CN112381758B - Method for calculating similarity of blood vessel tree - Google Patents
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Abstract
The invention relates to a method for calculating similarity of a blood vessel tree, which comprises the following steps: s1, constructing a multi-branch tree model of a blood vessel; s2, calculating the branch distance of the multi-branch tree model; s3, calculating the subtree distance of the multi-tree model; s4, calculating the distance of the multi-tree model according to the branch distance and the subtree distance; s5, calculating the blood vessel similarity according to the distance of the multi-tree model; the method realizes the calculation method of the three-dimensional vessel tree similarity comprehensively considering topology and geometry, comprehensively considers each characteristic in geometric comparison, and firstly proposes the calculation of the vessel branch shape difference by utilizing the combined curve of the skeleton line and the diameter.
Description
Technical Field
The invention belongs to the technical field of biomedical imaging, and particularly relates to a method for calculating similarity of a blood vessel tree.
Background
In the biomedical imaging field, with the development of digital medical treatment and the mass use of three-dimensional scanning devices, medical workers and researchers can conveniently obtain model data of three-dimensional blood vessels. These three-dimensional blood vessels contain blood vessel tissue of various parts such as neurons, lung airways, abdominal arteries, coronary arteries and the like, and the shape of these blood vessel structures is mostly described by mathematical tree structures. The computation of the similarity of the blood vessel trees is the basis of the problems of blood vessel correspondence, identification, classification and the like, and doctors often compare whether two groups of blood vessel trees are similar or not to find the lesion part. Perceptually similarity is a relatively fuzzy concept, and the degree of similarity of blood vessels is often judged differently according to different experiences of different individuals, so that it is necessary to make uniform rules and calculate the similarity of the blood vessel tree by means of a computer.
The comparison of the shapes of the objects needs to comprehensively consider the geometry and the topology, and the three-dimensional vessel tree has the characteristics of topoisomerase, geometric large deformation and the like, so that the problems of correspondence, identification, classification and the like of the three-dimensional vessel tree are correspondingly more complex. The dataset of a three-dimensional vascular tree typically contains vascular tissue at only a certain location. Compared with the data set of a general three-dimensional tree structure, the data set of the same blood vessel organization is usually composed of branches which are similar in topology and have relatively large geometric differences, and branches between two data are generally in one-to-one matching relationship, or a situation of branch missing exists, and a situation of one-to-many is rarely generated. Whether the branches of the blood vessel tree are matched depends on the comparison of branch differences, and the accuracy of the matching results of the branches influences the calculation of the similarity of the blood vessel tree, so that it is important to define a method capable of calculating the branch differences more comprehensively. The geometry of the branches can be represented in the form of a discrete curve, a continuous curve, etc., the calculation using the discrete form is relatively simple, and the difference of the branches calculated using the continuous form is more closely related to the real difference.
There are three types of methods for comparing the differences in the shape of the vascular tree: firstly, analyzing the shape of a blood vessel tree by means of extracting image features, wherein most of the methods neglect the topological structure of the blood vessel tree, mainly extracting geometrical information in a blood vessel tree model or image which is interested by researchers, and then quantitatively analyzing the geometrical information; secondly, the topological information is singly used for comparing the vascular tree structure, the geometrical information of the vascular tree is basically ignored or simplified by the method, the comparison of the whole vascular tree structure is focused on according to the topological relation of the branches of the vascular tree, and the most famous and most widely applied method is tree editing distance (Tree Edit Distance, TED); thirdly, the analysis and comparison are carried out on the shape of the blood vessel tree by combining the geometry and the topology comprehensively, and the method comprehensively compares the geometry and the topology of the shape of the blood vessel tree, but the geometric comparison still has the defects. Among these are the geometric shapes that take the form of sampling points to represent the branches of the vessel tree, which, although simpler to calculate, lack a great deal of geometric information. In addition, the method adopts a continuous curve form to represent the geometry and shape of the branches of the blood vessel tree, and adopts an elastic shape analysis framework (Elastic Shape Analysis Framework, ESAF) to calculate the shape similarity of the curves, and the method comprehensively compares the geometry of the branch skeleton lines. However, the vessel tree branches are tubular, so that not only the geometry of the skeleton line but also the diameter information is taken into account when comparing the vessel tree branches. At present, a method for integrating topology and geometry and adding diameter information comparison in branch geometry difference calculation is lacking.
