Isometry-Invariant Shape Analysis

Shape analysis aims to describe either a single shape or a population of shapes in an efficient and informative way. This is a key problem in various applications such as mesh deformation and animation, object recognition, and mesh parameterization.

I will present a number of approaches to process shapes that are nearly isometric. The first approach computes the correspondence information between a population of shapes in this setting. Second and third are approaches to morph between two shapes and to segment a population of shapes into near-rigid components. Next, I will present an approach for isometry-invariant shape description and feature extraction.

Furthermore, I will present an algorithm to compute the correspondence information between human bodies in varying postures. In addition to being nearly isometric, human body shapes share the same geometric structure, and we can take advantage of this prior geometric information to find accurate correspondences. Finally, I will discuss some applications of shape analysis in computer-aided design.