Shape Indexing through Laplacian Spectra

Abstract

With ever growing databases containing multimedia data, indexing has become a necessity to avoid a linear search. We propose a novel technique for indexing multimedia databases, whose entries can be represented as graph structures. In our method, the topological structure of a graph as well as that of its subgraphs are represented as vectors in which the components correspond to the sorted Laplacian eigenvalues of the graph or subgraphs. We draw from recently-developed techniques in the field of spectral integral variation to overcome the problem of computing the Laplacian spectrum for every subgraph individually. By doing a nearest neighbor search around the query spectra, similar but not necessarily isomorphic graphs are retrieved. The novelties of the proposed method come from the powerful representation of the graph topology and successfully adopting the concept of spectral integral variation in an indexing algorithm. Our experiments, consisting of recognition trials in the domain of 2D and 3D object recognition, including a comparison with a competing indexing method, demonstrate both the robustness and efficacy of the approach.