Research On Algorithms Of Point Pattern Matching Based On Graph Spectral Theory

Image matching is an important part in the research areas of image processing, pattern recognition and computer vision. It makes space transform for images from different perspectives, different times or different imaging mode, so that they are corresponding to each other in geometry. Technically, image matching can be roughly divided into gray-based matching and feature-based matching, of which feature-based matching has very prominent advantages in terms of reliability and robustness. Point pattern is an important feature for images, in recent years, more and more researchers focus on it owing to its important theoretical and practical value.Based on the theory of graph spectrum as the main theoretical tool, we have researched on the algorithms of point pattern matching and proposed three matching algorithms in this paper. The main research contents and the achievements are as follows:First of all, a kind of image layered matching algorithm based on the median is proposed. First, this algorithm figures out the medians of two images that will be matched, and treats them as a reference in the image of the feature points stratified. Second, constructs the Gauss-Laplace matrix corresponding to every layer respectively, and conceives the relationship matrix that reflects the matching degree of each feature point according to the result of SVD analysis. Last, obtains the matching result of the entire image by the feature points matched. Experimental results demonstrate the feasibility and effectiveness of the approach.Secondly, an algorithm of image feature points matching by representing geometric structure of images basing on the angle between spectral coefficient vectors is proposed. The algorithm uses Harris angular point detecting method to find angular points from two images to be matched, those angular points which reflect image structural feature are treated as nodes when constructing complete graph, and then builds Gaussian-weighted Laplacian matrices based on complete graph, obtains the eigenvalues and eigenvectors corresponding to each feature point by the singular value decomposition on the two matrices; Gains a symmetric matrix with the cosine value of the angle between the weight; Then with the result of the decomposition of the symmetric matrix, gets a relationship matrix which denoted the matching degree among feature points; Finally, the algorithm achieves feature points matching of the two images with the relationship matrixes. Experiments on synthetic images, real-world images and synthetic data demonstrate the effectiveness and feasibility of the approach.Finally, an iterative matching algorithm which combines texture matching algorithm and Lapacian spectrum matching algorithm is proposed. First, it applies texture matching algorithm and Lapacian spectrum matching algorithm to gain the matching results from two images to be matched independently, and finds the same matching points, and then removes them from the feature points; Next, it makes the rest points which are not matched as initial feature points, and for the same treatment as the first step, then iterates until there are no same matching points between the matching results of the two algorithms, and gains matching results by the algorithm of Laplacian spectrum based on the rest unmatched points; Last, obtains ultimate matching results according to matching points of each iterations. Experimental results demonstrate that the approach can receive a high matching accuracy.