CN110853020B - Method for measuring retinal vascular network similarity based on topological structure and map - Google Patents

Method for measuring retinal vascular network similarity based on topological structure and map Download PDF

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CN110853020B
CN110853020B CN201911106308.3A CN201911106308A CN110853020B CN 110853020 B CN110853020 B CN 110853020B CN 201911106308 A CN201911106308 A CN 201911106308A CN 110853020 B CN110853020 B CN 110853020B
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李慧琦
吴冠男
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Abstract

The invention relates to a method for measuring the similarity of a retinal vascular network based on a topological structure and a map, and belongs to the technical field of target feature description and comparison. The method comprises the following steps: the method comprises the following steps: retinal vessel tracking; step two: calculating topological distance between the blood vessel trees, namely tree editing distance, matching the blood vessel trees according to the topological distance, and generating a matched blood vessel tree pair; step three: calculating the spectral distance between the vessel trees; sampling data of each pair of matched blood vessel trees in the second step, then performing spectrum mapping on the sampled data, and calculating the spectral distance of the pair of blood vessel trees according to the data after the spectrum mapping; step four: the weighting integrates the topological distance and the spectral distance. According to the method, vessel parameters of the vessel trees with similar topological and geometric shapes are compared through local vessel tree matching, so that more accurate measurement of the similarity of the vessel network is realized; by utilizing the clustering characteristic of the spectrum mapping, the parameter difference of the blood vessel tree is more obvious, and the precision of similarity measurement is effectively improved.

Description

Method for measuring retinal vascular network similarity based on topological structure and map
Technical Field
The invention relates to a method for measuring the similarity of a retinal vascular network based on a topological structure and a map, and belongs to the technical field of target feature description and comparison.
Background
The retinal vascular network is the only blood circulation system in the human body that can be observed by non-invasive methods and can provide a lot of meaningful medical research information. Morphological changes of retinal blood vessels are associated with a number of major diseases, such as hypertension, diabetes, etc. The correlation of the disease and the blood vessel shape and the parameters can be analyzed by observing the change of the blood vessel shape and the parameters of the retina of the same patient; the physician can be assisted in diagnosing whether the disease is ill and the degree of the disease by comparing the difference of the retinal vascular morphology and parameters of different patients. Therefore, it is important to compare the similarity of retinal vascular network morphology and parameters. However, due to the complexity and individual variability of retinal vascularity, there remains a challenge in objectively and effectively comparing retinal vascular networks.
The existing retinal vessel morphology similarity measurement method is mainly based on the topological structure of a vessel network, and does not compare vessel parameters. On the other hand, for the research on retinal vascular parameters, a method of averaging related parameters is mostly adopted, the topological structure of blood vessels and the local difference of a blood vessel network are not considered, and the averaging method reduces the difference of the vascular parameters to a certain extent, so that the comparison accuracy is poor.
Disclosure of Invention
The invention aims to provide a method for measuring the similarity of a retinal vascular network based on a topological structure and a map, aiming at the technical defects of poor accuracy, insufficient information quantity and the like of the conventional method for measuring the similarity of the retinal vascular network.
