CN109697692B - Feature matching method based on local structure similarity - Google Patents
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Abstract
The invention provides a feature matching method based on local structure similarity, which is used for solving the problem that the matching result is not ideal due to noise interference in the image registration process. The method comprises the following steps: step 1, performing feature extraction and initial matching on two images to be matched; step 2, establishing a neighborhood affine coefficient matrix of the feature points; step 3, calculating the difference of the neighborhood affine coefficient matrixes of the feature points associated with each matching in the initial matching set; step 4, optimizing the neighborhood affine coefficient matrix to obtain the difference degree of the local structure; and 5, setting a comparison threshold according to the local structure difference value of each matched and associated feature point, and determining a final feature matching pair as a matching relation result of the image to be matched. The invention technically overcomes the problems of complex optimization process and slow convergence in the prior art, and effectively improves the matching efficiency.
Description
Technical Field
The invention belongs to the field of image processing, particularly relates to image processing when matching is not accurate enough under the influence of image noise, and particularly relates to a feature matching method based on local structure similarity.
Background
With the rapid development of multimedia technology, images have become important carriers for transmitting information, and digital image processing technology has highlighted its importance, wherein image matching technology is the key content of people's attention in recent years. Because other research directions of digital image processing technology, such as image recognition, image retrieval, and target recognition, target tracking, etc., are further developed on the basis of image matching technology. It can be said that the progress of the image matching technology can drive the development of the digital image processing technology as a whole. However, the image matching technology is not only a research hotspot, but also a research difficulty. The matching is aimed at finding an exact correspondence relation for the same object in the image, but the implementation process is limited. For example, the images to be matched may come from different photographic devices, different shooting scenes, or even different shooting times. The differences of the storage devices, the transformation of the visual angle and the illumination and the clutter of the background bring about the distortion of objects, geometric deformation, noise interference and the like, and the influences undoubtedly bring about huge tests for the image matching technology.
In recent years, a great deal of research has been carried out on image matching techniques by a large number of scholars, and a good academic achievement is achieved. A general image matching method is performed based on image feature points and feature description vectors. An initial set of matches is obtained by computing the distance between the feature descriptions. Because the common feature extraction algorithm has good distinguishability and scale invariance, a great part of initial matching set obtained through feature description can be ensured to be correct matching pairs. The subsequent algorithm is to remove the error matching in the initial matching set by setting geometric constraint or relationship constraint to obtain the final correct matching set. Most commonly, the optimization process of the matching set is implemented by using a graph matching algorithm. The vertex in the graph represents image characteristic points, the edge in the graph represents image characteristic point association, the similarity between points and the similarity between the edges are represented by energy functions, and the matching constraint effect is achieved by minimizing the functions. And performing secondary optimization on the basis, selecting 3 neighbor points around the key point to linearly represent the point, acting the obtained coefficient matrix on the corresponding matching point, substituting the coefficient matrix into an energy function formula, solving by using linear programming, and determining a final matching result. However, the selection of the neighbor points is not flexible enough, the subsequent solving process is too complex, the time and the cost are large, and the high efficiency of matching cannot be realized.
Disclosure of Invention
Aiming at the problems existing in the matching method, the invention provides a feature matching method based on local linear structure similarity. Compared with the prior art, the method flexibly utilizes the image structure information, simplifies the calculated amount in the optimization process, and greatly improves the matching accuracy and recall rate.
The invention aims to: the invention aims to solve the problem that the existing matching method is insufficient, and provides a feature matching method based on local structure similarity.
The technical scheme is as follows: the invention relates to a characteristic matching method based on local structure similarity, which is characterized in that image characteristic description is extracted to obtain an initial matching set, adjacent points of key points are used for linearly representing the key points to obtain a coefficient matrix, and measuring the geometric consistency of the local areas of the key points of the matching pairs based on the coefficient matrix, taking the consistency as a confidence judgment standard, deleting the matching pairs with small confidence, keeping the high confidence, and determining a final matching set. The method specifically comprises the following steps:
step 1, performing feature extraction and initial matching on two images to be matched so as to obtain a relation set corresponding to the initial matching;
step 2, determining neighbor points of each feature point for the feature points determined in the initial matching set obtained in the step 1, and establishing a neighborhood affine coefficient matrix of the feature points according to the neighbor points;
and 3, calculating the difference of the neighborhood affine coefficient matrixes of the feature points associated with the initial matching set for each matching in the initial matching set, and expressing the local structural similarity between the feature points associated with each matching by using the difference. The smaller the difference value is, the higher the local structural similarity is, the larger the difference is, the lower the local structural similarity is;
step 4, optimizing the neighborhood affine coefficient matrix, defining a function formula for calculating the local structure difference degree by taking the neighborhood affine coefficient matrix as a variable, solving the corresponding neighborhood affine coefficient matrix when the function formula is used for taking an extreme value, and substituting the coefficient matrix into the function formula for calculating the local structure difference degree of the characteristic point;
and 5, setting a comparison threshold according to the local structure difference value of each matched and associated feature point obtained in the step 4, keeping the matching with the difference value lower than the threshold, deleting the matching with the difference value not lower than the threshold, and determining the final feature matching pair as the matching relation result of the image to be matched.
Further, the detailed steps of the invention are as follows:
step 1, image feature extraction and initial matching: and extracting local characteristic points of the image to be matched, namely finding distinguishable key points which have stronger robustness on image transformation and high detection repetition rate in the image. And performing gradient statistical calculation on the detected local area of the feature point to complete the feature description process of the feature point. And calculating the Euclidean distance value between the descriptor of any one feature point and the description of other feature points, and selecting the feature point with the minimum Euclidean distance value as the matching point of the feature point. Collecting all the characteristic points and the matching points thereof to form an initial image matching set;
step 2, establishing a neighborhood affine coefficient matrix of key points in the matching pair: on the basis of obtaining an initial matching set in the step 1, for each local feature point in the matching set, finding other feature points within a certain range from the local feature point as neighborhood feature points of the local feature point, linearly representing the key point by using the neighborhood feature points, and obtaining a corresponding affine coefficient matrix;
step 3, measuring the local structure difference degree based on the neighborhood affine coefficient matrix: for each match in the initial matching set obtained in step 1, obtaining a neighborhood affine coefficient matrix of the feature point associated with each match through step 2, and calculating a difference value of the two neighborhood affine coefficient matrices, wherein the difference value represents the local structure difference degree of the feature point associated with each match. The smaller the difference value is, the higher the local structural similarity is, the larger the difference is, the lower the local structural similarity is;
step 4, neighborhood affine coefficient matrix optimization: defining a function formula for calculating the local structure difference degree by taking a neighborhood affine coefficient matrix as a variable, wherein the function formula consists of the sum of two data items, the two data items are respectively the difference of affine combinations consisting of characteristic points corresponding to initial matching set matching and the neighborhood affine coefficient matrix, the aim of solving the formula is to make the value of the function as close to zero as possible, obtain the neighborhood affine coefficient matrix corresponding to the function formula at an extreme point, and bring the neighborhood affine coefficient matrix into the function formula to calculate the local structure difference degree of the characteristic points;
and 5, comparing the threshold value of the local structure difference value corresponding to each matching in the step 4, wherein when the difference value is smaller than a specified threshold value, the corresponding characteristic point pair belongs to a correct matching pair, and when the difference value is not smaller than the specified threshold value, the corresponding characteristic point pair belongs to an incorrect matching pair, removing the incorrect matching pair from the initial matching corresponding relation set, and taking all the remaining matching pairs as final correct matching results and outputting the final correct matching results.
Further, the implementation process of step 1 is specifically as follows: step 1.1, image feature extraction: and (3) extracting image features by adopting a classical Scale Invariant Feature Transform (SIFT) feature description operator. Taking a pair of images I and I' to be matched as input of an SIFT algorithm to perform feature extraction, and acquiring SIFT feature points and 128-dimensional feature description vectors corresponding to the feature points;
step 1.2, initially matching features: according to the characteristic vectors obtained in the step 1.1, the single characteristic description vectors of the two images I and I' to be matched are respectively X i 、X j Calculating the Euclidean distance d (X) between two vectors i ,X j ) If and only if X i Distance to d (X) of all other feature description vectors i ,X j ) When the ratio of (A) to (B) is greater than a set threshold value, we consider X to be i And X j And if the ratio is less than or equal to the set threshold value, the corresponding characteristic points are considered as unmatched. The distance between feature description vectors is formulated as:
where k denotes the 128-dimensional eigenvector dimension index number, the range is [1,128 ]]。X ik Representing vector X i The k-th dimension component, X jk Representing vector X j The k-th dimension component of (a);
in other words, the present step is: giving an image pair to be matched, measuring the distance values of all the feature description vectors in one image and the feature description vectors in the other image one by one, and selecting the corresponding feature point with the minimum distance value as the initial matching, so that each matching pair corresponds to the feature region in the image to be matched. And collecting all the initial matching pairs to form an initial matching set of the image to be matched.