For example, chinese patent application number CN200810047853.5 discloses a dynamic model guided angiography three-dimensional reconstruction method, which belongs to the crossing field of digital image processing and medical imaging, and aims to meet the special requirements of auxiliary detection and surgical navigation of cardiovascular diseases in chinese clinical medicine. The method comprises a pretreatment step of an image forming map, a blood vessel segmentation step, a blood vessel framework and radius extraction step, a model guiding blood vessel primitive identification step, a blood vessel matching step and a blood vessel three-dimensional reconstruction step. The invention also provides a cardiovascular dynamic model building method, which comprises a cardiovascular slice data extraction step, a heart static and dynamic modeling step and a cardiovascular system static and dynamic modeling step. Although the invention can obtain good angiography three-dimensional reconstruction results, the invention effectively assists in the detection and operation navigation of cardiovascular diseases and meets clinical requirements. But the invention lacks a comparison of shape by integrating topology and geometry and adding diameter information in the calculation of branch geometry differences.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for calculating the similarity of a blood vessel tree.
In order to achieve the technical purpose, the technical scheme of the invention is realized as follows:
the method for calculating the similarity of the blood vessel tree comprises the following steps:
s1, constructing a multi-branch tree model of a blood vessel tree;
s2, calculating the branch distance of the multi-branch tree model;
s3, calculating the subtree distance of the multi-tree model;
s4, calculating the distance of the multi-tree model according to the branch distance and the subtree distance;
and S5, calculating the blood vessel similarity according to the distance of the multi-tree model.
Further, S1, the constructing a multi-tree model of a vessel tree includes:
s1.1, defining a multi-tree model of a blood vessel tree:
the vessel multi-way tree model is t= (V, E, r), where v= { V 1 ，v 2 ，...，v n The set of vertices, e= { E } is 1 ，e 2 ，...，e n Is the collection of branches, r is the root branch marked in the vessel tree, and the 3D branch skeleton line function is beta s ：[0，1]→R 3 Diameter function beta d ：[0，1]→R 1 Each branch in E is noted as a 4D combination curve β: [0,1]→R 4 ，Root branch r is also a 4D combined curve;
s1.2, constructing a unified multi-tree model of two vessel tree topologies:
assuming that the missing branch of the blood vessel tree exists and the missing branch is regarded as a virtual branch, the virtual branch is expressed as a point on the mother branch, the solid line part in the unified model is the branch in which the blood vessel tree exists normally, and the unified multi-branch tree model capable of describing the topology of the two blood vessel trees is constructed by traversing the topology in the data of the two blood vessel trees.
Further, S2, the calculating a branching distance of the multi-tree model includes:
s2.1, calculating branch geometric differences, branch direction differences, branch position differences and branch length differences respectively:
the calculation formula of the branch geometric difference is as follows (1):
in the above formula (1), a represents a branch, b represents b branch, S 1 For branch geometry difference d 4D (β a ，β b ) For the combined curve beta a And beta b Shape distance of (2);
the calculation formula of the branching direction difference is the following formula (2):
in the above formula (2), a represents a branch, b represents b branch, S 2 For the difference of branch direction phi a For the branch direction of branch a, phi b A branch direction of the branch b;
the calculation formula of the branch position difference is the following formula (3):
in the above formula (3), a represents a branch, b represents a branch, S3 represents a difference in branch position, l a Is the length l from the starting point to the intersection point with the a branch on the a branch mother b For the length from the starting point to the intersection point with the b branch on the b branch mother, L A For length of a branch mother, L B Length of mother for b branches;
the calculation formula of the branch length difference is the following formula (4):
in the above formula (4), a represents a branch, b represents b branch, S 4 For the difference of branch lengths, L a For the length of the a branch, L b Length of branch b;
s2.2, calculating a branch distance according to the branch geometric difference, the branch direction difference, the branch position difference and the branch length difference, wherein the calculation formula is as follows (5):
d e (a，b)＝w 1 S 1 (a，b)+w 2 S 2 (a，b)+w 3 S 3 (a，b)+w 4 S 4 (a，b)......(5)，
in the above formula (5), d e (a, b) is the branch distance of the a branch and the b branch, w 1 Is the weight of branch geometric difference, S 1 For branch geometry differences, w 2 Is the weight of the branch direction difference, S 2 For the difference in branch direction, w 3 Is the weight of the branch position difference, S 3 For branch position difference, w 4 Is the weight of the branch length difference, S 4 Is the difference in branch length.
