CN106530341B - Point registration algorithm for keeping local topology invariance - Google Patents

Abstract

The invention discloses a point registration algorithm for keeping local topology invariance, which converts the registration problem of points into the matching problem of a graph; wherein, the points in the point set are used as nodes in the graph; defining a neighborhood of nodes in the graph; the node and one point in the neighborhood of the node are connected to form one edge in the local subgraph; dynamically planning the local subgraphs to obtain the matching probability among the local subgraphs; processing the global matching probability through the matching probability between local subgraphs and a relaxation marking method to obtain the corresponding relation between point pairs; and according to the corresponding relation between the point pairs, performing elastic deformation regularization processing on the point set through a thin plate spline function to obtain model parameters. The point registration algorithm for keeping the local topology invariance accurately quantifies the local topology difference, improves the accuracy of the non-rigid registration when large deformation occurs, and improves the robustness of the algorithm when abnormal points exist.

Description

Point registration algorithm for keeping local topology invariance

Technology neighborhood

The invention relates to a point registration algorithm for keeping local topology invariance.

Background

The image registration technology is a very important research subject in the fields of computer vision and image processing, and has been successfully applied to a plurality of important fields such as pattern recognition, medical image processing, digital media and the like; particularly, at present, virtual reality and reality augmentation technologies have gradually come out of laboratories to the lives of people, and are about to become the next economic growth point. And the registration algorithm is a key core algorithm for whether the technology can be successfully applied. The method can be divided into a gray level registration algorithm and a point registration algorithm according to a registration object; the point registration algorithm can effectively reduce the complexity of the algorithm and give consideration to the registration precision, so that the method has high practical application value; therefore, point registration techniques are of particular interest; currently, the point registration technology is classified into a classification-based method and a graph matching-based method according to technical lines.

The registration algorithm based on classification mainly applies a finite mixture model, particularly a Gaussian mixture model; the Chui and Rangarajan convert the feature point registration problem into the maximum likelihood estimation problem through a hybrid model, and the method uses a deterministic annealing mechanism to realize an expectation maximization algorithm, so that the corresponding ambiguity between the point pairs can be directly controlled; the consistency point drift algorithm defines a velocity field function for a centroid in the Gaussian mixture model, namely a template point set in two point sets to be registered, and calculates unknown parameters in the Gaussian mixture model through an expectation maximization algorithm to realize registration.

Horaud et al propose a conditional expectation maximization point registration algorithm, which utilizes an anisotropic covariance model and a conditional expectation maximization algorithm to calculate the registration problem of rigidity and hinge points, and adds an additional uniform component in a mixed model in order to enhance the robustness of the algorithm; but the strategy cannot simultaneously fit abnormal points mixed in two point sets; sanroma et al proposed a rigid point registration algorithm using point-neighborhood relations and extended a non-rigid registration version.

However, these methods assume an average mixing weight as an inappropriate prior probability, and in fact use a simplified posterior probability; the abnormal points appearing in the two point sets are not accurately fitted in the mixed model, so that the robustness of the algorithm to the abnormal points is reduced, and particularly when the abnormal points appear in the two point sets at the same time, the registration accuracy is obviously reduced.

The method based on graph matching is to convert the point registration problem into the graph matching problem, in the method, points in a point set are used as nodes in a graph, and connecting lines between the points lower than a set threshold are used as edges of the graph; the registration of the sets of points is achieved by maximizing the number of matched edges, each added by a row and a column for fitting outliers in the two sets of points when computing the similarity matrix between the two sets of points.

Chui et al propose a robust point registration method, integrate the point deformation and correspondence into an objective function, and solve the optimization problem through soft distribution and deterministic annealing; zheng et al propose to maintain the neighborhood relations between local points in the registration process and define a matching probability function that computes the point neighborhood relations based on the shape context.

However, when the point neighbor relation is calculated, the matching probability among all neighborhood points is counted, and a large amount of redundant information is contained; lee et al used the label relaxation method and quantified the matching correlation between pairs of points by discrete angle and radius differences; when the topological difference between the comparison point and the adjacent domain is compared, the similarity probability is calculated in a one-to-many mode; the method ignores prior probability among local matching points, namely ignores the similarity probability among local point pairs when calculating local similarity, and does not establish a corresponding relation among neighborhood points, thereby reducing the accuracy of registration.

