Spectral representation for matching and recognition

In this thesis, we aim to use the spectral graph theory to develop a framework to solve the problems of computer vision. The graph spectral methods are concerned with using the eigenvalues and eigenvectors of the adjacency matrix or closely related Laplacian matrix. In this thesis we develop four methods using spectral techniques: (1) We use a Hermitian property matrix for point pattern matching problem; (2) We use coefficients of symmetric polynomials to cluster similar human poses using the skeletal representation acquired from Microsoft Kinect; (3) We use coefficients of the elementary symmetric polynomials to make the direction of the eigenvectors of the proximity matrices consistent with each other for the problem of correspondence matching; (4) We use commute time embedding to construct a 3D shape descriptor for the purpose of 3D shape classification. In Chapter 3 we address the problem of correspondence matching. We extend the Laplacian matrix to the complex domain by constructing a Hermitian property matrix. We construct a Hermitian property matrix from the spatial locations