Further, S3, the calculating a subtree distance of the multi-tree model includes:
s3.1, determining a recursive method of the subtree distance of the multi-tree model:
vessel tree T 1 And T 2 Is a subtree T of (2) 1 (a) And T 2 (b) The calculation formula of the subtree distance of (2) is as follows:
in the above formula (6), d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, where λ is [0,1]A variable in between for regulating the influence of the offspring branch on the overall shape of the blood vessel tree, d e For the branching distance L 1 (a)<i>Is T 1 Branches of layer i, L 2 (a)<i>Is T 2 Branching of the i-th layer;
a method of adapting the computation of the subtree distance to be recursive, the following equation (7):
in the above formula (7): d, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, where λ is [0,1]A variable in between for regulating the influence of the offspring branch on the overall shape of the blood vessel tree, d e For the branching distance L 1 (a)<1>Is T 1 Branching of layer 1, L 2 (a)<1>Is T 2 Branching of layer 1;
s3.2, calculating the matching cost of the first layer branch of the subtree distance, wherein the calculation formula is as follows (8):
in the above formula (8), cost (a, b) is the matching cost of the a branch and the b branch, d e (a, b) is the branch distance of the a branch and the b branch, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, lambda is a constant;
s3.3, calculating the subtree distance of the multi-tree model according to the matching cost of the first layer branch, wherein the calculation formula is as follows (9):
in the above formula (9), d st (T 1 (a)，T 2 (b) A branch and b branch subtree distance d) e (a, b) is the branch distance of the a branch and the b branch, and i, j and lambda are constants.
Further, S4, the calculating the distance of the multi-tree model according to the branch distance and the subtree distance includes:
s4.1, determining the distance of the multi-tree model, wherein the calculation formula is as follows (10):
in the above formula (10), d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multiple tree model distance, d, of model 4D (β r1 ，β r2 ) For the combined curve beta r1 And beta r2 Shape distance d of (2) st (T 1 (r 1 )，T 2 (r 2 ) Is r) 1 Branching sum r 2 Branch subtree distance;
s4.2, simplifying a calculation formula of the multi-tree model distance, wherein the calculation formula is as follows (11):
d T (T 1 ，T 2 )＝d 4D (β r1 ，β r2 )+d st (T 1 (r 1 )，T 2 (r 2 ))......(11)，
in the above formula (11), d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multiple tree model distance, d, of model 4D (β r1 ，β r2 ) For the combined curve beta r1 And beta r2 Shape distance d of (2) st (T 1 (r 1 )，T 2 (r 2 ) Is r) 1 Branching sum r 2 Branch subtree distance.
Further, S5, the calculating the blood vessel similarity according to the distance of the multi-tree model is as follows (12):
in the above formula (12), s (T) 1 ，T 2 ) Is T 1 Model and T 2 Similarity of blood vessels of model, d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multi-way tree model distance of the model.
The method has the beneficial effects that:
1. the method realizes the calculation method of the three-dimensional vessel tree similarity comprehensively considering topology and geometry, comprehensively considers each characteristic in geometric comparison, and firstly proposes the calculation of the vessel branch shape difference by utilizing the combined curve of the skeleton line and the diameter.
2. In the method, different difference calculation methods when branches are missing are provided on topology comparison, and meanwhile, the matched branches are one-to-one and are in the same level, and the branch matching result provides reference for clinical diagnosis of doctors, so that disease diagnosis is more objective.
3. The method of the invention utilizes calculation to obtain the similarity, and is convenient for classifying the blood vessel data set, thereby distinguishing normal and pathological blood vessel data and facilitating the doctor to apply to treating pathological blood vessels of patients.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a flow chart of constructing a unified multi-way tree model in the method of the present invention;
FIG. 3 is a schematic diagram of a branch direction calculation in the method of the present invention;
FIG. 4 is a schematic representation of a sub-tree model in the method of the present invention;
FIG. 5 is a flow chart of the best matching algorithm in the method of the present invention;
FIG. 6 is a graph of abdominal vascular branch matching results in the method of the present invention;
fig. 7 is a neurone dataset similarity confusion matrix in the method of the invention.
