Complexity Fusion for Indexing Reeb Digraphs

In this paper we combine different quantifications of heat diffusion-thermodynamic depth on digraphs in order to match directed Reeb graphs for 3D shape recognition. Since different real valued functions can infer also different Reeb graphs for the same shape, we exploit a set of quasi-orthogonal representations for comparing sets of digraphs which encode the 3D shapes. In order to do so, we fuse complexities. Fused complexities come from computing the heat-flow thermodynamic depth approach for directed graphs, which has been recently proposed but not yet used for discrimination. In this regard, we do not rely on attributed graphs as usual for we want to explore the limits of pure topological information for structural pattern discrimination. Our experimental results show that: a) our approach is competitive with information-theoretic selection of spectral features and, b) it outperforms the discriminability of the von Neumann entropy embedded in a thermodynamic depth, and thus spectrally robust, approach.