CN112381758A - Method for calculating similarity of vessel tree - Google Patents
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Abstract
The invention relates to a method for calculating the similarity of a vessel tree, which comprises the following steps: s1, constructing a multi-branch tree model of the blood vessel; s2, calculating the branch distance of the multi-branch tree model; s3, calculating the subtree distance of the multi-branch tree model; s4, calculating the distance of the multi-branch tree model according to the branch distance and the subtree distance; s5, calculating the similarity of the blood vessels according to the distance of the multi-branch tree model; the method realizes the calculation of the three-dimensional vessel tree similarity by comprehensively considering topology and geometry, comprehensively considers all the characteristics in the aspect of geometric comparison, and firstly proposes to calculate the vessel branch shape difference by using a combined curve combining skeleton lines and diameters.
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 field of biomedical imaging, with the development of digital medical treatment and the heavy use of three-dimensional scanning equipment, medical workers and researchers can conveniently obtain model data of a three-dimensional blood vessel. These three-dimensional blood vessels include blood vessel structures in various regions such as neurons, pulmonary airways, abdominal arteries, and coronary arteries, and the shapes of these blood vessel structures are described mostly by mathematical tree structures. The calculation 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 the two groups of blood vessel trees are similar to find the diseased part. Perceptually similarity is a fuzzy concept, and generally the judgment of the similarity of blood vessels is different due to different experiences of different individuals, so that it is necessary to make a uniform rule and calculate the similarity of blood vessel trees by means of a computer.
The geometry and the topology need to be considered comprehensively for the comparison of the object shapes, and the three-dimensional blood vessel tree has the characteristics of topological isomerism, large geometric deformation and the like, so that the problems of correspondence, identification, classification and the like of the three-dimensional blood vessel tree are correspondingly more complicated. The data set of a three-dimensional vessel tree usually contains only vessel tissue at a certain location. Compared with a general three-dimensional tree-structured data set, the data set of the same vascular tissue is generally composed of branches which are similar in topology but have relatively large geometric difference, and the branches between two data are generally in a one-to-one matching relationship or in the case of branch deletion, the one-to-many situation rarely occurs. Whether the branches of the blood vessel tree are matched or not depends on the comparison of the branch differences, and the accuracy of the matching result of the branches influences the calculation of the similarity of the blood vessel tree, so that the method for comprehensively calculating the branch differences is very important to define. The geometry of the branches can be represented in the form of discrete curves, continuous curves and the like, the calculation is relatively simple by using the discrete form, and the branch difference calculated by using the continuous form is closer to the real difference.
There are three types of methods for comparing the shape difference of blood vessel trees: firstly, the morphology of the blood vessel tree is analyzed by means of extracting image features, most of the methods ignore the topological structure of the blood vessel tree, mainly extract the geometric information in the blood vessel tree model or image which researchers are interested in, and then carry out quantitative analysis on the geometric information; secondly, the topological information is singly used for comparing the vessel Tree structures, the methods basically ignore or simplify the geometric information of the vessel Tree and concentrate on comparing the whole vessel Tree structure according to the topological relation of the vessel Tree branches, and the most famous and most widely applied method in the methods is Tree Edit Distance (TED); thirdly, the vessel tree shapes are comprehensively analyzed and compared in a comprehensive geometric and topological way, although the method comprehensively compares the geometric and topological of the vessel tree shapes, the geometric comparison is still insufficient. Some of the methods use sampling points to represent the geometry of branches of the vessel tree, and although the calculation is simple, a large amount of geometric information is lost. In addition, the geometry and the Shape of the branches of the blood vessel tree are represented in the form of continuous curves, and the Shape similarity of the curves is calculated by using an Elastic Shape Analysis Framework (ESAF), and the method comprehensively compares the geometries of the branch skeleton lines. However, the vessel tree branches are tubular, so not only the geometry of the skeleton line but also the diameter information needs to be considered when comparing the vessel tree branches. At present, a method capable of integrating topology and geometry and adding diameter information comparison in branch geometry difference calculation is also lacked.
For example, chinese patent application No. CN200810047853.5 discloses a dynamic model-guided angiography three-dimensional reconstruction method, which belongs to the cross field of digital image processing and medical imaging, and aims to meet the special requirements of cardiovascular disease auxiliary detection and surgical navigation in chinese clinical medicine. The method comprises the steps of angiogram preprocessing, blood vessel segmentation, blood vessel skeleton and radius extraction, model-guided blood vessel primitive recognition, blood vessel matching and three-dimensional blood vessel reconstruction. The invention also provides a cardiovascular dynamic model establishing 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 the detection and operation navigation of cardiovascular diseases and meets the clinical requirements. But the invention lacks a comparison of shapes that integrate topology and geometry to add diameter information in the branch geometry difference calculations.
