CN115239980A - Method for realizing shape matching based on quantum simulation bifurcation algorithm - Google Patents
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Abstract
The invention relates to a method for realizing shape matching based on a quantum simulation bifurcation algorithm. The method comprises the steps of constructing geodesic matrixes among data points in different shapes by utilizing data sets in different shapes, initializing node arrangement of paired data, selecting sub-node sets from the node arrangement and constructing corresponding energy sub-matrixes, generating a cyclic list according to the sub-node sets, and solving binary parameters of cyclic variables of a coupling matrix based on the cyclic list and the energy quantum matrixes by a quantum simulation bifurcation algorithm.
Description
Technical Field
The invention mainly relates to the field of computer vision, in particular to a method for realizing shape matching based on a quantum simulation bifurcation algorithm.
Background
Computer vision, also known as machine vision, performs the perceived activities of the three-dimensional world by using a computer or some other similar device to help translate the line-of-sight things into pictures. The rapid development of computers, without departing from the research and development in neuropsychology and psychology and cognitive science, the development direction of computer vision detection technology is to sense and analyze the surrounding three-dimensional space. Once in possession of this capability, the computer is not only aware of the general environment around it, but also has the capability to describe, recognize, understand and store objects.
The important aspect for realizing computer processing of artificial intelligence and vision is that in the field of computer vision application, a computer needs to understand image information, and a series of data processing processes such as digital image processing must be performed. The processing of the digital image comprises five steps: image pre-processing (noise removal), segmentation processing of segmented regions, measurement, image interpretation and image techniques. Different image technologies can be divided into three levels according to the abstraction level and processing method: image processing, image analysis, and image understanding. The organic integration of these three layers is also referred to as image engineering.
Computer vision (Computer vision) is the perception, recognition and understanding of three-dimensional scenes in the objective world by using a Computer to realize human visual functions. Visual inspection can be broadly divided into visual inspection of binary images, grayscale images, and color and depth images, depending on the type of data it processes. In addition, X-ray, ultrasound and infrared detection are also possible.
Shape is a high level of visual information, and in the field of computer vision research, shape is an important attribute for describing objects. Shape representation and matching have played an important role in many fields, such as target detection and medical analysis, ancient text research, etc., as a key and fundamental problem in the field of computer vision. Among various shape matching methods, the method of combining contour and region information includes richer shape information. In order to solve the problems that the probability of successful matching is greatly limited due to the fact that a linear equation is constrained forcibly in shape matching, the method is suitable for finding the quadratic distribution problem of shape matching.
Disclosure of Invention
The application relates to a method for realizing shape matching based on a quantum simulation bifurcation algorithm, which comprises the following steps:
the method comprises the steps that a geodesic matrix between data points in different shapes is built by utilizing data sets in different shapes, node arrangement of paired data is initialized, a sub-node set is selected from the node arrangement, and a corresponding energy sub-matrix is built;
and generating a circulation list according to the child node set, and solving a binary parameter of a circulation variable of a coupling matrix based on the circulation list and the energy quantum matrix by a quantum simulation bifurcation algorithm.
The method described above, wherein:
the child node sets are pairs of child node sets with different selected matching degrees and different requirements in the node arrangement.
The method described above, wherein:
and randomly generating a cyclic permutation with disjoint cycles according to the child node set, and changing the position of each disjoint cycle in the generated cyclic permutation to generate the cyclic list containing the cyclic permutation.
The method described above, wherein:
and constructing a coupling matrix of a binary quadratic unlimited optimization problem by taking the cycle number as a binary parameter according to the cycle list and the energy submatrix.
The method described above, wherein:
and when the binary parameters of the cyclic variables of the coupling matrix are solved by using a quantum simulation bifurcation algorithm, changing the arrangement position of the nodes of the data according to the binary parameters.
The method described above, wherein:
the geodesic matrix d is a square matrix, the dimension of the geodesic matrix d is equal to the number of data points, the elements on the diagonal are all 0, and the matrix element d ij Showing the geodesic distance of the ith and j data points.
