Differentiable Surface Triangulation

Marie-Julie Rakotosaona, Noam Aigerman, Niloy J. Mitra, Maks Ovsjanikov, Paul Guerrero

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably perturbed weighted Delaunay triangulation. We translate this result into a computational algorithm by proposing a soft relaxation of the classical weighted Delaunay triangulation and optimizing over vertex weights and vertex locations. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints. We demonstrate the efficacy of our method on various planar and surface meshes on a range of difficult-to-optimize objective functions. Our code can be found online: https://github.com/mrakotosaon/diff-surface-triangulation.
Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalACM Transactions on Graphics
Volume40
Issue number6
DOIs
StatePublished - Dec 10 2021
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-05-25
Acknowledged KAUST grant number(s): CRG-2017-3426
Acknowledgements: Parts of this work were supported by the KAUST OSR Award No. CRG-2017-3426, the ERC Starting Grant No. 758800 (EXPROTEA), the ANR AI Chair AIGRETTE, gifts from Adobe, the UCL AI Centre and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant PRIME No. 956585.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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