Disclosure of Invention
In view of the shortcomings of the prior art, the invention aims to provide a method for calculating the similarity of a 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 the blood vessel tree;
s2, calculating the branch distance of the multi-branch tree model;
s3, calculating the subtree distance of the multi-branch tree model;
s4, calculating the distance of the multi-branch tree model according to the branch distance and the subtree distance;
and S5, calculating the similarity of the blood vessels according to the distance of the multi-branch tree model.
Further, S1, the constructing the multi-branch tree model of the blood vessel tree includes:
s1.1, determining the definition of a multi-branch tree model of a blood vessel tree:
the vessel multi-branch tree model is T ═ (V, E, r), where V ═ V1，v2，...，vnIs the set of vertices, E ═ E1，e2，...，enIs the set of branches, r is the root branch marked in the vessel tree, and the 3D branch skeleton line function is βs：[0，1]→R3Function of diameter of betad：[0，1]→R1In E, each branch is marked as a 4D combination curve β: [0,1]→R4，
The root branch r is also a 4D composite curve;
s1.2, constructing a unified multi-branch 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 represented as a point on the mother branch, and the solid line part in the unified model is the branch in which the blood vessel tree normally exists, and a 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 the branch distance of the multi-branch tree model includes:
s2.1, respectively calculating branch geometric difference, branch direction difference, branch position difference and branch length difference:
the calculation formula of the branch geometric difference is the following formula (1):
in the above formula (1), a represents a branch, b represents b branch, S1Is the difference in branch geometry, d4D(βa，βb) Is a combined curve betaaAnd betabThe shape distance of (2);
the calculation formula of the difference in the branch direction is the following formula (2):
in the above formula (2), a represents a branch, b represents b branch, S2Is the difference in branch direction, phiaIs the branch direction of the a branch, phibThe branch direction is b branch;
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 b branch, S3 represents a difference in branch position, laIs the length from the starting point on the mother of branch a to the intersection point with branch a, lbIs the length from the starting point on the b-branch mother to the intersection point with the b-branch, LAA length of the mother of the branch, LBB length of the mother of the bifurcation;
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, S4Is a difference in branch length, LaIs the length of the a branch, LbIs the length of the b branch;
s2.2, calculating 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):
de(a，b)＝w1S1(a，b)+w2S2(a，b)+w3S3(a，b)+w4S4(a，b)......(5)，
in the above formula (5), de(a, b) is the branch distance of the a branch and the b branch, w1As a weight of the branch geometric difference, S1Is the difference in branch geometry, w2Is the weight of the branch direction difference, S2Is a difference in branch direction, w3As a weight of the branch position difference, S3Is a difference in branch position, w4Is the weight of the branch length difference, S4Is the branch length difference.
Further, S3, the calculating subtree distances of the multi-way tree model includes:
s3.1, determining a recursive method of subtree distance of the multi-branch tree model:
vascular tree T1And T2Subtree T of1(a) And T2(b) The calculation formula of the subtree distance of (2) is as follows:
in the above formula (6), dst(T1(a)，T2(b) A subtree distance of a-branch and b-branch, where λ is [0, 1 ]]A variable between, which regulates the magnitude of the influence of the offspring branches on the overall shape of the vessel tree, deIs the branch distance, L1(a)<i>Is T1Branches of the i-th layer, L2(a)<i>Is T2A branch of the ith layer;
a method of adapting the calculation of the subtree distance to recursion, as shown in the following equation (7):
in the above formula (7): dst(T1(a)，T2(b) A subtree distance of a-branch and b-branch, where λ is [0, 1 ]]A variable between, which regulates the magnitude of the influence of the offspring branches on the overall shape of the vessel tree, deIs the branch distance, L1(a)<1>Is T1Branch of layer 1, L2(a)<1>Is T2A branch 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, de(a, b) is the branch distance of the a branch and the b branch, dst(T1(a)，T2(b) A subtree distance of a branch and b branch, λ is constant;
s3.3, calculating the subtree distance of the multi-branch 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), dst(T1(a)，T2(b) A subtree distance of a branch and b branch, deAnd (a, b) is the branch distance of the branch a and the branch b, and i, j and lambda are constants.
