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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
