3D Shape Segmentation and Matching using Graph Spectral Methods

In the era of perpetually increasing computational capabilities, multi-camera acquisition systems are being increasingly used to capture parameterization-free articulated 3D shapes. These systems allow marker-less shape acquisition and are useful for a wide range of applications in the entertainment, sports, surveillance industries and also in interactive, and augmented reality systems. The availability of vast amount of 3D shape data has increased interest in 3D shape analysis methods. Segmentation and Matching are two important shape analysis tasks. 3D shape segmentation is a subjective task that involves dividing a given shape into constituent parts by assigning each part with a unique segment label.

In the case of 3D shape matching, a dense vertex-to-vertex correspondence between two shapes is desired. However, 3D shapes analysis is particularly difficult in the case of articulated shapes due to complex kinematic poses. These poses induce self-occlusions and shadow effects which cause topological changes such as merging and splitting. In this work we propose robust segmentation and matching methods for articulated 3D shapes represented as mesh-graphs using graph spectral methods.

This talk is divided into two parts. Part one of the talk will focus on 3D shape segmentation, attempted both in an unsupervised and semi-supervised setting by analysing the properties of discrete Laplacian eigenspaces of mesh-graphs. In the second part, 3D shape matching is analysed in a multi-scale heat-diffusion framework derived from Laplacian eigenspace. We believe that this framework is well suited to handle large topological changes and we substantiate our beliefe by showing promising results on various publicly available real mesh datasets.