Further, S4, the calculating the distance of the multi-way tree model according to the branch distance and the sub-tree distance includes:
s4.1, determining the distance of the multi-branch tree model, wherein the calculation formula is as the following formula (10):
in the above formula (10), dT(T1，T2) Is T1Model and T2Model distance of the model, d4D(βr1，βr2) Is a combined curve betar1And betar2Distance of shape of dst(T1(r1)，T2(r2) Is r)1Branch sum r2Branch subtree distance;
s4.2, simplifying a calculation formula of the distance of the multi-branch tree model, wherein the calculation formula is as follows (11):
dT(T1，T2)＝d4D(βr1，βr2)+dst(T1(r1)，T2(r2))......(11)，
in the above formula (11), dT(T1，T2) Is T1Model and T2Model distance of the model, d4D(βr1，βr2) Is a combined curve betar1And betar2Distance of shape of dst(T1(r1)，T2(r2) Is r)1Branch sum r2Branch subtree distance.
Further, S5, the calculating the blood vessel similarity according to the distance of the multi-branch tree model is as follows (12):
in the above formula (12), s (T)1，T2) Is T1Model and T2Vascular similarity of the model, dT(T1，T2) Is T1Model and T2Model distance of the model.
The method has the beneficial effects that:
1. the method realizes the calculation of the three-dimensional vessel tree similarity by comprehensively considering topology and geometry, comprehensively considers all the characteristics in the aspect of geometric comparison, and firstly proposes to calculate the vessel branch shape difference by using a combined curve combining skeleton lines and diameters.
2. According to the method, different difference calculation methods are given when the branches are missing on the aspect of topology comparison, meanwhile, the branch matching is specified to be one-to-one, the matched branches are located at the same level, and the branch matching result provides reference for clinical diagnosis of doctors, so that the disease diagnosis is more objective.
3. The method of the invention obtains the similarity by calculation, and is convenient for classifying the blood vessel data sets, thereby distinguishing the normal blood vessel data from the diseased blood vessel data and being convenient for doctors to apply to treating the diseased blood vessel of the patient.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a flow chart of the method of the present invention for constructing a unified multi-way tree model;
FIG. 3 is a schematic diagram of branch direction calculation in the method of the present invention;
FIG. 4 is a schematic diagram of a subtree model in the method of the present invention;
FIG. 5 is a flow chart of an optimal matching algorithm in the method of the present invention;
FIG. 6 is a graph of the results of abdominal vessel branch matching in a method of the present invention;
FIG. 7 is a neuron dataset similarity confusion matrix in the method of the invention.
Detailed Description
The following description will be made in further detail with reference to the accompanying fig. 1 to 7.
As shown in fig. 1, the method comprises the steps of:
s1, constructing a multi-branch tree model of the blood vessel tree:
s1.1, determining the definition of a multi-branch 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 a connecting point, defining the commonly existing branch in the blood vessel data set as a root branch, and traversing sub-branches from the root branch to construct a multi-branch tree model of one layer of the blood vessel;
defining the vessel multi-branch tree model as T ═ (V, E, r), where V ═ { V ═ V1，v2，...，vnIs the set of vertices, E ═ E1，e2，...，enIs the set of branches, r is the labeled root branch in the vessel tree, defining a 3D branch-skeleton function as βs：[0，1]→R3Function of diameter of betad：[0，1]→R1In E, each branch is marked as a 4D combination curve β: [0,1]→R4，
The root branch r is also a 4D combined curve, and a unified multi-branch tree model of the blood vessel is constructed, as shown in FIG. 2;
s1.2, constructing a unified multi-branch tree model of two vessel tree topologies:
starting from a root node, constructing a topology 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 topology model is regarded as a node, the connection between two nodes indicates that the two branches are in a parent-child relation, the node of the lower layer is a descendant branch of the node of the upper layer, the branch connected with the root branch is defined as a branch of the 1 st layer and is marked as L <1>, the descendant branch connected with the branch of the 1 st layer is a branch of the 2 nd layer and is marked as L <2>, and the rest is done in the same way, and the branch of the x-th layer is marked as L < x >;
the two vessel trees usually have a topological heterogeneous problem of branch deletion, the problem is solved by constructing a unified multi-branch tree model, assuming that the branch of the vessel tree is deleted and regarding the deleted branch as a virtual branch, the virtual branch is represented as a point on a mother branch, and a solid line part in the unified model is a branch in which the vessel tree normally exists, and the unified multi-branch tree model which can satisfy the description of 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, respectively calculating branch geometric difference, branch direction difference, branch position difference and branch length difference:
