Deep functional maps have recently emerged as a successful paradigm for
non-rigid 3D shape correspondence tasks. An essential step in this pipeline
consists in learning feature functions that are used as constraints to solve
for a functional map inside the network. However, the precise nature of the
information learned and stored in these functions is not yet well understood.
Specifically, a major question is whether these features can be used for any
other objective, apart from their purely algebraic role in solving for
functional map matrices. In this paper, we show that under some mild
conditions, the features learned within deep functional map approaches can be
used as point-wise descriptors and thus are directly comparable across
different shapes, even without the necessity of solving for a functional map at
test time. Furthermore, informed by our analysis, we propose effective
modifications to the standard deep functional map pipeline, which promote
structural properties of learned features, significantly improving the matching
results. Finally, we demonstrate that previously unsuccessful attempts at using
extrinsic architectures for deep functional map feature extraction can be
remedied via simple architectural changes, which encourage the theoretical
properties suggested by our analysis. We thus bridge the gap between intrinsic
and extrinsic surface-based learning, suggesting the necessary and sufficient
conditions for successful shape matching. Our code is available at
this https URL

本文探讨了深度函数地图方法中所学特征函数的本质以及如何将其用于点描述，在此基础上，我们提出了一种改进的方法来使学习特征的结构显著改进匹配结果，并成功地将内在和外在表面学习框架结合起来。