the sub-interfaces of the volume data; a is that P Is a node attribute feature and represents the number of representing sub-interfaces; a is that E Is an edge attribute feature, namely A E ＝{E ne ，E in ，E dis E, where E ne Is the adjacent relation of the sub-interface, and is represented by the representation method of the adjacent relation edge in the step 1.2; e (E) in The sub-interfaces contain relations, and the relation is represented by a representation method containing relation edges in the step 1.2; e (E) dis Representing the sub-interface separation relationship, and not carrying out edge representation;
step 2.1: analyzing the obtained skeleton characteristics of each sub-interface, and determining the number of skeleton endpoints, the number of skeleton bifurcation nodes and the total number of skeleton branches of each sub-interface;
step 2.2: and (3) according to the number of skeleton endpoints, the number of skeleton bifurcation nodes and the total number of skeleton branches determined in the step (2.1), carrying out skeleton shape feature vector representation of the volume data, wherein the skeleton shape feature vector of the volume data is as follows: t= [ T ] 1 T 2 T 3 ...T n ]，T i The skeleton characteristics representing the ith sub-interface, i=1.2.3..n, T i ＝[B F N]B represents the number of skeleton end points corresponding to the ith sub-interface, F represents the number of skeleton bifurcation nodes corresponding to the ith sub-interface, and N represents the total number of skeleton branches corresponding to the ith sub-interface;
step 3, ridge-valley shape characteristic representation of the volume data; the method comprises the following steps:
step 3.1, all coordinates of the ridge point and the valley point of each sub-interface are extracted respectively, and eight vertex coordinates of the minimum direction bounding box are obtained, namely (X) min ,Y min ,Z min )、(X max ,Y min ,Z min )、(X min ,Y max ,Z min )、(X max ,Y max ,Z min )、(X min ,Y min ,Z max )、(X max ,Y min ,Z max )、(X min ,Y max ,Z max )、(X max ,Y max ,Z max ) Wherein X is min ，X max ，Y min ，Y max ，Z min ，Z max Respectively representing the minimum coordinate, the maximum coordinate, the minimum coordinate, the maximum coordinate and the minimum coordinate of the minimum bounding box in the X axis, the minimum coordinate and the maximum coordinate in the Y axis and the minimum coordinate and the maximum coordinate in the Z axis of the point set;
step 3.2, equally dividing the whole bounding box to obtain grids, numbering the grids to respectively realize three-dimensional rasterization of ridge points and valley points of sub-interfaces, as shown in fig. 3;
step 3.3, determining a space density histogram according to the number of ridge points and valley points in each grid and the number of total ridge points and valley points of the sub-interfaces, wherein the density histogram is a one-dimensional discrete function, and the calculation is shown in a formula (2):
wherein f is the total number of ridge points or valley points of the sub-interface, N i The number of the ridge points or the valley points in the ith grid;
step 3.4, calculating the average distance in each grid by respectively calculating the distances from all the ridge points and the valley points in each grid after three-dimensional rasterization to the center of mass of the sub-interface point set, and respectively generating a distance characteristic histogram of the ridge points and the valley points;
and 3, step 3.5, representing ridge-valley shape feature vectors of the volume data: the ridge-valley shape feature vector of the volume data is: h= [ H ] 1r H 1v ；H 2r H 2v ；...；H nr H nv ]，H nr ＝[ρ r d r ]Ridge point density histogram and distance histogram features representing a sub-interface ρ r Representing the density of the ridge points corresponding to the sub-interfaces, d r Represents the distance of the ridge point corresponding to the sub-interface, H nv ＝[ρ v d v ]Density histogram and distance histogram features, ρ, representing a subinterface dip v Represents the density of the valley point corresponding to the sub-interface, d v Representing the distance of the ridge point corresponding to the sub-interface;
step 4, constructing a tree structure topological graph and carrying out vector representation on the tree structure topological graph to realize comprehensive and effective representation of three-dimensional space characteristics of the internal structure of the volume data, wherein the method specifically comprises the following steps:
step 4.1, determining characteristic expressions of directional skeleton trees, skeletons of sub-interfaces and ridges and valleys of the sub-interfaces in the volume data on the basis of the step 1-3, and constructing a tree topology diagram of the volume data, as shown in fig. 4;
step 4.2, the feature vector of the entire tree structure topology is m= [ Tr T H]Wherein Tr is a feature vector of the directed skeleton tree of the volume data, T is a skeleton shape feature vector of the volume data, H is a ridge valley vector of the volume data, and the feature vector Tr= [ N ] of the directed skeleton tree of the volume data P N Ene N Ein N Edis ]Wherein N is p Representing the number of sub-interfaces; n (N) Ene Representing the number, N, of sub-interface adjacency relations Ein Representing the number, N, of sub-interface inclusion relationships Edis Characteristic vector Tr= [ N ] of directed skeleton tree of volume data representing number of separation relations between sub-interfaces P N Ene N Ein N Edis ]The method is obtained by inquiring and reading the spatial incidence matrix of the directed skeleton tree, wherein the spatial incidence matrix of the directed skeleton tree is as follows:
wherein P is i And P j Respectively representing the ith sub-interface and the jth sub-interface, when the sub-interface interfaces are inclusion relations, psi (i, j) = 2 and psi (i, j) = -2 are in one-to-one correspondence in the spatial relation matrix, and only one sub-interface is taken when the vector is acquired, as shown in fig. 2.