Detailed Description
The following describes in further detail the embodiments of the method according to the invention in connection with the accompanying figures 1 to 7 of the description.
As shown in fig. 1, the method comprises the steps of:
s1, constructing a multi-tree model of a blood vessel tree:
s1.1, defining a multi-tree model of a blood vessel tree:
firstly integrating the segments of branches in the blood vessel data, judging whether the two segments belong to the same branch according to the tangential offset of the two segments at the connecting point, defining the ubiquitous branches in the blood vessel data set as root branches, and constructing a multi-branch tree model of a blood vessel layer by traversing the sub-branches from the root branches;
defining a vessel multi-way tree model as t= (V, E, r), wherein v= { V 1 ，v 2 ，...，v n The set of vertices, e= { E } is 1 ，e 2 ，...，e n Is the collection of branches, r is the root branch marked in the vessel tree, defining the 3D branch skeleton line function as β s ：[0，1]→R 3 Diameter function beta d ：[0，1]→R 1 Each branch in E is noted as a 4D combination curve β: [0,1]→R 4 ，The root branch r is also a 4D combined curve, and a unified vessel multi-branch tree model is constructed, as shown in figure 2;
s1.2, constructing a unified multi-tree model of two vessel tree topologies:
starting from a root node, constructing a topological model of a multi-branch tree of a blood vessel from top to bottom according to a connection relation, wherein each branch of an original blood vessel in the topological model is regarded as a node, the connection between two nodes shows that the two branches are in a parent-child relation, the node at the lower layer is a descendant branch of the node at the upper layer, the branch connected with the root branch is specified to be a layer 1 branch and is marked as L <1>, the descendant branch connected with the layer 1 branch is marked as a layer 2 branch and is marked as L <2>, and the like, and the branch at the x layer is marked as L < x >;
the problem of topoisomerase of branch deficiency usually exists in two vessel trees, the problem is solved by constructing a unified multi-way tree model, the existence of the branch deficiency of the vessel tree is assumed, the branch deficiency is regarded as a virtual branch, the virtual branch is expressed as a point on a mother branch, the solid line part in the unified model is the branch of the normal existence of the vessel tree, and the unified multi-way tree model capable of describing the topology of the two vessel trees is constructed by traversing the topology in the data of the two vessel trees;
s2, calculating the branch distance of the multi-branch tree model:
s2.1, calculating branch geometric differences, branch direction differences, branch position differences and branch length differences respectively:
the calculation formula of the branch geometric difference is as follows (1):
in the above formula (1), a represents a branch, b represents b branch, S 1 Is the difference of branch geometryDifferent, d 4D (β a ，β b ) For the combined curve beta a And beta b Shape distance of (2);
the calculation formula of the branching direction difference is the following formula (2):
in the above formula (2), a represents a branch, b represents b branch, S 2 For the difference of branch direction phi a For the branch direction of branch a, phi b The branching direction of the branch b is shown in fig. 2;
the calculation formula of the branch position difference is as follows (3):
in the above formula (3), a represents a branch, b represents a b branch, S 3 For branch position difference, l a Is the length l from the starting point to the intersection point with the a branch on the a branch mother b For the length from the starting point to the intersection point with the b branch on the b branch mother, L A For length of a branch mother, L B Length of mother for b branches;
the calculation formula of the branch length difference is the following formula (4):
in the above formula (4), a represents a branch, b represents b branch, S 4 For the difference of branch lengths, L a For the length of the a branch, L b Length of branch b;
s2.2, calculating a branch distance according to the branch geometric difference, the branch direction difference, the branch position difference and the branch length difference, wherein the calculation formula is as follows (5):
d e (a，b)＝w 1 S 1 (a，b)+w 2 S 2 (a，b)+w 3 S 3 (a，b)+w 4 S 4 (a，b)......(5)，