The method described above, wherein:
when the number of nodes of the shape is n, the size of the energy matrix is n 2 ×n 2 The elements of the two shape-matched energy matrices W are represented as:
W ikjl ＝W i·n+k,j·n+l ＝|d A (i,j)-d B (k,l)|
where i, j and k, l are the nodes of two shapes A and B, respectively, the matrix element describing the case of the geodesic distance between two matches (i, k), (j, l), d A And d B Representing a square matrix of shapes a and B.
The method described above, wherein:
the cycle number, i.e., 2-cycle c, is composed of 2 positions, and c = (a, b) is expressed as:
wherein x is a matrix of cyclic c visualization, which is used for exchanging the position a and the position b of the arrangement P;
x ij the case where =1 is the case where the first type condition i, j = a, b or b, a is satisfied;
x ii the case where =1 is that the second type condition i ≠ a and i ≠ b is satisfied; and
x ij the case of =0 is the case other than the first and second types of conditions.
The application relates to a method for realizing shape matching based on a quantum simulation bifurcation algorithm, which comprises the following steps:
s1, constructing a geodesic matrix between data points in different shapes based on data sets in two shapes, and initializing the arrangement of paired data nodes;
s2, selecting paired sub-node sets with inconsistent matching degrees and requirements from the paired node arrangement;
s3, constructing a corresponding energy sub-matrix according to the sub-node set;
s4, randomly generating a cyclic arrangement with disjoint cyclic numbers according to the child node set, changing the position of each disjoint cyclic number in the generated cyclic arrangement, and generating a cyclic list containing the cyclic arrangement;
s5, constructing a coupling matrix of a binary secondary unlimited optimization problem by taking the cycle number as a binary parameter according to the cycle list and the energy submatrix;
and S6, solving binary parameters of the cyclic variables of the step coupling matrix by using a quantum simulation bifurcation algorithm, and changing the arrangement position of the data nodes according to the binary parameters.
The method described above, further comprising:
s7, repeating the operations of S5-S6, and traversing each circular arrangement in the circular list generated in S4 once;
and S8, repeating the operations of S2-S7 according to the new arrangement of the update point set generated in S7 until the result is converged.
The application relates to the field of quantum computer vision application, and aims to solve the problems that the probability of successful matching is greatly limited and the number of solving variables is huge to cause difficulty in solving due to the fact that a linear equation is constrained forcibly in shape matching by a punishment item. In alternative embodiments, the method is particularly directed to a subspace solution of quantum iteration and is suitable for finding a quadratic assignment problem of shape matching. Therefore, the method for realizing the shape matching based on the quantum simulation bifurcation algorithm in the application comprises the method of quantum iteration subspace solution.
Shape matching is at the heart of many computer vision and graphics applications because knowing the relationships between points can pass information to new shapes. It has been a challenging problem since they are often expressed as a combined Quadratic Assignment Problem (QAPS) with permutation matrix constraints, which is a property of the N-P problem. How quantum computing helps solve the problem of computer vision remains a relatively unexplored problem.
As quantum computing considers practical implementation from theoretical considerations, it becomes increasingly attractive to handle the N-P problem in computer vision. Unfortunately, constrained problems such as this cannot be solved directly with quantum computation and must be converted to quadratic unconstrained binary optimization problems, which greatly limits the probability of success of such approaches. Meanwhile, the traditional shape matching combined optimization solving method has high requirement on the number of solving variables, thereby greatly limiting the possibility of matching and solving the large-scale node shape problem. The present application has the advantage of solving these problems.
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In order that the above objects, features and advantages will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to the appended drawings, which are illustrated in the appended drawings.
FIG. 1 is an arrangement for constructing a geodetic matrix and initializing pairs of data nodes.
FIG. 2 is a selection of a set of matched child nodes from a paired node arrangement.