The invention discloses a multi-domain substance body data internal structure feature expression method, which is characterized in that a directed skeleton tree is constructed based on the acquired sub-interfaces of the body data, the feature expression is carried out on the skeleton shape feature of the acquired sub-interfaces and the ridge-valley shape feature structure thereof, and finally, a body data tree structure topological graph with three-dimensional features is established, so that the complete description of the shape feature of the body data interfaces is realized.
Claims (3)
1. The method for expressing the internal structural characteristics of the multi-domain substance body data is characterized by comprising the following steps of:
step 1, acquiring a volume data sub-interface, analyzing the interrelation between the volume data sub-interfaces, and constructing a directed skeleton tree;
in the step 1, the interrelationship between the sub-interfaces of the volume data is analyzed, and the construction of the directed skeleton tree is specifically as follows:
step 1.1, determining the number of sub-interfaces based on acquired volume data sub-interfaces, wherein the relation among all the sub-interfaces comprises inclusion, adjacency and separation;
step 1.2, mapping the inclusion relation between child interfaces into a directed skeleton tree, converting the inclusion relation into a parent-child relation, and using a solid line of a unidirectional arrow to indicate that if the child interface A contains the child interface B, the parent node B is a child node, and the parent-child relation is indicated as A-B;
mapping the adjacent relation between the sub-interfaces into a brother relation in the directed skeleton tree, and using a dotted line of a bidirectional arrow to indicate that if the sub-interface A is adjacent to the interface B, the A and the B are the brother relation, and the brother relation is expressed as A≡ … - & gt B;
the separation relation between the sub-interfaces is not represented by edges;
step 1.3, constructing a directed skeleton tree, wherein the directed skeleton tree is expressed as G=<P,E,A P ,A E >Wherein P is a set of nodes in the directed skeletal tree representing sub-interfaces; e is an edge set in the directed skeleton tree and represents the topological relation between the sub-interfaces of the volume data; a is that P Is a node attribute feature and represents the number of representing sub-interfaces; a is that E Is an edge attribute feature, namely A E ＝{E ne ，E in ，E dis E, where E ne Is the adjacent relation of the sub-interface, and is represented by the representation method of the adjacent relation edge in the step 1.2; e (E) in The sub-interfaces contain relations, and the relation is represented by a representation method containing relation edges in the step 1.2; e (E) dis Representing the sub-interface separation relationship, and not carrying out edge representation;
step 2, skeleton shape characteristic representation of the volume data;
step 2.1: analyzing the obtained skeleton characteristics of each sub-interface, and determining the number of skeleton endpoints, the number of skeleton bifurcation nodes and the total number of skeleton branches of each sub-interface;
step 2.2: and (3) according to the number of skeleton endpoints, the number of skeleton bifurcation nodes and the total number of skeleton branches determined in the step (2.1), carrying out skeleton shape feature vector representation of the volume data, wherein the skeleton shape feature vector of the volume data is as follows: t= [ T ] 1 T 2 T 3 ...T n ]，T i The skeleton characteristics representing the ith sub-interface, i=1.2.3..n, T i ＝[B F N]B represents the number of skeleton end points corresponding to the ith sub-interface, F represents the number of skeleton bifurcation nodes corresponding to the ith sub-interface, and N represents the total number of skeleton branches corresponding to the ith sub-interface;
step 3, ridge-valley shape characteristic representation of the volume data;
step 3.1, all coordinates of the ridge point and the valley point of each sub-interface are extracted respectively, and eight vertex coordinates of the minimum direction bounding box are obtained, namely (X) min ,Y min ,Z min )、(X max ,Y min ,Z min )、(X min ,Y max ,Z min )、(X max ,Y max ,Z min )、(X min ,Y min ,Z max )、(X max ,Y min ,Z max )、(X min ,Y max ,Z max )、(X max ,Y max ,Z max ) Wherein X is min ，X max ，Y min ，Y max ，Z min ，Z max Respectively representing the minimum coordinate, the maximum coordinate, the minimum coordinate, the maximum coordinate and the minimum coordinate of the minimum bounding box in the X axis, the minimum coordinate and the maximum coordinate in the Y axis and the minimum coordinate and the maximum coordinate in the Z axis of the point set;
