Memory-Scalable and Simplified Functional Map Learning
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.