The method for measuring the similarity of the retinal vascular network comprises the following steps:
the method comprises the following steps: the retinal blood vessel tracking method specifically comprises the following sub-steps:
step 1.1: respectively determining the center and the radius of the optic disc of each of the two color fundus images subjected to similarity comparison;
wherein, for two color fundus images for similarity comparison, the first fundus image is called as image a, and the second fundus image is called as image b;
step 1.2: determining the tracking starting position of each blood vessel tree at k times of the radius of the optic disc from the center of the optic disc; wherein the value range of k is 1 to 2;
step 1.3: starting from the initial position, carrying out blood vessel tracking, determining the topological structure of the blood vessel tree and the boundary points of the blood vessel, and measuring relevant parameters of the blood vessel according to tracking data;
the vessel tracking is based on vessel segmentation, semi-ellipse dynamic search and feature point detection;
step two: calculating topological distance between the blood vessel trees, namely tree editing distance, matching the blood vessel trees according to the topological distance, and generating a matched blood vessel tree pair, which specifically comprises the following substeps:
step 2.1: for two fundus images for similarity comparison, an image a and an image b, numbering blood vessel trees in the two images respectively, describing each blood vessel section as a node for each blood vessel tree, and connecting the nodes by edges according to the connection relationship among the blood vessel sections to form a tree-shaped data structure;
step 2.2: calculating a tree edit distance d for each vessel tree in graph a and each vessel tree in graph btop(ai,bj)；
Wherein, aiRepresenting the ith vessel tree in a, bjRepresents the jth vessel tree in diagram b; the tree editing distance has three editing operations, namely inserting nodes, deleting nodes and changing node labels; each operation needs to be assigned a cost, and the cost for the editing operation according to the direction and the length of the blood vessel section is assigned as shown in the formula (1):
Figure BDA0002271410130000031
wherein R represents the level of the vessel segment, L represents the length of the vessel segment, L1 and L2 represent the length of the longer and shorter vessel segment, respectively, of the two vessel segments, and θ represents the angle of the smaller included angle between the two vessel segments;
step 2.3: matching the vessel trees of the two fundus images according to the tree editing distance; respectively matching different blood vessel trees which are nearest to the blood vessel trees in the other fundus picture with a smaller number of blood vessel trees;
so far, through the steps 2.1 to 2.3, a matched blood vessel tree pair is generated;
step three: calculating the spectral distance between the vessel trees; sampling data of each pair of matched blood vessel trees in the second step, then performing spectrum mapping on the sampled data, and calculating the spectral distance of the pair of blood vessel trees according to the data after the spectrum mapping; the method specifically comprises the following substeps:
step 3.1: sampling data points; for the pair of vessel trees matched in the second step, it is marked as aiAnd bjRespectively sampling the tracking data points, and setting a default value of a sampling interval as t, wherein t isThe value range is 2 to 5;
step 3.2: extracting a feature vector; for each sampling point, extracting the blood vessel related parameters at the sampling point as the feature vector x of the pointk＝(y1,y2…yn)；
Wherein x iskIs the feature vector at the kth sampling point, ynA certain blood vessel parameter at the sampling point; thus for the vessel tree aiExtracting N feature vectors
Figure BDA0002271410130000032
For the vessel tree bjExtracting M feature vectors
Figure BDA0002271410130000033
Wherein N and M are respectively a vessel tree ai，bjThe number of the sampling points of (a),
Figure BDA0002271410130000034
and
Figure BDA0002271410130000035
respectively a vessel tree aiAnd bjThe feature vector extracted at the kth sampling point of (1);
step 3.3: constructing a combined normalized Laplace matrix, and specifically connecting feature vectors extracted from two vessel trees to form a combined feature vector X ═ X (X)i，Xj) Reconstructing the joint adjacency matrix W (W)nm)(N+M)×(N+M)And calculates its degree matrix D (D)nm)(N+M)×(N+M)Further calculating a combined Laplace matrix L and a normalized combined Laplace matrix;
wherein the joint adjacency matrix W (W)nm)(N+M)×(N+M)Is a matrix of dimensions (N + M) × (N + M);
wherein the value w of the n-th row and the m-th columnnmThe distance between the nth characteristic vector and the mth characteristic vector in the combined characteristic vector X is obtained;