The step 2 is as follows: step 2.1, selecting key neighborhood points: obtaining an initial matching set of the image according to the step 1.2, and enabling any matching M in the matching set to correspond to the feature point pair (p, p '), wherein the feature point p belongs to the image I to be matched, and p'Correspondingly, points matched with the characteristic points p in the image I' to be matched are obtained; find other matches that match M neighbors and let the corresponding pairs of feature points be (q) i ,q i ') to a host; when the feature points p and q are i Simultaneous feature points p' and q i When the spatial distance value of' is smaller than a prescribed threshold value, we consider the feature point q i Neighbor points belonging to feature point p, feature point p' belonging to feature point q i ' and when the distance value is greater than or equal to a prescribed threshold value, we consider the feature points p and q i P' and q i ' has no neighbor relation; the neighbor relation judgment formula is as follows:
||p-q i ||＜τ,and||p'-q i '||＜τ,
where τ represents a similarity threshold between a keypoint and its neighbors. The tau is set to ensure that the key point p of the image to be matched has k nearest neighbors on average, and the setting of the k value can be specifically set according to the local neighborhood information of the key point, so that the structural information of the key point can be more accurately represented. i represents the number of neighbor points of the characteristic point p, the value range is [1,k ], and the value of tau can be adjusted in experiments so as to flexibly change the size of k. Calculating a neighbor relation judgment formula of each feature point and other feature points to obtain a neighbor point set of each feature point; namely, the neighbor points of the image points to be matched are determined through the step;
step 2.2, establishing a neighborhood affine coefficient matrix of key points in the matching pair: based on the step 2.1, determining the neighbor points of the image points to be matched, and integrally representing the neighbor points of the corresponding feature points p of any matching M in the image I as
Where k denotes the number of neighbors of a feature point p, q i The ith neighbor point representing p; following the local Linear Embedding (localization Linear Embedding) theory, the geometry near the image feature point p can be represented by its neighborhood affine coefficient matrix w = [ w = ] 1 ,...,w i ,...] T To depict, the feature point p uses its determined neighbor point set
Is expressed as: p = ∑ w i q i Where Σ w i =1; and for the matched feature point p 'corresponding to the feature point p on the image I', using a neighborhood affine coefficient matrix w '= [ w' 1 ,...,w' i ,...] T P ' = Sigma w ' is obtained ' i q' i Of which is ∑ w' i =1, thus completing the establishment of the key point neighborhood affine coefficient matrix;
the step 3 is as follows: and (3) judging the local structural similarity of the matching points: through the processing of the image feature points in the step 2, neighborhood affine transformation matrixes w and w ' of feature point pairs (p, p ') associated with any matching M in the initial matching set are obtained, because the neighborhood affine coefficient matrixes describe the local structural geometric properties of the feature points, the corresponding matching pairs are correctly represented if the corresponding matching pairs are consistently represented by the neighborhood coefficient matrixes of the matching feature point pairs, namely when w = w ', the corresponding matching pairs are reserved as correct matching pairs, and if the two are not equal, the matching pairs are determined as wrong matching pairs and deleted;
and 4, optimizing the feature point neighborhood affine coefficient matrix as follows: in order to optimize the neighborhood affine coefficient matrix of the feature points, an optimal neighborhood affine coefficient matrix is found
Neighbor point set with feature point p
Linear combination, subtraction with characteristic point p, obtaining difference value of the two and carrying out normal form processing, and using optimal affine coefficient matrix coefficient vector
Set of neighbor points of matching point p' with feature point p
Linearly combined, thereafter withSubtracting the characteristic points p' and carrying out normal form processing; defining matrix covariance J composed of the sum of the above two normal forms, and representing the local structure difference degree of the matching point pair; the matrix covariance J is specified as follows:
the feature points associated in the same image for correct matching of the same object in the images to be matched are usually adjacent in spatial position, and similar topological structures are shared between the two images to be matched due to physical constraints, so that the solution goal of the corresponding matrix covariance is to make the value of J as small as possible. And correspondingly, geometric structures represented by the feature points of the adjacent areas of the feature points which are in the mismatching correspondence are difficult to keep consistent on different images, so the matrix covariance J provides a good judgment method for judging the local structural similarity of the feature points, namely the accuracy of the matching in the initial matching set.
The step 5 is as follows: and (5) obtaining the difference degree of the local structure of each matched and corresponding characteristic point, namely the value of the matrix covariance, based on the step 4. Setting a smaller threshold, and defining that when the matrix covariance of the feature point is less than the set threshold, the matching associated with the feature point is considered to be correct matching and is retained to a final matching set, otherwise, when the matrix covariance of the feature point is greater than the set threshold, the matching associated with the feature point is considered to be wrong matching and is deleted; and finally, taking all the reserved matching sets as a final image matching result set.
Advantageous technical effects
The feature matching method provided by the invention is used for solving the problem that the matching result is not ideal due to noise interference in the image registration process. A feature matching method based on local structural similarity is adopted. The method comprises the following steps: step 1, performing feature extraction and initial matching on two images to be matched so as to obtain a relation set corresponding to the initial matching; step 2, determining the neighbor points of each feature point for the feature points determined in the obtained initial matching set, and establishing a neighborhood affine coefficient matrix of the feature points according to the neighbor points; step 3, calculating the difference of the neighborhood affine coefficient matrixes of the feature points associated with the initial matching set for each matching in the initial matching set, and expressing the local structural similarity between the feature points associated with each matching by using the difference; step 4, optimizing the neighborhood affine coefficient matrix, defining a function for calculating the local structure difference degree by taking the neighborhood affine coefficient matrix as a variable, taking an extreme value of the function and further obtaining the local structure difference degree; and 5, setting a comparison threshold according to the local structure difference value of each matched and associated feature point, keeping the matching with the difference value lower than the threshold, deleting the matching with the difference value not lower than the threshold, and determining the final feature matching pair as the matching relation result of the image to be matched.
The invention relates to an image matching method based on local structure similarity, which is an effective solution designed aiming at the problem of noise interference which cannot be avoided by the current image matching technology. Definition by affine relation between image characteristic point and its neighbor pointSpecially for treating diabetes The local structure description of the characteristic points is compared with the local structure of the matched characteristic points to delete the error matching, thereby removing the noise The object of (1). The invention mainly establishes the idea that the matching pair which maps the same object in the image to be matched is usually positioned in the adjacent area On the basis of thinking, the noise point cannot simultaneously satisfy two constraints of a neighborhood point range and a similar local structure, so that the noise point can be effectively used Ground excludes noise. In the course of this particular implementation of the invention,the self structural information of the image is flexibly utilized, the constraint of affine relation is given, the image matching is accurately realized, the calculation process is simplified, the problems of complexity and slow convergence of the optimization process in the prior art are technically solved, and the matching efficiency is effectively improved.
