A Data-Driven Approach to Functional Map Construction and Bases Pursuit

Omri Azencot, Rongjie Lai

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)97-110
Number of pages14
JournalComputer Graphics Forum
Volume40
Issue number5
DOIs
StatePublished - 1 Aug 2021

Keywords

  • CCS Concepts
  • • Computing methodologies → Shape analysis

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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