wnmmeter (2)The calculation formula is shown as formula (2):
Figure BDA0002271410130000041
where β controls the size of the Gaussian function window, xn、xmRespectively, are combined eigenvectors X ═ Xi，Xj) Is the nth and mth feature vectors, | is the vector l2A norm;
degree matrix D (D) of joint adjacency matrixnm)(N+M)×(N+M)The calculation formula (2) is shown as formula (3):
Figure BDA0002271410130000042
the joint Laplace matrix L is calculated by L ═ D-W, and the joint Laplace matrix L is normalized*By passing
Figure BDA0002271410130000043
Calculating;
step 3.4: performing spectrum mapping on the sampled data; performing eigen decomposition on the normalized joint Laplace matrix, i.e. solving for L*v is lambda v, and the feature vector corresponding to the minimum non-zero feature value is selected as the spectrum mapping vector of the data;
wherein λ is a matrix L*V is a eigenvector corresponding to λ; matrix L*With a total of N + M characteristic values, i.e. 0 ═ λ0<λ1<λ2<…<λN+MTheir corresponding feature vectors are respectively v0,v1,v2,…vN+M(ii) a Selecting the eigenvector corresponding to the smallest non-zero eigenvalue, i.e. lambda1Corresponding feature vector v1＝(s1,s2,…sN,sN+1,sN+2,…sN+M)ΤA spectral mapping vector as data;
step 3.5: calculating the spectral distance between two vessel trees, i.e. the coordinates after spectral mapping, i.e. v1＝(s1,s2,…sN,sN+1,sN+2,…sN+M)ΤIs mapped to [0,1 ]]Interval, then [0,1 ]]The interval is equally divided into R small intervals, wherein R ranges from 5 to 20, and v is calculated respectively1The proportion of the middle and front N values and the rear M values in each interval, namely calculating a data distribution histogram,
Figure BDA0002271410130000051
and
Figure BDA0002271410130000052
wherein h isiAnd hjDistribution histograms for the first N values and the last M values respectively,
Figure BDA0002271410130000053
and
Figure BDA0002271410130000054
the number of the first N values and the number of the second M values falling on the kth interval respectively account for the proportion; finally calculating the spectral distance d of the two vessel treesspec(ai,bj)＝‖hi-hjII is a vector of2A norm;
step four: weighting and integrating the topological distance and the spectral distance; the method specifically comprises the following substeps:
step 4.1: for a pair of matched blood vessel trees a in the two fundus images a and biAnd bjThe calculation formula of the similarity d between them is shown in formula (4):
d＝λdtop(ai,bj)+(1-λ)dspec(ai,bj) (4)
wherein, λ is the weight of topological distance of two vascular trees, which is used to balance the influence of topological distance and spectral distance; calculating the similarity of each pair of matched vessel trees according to the formula (4);
step 4.2: calculating the similarity sim of the whole blood vessel network, as shown in formula (5):
Figure BDA0002271410130000055
wherein d iskFor similarity between matching kth pair of vessel trees, αkFor their respective weights, αkCalculating the average data point number according to the pair of the blood vessel trees;
wherein the weight αkThe calculation process of (2) is as follows:
first, the average number of data points μ of all matched pairs of vessel trees is calculated1,μ2,…μN；
Wherein, mukThe average value of the data points of the kth pair of two matched blood vessel trees is obtained;
then find all μkMaximum value of (1) is μt＝max(μ1,μ2,…μN)；
Third, αkIs calculated as shown in equation (6):
Figure BDA0002271410130000061
from the first step to the fourth step, the method for measuring the similarity of the retinal vascular network based on the topological structure and the map is completed.
Advantageous effects
Compared with the existing method for measuring the similarity of the retinal vascular network, the method for measuring the similarity of the retinal vascular network based on the topological structure and the map has the following beneficial effects:
1. the invention provides a method for measuring the similarity of retinal fundus vascular networks based on a topological structure and a map, which can effectively compare the difference between the topological structure of the vascular network and the vascular parameters, thereby providing help for the work of clinical diagnosis, observation of the development of related diseases, exploration of the relationship between the vascular parameters and the related diseases and the like;
2. the method of the invention compares the vessel parameters of the vessel trees with similar topological and geometric shapes through local vessel tree matching, thus realizing more accurate measurement of the similarity of the vessel network;
3. the method of the invention utilizes the clustering characteristic of the spectrum mapping to make the parameter difference of the blood vessel tree more obvious and effectively improve the precision of similarity measurement.