Drawings
FIG. 1 is a basic flow diagram of the process of the present invention
FIG. 2 is a diagram showing the relationship between feature points and their neighboring points
FIG. 3 is a diagram of the experimental matching effect
The invention is further described below with reference to the accompanying drawings:
referring to fig. 1, a matching method based on local structural similarity, which sequentially processes a pair of images to be matched as follows:
step 1, performing feature extraction and initial matching on two images to be matched so as to obtain a relation set corresponding to the initial matching; step 2, determining neighbor points of each feature point for the feature points determined in the initial matching set obtained in the step 1, and establishing a neighborhood affine coefficient matrix of the feature points according to the neighbor points; and 3, calculating the difference of the neighborhood affine coefficient matrixes of the feature points associated with each match in the initial matching set, and expressing the local structural similarity between the feature points associated with each match by using the difference. The smaller the difference value is, the higher the local structural similarity is, the larger the difference is, the lower the local structural similarity is; step 4, optimizing the neighborhood affine coefficient matrix, defining a function formula for calculating the local structure difference degree by taking the neighborhood affine coefficient matrix as a variable, solving the corresponding neighborhood affine coefficient matrix when the function formula is used for taking an extreme value, and substituting the coefficient matrix into the function formula for calculating the local structure difference degree of the characteristic point; and 5, setting a comparison threshold according to the local structure difference value of each matched and associated feature point obtained in the step 4, keeping the matching with the difference value lower than the threshold, deleting the matching with the difference value not lower than the threshold, and determining the final feature matching pair as the matching relation result of the image to be matched.
Further, the method comprises the following specific steps: step 1, image feature extraction and initial matching: and extracting local characteristic points of the image to be matched, namely finding distinguishable key points which have strong robustness on image transformation and high detection repetition rate in the image. And performing gradient statistical calculation on the local area of the detected characteristic point to finish the characteristic description process of the characteristic point. And calculating the Euclidean distance value between the descriptor of any one feature point and the description of other feature points, and selecting the feature point with the minimum Euclidean distance value as the matching point of the feature point. Collecting all the characteristic points and the matching points thereof to form an initial image matching set;
step 2, establishing a neighborhood affine coefficient matrix of key points in the matching pair: on the basis of obtaining an initial matching set in the step 1, for each local feature point in the matching set, finding other feature points within a certain range from the local feature point as neighborhood feature points of the local feature point, linearly representing the key point by using the neighborhood feature points, and obtaining a corresponding affine coefficient matrix;
step 3, measuring the local structure difference degree based on the neighborhood affine coefficient matrix: for each match in the initial matching set obtained in the step 1, obtaining a neighborhood affine coefficient matrix of the feature point associated with each match through the step 2, and calculating a difference value of the two neighborhood affine coefficient matrices, wherein the difference value represents the local structure difference degree of the feature point associated with each match. The smaller the difference value is, the higher the local structural similarity is, the larger the difference is, the lower the local structural similarity is;
step 4, neighborhood affine coefficient matrix optimization: defining a function formula for calculating the local structure difference degree by taking a neighborhood affine coefficient matrix as a variable, wherein the function formula consists of the sum of two data items, the two data items are respectively the difference between the feature points corresponding to the initial matching set and the affine combination consisting of the domain affine coefficient matrix, the objective of solving the formula is to make the value of the function as close to zero as possible, obtain the neighborhood affine coefficient matrix corresponding to the function formula at the extreme point, and bring the neighborhood affine coefficient matrix into the function formula to calculate the local structure difference degree of the feature points;
and 5, comparing the threshold value of the local structure difference value corresponding to each matching in the step 4, wherein when the difference value is smaller than a specified threshold value, the corresponding characteristic point pair belongs to a correct matching pair, and when the difference value is not smaller than the specified threshold value, the corresponding characteristic point pair belongs to an incorrect matching pair, removing the incorrect matching pair from the initial matching corresponding relation set, and taking all the remaining matching pairs as final correct matching results and outputting the final correct matching results.
As shown in the flowchart of fig. 1, the method is a serial matching process: firstly, extracting image feature points and feature descriptors, and acquiring an initial image matching set according to the described similarity. And then searching adjacent points of each feature point, establishing a neighborhood affine coefficient matrix of the key points of the matching pairs in the initial matching set, defining a matrix covariance formula to optimize the neighborhood affine coefficient matrix of the feature points, finally keeping the matching of which the corresponding matrix covariance is less than a specified threshold, deleting the matching of which the corresponding matrix covariance is not less than the specified threshold, and determining a final feature matching set as a matching result of the image to be matched.
Specifically, as shown in fig. 1, the present invention discloses a matching method based on local line structure similarity. The method mainly comprises the following steps:
step 1, image feature extraction and initial matching: extracting the feature points and feature description of the image to be matched, and acquiring an initial image matching set based on the described similarity.
