A Data-Driven Approach to Functional Map Construction and Bases Pursuit
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Date
2021
Authors
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Journal ISSN
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Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace-Beltrami operator and thus favor low-frequency eigenfunctions, we aim for a basis that allows for better feature matching. This change of perspective introduces many degrees of freedom into the problem allowing to better exploit non-smooth descriptors. To effectively search in this high-dimensional space of solutions, we incorporate into our minimization state-of-the-art regularizers. We solve the resulting highly non-linear and non-convex problem using an iterative scheme via the Alternating Direction Method of Multipliers. At each step, our optimization involves simple to solve linear or Sylvester-type equations. In practice, our method performs well in terms of convergence, and we additionally show that it is similar to a provably convergent problem. We show the advantages of our approach by extensively testing it on multiple datasets in a few applications including shape matching, consistent quadrangulation and scalar function transfer.
Description
@article{10.1111:cgf.14360,
journal = {Computer Graphics Forum},
title = {{A Data-Driven Approach to Functional Map Construction and Bases Pursuit}},
author = {Azencot, Omri and Lai, Rongjie},
year = {2021},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14360}
}