Drawings
Fig. 1 is a schematic flow chart of a retinal vascular network similarity measurement method and an embodiment based on a topological structure and a map according to the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
Example 1
Fig. 1 is a flowchart of a method for measuring similarity of retinal vascular networks according to an embodiment of the present invention, which specifically includes the following steps:
step A: retinal vessel tracking; selecting two color fundus images provided by Beijing Anzhen hospital as samples to be compared, respectively named as image a and image b, and comparing the similarity of the two vascular networks; firstly, respectively tracking retinal blood vessels and measuring related parameters, and specifically comprises the following substeps:
step A.1: respectively determining the center and the radius of an optic disc of each color fundus image a and b subjected to similarity comparison;
step A.2: determining a tracking start position of each vessel tree at k times of the optic disc radius from the optic disc center, wherein k is set to 1.5;
step A.3: starting from the initial position, carrying out blood vessel tracking, determining the topological structure of the blood vessel tree and the boundary points of the blood vessel, and measuring relevant parameters of the blood vessel according to tracking data; it should be noted that any method that is effective for vessel tracking is suitable for use with the present invention;
and B: calculating topological distance between the vessel trees, namely tree editing distance, and performing vessel tree matching according to the topological distance, specifically comprising the following substeps:
step B.1: for two fundus images for similarity comparison, images a and b, the blood vessel trees in the two images are numbered respectively; for each blood vessel tree, describing each blood vessel segment as a node, and connecting the nodes by edges according to the connection relation among the blood vessel segments to form a tree-shaped data structure; in order to reduce the influence of the error of vessel tracking, only the first three-level vessel segment of each vessel tree is taken;
step B.2: calculating a tree edit distance d for each vessel tree in graph a and each vessel tree in graph btop(ai,bj) Wherein a isiRepresenting the ith vessel tree in a, bjRepresents the jth vessel tree in diagram b;
the tree edit distance is a method for measuring the similarity of the topological structures of the tree data, and is widely applied to the field of bioinformatics; the tree editing distance is that one tree is converted into another tree through three editing operations, namely node insertion, node deletion and node tag change; assigning a certain cost for each editing operation, wherein the sum of the costs of the operations required by the final conversion is the tree editing distance of the two trees;
the cost for the editing operation is assigned according to the direction and length of each blood vessel segment in the blood vessel tree, and is shown in the formula (7):
Figure BDA0002271410130000081
wherein, R represents the grade of the blood vessel segment, wherein R is respectively set to 1, 0.8 and 0.6 for the primary blood vessel, the secondary blood vessel and the tertiary blood vessel; l represents the length of the blood vessel section, L1 and L2 represent the length of the longer and shorter blood vessel section of the two blood vessel sections respectively, theta represents the smaller included angle between the directions of the two blood vessel sections, and the direction of the blood vessel section is from one end close to the optic disc to one end far away from the optic disc;
step B.3: matching the vessel trees of the two fundus images according to the tree editing distance; respectively matching different blood vessel trees which are nearest to the blood vessel trees in the other fundus picture with a smaller number of blood vessel trees; assuming that the number of vessel trees in graph a is smaller than that in graph b, each vessel tree in graph a matches a vessel tree in graph b, which is the smallest distance from the vessel tree in graph b, and is different from each other;
