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Optical Engineering

Shape signature based on Ricci flow and optimal mass transportation
Author(s): Wei Luo; Zengyu Su; Min Zhang; Wei Zeng; Junfei Dai; Xianfeng D. Gu
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Paper Abstract

A shape signature based on surface Ricci flow and optimal mass transportation is introduced for the purpose of surface comparison. First, the surface is conformally mapped onto plane by Ricci flow, which induces a measure on the planar domain. Second, the unique optimal mass transport map is computed that transports the new measure to the canonical measure on the plane. The map is obtained by a convex optimization process. This optimal transport map encodes all the information of the Riemannian metric on the surface. The shape signature consists of the optimal transport map, together with the mean curvature, which can fully recover the original surface. The discrete theories of surface Ricci flow and optimal mass transportation are explained thoroughly. The algorithms are given in detail. The signature is tested on human facial surfaces with different expressions accquired by structured light 3-D scanner based on phase-shifting method. The experimental results demonstrate the efficiency and efficacy of the method.

Paper Details

Date Published: 25 April 2014
PDF: 19 pages
Opt. Eng. 53(11) 112209 doi: 10.1117/1.OE.53.11.112209
Published in: Optical Engineering Volume 53, Issue 11
Show Author Affiliations
Wei Luo, Zhejiang Univ. (China)
Zengyu Su, Stony Brook Univ. (United States)
Min Zhang, Stony Brook Univ. (United States)
Wei Zeng, Florida International Univ. (United States)
Junfei Dai, Zhejiang Univ. (China)
Xianfeng D. Gu, Stony Brook Univ. (United States)

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