Schrödinger Diffusion for Shape Analysis with Texture

Jose A. Iglesias and Ron Kimmel

Abstract. In recent years, quantities derived from the heat equation have become popular in shape processing and analysis of triangulated surfaces. Such measures are often robust with respect to different kinds of perturbations, including near-isometries, topological noise and partialities. Here, we propose to exploit the semigroup of a Schrödinger operator in order to deal with texture data, while maintaining the desirable properties of the heat kernel. We define a family of Schrödinger diffusion distances analogous to the ones associated to the heat kernels, and show that they are continuous under perturbations of the data. As an application, we introduce a method for retrieval of textured shapes through comparison of Schrödinger diffusion distance histograms with the earth’s mover distance, and present some numerical experiments showing superior performance compared to an analogous method that ignores the texture.

Keywords: Laplace-Beltrami operator, textured shape retrieval, diffusion distance, Schrödinger operators, earth mover’s distance

LNCS 7583, p. 123 ff.

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