Shape signature based on Ricci flow and optimal mass transportation

Wei Luo; Zengyu Su; Min Zhang; Wei Zeng; Junfei Dai; Xianfeng D. Gu

doi:10.1117/1.OE.53.11.112209

25 April 2014 Shape signature based on Ricci flow and optimal mass transportation

Wei Luo, Zengyu Su, Min Zhang, Wei Zeng, Junfei Dai, Xianfeng D. Gu

Author Affiliations +

Optical Engineering, Vol. 53, Issue 11, 112209 (April 2014). https://doi.org/10.1117/1.OE.53.11.112209

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.

Citation Download Citation

Wei Luo, Zengyu Su, Min Zhang, Wei Zeng, Junfei Dai, and Xianfeng D. Gu "Shape signature based on Ricci flow and optimal mass transportation," Optical Engineering 53(11), 112209 (25 April 2014). https://doi.org/10.1117/1.OE.53.11.112209

Published: 25 April 2014

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