the calculation formula of the branch geometric difference is the following formula (1):
in the above formula (1), a represents a branch, b represents b branch, S1Is the difference in branch geometry, d4D(βa，βb) Is a combined curve betaaAnd betabThe shape distance of (2);
the calculation formula of the difference in the branch direction is the following formula (2):
in the above formula (2), a represents a branch, b represents b branch, S2Is the difference in branch direction, phiaIs the branch direction of the a branch, phibThe branch direction of the b branch, as shown in FIG. 2;
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 b branch, S3Is the difference in branch position,. laIs the length from the starting point on the mother of branch a to the intersection point with branch a, lbIs the length from the starting point on the b-branch mother to the intersection point with the b-branch, LAA length of the mother of the branch, LBB length of the mother of the bifurcation;
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, S4Is a difference in branch length, LaIs a length of branch aDegree, LbIs the length of the b branch;
s2.2, calculating 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):
de(a，b)＝w1S1(a，b)+w2S2(a，b)+w3S3(a，b)+w4S4(a，b)......(5)，
in the above formula (5), de(a, b) is the branch distance of the a branch and the b branch, w1As a weight of the branch geometric difference, S1Is the difference in branch geometry, w2Is the weight of the branch direction difference, S2Is a difference in branch direction, w3As a weight of the branch position difference, S3Is a difference in branch position, w4Is the weight of the branch length difference, S4Is the branch length difference;
s3, calculating subtree distance of the multi-branch tree model:
s3.1, determining a recursive method of subtree distance of the multi-branch tree model:
the subtree models of different sizes in the multi-branch tree model shown in fig. 4, where T ═ T (r), define the subtree of branch a in the vessel multi-branch tree T (r) as: t (a) ((e) (a)), where e (a) is a set of subtree branches, consisting of all descendant branches of branch a, denoted as e (a) { a ═ a1，a2，...，am，...，anA, a sub-tree T (a) is a subset of the tree T, E (a) is a subset of E, a is a root node of the sub-tree T (a), in order to distinguish the root of the sub-tree from the root of the whole tree, the root of the sub-tree is called mother branch, the mother branch is any node except leaf node in the tree model, in the sub-tree T (a), the branch at the x-th layer is marked as L (a)<x>；
Vascular tree T1And T2Subtree T of1(a) And T2(b) Distance d of subtreestIs calculated as the following formula (6):
in the above formula (6): dst(T1(a)，T2(b) A subtree distance of a-branch and b-branch, where λ is [0, 1 ]]A variable between, which regulates the magnitude of the influence of the offspring branches on the overall shape of the vessel tree, deIs the branch distance, L1(a)<i>Is T1Branches of the i-th layer, L2(a)<i>Is T2A branch of the ith layer;
the method of rewriting the calculation of the subtree distance to recursion is shown in the following equation (7):
in the above formula (7): dst(T1(a)，T2(b) A subtree distance of a-branch and b-branch, where λ is [0, 1 ]]A variable between, which regulates the magnitude of the influence of the offspring branches on the overall shape of the vessel tree, deIs the branch distance, L1(a)<1>Is T1Branch of layer 1, L2(a)<1>Is T2A branch of layer 1;
s3.2, calculating the matching cost of the first-layer branch of the subtree distance:
the optimal matching process is shown in FIG. 5, which divides the matching problem of all branches into sub-problems of the first-level branch matching of each sub-tree, and for the sub-tree T1(a) And T2(b) N and m are L1(a)<1>And L2(b)<1>K ═ max { n, m }; updating L1(a)<1>＝{a1，...，akAnd L2(b)<1>＝{b1，...，bk-wherein the newly added element is a virtual branch; calculating all matching costs of each pair of possibly matched branches in the first layer of the subtree, and constructing a new matching cost matrix DCA k by k matrix, DC(i，j)＝cost(ai，bj) The calculation formula of the matching cost of the first-level 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, de(a, b) is the branch distance of the a branch and the b branch, dst(T1(a)，T2(b) A subtree distance of a branch and b branch, λ is constant;
s3.3, calculating the subtree distance of the multi-branch tree model according to the matching cost of the first layer of branches:
defining a matching function M: (1, 2.., k) × (1, 2.,. k):
function satisfaction
Meaning T1Can only be connected with T2And vice versa, define MkFor the set of all possible matching combinations of k pairs of branches, the optimal matching function of the first level branch of the sub-tree
