The prediction of eigenvalues of the normalized laplacian matrix for image registration

Spectral graph theory can characterize the global properties and extract structural information of a graph. The normalized Laplacian matrix of a graph has positive or zero eigenvalues, and the largest eigenvalues is less than or equal to 2. In this paper, the internal rules of the eigenvalues of the normalized Laplacian matrix will be proposed. The range of the eigenvalues is further narrowed and the distribution of the eigenvalues is given, so the prediction of eigenvalues will conduct the research of the spectral graph theory. We apply this technique to image registration; the experimental results on image registration are very encouraging.