Fig. 3 is a main flow chart of a method for realizing shape matching based on a quantum simulation bifurcation algorithm.
Fig. 4 is a traversal for each circular permutation in the generated circular list.
Fig. 5 is a flowchart for repeating the entire process until the result converges in accordance with the new arrangement of the generated update point set.
Detailed Description
The present invention will be described more fully hereinafter with reference to the accompanying examples, which are intended to illustrate, but not to limit the invention to the particular forms disclosed, and which are included within the scope of the invention as defined by the appended claims.
Referring to fig. 1, the present application proposes solving a shape matching problem using a simulated bifurcation optimization algorithm.
Inspired by the quantum adiabatic optimization computing technology using a nonlinear oscillation network, a method for solving the yixin problem by using Simulated Bifurcations (SB) on a classical computer is proposed in the industry. The method carries out numerical simulation on the bifurcation phenomenon of the classical Hamilton system in the adiabatic evolution process. The classical computer simulates the hamiltonian system more efficiently than the quantum adiabatic evolution phenomenon on the classical computer. Compared with simulation annealing, which updates one variable at each step to ensure convergence, simulation bifurcation can update multiple or even all variables at the same time, accelerate the convergence of the problem and enable a simulation bifurcation algorithm to well utilize multi-core parallel computation.
Referring to fig. 1, the method for implementing shape matching based on quantum simulation bifurcation algorithm includes: the method comprises the steps of constructing geodesic matrixes among data points in different shapes by utilizing data sets in different shapes, initializing node arrangement of paired data, selecting a sub-node set from the node arrangement and constructing a corresponding energy sub-matrix. For example, by using datasets of different shapes (exemplified by a set of shapes a and B but allowing the number of shapes to be adjusted according to practice) to construct a geodesic matrix, such as matrix d, between the data points of different shapes, such as a and B.
Referring to fig. 2, it is known to select a set of sub-nodes from a node arrangement (for example, a pair of sub-node sets with the worst matching degree are selected as the sub-node sets) and construct a corresponding energy sub-matrix, and in an alternative embodiment, some sub-node sets LT1 are selected from the node arrangement LT and construct a corresponding energy sub-matrix W. Preferably, the paired sub-node sets with the worst matching degree are selected from the paired node arrangements, and the energy sub-matrix corresponding to the point set is constructed according to the node set with the worst matching degree. In an alternative embodiment, the child node sets are pairs of child node sets with different matching degrees and different requirements selected from the node arrangements, and the matching degree and the different requirements are illustrated below by taking the pair of child node sets with the worst matching degree as an example.
Referring to fig. 2, a circular list is generated according to the child node set LT1, and binary parameters of a circular variable of a coupling matrix based on the circular list and an energy quantum matrix are solved by a quantum simulation bifurcation algorithm. In an alternative example, a cyclic permutation composed of disjoint numbers of cycles or cycle information (typically, a number of cycles or cycle information such as a plurality of 2-cycles) is randomly generated according to the generated child node set, and the position of each disjoint number of cycles or cycle information in the generated cyclic permutation may be changed, for example, the position of 2-cycle, and a list composed of cyclic permutations is generated.
Referring to fig. 2, a coupling matrix of a binary quadratic infinite optimization problem with cycles as binary parameters is constructed according to the generated cyclic list and the energy submatrix W generated in the previous step. And when the binary parameters of the cyclic variables of the coupling matrix are solved by using a quantum simulation bifurcation algorithm, changing the arrangement position of the nodes of the data according to the binary parameters. Examples of the circular list and the energy quantum matrix and the arrangement position of the nodes for changing data will be described in detail below.
Referring to fig. 1, in an alternative embodiment, assume that the geodetic matrix d is a square matrix, the size of the matrix dimension is equal to the number of data points, the elements on the diagonal are all 0 and the element d is a matrix element ij The geodesic distance of the ith and j data points is shown.
