  Deep functional map frameworks are widely employed for 3D shape matching.
However, most existing deep functional map methods cannot adaptively capture
important frequency information for functional map estimation in specific
matching scenarios, i.e., lacking \textit{frequency awareness}, resulting in
poor performance when dealing with large deformable shape matching. To this
end, we propose a novel unsupervised learning-based framework called Deep
Frequency-Aware Functional Maps, which can gracefully cope with various shape
matching scenarios. We first introduce a general constraint called Spectral
Filter Operator Preservation to compute desirable functional maps, where the
spectral filter operator encodes informative frequency information and can
promote frequency awareness for deep functional map frameworks by learning a
set of filter functions. Then, we directly utilize the proposed constraint as a
loss function to supervise functional maps, pointwise maps, and filter
functions simultaneously, where the filter functions are derived from the
orthonormal Jacobi basis, and the coefficients of the basis are learnable
parameters. Finally, we develop an effective refinement strategy to improve the
final pointwise map, which incorporates our constraint and learned filter
functions, leading to more robust and accurate correspondences during the
inference process. Extensive experimental results on various datasets
demonstrate that our approach outperforms the existing state-of-the-art
methods, especially in challenging settings like datasets with non-isometric
deformation and inconsistent topology.
