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

• URL: http://arxiv.org/abs/2205.04800v1
• Date: Tue, 10 May 2022 11:02:14 GMT
• Title: Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases
• Authors: Mikhail Panine, Maxime Kirgo and Maks Ovsjanikov
• Abstract summary: We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. We focus instead on near-conformal maps that preserve landmarks exactly. Our method is descriptor-free, efficient and robust to significant variability mesh.
• Score: 27.403848280099027
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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