Graph Characterization Using Wave Kernel Trace

Graph based methods have been successfully used in computer vision for classification and matching. This is due to the fact that shapes can be conveniently represented using graph structures. In this paper we explore the use of a spectral invariant which is based on the wave kernel trace to characterize graphs. The wave kernel is the solution of wave equation defined using the Edge-based Laplacian of a graph. The advantage of using the edge-based Laplacian over its vertex-based counterpart is that it can be used to translate equations from continuous analysis to the discrete graph theoretic domain, that have no meanings if defined using vertex-based Laplacian. To illustrate the utility of the proposed method we apply it to graphs extracted from both three-dimensional shapes and images.