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

Abstract

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.