Surface Comparison using Conformal Geometry
Speaker: Yaron Lipman, Princeton University
Location: Warren Weaver Hall 1302
Date: February 11, 2011, 11:30 a.m.
Host: Denis Zorin
One of the core problems in geometry processing is the problem of comparing shapes and finding correspondences between different, but similar shapes. Maybe the most popular instance of this problem is matching and comparing surfaces (2-dimensional manifolds), a crucial component in a large number of applications ranging from matching of cortical surfaces, faces, bones or other biological surfaces, to more synthetic applications like shape morphing and attribute transfer. In this talk we will present a few applications of conformal geometry to the problems of surface matching and comparison. In particular, we will show how certain ideas originated in the theory of conformal geometry can be used to define novel metrics measuring dissimilarities and finding correspondences betweens pairs of surfaces automatically. The key idea is to utilize the prominent low-dimensionality of conformal mappings to construct metrics that are computationally efficient. I will report results on a few datasets of biological surfaces as well as other standard 3D surface datasets.
I will end the talk with a broader picture of how ideas originated from differential geometry can be proven useful in describing and constructing algorithms for solving different geometric problems.
Yaron Lipman is a Postdoctoral Fellow in the Computer Science Department, and the Program in Applied and Computational Mathematics at Princeton University. His research interests are mainly in geometric processing and modeling, discrete differential geometry, and approximation theory with applications. Dr. Lipman received his B.Sc. in Computer Science and Mathematics, and a Ph.D. in Applied Mathematics from Tel-Aviv University. He received the 2009 Eurographics Young Researcher award and the 2010 Blavatnik Award for Young Scientists (postdoc category).
In-person attendance only available to those with active NYU ID cards.