Step 1.1, image feature extraction: using classic rulesDegree invariant feature transform (SIFT) feature description operator extraction And (4) image characteristics. Taking a pair of images I and I' to be matched as input of an SIFT algorithm to carry out feature extraction, and obtaining SIFT feature points And 128-dimensional feature description vectors corresponding to the feature points;
step 1.2, initially matching features: according to the characteristic vectors obtained in the step 1.1, the single characteristic description vectors of the two images I and I' to be matched are respectively X i 、X j Calculating the Euclidean distance d (X) between two vectors i ,X j ) If and only if X i Distance to d (X) of all other feature description vectors i ,X j ) When the ratio of (A) to (B) is greater than a set threshold value, we consider X to be i And X j And if the ratio is less than or equal to the set threshold value, the corresponding characteristic points are considered as unmatched. The distance between feature description vectors is formulated as:
wherein X ik Representing vector X i The threshold value is taken to be 1.1 for the k-th dimension component of (2).
Giving an image pair to be matched, and carrying out one-by-one treatment on all feature description vectors in one image and feature description vectors in the other imageMeasuring distance value, selecting the corresponding characteristic point with the minimum distance value asAnd matching points.Thus each matching pair will correspond to a respective feature region in the image to be matched. And collecting all the initial matching pairs to form an initial matching set of the image to be matched.
Step 2, establishing a neighborhood affine coefficient matrix of key points in the matching pair: further explained in conjunction with fig. 2, step 2.1, selecting key neighborhood points: obtaining an initial matching set of the image according to the step 1.2, and randomly matching M corresponding feature point pairs (p, p ') in the matching set, wherein the feature point p belongs to the image I to be matched, and the point p ' corresponds to the point matched with the feature point p in the image I ' to be matched; find other matches that match M neighbors and let the corresponding pairs of feature points be (q) i ,q i ') to a test; when the feature points p and q are i Simultaneous feature points p' and q i When the spatial distance value of' is smaller than a prescribed threshold value, we consider the feature point q i Neighbor points belonging to feature point p, feature point p' belonging to feature point q i ' and when the distance value is greater than or equal to a specified threshold, we consider the feature points p and q i P' and q i ' has no neighbor relation; the neighbor relation judgment formula is as follows:
||p-q i ||＜τ,and||p'-q i '||＜τ,
wherein τ represents a similarity threshold between the key point and the adjacent point, and the value is 10. The tau is set to ensure that the key point p of the image to be matched has k nearest neighbors on average, and the setting of the k value can be specifically set according to the local neighborhood information of the key point, so that the structural information of the key point can be more accurately represented. i represents the number of neighbor points of the characteristic point p, the value range is [1,k ], and the value of tau can be adjusted in the experiment to flexibly change the size of k, so that the experiment can show better effect.
Step 2.2, establishing a neighborhood affine coefficient matrix of key points in the matching pairs: on the basis of the step 2.1, the adjacent local points of the image points to be matched are determined, and the adjacent points of the corresponding characteristic points p of any matching M in the image I are integrally expressed as
Wherein k represents the number of neighbor points of the feature point p, and qi represents the ith neighbor point of p; following the local Linear Embedding (localization Linear Embedding) theory, the geometry near the image feature point p can be represented by its neighborhood affine coefficient matrix w = [ w = ] 1 ,...,w i ,...] T To depict, the feature point p uses its determined neighbor point set
An affine combination of (1) is represented as: p = ∑ w i q i Where Σ w i =1; and for the matched feature point p 'corresponding to the feature point p on the image I', using a neighborhood affine coefficient matrix w '= [ w' 1 ,...,w' i ,...] T P ' = Sigma w ' is obtained ' i q' i Wherein Σ w' i =1, thus completing the establishment of the key point neighborhood affine coefficient matrix;
step 3, judging the local structural similarity of the matching points: through the processing of the image feature points in the step 2, neighborhood affine transformation matrixes w and w ' of feature point pairs (p, p ') associated with any matching M in the initial matching set are obtained, because the neighborhood affine coefficient matrixes describe the local structural geometric properties of the feature points, the corresponding matching pairs are correctly represented if the corresponding matching pairs are consistently represented by the neighborhood coefficient matrixes of the matching feature point pairs, namely when w = w ', the corresponding matching pairs are reserved as correct matching pairs, and if the two are not equal, the matching pairs are determined as wrong matching pairs and deleted;
and 4, optimizing the feature point neighborhood affine coefficient matrix: in order to optimize the neighborhood affine coefficient matrix of the feature points, an optimal neighborhood affine coefficient matrix is found
Neighbor point set with feature point p
Linear combination is carried out, and the difference value of the characteristic point p and the characteristic point p is obtained and then is subjected to parallel operationRow pattern processing, reuse of optimal affine coefficient matrix coefficient vectors
Neighbor point set of matching point p' with feature point p
Linear combination, and then subtraction is carried out on the linear combination and the characteristic point p' and normal form processing is carried out; defining matrix covariance J composed of the sum of the above two normal forms, and representing the local structure difference degree of the matching point pair; the matrix covariance J is specified as follows:
the magnitude of the J value indicates the degree of difference in the local structures of the feature points p and p ', and a smaller value of J indicates that the local structures of the feature points p and p' are more similar. In principle, correct matches that map the same object in the images to be matched tend to cluster in adjacent regions, and similar topologies are shared between the images due to physical constraints, so the corresponding J values are small. However, the geometric layout of the matching points near the mismatch is difficult to be consistent among different images, so that the corresponding J value is large. Therefore, the matrix covariance J provides a good method for evaluating the correctness of matching. And setting a smaller comparison threshold, when the matrix covariance J is less than the set threshold, considering that the corresponding match is a correct match, and keeping the match in the initial matching set, and when the matrix covariance J is not less than the set threshold, considering that the corresponding match is a wrong match, and deleting the match in the initial matching set.
