报告题目：Discrete Surface Ricci Flow and Optimal Transportation
报告人：顾险峰(David Gu)，Stony Brook University
时 间：2016年12月28日 下午2:30-3:30
地 点：1518
内容提要：
This talk introduces two fundamental theoretic tools in geometric processing, surface Ricci flow and optimal transportation.
Surface mapping will introduce distortions, which can be classified to angle distortion and area distortion. Ricci flow can produce angle-preserving mappings, optimal mass transportation can induce area-preserving mappings.
Surface Ricci flow deforms the surface Riemannian metric proportional to the current curvature, such that the curvature evolves according to a diffusion and reaction process, and eventually the curvature converges to a constant. We formulate the discrete surface Ricci flow as a variational problem, and use Newton’s method for the convex optimization. Furthermore, we prove the existence and the uniqueness of the solution to the discrete surface Ricci flow, which implies the classical surface uniformization theorem. The methods can design Riemannian metrics from prescribed curvatures.
Optimal mass transportation produces a homeomorphism which maps one probability measure to the other in the most economical way. Optimal transportation has intrinsic relation to the Minkowski problem in convex geometry, and can be reduced to solve Monge-Ampere equation. We give a variational approach to solve the Monge-Ampere equation, which leads to a novel proof of Alexandrov theorem. The method can be applied for computing Wasserstein distance between probability measures.
报告人简介：
David Gu is an associate professor (with tenure) at the Department of Computer Science, Stony Brook University. He received his PhD degree from the Department of Computer Science, Harvard University in 2003 and B.S. degree from the Tsinghua University, Beijing, China in 1995.
David Gu’s research focuses on applying modern geometry in engineering and medical fields. With his collaborators, David systematically develops discrete theories and computational algorithms in the interdisciplinary field: Computational Conformal Geometry, and apply them in Computer Graphics, Computer Vision, Geometric Modeling, Geometric Processing, Networking and Medical Imaging.