for example, if the vessel tree 1 in fig. a is closest to the vessel tree 2 in fig. b, then the two vessel trees match; if a plurality of vessel trees are matched with the same vessel tree, the matching with the minimum distance is established; for example, if both the vessel tree 1 and the vessel tree 2 in fig. a match the vessel tree 2 in fig. b, the distances between the two are compared with the vessel tree 2 in fig. b, and if d is the casetop(a1,b2)<dtop(a2,b2) Then the vessel tree 1 in fig. a matches the vessel tree 2 in fig. b; the vessel tree 2 in the graph a continues to search for a vessel tree with a second smallest distance in the graph b for matching until a different vessel tree is matched for each vessel tree in the graph a;
so far, through the steps B.1 to B.3, the blood vessel tree matching is realized according to the similarity of the blood vessel topological structures, and the local comparison of the retina blood vessel network is realized through the matching of the blood vessel tree; compared with the existing method for measuring the similarity of the retinal vascular network by a global comparison method, the method can more accurately position the positions where the differences are generated, so that the similarity of the retinal vascular network can be more accurately measured;
and C: calculating the spectral distance between the vessel trees; sampling data of the two matched blood vessel trees, then performing spectrum mapping on the sampled data, and calculating the spectral distance of the two blood vessel trees according to the data after the spectrum mapping; the method specifically comprises the following substeps:
step C.1: sampling data points; because the tracking data has certain errors, the blood vessel tree tracking data is sampled when the blood vessel parameters are analyzed, so that the influence of the errors is reduced; for two matched vessel trees aiAnd bjRespectively sampling the tracking data points, and setting a sampling interval t to be 3;
step C.2: extracting a feature vector; for each sampling point, extracting the blood vessel related parameters at the point as the feature vector x of the pointk＝(y1,y2…yn) Wherein x iskIs the feature vector at the kth sampling point, ynIs a certain blood vessel parameter at the point. Thus for the vessel tree aiExtracting N feature vectors
Figure BDA0002271410130000091
For the vessel tree bjExtracting M feature vectors
Figure BDA0002271410130000092
Wherein N and M are respectively a vessel tree ai，bjThe number of the sampling points of (a),
Figure BDA0002271410130000093
and
Figure BDA0002271410130000094
respectively a vessel tree aiAnd bjThe extracted feature vector at the kth sampling point of (a);
step C.3: constructing a combined normalized Laplace matrix; connecting the feature vectors extracted from two vascular trees to form a combined feature vector X ═ Xi，Xj) (ii) a Constructing a Joint Adjacency matrix W (W)nm)(N+M)×(N+M)(ii) a The joint adjacency matrix is a matrix of (N + M) × (N + M) dimensions, in which the value w of the nth row and mth columnnmThe distance between the nth characteristic vector and the mth characteristic vector in the joint characteristic vector is obtained; w is anmThe calculation formula (2) is shown as the formula (8):
Figure BDA0002271410130000101
wherein β controls the size of the gaussian window, with the value set to 2; x is the number ofn、xmRespectively, are combined eigenvectors X ═ Xi，Xj) Is the nth and mth feature vectors, | is the vector l2A norm;
calculating a degree matrix D (D) thereof according to the joint adjacency matrixnm)(N+M)×(N+M)The calculation formula of the degree matrix is shown as formula (9):
Figure BDA0002271410130000102
the joint laplacian matrix is L ═ D-W, and the normalized joint laplacian matrix is
Figure BDA0002271410130000103
Figure BDA0002271410130000104
Step C.4: performing spectrum mapping on the sampled data; performing characteristic decomposition on the normalized combined Laplace matrix, and solving L*v ═ λ v, where λ is the matrix L*V is a eigenvector corresponding to λ; matrix L*With a total of N + M characteristic values, i.e. 0 ═ λ0<λ1<λ2<…<λN+MTheir corresponding feature vectors are respectively v0,v1,v2,…vN+MEach feature vector is N + M dimensions; selecting the eigenvector corresponding to the smallest non-zero eigenvalue, i.e. lambda1Corresponding feature vector v1＝(s1,S2,…SN,SN+1,sN+2,…sN+M)ΤAs a coordinate after data spectrum mapping, where skNamely the coordinates of the kth feature vector in the combined feature vector X in the spectrum space;
