Variance-Minimizing Transport Plans for Inter-surface Mapping

Manish Mandad, David Cohen-Steiner, Leif Kobbelt, Pierre Alliez, Mathieu Desbrun

We introduce an efficient 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-to-fine 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.

» Show BibTeX

author = "Mandad, Manish and Cohen-Steiner, David and Kobbelt, Leif and Alliez, Pierre and Desbrun, Mathieu",
title = "Variance-Minimizing Transport Plans for Inter-surface Mapping",
journal = "ACM Transactions on Graphics",
volume = 36,
number = 4,
year = 2017,
articleno = {39},

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