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Journal Articles ACM Transactions on Graphics Year : 2017

Variance-Minimizing Transport Plans for Inter-surface Mapping

Abstract

We introduce an effcient computational method for generating dense and low distortion maps between two arbitrary surfaces of same genus. Instead of relying on semantic correspondences or surface parameterization, we directly optimize a variance-minimizing transport plan between two input surfaces that defines an as-conformal-as-possible inter-surface map satisfying a user-prescribed bound on area distortion. The transport plan is computed via two alternating convex optimizations, and is shown to minimize a generalized Dirichlet energy of both the map and its inverse. Computational efficiency is achieved through a coarse-tone approach in diffusion geometry, with Sinkhorn iterations modified to enforce bounded area distortion. The resulting inter-surface mapping algorithm applies to arbitrary shapes robustly, with little to no user interaction.
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Dates and versions

hal-01519006 , version 1 (05-05-2017)

Identifiers

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Manish Mandad, David Cohen-Steiner, Leif Kobbelt, Pierre Alliez, Mathieu Desbrun. Variance-Minimizing Transport Plans for Inter-surface Mapping. ACM Transactions on Graphics, 2017, 36, pp.14. ⟨10.1145/3072959.3073671⟩. ⟨hal-01519006⟩
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