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 belief by showing promising
results on various publicly available real mesh datasets.