The effectiveness of formula J is established in a neighborhood affine coefficient matrix
On the assumption that local geometric changes between images remain unchanged. In the document of feature matching, it is generally assumed that the corresponding local regions are affine invariant. The specific demonstration method is as follows: for any match M in the initial matching set, a matching point pair (p, p') exists, and its adjacent matches M exist i And (3) corresponding to the matching point pair (q, q'). The feature point p 'can be approximated by its matching feature point p through a 2 × 2 rotation scaling matrix a and a 2 × 1 translation vector t, and at the same time, the feature points of the neighboring region have similar transformation, so the neighbor point q of the feature point p can also be approximated by its matching point q' through the rotation scaling matrix a and the translation vector t. Then:
wherein
This constraint ensures invariance of the transition. Thus proving the affine coefficient matrix of the neighborhood
For local geometric changes between images, i.e. if
Then
This is true. The above formula may not hold if more severe image distortion occurs near the keypoint p or p'. Fortunately, it is not always the case that the image is severely distorted. In summary, we demonstrate here that when a match M and its neighboring matches M i If it is a correct match, the local region structure is affine invariant.
Since the initial matching set may contain false matches, jointly constructing pairs of matched feature points with respective neighborhood linear combinations in each image may reduce noise-induced errors. And can also be optimized for pure error matching, thereby providing stronger robust processing for matching under noise interference. The specific optimization process is as follows:
equation J can be written as:
wherein X = [ p-q ] 1 ,...,p-q i ,...]，Y＝[p'-q' 1 ,...,p'-q' i ,...]. Set of settings C = X T X+Y T And Y. Then introduce lagrange multiplier lambda to perform
The formula can be converted again to:
wherein 1= [1,.. 1, 1=] T Is a column vector of | N | × 1. By taking the gradient of J and setting it to zero,
can be calculated as
Formula (II)
The solution of (C) requires explicit computation of the inverse of the matrix C, which by definition is symmetric and semi-positive. However, because the number of contiguous matching sets of matches M is typically greater than 2, the matrix C may be singular. In order to make the formula linearly solvable, in practical applications, we further add a small product of the identity matrix I as a regularization term to the matrix C.
C new ＝C+εI,
ε is set to a smaller value than the trace of C, and is set to 10 throughout the experiment -3 tr (C). We can solve a system of linear equations
And adjusting
To obtain
Thereby making
After being processed
Then, the calculated
And substituting the matrix covariance J into a formula to calculate a corresponding J value, and further obtaining a local structure difference value of each matched corresponding characteristic point pair.
And 5, based on the difference degree of the local structure of each matched and corresponding characteristic point obtained in the step 4, namely the value of the matrix covariance. Setting a smaller threshold value, wherein the value of the threshold value is 8, and defining that when the matrix covariance of the feature point is smaller than the set threshold value, the matching associated with the feature point is considered to be correct matching and is reserved to a final matching set, otherwise, when the matrix covariance of the feature point is larger than the set threshold value, the matching associated with the feature point is considered to cause wrong matching and is deleted; and finally, taking all the reserved matching sets as a final image matching result set.
Examples
The experimental hardware environment of the invention is: intel (R) Core (TM) i5-4590CPU@3.30GHz 3.30GHz,8G memory, microsoft Windows7 flagship edition, programming environment is Visual Studio 2015, MATLAB (R2016 a) 64 bits, test charts (see the experimental matching effect chart shown in FIG. 3 in detail) are derived from a multi-target object matching standard image set disclosed on the Korean Seoul National University (SNU) network.
All images of the SNU image set are selected, 6 groups of images to be matched are provided, the names of the images are Books, bulletins, jigsaws, mickeys, minnies and Toys, each image comprises a plurality of objects, different view angle changes, different illumination and different self changes exist between each pair of objects to be matched, and the matching technology adopting the images faces a great challenge.
The invention carries out comparison of accuracy and recall ratio with other Matching methods on the basis of realization of Matching technology, and the Matching methods adopting comparison comprise a Hough voting characteristic Matching method HV (Feature Matching with alternative Hough and invoked Hough Transforms), a Discrete topology searching Matching method DTS (Discrete Tabu Search For Graph Matching), a weighted Random walk Graph Matching method RRWM (weighted Random walk For Graph Matching) and a Spatial Matching method EWGR (Spatial Matching as sensitive of weak geometric relations). In the matching process, SIFT description operators are used for feature description, and the aim of removing the error matching in the initial matching set is to obtain the initial matching set. All the parameters in the comparison method are selected to be the corresponding parameters when the experiment effect performance is best. The performance of each method is expressed by accuracy and recall rate. The comparative results are as follows:
| HV | RRWM | DTS | EWGR | Ours | |
| Precision(％) | 71.36 | 77.68 | 78.22 | 85.19 | 95.45 |
| Recall(％) | 94.04 | 90.05 | 94.17 | 71.49 | 97.50 |
as can be seen from the data in the table, the matching method of the invention has better effect than other matching methods in the data representation of accuracy and recall rate, thereby proving the significance of the invention.
