A Splitting Scheme for Flip-Free Distortion Energies
Name
21m1433058.pdf
Description
Published version
Size
31.27 MB
Format
Adobe PDF
Checksum (MD5)
569459daa5f2844135a8964ea1989a1f
Author(s)
Stein, Oded
Li, Jiajin
Solomon, Justin
Date Issued
June 2022
Journal
SIAM Journal on Imaging Sciences
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
We introduce a robust optimization method for flip-free distortion energies used, for example, in parametrization, deformation, and volume correspondence. This method can minimize a variety of distortion energies, such as the symmetric Dirichlet energy and our new symmetric gradient energy. We identify and exploit the special structure of distortion energies to employ an operator splitting technique, leading us to propose a novel alternating direction method of multipliers (ADMM) algorithm to deal with the nonconvex, nonsmooth nature of distortion energies. The scheme results in an efficient method where the global step involves a single matrix multiplication and the local steps are closed-form per-triangle/per-tetrahedron expressions that are highly parallelizable. The resulting general-purpose optimization algorithm exhibits robustness to flipped triangles and tetrahedra in initial data as well as during the optimization. We establish the convergence of our proposed algorithm under certain conditions and demonstrate applications to parametrization, deformation, and volume correspondence.
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DOI of Published Version
https://doi.org/10.1137/21M1433058