in the above formula (5), d e (a, b) is the branch distance of the a branch and the b branch, w 1 Is the weight of branch geometric difference, S 1 For branch geometry differences, w 2 Is the weight of the branch direction difference, S 2 For the difference in branch direction, w 3 Is the weight of the branch position difference, S 3 For branch position difference, w 4 Is the weight of the branch length difference, S 4 Is the difference of branch lengths;
s3, calculating the subtree distance of the multi-tree model:
s3.1, determining a recursive method of the subtree distance of the multi-tree model:
a subtree model of different sizes in the multi-tree model as shown in fig. 4, where t=t (r), defines the subtree of branch a in vessel multi-tree T (r) as: t (a) = (E (a), a), where E (a) is a set of sub-tree branches, made up of all descendant branches of branch a, denoted as E (a) = { a 1 ，a 2 ，...，a m ，...，a n Subtree T (a) is a subset of tree T, E (a) is a subset of E, a is the root node of subtree T (a), to distinguish the root of subtree from the root of the entire tree, the root of subtree is called the maternal branch, which is any node in the tree model other than the leaf node, in subtree T (a), the branch of the x-th layer is marked L (a)<x>；
Vessel tree T 1 And T 2 Is a subtree T of (2) 1 (a) And T 2 (b) Is the subtree distance d of (2) st The formula (1) is represented by the following formula (6):
in the above formula (6): d, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, where λ is [0,1]A variable in between for regulating the influence of the offspring branch on the overall shape of the blood vessel tree, d e For the branching distance L 1 (a)<i>Is T 1 Branches of layer i, L 2 (a)<i>Is T 2 Branching of the i-th layer;
a method of rewriting the computation of the subtree distance to recursion, as shown in the following formula (7):
in the above formula (7): d, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, where λ is [0,1]A variable in between for regulating the influence of the offspring branch on the overall shape of the blood vessel tree, d e For the branching distance L 1 (a)<1>Is T 1 Branching of layer 1, L 2 (a)<1>Is T 2 Branching of layer 1;
s3.2, calculating the matching cost of the first-layer branches of the subtree distance:
the optimal matching flow is shown in FIG. 5, and the matching problem of all branches is divided into sub-problems of the first-layer branch matching of each sub-tree, for sub-tree T 1 (a) And T 2 (b) N and m are L 1 (a)<1>And L 2 (b)<1>K=max { n, m }; updating L 1 (a)<1>＝{a 1 ，...，a k Sum L 2 (b)<1>＝{b 1 ，...，b k -wherein the newly added element is a virtual branch; calculating all matching costs of each pair of possible matching branches in the first layer of the subtree, and constructing a new matching cost matrix D C A matrix of k x k, D C (i，j)＝cost(a i ，b j ) The calculation formula of the matching cost of the first layer branch of the subtree distance is as follows (8):
in the above formula (8), cost (a, b) is the matching cost of the a branch and the b branch, d e (a, b) is the branch distance of the a branch and the b branch, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, lambda is a constant;
s3.3, calculating the subtree distance of the multi-tree model according to the matching cost of the first-layer branch:
defining a matching function M: (1, 2., k) x (1, 2., k):
the function satisfiesMeaning T 1 Each branch of (a) can only be connected with T 2 One branch of (a) matches and vice versa defines M k For the set of all possible matching combinations of k pairs of branches, the best matching function of the first layer branch of the subtree +.>Then the calculation by hungarian algorithm:
the calculation formula for calculating the subtree distance is the following formula (9):
in the above formula (9), d st (T 1 (a)，T 2 (b) A branch and b branch subtree distance d) e (a, b) is the branch distance of the a branch and the b branch, i, j and lambda are constants;
s4, calculating the distance of the multi-tree model according to the branch distance and the subtree distance:
s4.1, determining the distance of the multi-tree model:
firstly, calculating the distance of a root branch of a blood vessel and adding the distance of a sub-tree of a maximum sub-tree in the blood vessel to obtain the distance of a blood vessel tree; for a unified vessel tree model with U-layer branches, its distance calculation is divided into two parts: root and all offspring branches; the comparison of shapes requires elimination of translational, rotational, and scaling effects; the calculation of all feature differences of the branch distances is performed under a local coordinate system, only ensuring that the distance of the root branch eliminates these effects; the calculation of the vessel tree distance is expressed as the following formula (10):