Claims (7)
1. A feature matching method based on local structure similarity is characterized in that: the method comprises the following steps of carrying out matching processing on a pair of images to be matched through a computer to obtain a feature point matching pair set with a similar local structure, wherein the matching pair set comprises the following steps:
step 1, performing feature extraction and initial matching on two images to be matched to obtain a relation set corresponding to the initial matching; when feature extraction is carried out, feature points of the initial matching corresponding relation set are obtained;
step 2, determining neighbor points of each feature point for the feature points determined in the initial matching corresponding relation set obtained in the step 1, and establishing a neighborhood affine coefficient matrix of the feature points according to the neighbor points;
step 3, for each match in the initial matching set, calculating the difference of the neighborhood affine coefficient matrixes of the feature points associated with the match, and expressing the local structural similarity between the feature points associated with each match by using the difference: the smaller the difference value is, the higher the local structure similarity is, the larger the difference is, and the lower the local structure similarity is;
step 4, optimizing the neighborhood affine coefficient matrix, calculating a function of the local structure difference degree by taking the neighborhood affine coefficient matrix as a variable, solving the corresponding neighborhood affine coefficient matrix when the function takes an extreme value, and substituting the coefficient matrix into the function to calculate the local structure difference degree of the characteristic point;
and 5, setting a comparison threshold according to the local structure difference value of each matched and associated feature point obtained in the step 4, keeping the matching with the difference value lower than the threshold, deleting the matching with the difference value not lower than the threshold, and determining the final feature matching pair as the matching relation result of the image to be matched.
2. The local structure similarity-based feature matching method according to claim 1, wherein: the method comprises the following specific steps in sequence:
step 1, image feature extraction and initial matching: extracting local characteristic points of the image to be matched, namely finding distinguishable key points which have strong robustness on image transformation and high detection repetition rate in the image; performing gradient statistical calculation on the local area of the detected feature points to complete the feature description process of the feature points; calculating Euclidean distance values between the descriptor of any one feature point and the descriptions of other feature points, and selecting the feature point with the minimum Euclidean distance value as a matching point of the feature point; collecting all the characteristic points and the matching points thereof to form an initial image matching set;
step 2, establishing a neighborhood affine coefficient matrix of key points in the matching pairs: on the basis of obtaining an initial matching set in the step 1, for each local feature point in the matching set, finding other feature points within a certain range from the local feature point as neighborhood feature points of the local feature point, linearly representing the key point by using the neighborhood feature points, and obtaining a corresponding affine coefficient matrix;
step 3, measuring the local structure difference degree based on the neighborhood affine coefficient matrix: for each match in the initial matching set obtained in the step 1, obtaining a neighborhood affine coefficient matrix of the feature point associated with each match through the step 2, and calculating a difference value of the two neighborhood affine coefficient matrices, wherein the difference value represents the local structure difference degree of the feature point associated with each match; the smaller the difference value is, the higher the local structural similarity is, the larger the difference is, the lower the local structural similarity is;
step 4, neighborhood affine coefficient matrix optimization: defining a function formula for calculating the local structure difference degree by taking a neighborhood affine coefficient matrix as a variable, wherein the function formula consists of the sum of two data items, the two data items are respectively the difference between affine combinations consisting of characteristic points corresponding to initial matching set matching and the neighborhood affine coefficient matrix, the solving objective of the formula is to make the value of the function as close to zero as possible, obtain the neighborhood affine coefficient matrix corresponding to the function formula at an extreme point, and bring the neighborhood affine coefficient matrix into the function formula to calculate the local structure difference degree of the characteristic points;
step 5, comparing the threshold value of each local structure difference value corresponding to the matching in the step 4:
when the difference value is smaller than a specified threshold value, the corresponding characteristic point pair belongs to a correct matching pair;
and when the difference value is not less than the specified threshold value, the corresponding characteristic point pairs belong to wrong matching pairs, the wrong matching pairs are removed from the initial matching corresponding relation set, and all the remaining matching pairs are used as final correct matching results and output.
3. A feature matching method based on local structure similarity according to claim 2, characterized in that: the step 1 is as follows:
step 1.1, image feature extraction: extracting the characteristics of the image to be matched by adopting a Scale Invariant Feature Transform (SIFT) characteristic description operator; taking a pair of images I and I' to be matched as input of an SIFT algorithm to perform feature extraction, and acquiring SIFT feature points and feature description vectors corresponding to the feature points; the feature description vector has 128 dimensions;
step 1.2, initial feature matching: according to the feature description vectors obtained in step 1.1, the single feature description vectors of the two images I and I' to be matched in step 1.1 are respectively X i 、X j Calculating X i Vector and X j The Euclidean distance of the vector is d (X) i ,X j ) If and only if X i Distance to d (X) of all other feature description vectors in image I i ,X j ) When the ratio of (A) is greater than a set threshold value, X is judged i And X j The corresponding feature points are matched; when the ratio is less than or equal to the set threshold, the corresponding characteristic points are considered as unmatched; the distance between feature description vectors is formulated as:
where k denotes the 128-dimensional eigenvector dimension index number, the range is [1,128 ]]；X ik Representing a vector X i The k-th dimension component, X jk Representing vector X j The k-th dimension component of (a);
and finally outputting an initial image matching relationship pair set by extracting the characteristics of the images I and I' to be matched in the step 1.1 and calculating the distance value between the characteristic descriptions in the step 1.2.