step 3.2, equally dividing the whole bounding box to obtain grids, numbering the grids, and respectively realizing three-dimensional rasterization of ridge points and valley points of the sub-interfaces;
step 3.3, determining a space density histogram according to the number of ridge points and valley points in each grid and the number of total ridge points and valley points of the sub-interfaces, wherein the density histogram is a one-dimensional discrete function, and the calculation is shown in a formula (2):
wherein f is the total number of ridge points or valley points of the sub-interface, N i The number of the ridge points or the valley points in the ith grid;
step 3.4, calculating the average distance in each grid by respectively calculating the distances from all the ridge points and the valley points in each grid after three-dimensional rasterization to the center of mass of the sub-interface point set, and respectively generating a distance characteristic histogram of the ridge points and the valley points;
step 3.5, representing ridge-valley shape feature vectors of the volume data: the ridge-valley shape feature vector of the volume data is: h= [ H ] 1r H 1v ；H 2r H 2v ；...；H nr H nv ]，H nr ＝[ρ r d r ]Ridge point density histogram and distance histogram features representing a sub-interface ρ r Representing the density of the ridge points corresponding to the sub-interfaces, d r Represents the distance of the ridge point corresponding to the sub-interface, H nv ＝[ρ v d v ]Density histogram and distance histogram features, ρ, representing a subinterface dip v Represents the density of the valley point corresponding to the sub-interface, d v Representing the distance of the ridge point corresponding to the sub-interface;
step 4, constructing a tree structure topological graph and carrying out vector representation on the tree structure topological graph to realize comprehensive and effective representation of three-dimensional space characteristics of the internal structure of the volume data;
step 4.1, determining characteristic expressions of directional skeleton trees, skeletons of sub-interfaces and ridges and valleys of the sub-interfaces in the volume data on the basis of the step 1-3, and constructing a tree topology graph of the volume data;
and 4.2, the feature vector of the whole tree structure topological graph is M= [ TrT H ], wherein Tr is the feature vector of the directed skeleton tree of the volume data, T is the skeleton shape feature vector of the volume data, and H is the ridge-valley vector of the volume data.
2. The method for expressing internal structural features of volumetric data of multi-domain substances according to claim 1, wherein the volumetric data has a feature vector tr= [ N ] of a directed skeletal tree P N Ene N Ein N Edis ]Wherein N is p Representing the number of sub-interfaces; n (N) Ene Representing the number, N, of sub-interface adjacency relations Ein Representing the number, N, of sub-interface inclusion relationships Edis The number of separation relations between sub-interfaces is shown.
3. The method for expressing internal structural features of volumetric data of multi-domain substances according to claim 2, wherein the volumetric data has a feature vector tr= [ N ] of a directed skeletal tree P N Ene N Ein N Edis ]The method is obtained by inquiring and reading the spatial incidence matrix of the directed skeleton tree, wherein the spatial incidence matrix of the directed skeleton tree is as follows:
wherein P is i And P j The i-th sub-interface and the j-th sub-interface are respectively represented, and when the sub-interface interfaces are containing relations, psi (i, j) = 2 and psi (i, j) = -2 are in one-to-one correspondence in the spatial relation matrix, and only one sub-interface is taken when a vector is acquired.
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| WO2001008263A2 (en) * | 1999-07-28 | 2001-02-01 | National University Of Singapore | Method and apparatus for generating atomic parts of graphic representation through skeletonization for interactive visualization applications |
| CN107330901A (en) * | 2017-06-29 | 2017-11-07 | 西安理工大学 | A kind of object component decomposition method based on skeleton |
| WO2019200683A1 (en) * | 2018-04-19 | 2019-10-24 | 浙江大学 | Sketch-based shape-preserving tree deformation animation method |
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