Disclosure of Invention

Aiming at the defects in the prior art, the point registration algorithm for maintaining the local topology invariance accurately quantifies the local topology difference, improves the accuracy of non-rigid registration when large deformation occurs, and improves the robustness of the algorithm when abnormal points exist.

In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a point registration algorithm for maintaining local topology invariance is provided, which comprises the following steps:

s1, converting point registration into matching of a graph; wherein, the points in the point set are used as nodes in the graph;

s2, defining a neighborhood of the nodes in the graph; the node and one point in the neighborhood of the node are connected to form one edge in the local subgraph;

s3, dynamically planning the local subgraphs to obtain the matching probability among the local subgraphs;

s4, processing the global matching probability through the matching probability among the local subgraphs and a relaxation marking method to obtain the corresponding relation among the point pairs;

and S5, according to the corresponding relation between the point pairs, performing elastic deformation regularization processing on the point set through a thin plate spline function to obtain model parameters.

Further, the detailed step of S2Comprises the following steps: let S_T＝{t₁,t₂...t_mDenotes a set of points T containing m points, for a given point T_i∈S_TDefinition of t_iIs a neighborhood ofWherein X is X at points t_iPoints within a circular neighborhood; point t_iAnd its neighborhoodForm a point t_iPartial subgraph of, t_iRespectively and neighborhoodThe points in (1) are connected into edges of the local subgraph.

Further, the radius of the neighborhood is S_TThe mean of the euclidean distances between all pairs of points in (a).

Further, the specific step of S3 is: dividing the dynamic programming into n stages, wherein n is expressed as the number of edges in the local subgraph; analyzing edges in the local subgraph to obtain the cost of each edge; calculating the cost difference between any two edges of each stage according to a cost difference calculation function formula; and planning the cost according to the matching function to obtain the matching probability among the local subgraphs.

Further, the specific step of S32 is: using log distance and polar coordinate angle to scale neighborhood, setting central point t_iIs 0, the farthest distance is 6, the distance from the center point to the neighborhood point isDividing 12 different angle values in 30 degrees; to be provided withRepresenting an angle value between the central point and the neighborhood points, wherein the distance line and the angle line divide the neighborhood range into 72 grids; by pointThe distance value and the angle value of the grid form a binary groupI.e. the cost of the edge.

Further, the cost difference is calculated by the formula Wherein, the parameters alpha and beta are respectively used for adjusting the weight occupied by the radius and the angle when calculating the cost difference, (u)_d,σ_d) And (u)_θ,σ_θ) The mean and variance of the corresponding radius and angle, respectively.

Further, the matching probability between local subgraphs is:

wherein the content of the first and second substances,denoted as point u in subgraph M corresponds to point v in subgraph N, ω is the weight parameter.

Further, the specific step of S4 is:

the corresponding probability between each pair of points is represented by a probability matrix P of (M +1) × (N + 1):

if point m and point n match, then probability p_mn1, otherwise p_mnAt this point, the extra row and column are used to fit the outliers in the set of points, while the matrix satisfies:

and updating the probability matrix P in an iterative manner, and endowing the corresponding relation between the point pairs according to the current maximum matching probability.

Further, the specific step of S5 is:

and performing elastic deformation regularization of the point set through the thin plate spline function, estimating deformation model parameters of the thin plate spline function by using matched point pairs in an iteration process, and then calculating the next deformation position of the template point set by using the obtained model parameters until the parameters converge to a global optimal solution.

The invention has the beneficial effects that: the point registration algorithm for keeping local topological invariance converts point registration into matching of a graph, and an accurate local topological relation is kept in the registration process; obtaining the topological difference among local subgraphs through dynamic planning, optimizing by using a relaxation marking method to obtain the corresponding relation among point pairs, and then performing elastic deformation regularization on a point set through a thin plate spline function; the global probability of matching between two point sets is guided through the matching probability between local subgraphs, the topological stability between the nodes and the neighborhood points is always kept in the process of point registration deformation, and the accuracy and the robustness of the algorithm are improved.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiment is only one embodiment of the present invention, and not all embodiments. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the protection scope of the present invention.

For simplicity, common technical knowledge known to those skilled in the art is omitted below.

The point registration algorithm for keeping local topological invariance comprises the following steps:

s1, converting point registration into matching of a graph; wherein the points in the point set are used as nodes in the graph.

