Journal article

Non-isometric shape matching via functional maps on landmark-adapted bases

  • Panine, Mikhail ORCID Istituto Dalle Molle di studi sull'intelligenza artificiale (IDSIA), Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
  • Kirgo, Maxime ORCID LIX, École Polytechnique, IP Paris, Palaiseau, France - EDF R&D, Palaiseau Cedex, France
  • Ovsjanikov, Maks ORCID LIX, École Polytechnique, IP Paris, Palaiseau, France
  • 2022
Published in:
  • Computer graphics forum. - 2022, vol. 41, p. 394-417
English We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional map framework, but rather than promoting isometries we focus on near-conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally-invariant energy that promotes high-quality landmark-preserving maps, and show how it can be optimized via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor-free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state-of-the-art performance on non-isometric benchmarks and near state-of-the-art performance on isometric ones.
  • English
Computer science and technology
Open access status
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