Metric geometry in action:<br/><br/>Non-rigid shape acquisition, processing and analysis

Monday, October 5, 2009 - 11:00am - 11:30am
Lind 305
Ron Kimmel (Technion-Israel Institute of Technology)
Gromov-Hausdorff distance (dGH) is a definition for the discrepancy
between metric
spaces. Until recently, it has been applied mainly in theoretical
exploration of metric spaces in metric geometry, as well as in theoretical
computer science, specifically, in the context of metric embedding of
graphs. A couple of years ago it was introduced into the field of
shape analysis by Memoli and Sapiro. In this talk we will explore the
relation between
the Gromov-Hausdorff distance and multi-dimensional scaling (MDS), a
classical approach for
embedding a given metric space into one in which distances can be
analytically computed. The
obvious example for such a target embedding space in MDS is Euclidean.
Alternatively, we
could use the Generalized MDS (GMDS) as a building block in numerically
approximating dGH.
This generalization deals with target spaces in which distances can be
numerically approximated
rather than evaluated analytically.

The exposition of ideas in metric geometry and numerical optimization would
be motivated through practical examples like 3D face recognition, texture
mapping in computer graphics, defining
and numerically exploring intrinsic symmetries and more. We will start from
the actual acquisition process and also present a 3D color video camera we
developed and demonstrate the potential of our computational tools on
various applications.

MSC Code: