Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases
This addresses shape matching for computer graphics and vision, offering a descriptor-free and efficient method, though it is incremental as it builds on the functional maps framework.
The paper tackles non-isometric shape matching by introducing a landmark-adapted basis and a conformally-invariant energy, achieving state-of-the-art performance on non-isometric benchmarks and near state-of-the-art on isometric ones.
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.