Surface meshes are widely used shape representations and capture finer
geometry data than point clouds or volumetric grids, but are challenging to
apply CNNs directly due to their non-Euclidean structure. We use parallel
frames on surface to define PFCNNs that enable effective feature learning on
surface meshes by mimicking standard convolutions faithfully. In particular,
the convolution of PFCNN not only maps local surface patches onto flat tangent
planes, but also aligns the tangent planes such that they locally form a flat
Euclidean structure, thus enabling recovery of standard convolutions. The
alignment is achieved by the tool of locally flat connections borrowed from
discrete differential geometry, which can be efficiently encoded and computed
by parallel frame fields. In addition, the lack of canonical axis on surface is
handled by sampling with the frame directions. Experiments show that for tasks
including classification, segmentation and registration on deformable geometric
domains, as well as semantic scene segmentation on rigid domains, PFCNNs
achieve robust and superior performances without using sophisticated input
features than state-of-the-art surface based CNNs.

通过平行帧场的工具，定义了 PFCNN 在表面网格上的应用。通过模拟标准的卷积方式，可以有效地实现表面网格上的特征学习。实验证明，在不使用比表面网格 CNN 更复杂的输入特征的情况下，PFCNN 在分类、分割、配准和场景分割等方面均实现了优异的性能。