Referring to FIG. 1, in an alternative embodiment, the number of nodes of the shape is n, and the energy matrix size is n 2 ×n 2 The elements of the two shape-matched energy matrices W are represented as:
W ikjl ＝W i·n+k,j·n+l ＝|d A (i,j)-d B (k,l)|
where i, j and k, l are the nodes of the two shapes A and B, respectively, and the matrix elements describe the case of geodesic distances between the two matches (i, k), (j, l). E.g. d A And d B Representing a square matrix of shapes a and B.
Referring to fig. 1, in an alternative embodiment, the number of cycles, e.g., 2-cycle c, consists of 2 positions, c = (a, b) is expressed as:
where x is a matrix of cyclic c visualizations, the effect is to swap positions a and b of the permutation P.
Note x ij The case of =1 is that the first type condition is satisfied: i. j = a, b or b, a.
And x ii The case of =1 is that the second type of condition is satisfied: i ≠ a and i ≠ b.
And x ij The case of =0 is: other than the first and second types of conditions. Such a situation, for example, in which neither the first type of condition nor the second type of condition is satisfied, is defined as a so-called other case.
Referring to fig. 3, in an alternative embodiment, the main flow of the method for implementing shape matching based on the quantum simulation bifurcation algorithm includes the following steps S1 to S6.
Referring to fig. 3, S1, a geodesic matrix between data points of different shapes is constructed based on the data sets of two shapes, and the arrangement of paired data nodes is initialized.
And S2, selecting a pair child node set with inconsistent matching degree and requirement from the pair node arrangement.
And 3, constructing a corresponding energy submatrix according to the child node set in S3.
Referring to fig. 3, S4, a cyclic permutation with disjoint cycles is randomly generated according to the child node set, and a cycle list including the cyclic permutation is generated by changing a position of each disjoint cycle in the generated cyclic permutation.
Referring to fig. 3, S5, a coupling matrix of a binary quadratic infinite optimization problem with the number of cycles as a binary parameter is constructed according to the cycle list and the energy submatrix.
Referring to fig. 3, S6, the quantum simulation bifurcation algorithm solves the binary parameters of the cyclic variables of the step coupling matrix, and changes the arrangement position of the data nodes according to the binary parameters.
Quantum computing is a complement to electronic chip computing, however, the operation of classical stereo matching algorithms on quantum chips cannot be handled in the way they are on electronic chips.
As related to quantum herein, the relevant matters regarding quantum devices and quantum data are as follows.
The term "quantum device" as used herein includes known quantum computing devices, quantum chips, and the like, and quantum hardware may be used instead of such terms. Typical "quantum devices" include, but are not limited to: quantum computers, quantum information processing systems or quantum cryptography systems, quantum simulators, all kinds of devices, apparatuses and machines that process quantum data.
By "quantum data" herein is meant information or data carried, held or stored by a quantum system, the smallest nontrivial system being a qubit, i.e., a system that defines a quantum information unit. It should be understood that the term "qubit" includes all quantum systems that can be appropriately approximated as two-level systems in the respective context. Such quantum systems typically include, for example, typical atomic, electronic, photonic, ionic, or superconducting qubits, among others.
Although the stereo matching problem achieves acceptable performance based on a classical solver, the solution module operation in the classical algorithm has high parallelism and consumes a large amount of computing resources. The method is based on a simulation bifurcation algorithm to replace a certain module in a classical stereo matching algorithm, and a pure quantum circuit and quantum classical mixed algorithm are used for processing the stereo matching problem. Thereby enabling the quantum chip and the electronic chip to work cooperatively for processing the stereo matching problem.
Referring to fig. 4, in an alternative embodiment, the main flow of the method for implementing shape matching based on the quantum simulation bifurcation algorithm includes the following step S7. Step S7 is to repeat operations S5-S6, and traverse each circular arrangement in the circular list generated in S4 once.
