Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching
This work addresses a critical bottleneck in shape matching for computer graphics and vision by improving robustness to non-isometric distortions, though it is incremental as it builds on existing functional map methods.
The paper tackles the problem of non-rigid shape matching by introducing a multi-resolution functional maps framework with spectral attention, which alleviates the need for manual spectral resolution tuning and achieves robust performance on both near-isometric and non-isometric benchmarks.
In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution hyperparameter, which can severely affect the overall accuracy or lead to overfitting, if not chosen carefully. In this paper, we show that spectral resolution tuning can be alleviated by introducing spectral attention. Our framework is applicable in both supervised and unsupervised settings, and we show that it is possible to train the network so that it can adapt the spectral resolution, depending on the given shape input. More specifically, we propose to compute multi-resolution functional maps that characterize correspondence across a range of spectral resolutions, and introduce a spectral attention network that helps to combine this representation into a single coherent final correspondence. Our approach is not only accurate with near-isometric input, for which a high spectral resolution is typically preferred, but also robust and able to produce reasonable matching even in the presence of significant non-isometric distortion, which poses great challenges to existing methods. We demonstrate the superior performance of our approach through experiments on a suite of challenging near-isometric and non-isometric shape matching benchmarks.