Memory-Scalable and Simplified Functional Map Learning
Authors: Robin Magnet, Maks Ovsjanikov

Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain the latest techniques have demonstrated that by promoting consistency between functional and pointwise maps leads to significant improvements in accuracy. Unfortunately existing approaches rely heavily on the computation of large dense matrices arising from soft pointwise maps which compromises their efficiency and scalability. To address this limitation we introduce a novel memory-scalable and efficient functional map learning pipeline. By leveraging the specific structure of functional maps we offer the possibility to achieve identical results without ever storing the pointwise map in memory. Furthermore based on the same approach we present a differentiable map refinement layer adapted from an existing axiomatic refinement algorithm. Unlike many functional map learning methods which use this algorithm at a post-processing step ours can be easily used at train time enabling to enforce consistency between the refined and initial versions of the map. Our resulting approach is both simpler more efficient and more numerically stable by avoiding differentiation through a linear system while achieving close to state-of-the-art results in challenging scenarios.