S2, defining a neighborhood of the nodes in the graph; the node and one point in the neighborhood of the node are connected to form one edge in the local subgraph; in a specific implementation, the registration of points is translated into matching of graphs, and the problem of the registration of points is translated into the problem of the number of matching edges in two graphs.

In actual practice, let S_T＝{t₁,t₂...t_mDenotes a set of points T, S containing m points_D＝{d₁,d₂...d_nDenotes a set of points D containing n points, the point matching being to find a matching functionEstablishing a corresponding relation between the two point sets; when the number of the points in the two point sets is not equal or the abnormal points exist in the point sets, a one-to-one corresponding relation cannot be formed; at this time, a pseudo point nil point is added to each of the two point sets to represent the unmatched points or abnormal points, and the two point sets are expanded to S'_T＝{t₁,t₂...t_MNil and S'_D＝{d₁,d₂...d_NNil }; at this time, the corresponding relationshipThen a one-to-one correspondence is satisfied and the points that cannot be matched or outliers will correspond to the pseudo-points nil.

When the two point sets are subjected to non-rigid deformation, the distance change between the points can be any; however, the nodes and the neighborhoods thereof keep relatively fixed relationships; namely, under the condition of non-rigid deformation, the local neighborhood relationship or the topological structure of the node still keeps the stability, and based on the principle, the corresponding optimization functionComprises the following steps:wherein the content of the first and second substances,

for a given point t_i∈S_TDefinition of t_iIs a neighborhood ofWherein X is X at points t_iPoints within a circular neighborhood; point t_iAnd its neighborhoodForm a point t_iPartial subgraph of, t_iRespectively and neighborhoodThe points in (1) are connected into the edge of the local subgraph; radius of neighborhood is S_TThe mean of the euclidean distances between all pairs of points in (a).

S3, dynamically planning the local subgraphs to obtain the matching probability among the local subgraphs; in a specific implementation, dynamic programming is divided into n stages, wherein n is expressed as the number of edges in a local subgraph; analyzing edges in the local subgraph to obtain the cost of each edge; calculating the cost difference between any two edges of each stage according to a cost difference calculation function formula; and planning the cost according to the matching function to obtain the matching probability among the local subgraphs.

In actual operation, the neighborhood is calibrated by using log distance and polar coordinate angle, and a central point t is set_iIs 0, the farthest distance is 6, the distance from the center point to the neighborhood point isDividing 12 different angle values in 30 degrees; to be provided withRepresenting an angle value between the central point and the neighborhood points, wherein the distance line and the angle line divide the neighborhood range into 72 grids; by pointThe distance value and the angle value of the grid form a binary groupI.e. the cost of the edge.

The cost difference between the two edges is calculated by the formula Wherein, the parameters alpha and beta are respectively used for adjusting the weight occupied by the radius and the angle when calculating the cost difference, (u)_d,σ_d) And (u)_θ,σ_θ) Respectively mean values and variances of corresponding radii and angles; at this time, the matching probability between the local subgraphs is:wherein the content of the first and second substances,denoted as point u in subgraph M corresponds to point v in subgraph N, ω is the weight parameter.

S4, processing the global matching probability through the matching probability among the local subgraphs and a relaxation marking method to obtain the corresponding relation among the point pairs; in a specific implementation, the probability matrix P of (M +1) × (N +1) is used to represent the corresponding probability between each pair of points:

if point m and point n match, then probability p_mn1, otherwise p_mnAt this point, the extra row and column are used to fit the outliers in the set of points, while the matrix satisfies:

and updating the probability matrix P in an iterative manner, and endowing the corresponding relation between the point pairs according to the current maximum matching probability.

S5, according to the corresponding relation between the point pairs, performing elastic deformation regularization processing on the point set through a thin plate spline function to obtain model parameters; in specific implementation, elastic deformation regularization of the point set is performed through a thin-plate spline function, deformation model parameters of the thin-plate spline function are estimated through matched point pairs in an iteration process, and then the next deformation position of the template point set is calculated through the obtained model parameters until the parameters converge to a global optimal solution.

