Spectral Analysis for Shape Matching

Spectral graph theory is widely used in Pattern Recognition and Image Processing. It has found a wide range of applications ranging from clustering, to dimension reduction, or image representation. Spectral analysis for image registration raises however some challenges are seldom addressed in the literature. The difficulty stems from the fact that the eigenspectrum and eigenspace of the Laplacian matrix (i.e. its eigenvalues and eigenvectors) cannot be uniquely defined and therefore cannot provide a priori, reliable representation of the image. In this paper, we address this issue and propose a practical scheme to align the Laplacian eigenspaces of two images. We show experimentally that this robust procedure can be applied to match and estimate the similarity of objects of different shapes.