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Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases

2022-05-10 11:02:14
Mikhail Panine, Maxime Kirgo, Maks Ovsjanikov

Abstract

We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead 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 solved 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.

Abstract (translated)

URL

https://arxiv.org/abs/2205.04800

PDF

https://arxiv.org/pdf/2205.04800.pdf


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