Referring to fig. 5, in an alternative embodiment, the method for implementing shape matching based on the quantum simulation bifurcation algorithm mainly includes the following step S8. The operations of S2-S7 are repeated mainly according to the new arrangement of the update point set generated in S7 (the update point set is, for example, a worst point set generated in S7), until the result converges.
Referring to fig. 3, in an alternative embodiment, the present application provides a method for implementing shape matching, which is a novel quantum iteration method for solving a simulated bifurcation algorithm based on quantum heuristics. Compared with the existing shape matching method, the method has the advantages that the arrangement is represented through a cycle set, and then the binary variable parameterization is used circularly, so that no constraint of any type is forced, the search in a solution space can be more effective, and the quality of a matching solution is improved.
Referring to fig. 3, in an alternative embodiment, the present application provides a method for implementing shape matching based on a quantum simulation bifurcation algorithm, and a specific scheme includes eight steps.
The method comprises the following steps: based on the data sets of two shapes, a geodesic matrix between data points of different shapes is constructed, and the arrangement P of paired data nodes is initialized 0 。
Step two: and selecting the paired child node set with the worst matching degree from the paired node arrangement.
Step three: and D, constructing an energy sub-matrix corresponding to the point set according to the node set with the worst matching obtained in the step two.
Step four: and D, randomly generating a cyclic arrangement formed by a plurality of disjoint 2-cycles according to the child node set generated in the step two, changing the position of each disjoint 2-cycle in the generated cyclic arrangement, and generating a list formed by the cyclic arrangement.
Step five: and constructing a coupling matrix of a binary secondary unlimited optimization problem by taking the circulation as a binary parameter according to the circulation list generated in the fourth step and the energy submatrix generated in the third step.
Step six: solving the binary parameters of the cyclic variables of the coupling matrix generated in the step five by using a quantum simulation bifurcation algorithm (allowing the bifurcation algorithm in the prior art to be used), and changing the arrangement positions of the nodes according to the binary variables.
Step seven: repeating the operations of the fifth step to the sixth step, and most importantly, traversing each circular arrangement in the list generated in the fourth step once.
Step eight: the operations of steps two through seven are repeated according to the new arrangement of a worst point set (e.g., referred to as an updated point set) generated in step seven until the results converge.
Referring to fig. 3, in an alternative embodiment, in step one, a geodesic matrix d corresponding to two shapes is constructed according to the characteristics of two shape nodes and the manifold surface. The geodesic line matrix d is a square matrix, the dimension is equal to the number of points, elements on the diagonal are all 0, and a matrix element d ij The geodesic distance of the ith and j points is shown.
Referring to fig. 3, in an alternative embodiment, in step one, the correlation matrix between the two position coordinates is constructed using a dot product of two property matrices in which the property matrix of the second shape is transposed. And solving the linear distribution solution of the incidence matrix to obtain rough initial matching arrangement between the two shape nodes.
Referring to fig. 3, in the second alternative embodiment, the quality of the matching degree is shown according to the difference between the geodetic distance sum of the two matching points and other points in the two shapes.
Referring to fig. 3, the matching principle is based on: if the two shapes A and B are completely the same and each point on A and B is perfectly matched, the geodetic distance from a certain point in the shape A to other points is always equal to the geodetic distance from a certain matching point in the shape B to other matching points, namely the sum of the geodetic distances from the matching points on A and B to other points is the same, and the difference is 0; the larger the difference between the absolute value of the geodesic distance sum of two matching points and other points is, the worse the matching degree of the two points is.
Referring to fig. 3, based on the principle, the sum of the differences between all matching points of the two shapes and the absolute value of the geodesic distance sum of other points is regarded as matching energy, and when the matching energy is 0, the two shapes are perfectly matched.
Referring to fig. 3, in an alternative embodiment, in step two, the differences between the absolute values of the geodesic distance sums of each matching point and other points are sorted according to the matching principle, and a specific number of pairs of points with the largest absolute value difference are selected as bad points and the bad points have the worst matching degree in the pair-wise arrangement, for example.