step C.5: calculating the spectral distance between two vessel trees; spectral mapping vector v1The first N values in (a) correspond to the vessel tree aiMiddle sampling point, the last M values correspond to the vessel tree bjSampling points in (1); coordinates after mapping the spectrum, i.e. v1＝(s1,s2,…sN,sN+1,sN+2,…sN+M)ΤIs mapped to [0,1 ]]Interval, then [0,1 ]]The interval is equally divided into R small intervals, R is set to be 10, and coordinate falls of sampling points of the two blood vessel trees after spectral mapping are respectively calculatedThe proportion in each interval, i.e. the calculated data distribution histogram,
Figure BDA0002271410130000111
Figure BDA0002271410130000112
and
Figure BDA0002271410130000113
hiand hjRespectively a vessel tree aiAnd the vascular tree bjA corresponding histogram of the distribution of the data points,
Figure BDA0002271410130000114
and
Figure BDA0002271410130000115
respectively a vessel tree aiAnd the vascular tree bjThe proportion of the number of points falling on the kth interval in the corresponding data points; finally calculating the spectral distance d of the two vessel treesspec(ai,bj)＝‖hi-hjII, wherein II is a vector of l2A norm;
so far, through the steps C.1 to C.5, relevant parameters of blood vessels are extracted, and the clustering characteristic of spectral mapping is utilized to make the difference between the relevant parameters of the blood vessels more obvious; the existing method for measuring the similarity of the retinal vascular network focuses more on the structural information of the vascular network, and the parameters of the blood vessels are not compared; on one hand, the method compares the parameters of the blood vessels, and on the other hand, the spectrum mapping is utilized to ensure that the difference of the related parameters of the blood vessels is more obvious, the distance between similar blood vessel networks is reduced, and the distance between dissimilar blood vessel networks is increased, thereby improving the accuracy of measuring the similarity of the blood vessel networks;
step D: weighting and integrating the topological distance and the spectral distance; the method specifically comprises the following substeps:
step D.1: for a pair of matched blood vessel trees a in the two fundus images a and biAnd bjSimilarity between themd is as shown in formula (10):
d＝λdtop(ai,bj)+(1-λ)dspec(ai,bj) (10)
wherein λ is the weight of the topological distance between two vascular trees, and the value is set to 0.4; calculating the similarity of each pair of matched vessel trees according to the formula (10);
step D.2: calculating the similarity sim of the whole blood vessel network, as shown in formula (11):
Figure BDA0002271410130000116
wherein d iskFor similarity between matching kth pair of vessel trees, αkFor their respective weights, αkAccording to the average data point number calculation of the pair of blood vessel trees, firstly, the average data point number mu of all matched blood vessel tree pairs is calculated1,μ2,…μNWherein, mukThe average value of the data points of the kth pair of two matched blood vessel trees is obtained; wherein the maximum value is mut＝max(μ1,μ2,…μN) Then alpha iskIs calculated as shown in equation (12):
Figure BDA0002271410130000121
thus, the whole process of the method for measuring the similarity of the retinal vascular network is completed; experiments prove that the method can effectively measure the similarity of retinal vascular networks of different fundus images and accurately compare the difference of vascular parameters, thereby assisting doctors in clinical diagnosis and clinical scientific research.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. The method for measuring the similarity of the retinal vascular network based on the topological structure and the map is characterized in that: the method comprises the following steps:
the method comprises the following steps: the retinal blood vessel tracking method specifically comprises the following sub-steps:
step 1.1: respectively determining the center and the radius of the optic disc of each of the two color fundus images subjected to similarity comparison;
wherein, for two color fundus images for similarity comparison, the first fundus image is called as image a, and the second fundus image is called as image b;