4. A feature matching method based on local structure similarity according to claim 2, characterized in that: the step 2 is specifically as follows:
step 2.1, selecting key neighborhood points: obtaining an initial matching set of the image according to the step 1.2, and randomly matching M corresponding feature point pairs (p, p ') in the matching set, wherein the feature point p belongs to the image I to be matched, and the point p ' corresponds to the point matched with the feature point p in the image I ' to be matched; find other matches that match M neighbors and let the corresponding pairs of feature points be (q) i ,q i ') to a host; when the feature points p and q are i Simultaneous feature points p' and q i When the spatial distance value of' is smaller than a prescribed threshold value, we consider the feature point q i Neighbor points belonging to feature point p, feature point p' belonging to feature point q i ' and when the distance value is greater than or equal to a specified threshold, we consider the feature points p and q i P' and q i ' having no neighborsA relationship; the neighbor relation judgment formula is as follows:
||p-q i ||＜τ,and||p'-q i '||＜τ,
wherein tau represents the similarity threshold value of the key point and the adjacent points; tau is set to ensure that key points p of the image to be matched have k nearest neighbors on average, and the setting of k value can be specifically set according to local neighborhood information of the key points so as to more accurately represent the structural information of the key points; i represents the number of neighbor points of the characteristic point p, and the value range is [1,k ]](ii) a Calculating a neighbor relation judgment formula of each feature point and other feature points to obtain a neighbor point set of each feature point; namely, the adjacent local points of the image feature points to be matched are determined through the step; step 2.2, establishing a neighborhood affine coefficient matrix of key points in the matching pair: on the basis of the step 2.1, the adjacent local points of the characteristic points of the image to be matched are determined, and the adjacent points of the corresponding characteristic points p of any matching M in the image I are integrally expressed as
Wherein k represents the number of neighbor points of the characteristic point p, and qi represents the ith neighbor point of p; following local Linear Embedding (local Linear Embedding) theory, the geometric structure near the image feature point p can be defined by its neighborhood affine coefficient matrix w = [ w ] 1 ,...,w i ,...] T To depict, the feature point p uses its determined neighbor point set
Is expressed as: p = ∑ w i q i Where Σ w i =1; and for the matched feature point p 'corresponding to the feature point p on the image I', using a neighborhood affine coefficient matrix w '= [ w' 1 ,...,w' i ,...] T To obtain p '= sigma w' i q' i Wherein Σ w' i =1; thus, the establishment of the key point neighborhood affine coefficient matrix is completed.
5. A local structure similarity-based feature matching method as claimed in any one of claims 2 or 4, characterized in that: the step 3 is as follows:
and (3) judging the local structural similarity of the matching points: through the processing of the image feature points in the step 2, neighborhood affine transformation matrixes w and w ' of each feature point pair (p, p ') associated with any matching M in the initial matching set are obtained, because the neighborhood affine coefficient matrixes describe the local structural geometric properties of the feature points, the corresponding matching pairs are retained as correct matching pairs if the corresponding matching pairs are represented in a consistent way by the neighborhood coefficient matrixes of the matching feature point pairs, namely w = w ', and the matching pairs are determined as incorrect matching pairs and deleted if the matching pairs are not equal to each other.
6. A local structure similarity-based feature matching method as claimed in any one of claims 2 or 4, characterized in that: the step 4 is specifically as follows:
optimizing a feature point neighborhood affine coefficient matrix: in order to optimize the neighborhood affine coefficient matrix of the feature points, an optimal neighborhood affine coefficient matrix is found
Neighbor point set with feature point p
Linear combination, subtracting the characteristic point p to obtain the difference value of the characteristic point p and carrying out normal form processing, and then using the coefficient vector of the optimal affine coefficient matrix
Set of neighbor points of matching point p' with feature point p
Linear combination, and then subtraction is carried out on the linear combination and the characteristic point p' and normal form processing is carried out; defining matrix covariance J composed of the sum of the above two normal forms, and representing the local structure difference degree of the matching point pair; the matrix covariance J is specified as follows:
7. the feature matching method based on local structure similarity as claimed in claim 2, wherein: the step 5 is as follows:
acquiring a matrix covariance value corresponding to each feature point in the initial matching set according to the step 4, setting a threshold value, and stipulating:
when the matrix covariance of the feature points is smaller than the set threshold, the matching associated with the feature points is considered to be correct matching, and the final matching set is reserved;
otherwise, when the covariance of the matrix of the feature point is larger than the set threshold value, the matching associated with the feature point is considered to cause the wrong matching, and the wrong matching is deleted;
and finally, taking all the reserved matching sets as a final image matching result set and outputting the final image matching result set.
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