The improvement of the point registration algorithm for keeping the local topology invariance and the specific implementation process thereof are as follows:

the point registration algorithm for keeping the local topology invariance converts the point registration problem into graph matching, points in a point set serve as nodes in a graph, and the nodes and one point in the neighborhood of the nodes form one edge in the graph; in this way, the point registration problem translates into a problem of the number of matching edges in the graph.

Let S_T＝{t₁,t₂...t_mAnd S_D＝{d₁,d₂...d_nRespectively representing a point set T containing m points and a point set D containing n points, wherein point matching is to find a matching functionEstablishing a corresponding relationship between the two point setsWhen the number of points in the two point sets is not equal or abnormal points exist in the point sets, a one-to-one corresponding relation cannot be formed; adding a pseudo point nil point to the two point sets respectively to represent the points which cannot be matched or abnormal points; then the two point sets are augmented to S'_T＝{t₁,t₂...t_MNil and S'_D＝{d₁,d₂...d_NNil }. At this time, the corresponding relationshipThen a one-to-one correspondence is satisfied and the points that cannot be matched or outliers will correspond to the pseudo-points nil.

When the two point sets are subjected to non-rigid deformation, the distance change between the points can be any; however, the nodes and the neighborhoods thereof keep relatively fixed relationships; namely, under non-rigid deformation, the local neighborhood relationship or the topological structure of the node still maintains stability, and based on the principle, the corresponding optimization function nil is as follows:wherein the objective function

Due to N_mIs a neighborhood of point m, while the neighborhood relationship is symmetric, i.e., if i ∈ N_mThen m ∈ N_i. f (m), f (n) represents a neighborhood system of corresponding points of the two point sets; d (f (m), f (n)) measures the distance between the two neighborhood systems, and a distance of 1 indicates that the two neighborhood systems match, i.e., the neighborhood relationship or topology is better maintained, otherwise 0.

In the non-rigid registration process, the better the stability of the local topological structure is kept, and the higher the accuracy and robustness of the registration algorithm is; since the elastic deformation of the set of points can be arbitrary, but if the topological relationship of the node and its neighborhood changes, thenThe deformation can be regarded as meaningless, at this time, the corresponding relation between the two point set shapes is lost, the Euclidean distance between the points is simply used in the algorithm of the prior art to describe the neighborhood relation and the difference between the neighborhoods, and at this time, the objective function is usedSubstitution formulaWherein the content of the first and second substances, the same applies to the remaining sets of points.

When the matching function f realizes the accurate one-to-one correspondence relationship, then Is zero; no matter Euclidean distance is used or radius angle difference is used, when local topological structure difference is quantified, the corresponding relation between local neighborhood points is ignored in the methods, only probability summation is carried out on all possible corresponding points, and the local matching probability between neighborhoods of two points is as follows: q. q.s_m,n＝∑_i∈M∑_j∈Ns_i,j。

For a given point t_i∈S_TDefinition of t_iIs a neighborhood ofWherein X is X at points t_iPoints within a circular neighborhood; point t_iAnd its neighborhoodForm a gateAt point t_iPartial subgraph of, t_iRespectively and neighborhoodThe points in (1) are connected into the edge of the local subgraph; radius of neighborhood is S_TThe mean of the euclidean distances between all pairs of points in (a).

The log distance and the polar coordinate angle are used for calibrating the neighborhood, and a central point t is set_iIs 0, the farthest distance is 6, the distance from the center point to the neighborhood point isDividing 12 different angle values in 30 degrees; to be provided withRepresenting an angle value between the central point and the neighborhood points, wherein the distance line and the angle line divide the neighborhood range into 72 grids; wherein, point t_iAnd its neighborhoodForm a point t_iPartial subgraph of, t_iRespectively and neighborhoodThe points in (1) are connected into the edge of the local subgraph; by pointThe distance value and the angle value of the grid form a binary groupI.e. the cost of the edge.

The cost difference between the two edges is calculated by the formula Wherein the content of the first and second substances,the parameters alpha and beta are respectively used for adjusting the weight occupied by the radius and the angle in the process of calculating the cost difference, (u)_d,σ_d) And (u)_θ,σ_θ) Respectively mean values and variances of corresponding radii and angles; obviously, the sum of the cost differences of all corresponding edges in the two local subgraphs at this time is the local topological structure difference of the current point; if the topology of the local subgraph m is identical to that of the local subgraph n, the sum of the cost differences of the corresponding edges is zero, and the similarity of the corresponding edges is the maximum.