in the above formula (10), d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multiple tree model distance, d, of model 4D (β r1 ，β r2 ) For the combined curve beta r1 And beta r2 Shape distance d of (2) st (T 1 (r 1 )，T 2 (r 2 ) Is r) 1 Branching sum r 2 Branch subtree distance;
the shape comparison of the vessel tree only considers the shape differences of the first layer branches when λ=0, and the shape comparison of the vessel tree considers the shape differences of all the offspring branches when λ=1, and the influence of each layer branch on the vessel tree shape as a whole is equivalent;
s4.2, simplifying a calculation formula of the multi-tree model distance:
the invention provides a subtree model to simplify calculation and ensure that all branches of a subtree of a blood vessel tree can be matched with branches of a subtree of the same level of another blood vessel tree;
the calculation formula of the distance of the multi-tree model is as follows (11):
d T (T 1 ，T 2 )＝d 4D (β r1 ，β r2 )+d st (T 1 (r 1 )，T 2 (r 2 ))......(11)，
in the above formula (11), d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multiple tree model distance, d, of model 4D (β r1 ，β r2 ) For the combined curve beta r1 And beta r2 Shape distance d of (2) st (T 1 (r 1 )，T 2 (r 2 ) Is r) 1 Branching sum r 2 Branch subtree distance;
s5, calculating the similarity of the blood vessel tree according to the distance of the multi-tree model:
obtaining the similarity value of the blood vessel tree according to the relationship of the negative correlation of the distance and the similarity, and when d (x, y) is a distance measure, e -d(x，y) Is a normalized similarity measure, 1-e -d(x，y) Is a standardized distance measure, and the calculation formula of the similarity of the blood vessel tree is as follows (12):
in the above formula (12), s (T) 1 ，T 2 ) Is T 1 Model and T 2 Similarity of blood vessels of model, d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multi-way tree model distance of the model.
The matching algorithm is applied to branch matching of abdominal blood vessels, as shown in fig. 6, branches with the same label can be accurately corresponding, redundant branches can be marked, and differences between normal blood vessels and lesion blood vessels can be effectively identified.
The present application is not limited to the embodiments described above, but any modifications, improvements, substitutions, etc. that can be conceived by a person skilled in the art without departing from the spirit of the invention, fall within the scope of protection of the present application.
Claims (2)
1. A method for computing similarity of a vessel tree, comprising the steps of:
s1, constructing a multi-tree model of a blood vessel tree:
s1.1, defining a multi-tree model of a blood vessel tree:
the vessel multi-branch tree model is t=(V, E, r), wherein v= { V 1 ，v 2 ，...，v n The set of vertices, e= { E } is 1 ，e 2 ，...，e n Is the collection of branches, r is the root branch marked in the vessel tree, and the 3D branch skeleton line function is beta s :[0，1]→R 3 Diameter function beta d :[0，1]→R 1 Each branch in E is marked as a 4D combination curve beta: [0,1 ]]→R 4 ，Root branch r is also a 4D combined curve;
s1.2, constructing a unified multi-tree model of two vessel tree topologies:
assuming that the missing branch of the blood vessel tree exists and regarding the missing branch as a virtual branch, representing the virtual branch as a point on a mother branch, and the solid line part in the unified model is the branch in which the blood vessel tree exists normally, and constructing a unified multi-branch tree model capable of meeting the description of the topology of the two blood vessel trees by traversing the topology in the data of the two blood vessel trees;
s2, calculating the branch distance of the multi-branch tree model:
s2.1, calculating branch geometric differences, branch direction differences, branch position differences and branch length differences respectively:
the calculation formula of the branch geometric difference is as follows (1):
in the above formula (1), a represents a branch, b represents b branch, S 1 For branch geometry difference d 4D (β a ，β b ) For the combined curve beta a And beta b Shape distance of (2);
the calculation formula of the branching direction difference is the following formula (2):
in the above formula (2), a represents a branch, b represents b branch, S 2 For the difference of branch direction phi a For the branch direction of branch a, phi b A branch direction of the branch b;
the calculation formula of the branch position difference is the following formula (3):