step 1.2: determining the tracking starting position of each blood vessel tree at r times of the radius of the optic disc from the center of the optic disc;
step 1.3: tracking blood vessels from an initial position, determining a topological structure of a blood vessel tree and a blood vessel boundary point, and measuring relevant parameters of the blood vessels according to tracking data;
step two: calculating topological distance between the blood vessel trees, namely tree editing distance, matching the blood vessel trees according to the topological distance, and generating a matched blood vessel tree pair, which specifically comprises the following substeps:
step 2.1: for two fundus images for similarity comparison, an image a and an image b, numbering blood vessel trees in the two images respectively, describing each blood vessel section as a node for each blood vessel tree, and connecting the nodes by edges according to the connection relationship among the blood vessel sections to form a tree-shaped data structure;
step 2.2: calculating a tree edit distance d for each vessel tree in graph a and each vessel tree in graph btop(as,bt)；
Wherein, asRepresents the s-th vessel tree in a, btRepresents the t-th vessel tree in diagram b; the tree editing distance has three editing operations, namely inserting nodes, deleting nodes and changing node labels; each operation needs to be assigned a cost, and the cost for the editing operation according to the direction and the length of the blood vessel section is assigned as shown in the formula (1):
Figure FDA0003213598180000021
wherein R represents the level of the vessel segment, L represents the length of the vessel segment, L1 and L2 represent the length of the longer and shorter vessel segment, respectively, of the two vessel segments, and θ represents the angle of the smaller included angle between the two vessel segments;
step 2.3: matching the vessel trees of the two fundus images according to the tree editing distance; respectively matching different blood vessel trees which are nearest to the blood vessel trees in the other fundus picture with a smaller number of blood vessel trees;
so far, through the steps 2.1 to 2.3, a matched blood vessel tree pair is generated;
step three: calculating the spectral distance between the vessel trees; sampling data of each pair of matched blood vessel trees in the second step, then performing spectrum mapping on the sampled data, and calculating the spectral distance of the pair of blood vessel trees according to the data after the spectrum mapping; the method specifically comprises the following substeps:
step 3.1: sampling data points; for the pair of vessel trees matched in the second step, it is marked as aiAnd bjRespectively sampling the tracking data points, and setting a default value of a sampling interval as t;
step 3.2: extracting a feature vector; for each sampling point, extracting the blood vessel related parameters at the sampling point as the feature vector x of the sampling pointu＝(y1,y2…yn)；
Wherein x isuIs the feature vector at the u-th sampling point, ynA certain blood vessel parameter at the sampling point; thus for the vessel tree aiExtracting N feature vectors
Figure FDA0003213598180000022
For the vessel tree bjExtracting M feature vectors
Figure FDA0003213598180000023
Wherein N and M are respectively a vessel tree ai，bjThe number of the sampling points of (a),
Figure FDA0003213598180000024
and
Figure FDA0003213598180000025
respectively a vessel tree aiAnd bjThe feature vector extracted at the u-th sampling point;
step 3.3: constructing a combined normalized Laplace matrix, and specifically connecting feature vectors extracted from two vessel trees to form a combined feature vector X ═ X (X)i，Xj) Then, a combined adjacent matrix W is constructed, a degree matrix D of the combined adjacent matrix W is calculated, and the combined Laplace matrix is further calculated to be L and a normalized combined Laplace matrix;
wherein the joint adjacency matrix W is a matrix of (N + M) × (N + M) dimensions;
wherein, the value of the n-th row and the m-th column of the joint adjacency matrix W is marked as WnmThe distance between the nth characteristic vector and the mth characteristic vector in the combined characteristic vector X is obtained;
wnmthe calculation formula (2) is shown as the following formula:
Figure FDA0003213598180000031