However, due to the lack of prior probability of local correspondence, equation q_m,n＝∑_i∈M∑_j∈Ns_i,jThe difference of the topological structure cannot be accurately quantified, and in order to obtain the corresponding probability of an edge in a local subgraph, namely the probability that an edge i in a local subgraph m corresponds to an edge j in a local subgraph n, the cost difference between the local subgraphs is solved and converted into a dynamic plan of an n-stage minimized objective function; at this time q_m,n＝∑_i∈M∑_j∈Ns_i,jConversion to q_m,n＝Min(∑_i∈M∑_j∈Ns_i,j)。

At this time, the number n of edges in the local subgraph represents n stages of the dynamic programming, and each stage is according to the cost differenceAnd calculating the cost difference of the two edges, and solving the minimum cost sum as the optimal solution according to the target function, wherein the sum of the obtained minimum cost difference is the required topological structure difference between the two local subgraphs.

When the local matching is converted into dynamic planning, a certain stage k is set, and each matched characteristic point is used as a stage; state variable x_KTo match the total candidate x k points ahead_K＝{x₁,x₂...x_n-k+1}; decision variable d_kA corresponding candidate point of the kth matching point; decision admission set of d_k∈x_K(ii) a The equation of state transition is x_K+1＝x_K-d_k(ii) a The stage index is V_k(x_k,d_k) (ii) a Recursive equationIs f_k(x_k)＝max{V_k(x_k,d_k)+f_k+1(x_k+1) }; initial conditions are f_K(x_K)＝V_K(x_K,d_k) (ii) a End point condition is f₁(x₁)＝max{V₁(x₁,d₁)+f₂(x₂) In which f₂(x₂) Can be obtained in the preceding step k-1.

The corresponding relation of points between subgraphs can be obtained by solving the dynamic programming problemIt represents that point u in the local subgraph M corresponds to point v in the local subgraph N; through the similarity measurement and dynamic planning between the point pairs, the prior probability of topological structure similarity between local subgraphs can be established; at this time, the matching probability between the local subgraphs isω is a weight parameter.

Then, processing the global matching probability through the matching probability between local subgraphs and a relaxation marking method to obtain the corresponding relation between point pairs; in the specific implementation, the graph matching optimization problem is solved by using a relaxation labeling method, a probability matrix P of (M +1) × (N +1) is used to represent the corresponding probability between each point pair, and the rate matrix is:

if point m and point n match, then probability p_mn1, otherwise p_mnAt this point, the extra row and column are used to fit the outliers in the set of points, while the matrix satisfies:

based on the probability matrix, the objective function can be obtained The rewrite is:by the formulaAnd iteratively updating the probability matrix P, and then endowing the corresponding relation between the point pairs according to the current maximum matching probability.

And finally, performing elastic deformation regularization of the point set by a thin plate spline function, estimating deformation model parameters by the matched point pairs in an iteration process, and then calculating the next deformation position of the template point set by using the obtained model parameters until the parameters converge to a global optimal solution.

In an actual experiment, firstly initializing parameters and assigning initial values; then calculating the matching probability between the shape context of the points in the two sets and the point pairs based on the shape context; then, initializing a matching probability matrix P by using the probability and regularizing; and according to the formulaCalculating the matching probability of the topological structure between the local subgraphs; using the formulaAnd updating the matching probability matrix P, and meanwhile, carrying out regularization processing on rows and columns of P.

Then, according to the matching probability of the point pairs in the P, calculating deformation parameters of the thin plate spline function; updating the next position of the point set according to the thin plate spline function deformation parameters; adding 1 to the iteration times in sequence, and when the maximum iteration number I is reached_maxTime or maximum matchAnd counting the number of points, ending, or restarting to calculate the matching probability between the shape context of the points in the two sets and the point pairs based on the shape context.

In a specific experiment, two point sets, namely a fish-shaped point set and a Chinese character shape point set, can be used, and for testing the performance of the algorithm, the model point set is subjected to degradation processing of non-rigid deformation, deformation and partial contour point deletion and abnormal point addition in different degrees; dividing each image into 5-6 degradation levels from weak to strong, and randomly generating 100 test point sets on each degradation level according to the degradation degree; the performance error of the algorithm is measured by the mean Euclidean distance of two point sets after registration, and meanwhile, the variance distribution of the error is given.