in the above formula (3), a represents a branch, b represents b branch, S 3 For branch position difference, l a Is the length l from the starting point to the intersection point with the a branch on the a branch mother b For the length from the starting point to the intersection point with the b branch on the b branch mother, L A For length of a branch mother, L B Length of mother for b branches;
the calculation formula of the branch length difference is the following formula (4):
in the above formula (4), a represents a branch, b represents b branch, S 4 For the difference of branch lengths, L a For the length of the a branch, L b Length of branch b;
s2.2, calculating a branch distance according to the branch geometric difference, the branch direction difference, the branch position difference and the branch length difference, wherein the calculation formula is as follows (5):
d e (a，b)＝w 1 S 1 (a，b)+w 2 S 2 (a，b)+w 3 S 3 (a，b)+w 4 S 4 (a，b)......(5)，
in the above formula (5), d e (a, b) is the branch distance of the a branch and the b branch, w 1 Is the weight of branch geometric difference, S 1 For branch geometry differences, w 2 Is the weight of the branch direction difference, S 2 For the difference in branch direction, w 3 Is the weight of the branch position difference, S 3 For branch position difference, w 4 For differences in branch lengthWeight, S 4 Is the difference of branch lengths;
s3, calculating the subtree distance of the multi-tree model:
s3.1, determining a recursive method of the subtree distance of the multi-tree model:
vessel tree T 1 And T 2 Is a subtree T of (2) 1 (a) And T 2 (b) The calculation formula of the subtree distance of (2) is as follows:
in the above formula (6), d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, where λ is [0,1]A variable in between for regulating the influence of the offspring branch on the overall shape of the blood vessel tree, d e For the branching distance L 1 (a)<i>Is T 1 Branches of layer i, L 2 (a)<i>Is T 2 Branching of the i-th layer;
a method of adapting the computation of the subtree distance to be recursive, the following equation (7):
in the above formula (7): d, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, where λ is [0,1]A variable in between for regulating the influence of the offspring branch on the overall shape of the blood vessel tree, d e For the branching distance L 1 (a)<1>Is T 1 Branching of layer 1, L 2 (a)<1>Is T 2 Branching of layer 1;
s3.2, calculating the matching cost of the first layer branch of the subtree distance, wherein the calculation formula is as follows (8):
in the above formula (8), cost (a, b) is a branch and bBranch matching cost, d e (a, b) is the branch distance of the a branch and the b branch, d st (T 1 (a)，T 2 (b) A) is the subtree distance of the a-branch and the b-branch, lambda is a constant;
s3.3, calculating the subtree distance of the multi-tree model according to the matching cost of the first layer branch, wherein the calculation formula is as follows (9):
in the above formula (9), d st (T 1 (a)，T 2 (b) A branch and b branch subtree distance d) e (a, b) is the branch distance of the a branch and the b branch, i, j and lambda are constants;
s4, calculating the distance of the multi-tree model according to the branch distance and the subtree distance;
s4.1, determining the distance of the multi-tree model, wherein the calculation formula is as follows (10):
in the above formula (10), d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multiple tree model distance, d, of model 4D (β r1 ，β r2 ) For the combined curve beta r1 And beta r2 Shape distance d of (2) st (T 1 (r 1 )，T 2 (r 2 ) Is r) 1 Branching sum r 2 Branch subtree distance;
s4.2, simplifying a calculation formula of the multi-tree model distance, wherein the calculation formula is as follows (11):
d T (T 1 ，T 2 )＝d 4D (β r1 ，β r2 )+d st (T 1 (r 1 )，T 2 (r 2 ))......(11)，
in the above formula (11), d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multiple tree model distance, d, of model 4D (β r1 ，β r2 ) For the combined curve beta r1 And beta r2 Shape distance d of (2) st (T 1 (r 1 )，T 2 (r 2 ) Is r) 1 Branching sum r 2 Branch subtree distance;
and S5, calculating the blood vessel similarity according to the distance of the multi-tree model.
2. The method for calculating the similarity of the blood vessel tree according to claim 1, wherein S5, the calculating the similarity of the blood vessel according to the distance of the multi-way tree model is represented by the following formula (12):
in the above formula (12), s (T) 1 ，T 2 ) Is T 1 Model and T 2 Similarity of blood vessels of model, d T (T 1 ，T 2 ) Is T 1 Model and T 2 Multi-way tree model distance of the model.
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