Referring to fig. 3, in an alternative embodiment, in step three, the energy sub-matrix W of the dead pixel obtained in the previous step two of the construction of the energy matrix W based on shape matching S 。
Referring to FIG. 3, in an alternative embodiment, where the number of nodes of a shape is n, the energy matrix has a size of n 2 ×n 2 The elements of the shape A and B matching energy matrix W are represented as
W ikjl ＝W i·n+k,j·n+l ＝|d A (i,j)-d B (k,l)|
Where i, j and k, l are the nodes of shapes A and B, respectively, the matrix element describes the case of geodesic distances between two matches (i, k), (j, l). I.e. reflects the degree of matching of the two matching pairs, whereas the energy matrix describes the degree of matching of all pair-wise properties.
Referring to FIG. 3, in an alternative embodiment, in step three, if only a subset of the energy matrices is taken as the sub-energy matrix, such as an immediate (W) S ) ikjl ＝W ikjl Only the matching degree of the paired characteristics between the child nodes is described, and the matching association between the selected child node and the non-selected child node cannot be described. The matching associations between the child nodes and the non-selected child nodes may be summed and reflected in the sub-energy matrix. The sub-energy matrix is represented as
And V \ S represents the part of the paired node set V with the selected sub-point set S removed. And taking the dead pixel obtained in the second step as a selected subset S to obtain a sub-energy matrix of the dead pixel.
Referring to fig. 3, in an alternative embodiment, in step four, a plurality of disjoint 2-loops are generated based on the bad points obtained in step two. The 2-cycle c consists of 2 positions, c = (a, b) is expressed as
Wherein x is a matrix of circular c visualization, the dimension is the same as the number of bad points, and the function of the matrix is to exchange the positions a and b of P for the arrangement P. The disjoint is that the positions of the multiple loops are not overlapped, that is, the visualization total matrix X of each disjoint circular arrangement can be described as the product form X = Π of each circular matrix X i x i ＝Π i c i . For a number n s Of disjoint cycles of n c ＝[n s /2]Wherein]Is a rounded symbol.
Referring to FIG. 3, in an alternative embodiment, in step four, the resulting single circular permutation has limited expression capacity. The method of generating a new cyclic permutation based on the previous cyclic permutation transformation may generate all possible permutations by: for cyclic permutation
When n is c When =2, the cycle after conversion is [ (a) 1 ,b 2 ),(b 1 ,a 2 )]。
When n is c In case of =3, the cycle after conversion is [ (+ a) 1 ,b 2 ),(b 1 ,b 3 ),(a 2 ,a 3 )](ii) a When n is c >At time 3, the cycle after the conversion is,
then all the resulting cyclic permutations are caused to form a loop, i.e. the first cyclic permutation is identical to the last cyclic permutation.
Referring to FIG. 3, in an alternative embodiment, in step five, each cycle c of the loop is arranged i Whether or not execution is treated as a binary variable alpha i When is alpha i If =1, the exchange of the positions corresponding to the cycles in the arrangement is executed; when alpha is i If =0, the exchange is not performed. Based on the binary parametrization, an arbitrary permutation P can be represented as the current permutation P 0 Product relationship with circulant matrix:
the matrix X (c, α) of whether a loop is executed or not is represented as:
the product relationship and matrix representation only holds if all cycles are independent.
Referring to FIG. 3, in step five, the energy based on shape matching represents E (P) i ,P j )＝v(P i ) T Wv(P j )。
Wherein v (P) i ) To be arranged P i The coded one-hot vector acts on the current permutation P by the execution matrix X (alpha) 0 The post permutation P is one-hot coded into a permutation vector, and the matching energy of the submatrix is expressed as:
wherein Q is the submatrix W S A circularly binary parametrized coupling matrix, the elements of the coupling matrix Q being represented as
Based on the representation of the matrix elements, a binary quadratic unconstrained optimization problem can be constructed.
