The spectral matching algorithm based on hyperbolic mahalanobis metric

Abstract

In order to solve the problem of the traditional image matching algorithm based on the spectral feature, the spectral matching algorithm based on hyperbolic mahalanobis metric is proposed in this paper. The algorithm first introduces a hyperbolic metric that has better adaptability to the sample data. And the hyperbolic mahalanobis metric is defined according to the statistical properties of the data. For a point in a given pointset, the sub point-set is selected according to the hyperbolic mahalanobis metric and the weighted graph of the sub point-set is constructed. The eigenvalue vector and the spectral gap vector are obtained by the singular value decomposition (SVD) of the adjacency matrix of the weighted graph, which construct the hyperbolic mahalanobis metric spectral feature. Finally, the matching matrix is constructed based on the similarity between the hyperbolic mahalanobis metric spectral feature and geometric relations between feature points. Thereby establish the matching mathematical model and introduce the greedy algorithm to obtain the matching results. A large number of experimental results show that the proposed algorithm improves the matching accuracy and the robustness. And the algorithm extends the application range of the spectral matching algorithm.