Then calculated by the Hungarian algorithm to obtain:
the calculation formula for calculating the subtree distance is the following formula (9):
in the above formula (9), dst(T1(a)，T2(b) A subtree distance of a branch and b branch, de(a, b) is the branch distance of the branch a and the branch b, i, j and lambda are constants;
s4, calculating the distance of the multi-branch tree model according to the branch distance and the subtree distance:
s4.1, determining the distance of the multi-branch tree model:
firstly, calculating the distance of a blood vessel root branch and adding the distance of the blood vessel root branch and the distance of a subtree of the largest subtree in a blood vessel to obtain the distance of a blood vessel tree; for a unified vessel tree model with U-layer branches, the distance calculation is divided into two parts: root and all offspring branches; the comparison of shapes requires eliminating the effects of translation, rotation, and scaling; the calculation of all the characteristic differences of the branch distance is carried out under a local coordinate system, and only the distance of the root branch needs to be ensured to eliminate the influences; the vessel tree distance is calculated as the following formula (10):
in the above formula (10), dT(T1，T2) Is T1Model and T2Model distance of the model, d4D(βr1，βr2) Is a combined curve betar1And betar2Distance of shape of dst(T1(r1)，T2(r2) Is r)1Branch sum r2Branch subtree distance;
when λ is 0, the shape comparison of the blood vessel tree only considers the shape difference of the branches of the first layer, and when λ is 1, the shape comparison of the blood vessel tree considers the shape difference of all the branches of the descendants, and the influence of each layer of branches on the whole shape of the blood vessel tree is equivalent;
s4.2, simplifying a calculation formula of the distance of the multi-branch tree model:
the invention provides a sub-tree model to simplify calculation and ensure that all branches of a sub-tree of a vessel tree can be matched with the branches of a sub-tree of the same level of another vessel tree;
the distance of the multi-branch tree model is calculated as the following equation (11):
dT(T1，T2)＝d4D(βr1，βr2)+dst(T1(r1)，T2(r2))......(11)，
in the above formula (11), dT(T1，T2) Is T1Model and T2Model distance of the model, d4D(βr1，βr2) Is a combined curve betar1And betar2Distance of shape of dst(T1(r1)，T2(r2) Is r)1Branch sum r2Branch subtree distance;
s5, calculating the similarity of the vessel tree according to the distance of the multi-branch tree model:
obtaining the value of the similarity of the vessel tree according to the relationship of the distance and the similarity, and when d (x, y) is distance measurement, e-d(x，y)Is a normalized similarity measure, 1-e-d(x，y)Is a normalized distance measure, the calculation of the vessel tree similarity is given by the following equation (12):
in the above formula (12), s (T)1，T2) Is T1Model and T2Vascular similarity of the model, dT(T1，T2) Is T1Model and T2Model distance of the model.
In addition, the invention applies the calculated similarity to the data set classification, such as the Wu neural data set similarity confusion matrix shown in fig. 7, and applies the classification algorithm through the confusion matrix to classify the data set.
The present application is not limited to the above-described embodiments, and any variations, modifications, and substitutions that may occur to those skilled in the art are intended to fall within the scope of the present application without departing from the spirit of the invention.
Claims (6)
1. A method for calculating the similarity of a vessel tree is characterized by comprising the following steps:
s1, constructing a multi-branch tree model of the blood vessel tree;
s2, calculating the branch distance of the multi-branch tree model;
s3, calculating the subtree distance of the multi-branch tree model;
s4, calculating the distance of the multi-branch tree model according to the branch distance and the subtree distance;
and S5, calculating the similarity of the blood vessels according to the distance of the multi-branch tree model.
2. The method of claim 1, wherein the constructing the multi-branch tree model of the vessel tree at S1 includes:
s1.1, determining the definition of a multi-branch tree model of a blood vessel tree:
the vessel multi-branch tree model is T ═ (V, E, r), where V ═ V1，v2，...，vnIs the set of vertices, E ═ E1，e2，...，enIs the set of branches, r is the root branch marked in the vessel tree, and the 3D branch skeleton line function is βs：[0，1]→R3Function of diameter of betad：[0，1]→R1In E, each branch is marked as a 4D combination curve β: [0,1]→R4，
The root branch r is also a 4D composite curve;
s1.2, constructing a unified multi-branch 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 represented as a point on the mother branch, and the solid line part in the unified model is the branch in which the blood vessel tree normally exists, and a 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.