The point registration algorithm for keeping the local topological invariance considers the local topological relation of points, and takes the corresponding relation between the local points as the prior probability of point registration; meanwhile, based on the position relation between the point pairs in the local subgraph, namely the corresponding relation of edges in the local subgraph, the topological difference between the local subgraphs is obtained through dynamic programming, and the global matching probability of matching between two point sets is guided through the local topological structure matching probability, so that the topological stability between the nodes and the neighborhood points is always kept in the process of point registration deformation.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

1. A point registration algorithm that preserves local topology invariance, comprising:

s1, converting point registration into matching of a graph; wherein, the points in the point set are used as nodes in the graph;

s2, defining a neighborhood of the node in the graph; the node and one point in the neighborhood of the node are connected to form one edge in the local subgraph;

the specific steps of S2 are as follows:

let S_T＝{t₁,t₂...t_mDenotes a set of points T containing m points, for a given point T_i∈S_TDefinition of t_iIs a neighborhood ofX is 1,2.. X; wherein X is X at points t_iPoints within a circular neighborhood; point t_iAnd its neighborhoodForm a point t_iPartial subgraph of, t_iRespectively and neighborhoodThe points in (1) are connected into the edge of the local subgraph;

s3, dynamically planning the local subgraphs to obtain the matching probability among the local subgraphs;

s4, processing the global matching probability through the matching probability among the local subgraphs and a relaxation marking method to obtain the corresponding relation among the point pairs;

and S5, according to the corresponding relation between the point pairs, performing elastic deformation regularization processing on the point set through a thin plate spline function to obtain model parameters.

2. The local topology invariance preserving point registration algorithm of claim 1, characterized by: radius of the neighborhood is S_TThe mean of the euclidean distances between all pairs of points in (a).

3. The local topology invariance preserving point registration algorithm of claim 1, characterized by: the specific steps of S3 are as follows:

s31, dividing the dynamic programming into n stages, wherein n represents the number of edges in a local subgraph;

s32, analyzing the edges in the local subgraph to obtain the cost of each edge;

s33, calculating the cost difference between any two edges of each stage according to a cost difference calculation function formula;

and S34, planning the cost according to a matching function to obtain the matching probability among the local subgraphs.

4. The point registration algorithm for maintaining local topology invariance as claimed in claim 3, wherein the specific steps of S32 are:

scaling the neighborhood using log distance and polar angle, setting a center point t_iIs 0, the farthest distance is 6, the distance from the center point to the neighborhood point isDividing 12 different angle values in 30 degrees; to be provided withRepresenting an angle value between the central point and the neighborhood points, wherein the distance line and the angle line divide the neighborhood range into 72 grids; by pointThe distance value and the angle value of the grid form a binary groupI.e. the cost of the edge.

5. The point registration algorithm for preserving local topology invariance as claimed in claim 4, wherein the cost difference calculation formula is:

wherein, the parameters alpha and beta are respectively used for adjusting the weight occupied by the radius and the angle when calculating the cost difference, (u)_d,σ_d) And (u)_θ,σ_θ) The mean and variance of the corresponding radius and angle, respectively.

6. The point registration algorithm for preserving local topology invariance as claimed in claim 1, wherein the matching probability between the local subgraphs is:

wherein the content of the first and second substances,denoted as point u in subgraph M corresponds to point v in subgraph N, ω is the weight parameter.

7. The point registration algorithm for maintaining local topology invariance as claimed in claim 1, wherein the specific steps of S4 are:

the corresponding probability between each pair of points is represented by a probability matrix P of (M +1) × (N + 1):

if point m and point n match, then probability p_mn1, otherwise p_mnAt this point, the extra row and column are used to fit the outliers in the set of points, while the matrix satisfies:

and updating the probability matrix P in an iterative manner, and endowing the corresponding relation between the point pairs according to the current maximum matching probability.

8. The point registration algorithm for maintaining local topology invariance as claimed in claim 7, wherein the specific steps of S5 are:

and performing elastic deformation regularization of the point set through the thin plate spline function, estimating deformation model parameters of the thin plate spline function by using matched point pairs in an iteration process, and then calculating the next deformation position of the template point set by using the obtained model parameters until the parameters converge to a global optimal solution.