Structural Descriptor Via Spectral Graph Analysis And Its Application In Point Pattern Matching

Serving as an important part in pattern recognition and computer vision, point pattern matching is a hotspot and critical issue in the related research fields. As graph is a powerful facility for characterizing point-set structure, point pattern matching is often formulated as graph matching problem. Graph matching via spectral graph analysis is one of the most active branches. However, the performance of the existing spectral matching methods degrades rapidly in the presence of positional jitter and outliers. To address these issues, in this dissertation, we focus on how to improve the robustness and accuracy of spectral matching methods for positional jitter and outliers. Our main contributions are as follows.1. To address the weakness of the single spectral representation, an algorithm is proposed for point pattern matching on the basis of multiple spectral representations. Firstly, the eigenvalue series obtained from various matrix representations of graphs are used as the descriptor of feature point. Secondly, the similarities between the given local structural descriptors are evaluated via the technique of multiview spectral embedding. Finally, combined with the geometric consistency, the correspondences are recovered by using the method of probabilistic relaxation. Comparative experiments conducted on both synthetic data and real images verify the effectiveness and robustness of the proposed method.2. A novel local spectral descriptor is proposed to represent the attribute domain of feature points. For a point in a point set, the weight graphs are constructed on its neighboring points and then their corresponding normalized Laplacian matrices are computed. According to the known spectral radius of the normalized Laplacian matrix, the distribution of the eigenvalues of these normalized Laplacian matrices is summarized as a histogram to describe a feature point. The proposed spectral descriptor is finally embedded into a graph matching framework for recovering correspondences between the matched point sets. Experimental results demonstrate the effectiveness of the proposed approach and its superiority to the existing methods.