Chapter 4 - Near-isometric motion analysis using spectral geometry

Abstract

This chapter presents a novel method to analyze a set of poses of 3D models that are represented with triangle meshes and unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectral domain defined by the Laplace–Beltrami operator. During this space-spectrum transform, all near-isometric deformations, mesh triangulations, and Euclidean transformations are filtered away. The different spatial poses from a 3D model are represented with near-isometric deformations, and therefore they have similar behaviors in the spectral domain. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectral domain. A semantic skeleton can be automatically built with joints detected as well. The method turns a rather difficult spatial problem into a spectral problem that is much easier to solve. The applications show that the 3D pose analysis method leads to a registration-free pose analysis and a high-level semantic part understanding of 3D shapes.