where β controls the size of the Gaussian function window, xn、xmRespectively, are combined eigenvectors X ═ Xi，Xj) Is the nth and mth feature vectors, | is the vector l2A norm;
the degree matrix D of the joint adjacency matrix is calculated by the formula (3):
Figure FDA0003213598180000032
the joint Laplace matrix L is calculated by L ═ D-W, and joint Laplace is normalizedThe Laplace matrix L*By passing
Figure FDA0003213598180000033
Calculating;
step 3.4: performing spectrum mapping on the sampled data; performing eigen decomposition on the normalized joint Laplace matrix, i.e. solving for L*v is lambda v, and the feature vector corresponding to the minimum non-zero feature value is selected as the spectrum mapping vector of the data;
wherein λ is a matrix L*V is a eigenvector corresponding to λ; matrix L*With a total of N + M characteristic values, i.e. 0 ═ λ0<λ1<λ2<…<λN+MTheir corresponding feature vectors are respectively v0,v1,v2,…vN+M(ii) a Selecting the eigenvector corresponding to the smallest non-zero eigenvalue, i.e. lambda1Corresponding feature vector v1＝(s1,s2,…sN,sN+1,sN+2,…sN+M)ΤA spectral mapping vector as data;
step 3.5: calculating the spectral distance between two vessel trees, i.e. the coordinates after spectral mapping, i.e. v1＝(s1,s2,…sN,sN+1,sN+2,…sN+M)ΤIs mapped to [0,1 ]]Interval, then [0,1 ]]The interval is equally divided into R small intervals, the proportions of the spectrum mapping coordinates of the front N points and the rear M points in each interval are respectively calculated, namely a data distribution histogram is calculated,
Figure FDA0003213598180000041
and
Figure FDA0003213598180000042
wherein h isiAnd hjDistribution histograms for the first N points and the last M points respectively,
Figure FDA0003213598180000043
and
Figure FDA0003213598180000044
the number of points falling on the s-th interval in the front N points and the rear M points respectively accounts for the proportion; finally calculating the spectral distance d of the two vessel treesspec(ai,bj)＝‖hi-hjII, wherein II is a vector of l2A norm;
step four: weighting and integrating the topological distance and the spectral distance; the method specifically comprises the following substeps:
step 4.1: for a pair of matched blood vessel trees a in the two fundus images a and biAnd bjAnd the similarity d between them is shown as formula (4):
d＝λdtop(ai,bj)+(1-λ)dspec(ai,bj) (4)
wherein, λ is the weight of topological distance of two vascular trees, which is used to balance the influence of topological distance and spectral distance; calculating the similarity of each pair of matched vessel trees according to the formula (4);
step 4.2: calculating the similarity sim of the whole blood vessel network, as shown in formula (5):
Figure FDA0003213598180000045
wherein d iskFor similarity between matching kth pair of vessel trees, αkFor their respective weights, αkCalculating the average data point number according to the pair of the blood vessel trees;
wherein the weight αkThe calculation process of (2) is as follows:
first, the average number of data points μ of all matched pairs of vessel trees is calculated1,μ2,…μk,…μN；
Wherein, mukThe average value of the data points of the kth pair of two matched blood vessel trees is obtained;
then, the maximum value of the number of data points of the k-th pair of two matched blood vessel trees is calculated to be mut＝max(μ1,μ2,…μN)；
Third, αkIs calculated as shown in equation (6):
Figure FDA0003213598180000051
from the first step to the fourth step, the method for measuring the similarity of the retinal vascular network based on the topological structure and the map is completed.
2. A method for measuring the similarity of retinal vascular networks based on topological structures and maps is characterized in that: in step 1.2, the value range of r is 1 to 2.
3. A method for measuring the similarity of retinal vascular networks based on topological structures and maps is characterized in that: in step 1.3, vessel tracking is based on vessel segmentation, semi-ellipse dynamic search and feature point detection.
4. A method for measuring the similarity of retinal vascular networks based on topological structures and maps is characterized in that: in step 3.1, the value range of t is 2 to 5.
5. A method for measuring the similarity of retinal vascular networks based on topological structures and maps is characterized in that: step 3.5R ranges from 5 to 20.
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