Spectral Methods for Non-Rigid Shape Analysis

Date: Friday, February 6, 2009
Time: 3:30pm - 4:30pm
Location: Bldg. 50F, Room 1647

Speaker:
Martin Reuter
Athinoula A. Martinos Center for Biomedical Imaging
Harvard Medical School

Abstract:
Complex geometric objects have gained much importance in many
different application fields such as medicine, computer aided design
or engineering. Modern sensor technologies produce large amounts of
3D (or higher dimensional) data, that need to be analyzed and
processed automatically. Methods to compare, recognize and process
shape (2D surfaces or 3D solid objects) are essential ingredien! ts
to achieve this goal. This talk will give an overview on different
applications of spectral methods in shape analysis. I will
demonstrate how the eigenvalues and eigenfunctions of the
Laplace-Beltrami operator yield powerful tools to describe and
analyze shape. Due to their isometry invariance they are optimally
suited to deal with non-rigid shapes often found in nature, such as
a body in different postures. The normed beginning sequence of the
spectrum can be used as a global signature for shape matching and
database retrieval, while the eigenfunctions and their topological
analysis, employing the Morse-Smale complex, persistence diagram or
the Reeb graph, can be applied for shape registration, segmentation
and local shape analysis. Examples of applications such as database
retrieval of near isometric shapes, statistical shape analysis of
subcortical structures and hierarchical segmentation of articulated
shapes will be presented.

Host of Seminar:

    Gunther Weber