An Algorithm for Point Correspondences Based on Laplacian Spectra of Graphs

This paper presents a novel algorithm of correspondence matching of point-sets by using Laplacian spectra of graphs. We make three contributions. Firstly, according to the two point sets to be matched, we define a Laplacian matrix with Euclidean distance, and give a closed form solution in terms of the matching matrix constructed on the vectors of eigenspace of the Laplacian matrix. Secondly, we theoretically prove that the algorithm acquires exact results under equilong or equiform transformation of image plane. Thirdly, we demonstrate how to combine this method with the algorithm of probabilistic relaxation. Experimental results of real-world data show that our method possesses comparatively high accuracy