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

TL;DR

This paper introduces a landmark-adapted basis within the functional maps framework to improve non-isometric shape matching, emphasizing landmark preservation and conformal maps, resulting in state-of-the-art performance.

Contribution

It develops a novel landmark-adapted basis using an intrinsic eigenproblem and extends the ZoomOut method for landmark-preserving non-isometric shape matching.

Findings

Achieves state-of-the-art results on non-isometric benchmarks.

Demonstrates robustness to mesh variability.

Provides a descriptor-free, efficient matching method.

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.