Pose-Consistent 3D Shape Segmentation Based on a Quantum Mechanical Feature Descriptor

Abstract

We propose a novel method for pose-consistent segmentation of non-rigid 3D shapes into visually meaningful parts. The key idea is to study the shape in the framework of quantum mechanics and to group points on the surface which have similar probability of presence for quantum mechanical particles. For each point on an object's surface these probabilities are encoded by a feature vector, the Wave Kernel Signature (WKS). Mathematically, the WKS is an expression in the eigenfunctions of the Laplace-Beltrami operator of the surface. It characterizes the relation of surface points to the remaining surface at various spatial scales. Gaussian mixture clustering in the feature space spanned by the WKS signature for shapes in several poses leads to a grouping of surface points into different and meaningful segments. This enables us to perform consistent and robust segmentation of new versions of the shape. Experimental results demonstrate that the detected subdivision agrees with the human notion of shape decomposition (separating hands, arms, legs and head from the torso for example). We show that the method is robust to data perturbed by various kinds of noise. Finally we illustrate the usefulness of a pose-consistent segmentation for the purpose of shape retrieval.