Referring to fig. 3, in an alternative embodiment, in step six, based on the coupling matrix obtained in step five, the execution parameter α is solved using a quantum simulation bifurcation algorithm. The quantum simulation bifurcation algorithm is based on the coherent Ishige machine inspiration, and effectively reduces the operation of the exponential power order of 2 to the square order by utilizing the natural evolution of quantum physics.
Referring to fig. 3, in an alternative embodiment, in step six, the specific location swap is performed on the current permutation based on the solution result of the quantum simulation bifurcation algorithm. Binary parameter alpha corresponding to each cycle i ，α i =1, the current permutation cycle c is executed i Exchanging positions; alpha (alpha) ("alpha") i When =0, the exchange is not performed.
Referring to fig. 5, in an alternative embodiment, in step seven, the permutation after the position exchange in step six is taken as the current permutation. For each cycle, a coupling matrix Q is generated, so that the quantum simulation bifurcation algorithm can be applied to solve execution parameters at the moment, and the current arrangement is updated.
Referring to fig. 5, in an alternative embodiment, in step eight, one step updates the arrangement for each loop of the loop list in step five, and re-matches the paired point set of dead pixels based on the updated arrangement until convergence. And the convergence is carried out until the matching energy iteration result in the step two is unchanged.
Advantages of the present application include the following: first, qubit based data representation capability is better. And secondly, the matching method based on the analog bifurcation algorithm can process data characteristics on quantum computing equipment and quantum chips in a highly parallel mode. Moreover, compared with the classical algorithm, the matching algorithm based on the simulated bifurcation algorithm has wider application scenes. And faster convergence to steady state during model training based on parameterized quantum wires.
While the above specification teaches the preferred embodiments with a certain degree of particularity, there is shown in the drawings and will herein be described in detail a presently preferred embodiment with the understanding that the present disclosure is to be considered as an exemplification of the principles of the invention and is not intended to limit the invention to the specific embodiment illustrated. Various alterations and modifications will no doubt become apparent to those skilled in the art after having read the above description. Therefore, the appended claims should be construed to cover all such variations and modifications as fall within the true spirit and scope of the invention. Any and all equivalent ranges and contents within the scope of the claims should be considered to be within the intent and scope of the present invention.
Claims (10)
1. A method for realizing shape matching based on a quantum simulation bifurcation algorithm is characterized by comprising the following steps:
the method comprises the steps that a geodesic matrix between data points in different shapes is built by utilizing data sets in different shapes, node arrangement of paired data is initialized, a sub-node set is selected from the node arrangement, and a corresponding energy sub-matrix is built;
and generating a circulation list according to the child node set, and solving a binary parameter of a circulation variable of a coupling matrix based on the circulation list and the energy quantum matrix by a quantum simulation bifurcation algorithm.
2. The method of claim 1, wherein:
the set of child nodes is a set of pairs of child nodes in the arrangement of nodes having a selected degree of mismatch and requirement.
3. The method of claim 1, wherein:
and randomly generating a cyclic permutation with disjoint cycles according to the child node set, and changing the position of each disjoint cycle in the generated cyclic permutation to generate the cyclic list containing the cyclic permutation.
4. The method of claim 1, wherein:
and constructing a coupling matrix of a binary secondary unlimited optimization problem by taking the cycle number as a binary parameter according to the cycle list and the energy submatrix.
5. The method of claim 1, wherein:
and when the binary parameters of the cyclic variables of the coupling matrix are solved by using a quantum simulation bifurcation algorithm, changing the arrangement position of the nodes of the data according to the binary parameters.
6. The method of claim 1, wherein:
the geodesic matrix d is a square matrix with dimensions equal to the number of data points, the diagonal elements are all 0 and the matrix element d ij The geodesic distance of the ith and j data points is shown.