3. The method for calculating the similarity of the vessel tree according to claim 1, wherein the calculating the branch distance of the multi-branch tree model at S2 includes:
s2.1, respectively calculating branch geometric difference, branch direction difference, branch position difference and branch length difference:
the calculation formula of the branch geometric difference is the following formula (1):
in the above formula (1), a represents a branch, b represents b branch, S1Is the difference in branch geometry, d4D(βa，βb) Is a combined curve betaaAnd betabThe shape distance of (2);
the calculation formula of the difference in the branch direction is the following formula (2):
in the above formula (2), a represents a branch, b represents b branch, S2Is the difference in branch direction, phiaIs the branch direction of the a branch, phibThe branch direction is b branch;
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 b branch, S3Is the difference in branch position,. laIs the length from the starting point on the mother of branch a to the intersection point with branch a, lbIs the length from the starting point on the b-branch mother to the intersection point with the b-branch, LAA length of the mother of the branch, LBB length of the mother of the bifurcation;
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, S4Is a difference in branch length, LaIs the length of the a branch, LbIs the length of the b branch;
s2.2, calculating 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):
de(a，b)＝w1S1(a，b)+w2S2(a，b)+w3S3(a，b)+w4S4(a，b)……(5)，
in the above formula (5), de(a, b) is the branch distance of the a branch and the b branch, w1As a weight of the branch geometric difference, S1Is the difference in branch geometry, w2Is the weight of the branch direction difference, S2Is a difference in branch direction, w3As a weight of the branch position difference, S3Is a difference in branch position, w4Is the weight of the branch length difference, S4Is the branch length difference.
4. The method of claim 1, wherein the step of calculating sub-tree distances of the multi-way tree model at S3 comprises:
s3.1, determining a recursive method of subtree distance of the multi-branch tree model:
vascular tree T1And T2Subtree T of1(a) And T2(b) The calculation formula of the subtree distance of (2) is as follows:
in the above formula (6), dst(T1(a)，T2(b) A sub-branch of a and bTree distance, where λ is [0, 1 ]]A variable between, which regulates the magnitude of the influence of the offspring branches on the overall shape of the vessel tree, deIs the branch distance, L1(a)<i>Is T1Branches of the i-th layer, L2(a)<i>Is T2A branch of the ith layer;
a method of adapting the calculation of the subtree distance to recursion, as shown in the following equation (7):
in the above formula (7): dst(T1(a)，T2(b) A subtree distance of a-branch and b-branch, where λ is [0, 1 ]]A variable between, which regulates the magnitude of the influence of the offspring branches on the overall shape of the vessel tree, deIs the branch distance, L1(a)<1>Is T1Branch of layer 1, L2(a)<1>Is T2A branch 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, de(a, b) is the branch distance of the a branch and the b branch, dst(T1(a)，T2(b) A subtree distance of a branch and b branch, λ is constant;
s3.3, calculating the subtree distance of the multi-branch 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), dst(T1(a)，T2(b) A subtree distance of a branch and b branch, deAnd (a, b) is the branch distance of the branch a and the branch b, and i, j and lambda are constants.
5. The method of claim 1, wherein the step of calculating the distance of the multi-branch tree model according to the branch distance and the sub-tree distance at S4 comprises:
s4.1, determining the distance of the multi-branch tree model, wherein the calculation formula is as the following formula (10):
in the above formula (10), dT(T1，T2) Is T1Model and T2Model distance of the model, d4D(βr1，βr2) Is a combined curve betar1And betar2Distance of shape of dst(T1(r1)，T2(r2) Is r)1Branch sum r2Branch subtree distance;
s4.2, simplifying a calculation formula of the distance of the multi-branch tree model, wherein the calculation formula is as follows (11):
dT(T1，T2)＝d4D(βr1，βr2)+dst(T1(r1)，T2(r2))……(11)，
in the above formula (11), dT(T1，T2) Is T1Model and T2Model distance of the model, d4D(βr1，βr2) Is a combined curve betar1And betar2Distance of shape of dst(T1(r1)，T2(r2) Is r)1Branch sum r2Branch subtree distance.
6. The method of claim 1, wherein the step of calculating the vessel tree similarity according to the distance of the multi-branch tree model at S5 is represented by the following formula (12):
in the above formula (12), s (T)1，T2) Is T1Model and T2Vascular similarity of the model, dT(T1，T2) Is T1Model and T2Model distance of the model.
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