7. The method of claim 6, wherein:
when the number of nodes of the shape is n, the size of the energy matrix is n 2 ×n 2 The elements of the two shape-matched energy matrices W are represented as:
W ikjl ＝W i·n+k，j·n+l ＝|d A (i，j)-d B (k，l)|
where i, j and k, l are the nodes of the two shapes A and B, respectively, the element of the matrix representing the case of the geodesic distance between the two matches (i, k), (j, l), d A And d B Representing a square matrix of shapes a and B.
8. The method of claim 1, wherein:
the cycle number, i.e., 2-cycle c, is composed of 2 positions, and c = (a, b) is expressed as:
wherein x is a matrix of cyclic c visualization, which is used for exchanging the position a and the position b of the arrangement P;
x ij the case where =1 is the case where the first type condition i, j = a, b or b, a is satisfied;
x ii the case where =1 satisfies the second type condition i ≠ a and i ≠ b; and
x ij the case of =0 is the case other than the first and second types of conditions.
9. A method for realizing shape matching based on a quantum simulation bifurcation algorithm is characterized by comprising the following steps:
s1, constructing a geodesic matrix between data points in different shapes based on two data sets in different shapes, and initializing the arrangement of paired data nodes;
s2, selecting paired sub-node sets with inconsistent matching degrees and requirements from the paired node arrangement;
s3, constructing a corresponding energy sub-matrix according to the sub-node set;
s4, randomly generating a cyclic arrangement with disjoint cyclic numbers according to the child node set, changing the position of each disjoint cyclic number in the generated cyclic arrangement, and generating a cyclic list containing the cyclic arrangement;
s5, constructing a coupling matrix of a binary quadratic unlimited optimization problem by taking the cycle number as a binary parameter according to the cycle list and the energy sub-matrix;
and S6, solving binary parameters of the cyclic variables of the step coupling matrix by using a quantum simulation bifurcation algorithm, and changing the arrangement position of the data nodes according to the binary parameters.
10. The method of claim 9, further comprising:
s7, repeating the operations of S5-S6, and traversing each cyclic arrangement in the cyclic list generated in S4 once;
and S8, repeating the operations of S2-S7 according to the new arrangement of the update point set generated in S7 until the result is converged.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104021229A (en) * | 2014-06-25 | 2014-09-03 | 厦门大学 | Shape representing and matching method for trademark image retrieval |
| US20150100289A1 (en) * | 2013-10-09 | 2015-04-09 | Technion Research & Development Foundation Limited | Method and system for shapewise comparison |
| CN111783704A (en) * | 2020-07-07 | 2020-10-16 | 中电万维信息技术有限责任公司 | Face recognition system based on particle swarm optimization radial basis |
| GB202117369D0 (en) * | 2021-12-01 | 2022-01-12 | Mastercard International Inc | Sub-graph isomorphism |
-
2022
- 2022-06-06 CN CN202210631046.8A patent/CN115239980A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20150100289A1 (en) * | 2013-10-09 | 2015-04-09 | Technion Research & Development Foundation Limited | Method and system for shapewise comparison |
| CN104021229A (en) * | 2014-06-25 | 2014-09-03 | 厦门大学 | Shape representing and matching method for trademark image retrieval |
| CN111783704A (en) * | 2020-07-07 | 2020-10-16 | 中电万维信息技术有限责任公司 | Face recognition system based on particle swarm optimization radial basis |
| GB202117369D0 (en) * | 2021-12-01 | 2022-01-12 | Mastercard International Inc | Sub-graph isomorphism |
Non-Patent Citations (2)
| Title |
|---|
| TAORUI JIA, ET AL: "Isometric Shape Matching Based on the Geodesic Structure and Minimum Cost Flow", 《2014 INTERNATIONAL CONFERENCE ON CYBERWORLDS 》, 15 October 2014 (2014-10-15) * |
| 潘珍: "基于轮廓的形状识别方法研究", 《中国优秀硕士学位论文全文数据库 信息科技辑》, vol. 2013, no. 02, 15 February 2013 (2013-02-15), pages 138 - 1329 * |
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