CNNs on Surfaces using Rotation-Equivariant Features

CNNs on Surfaces using Rotation-Equivariant Features

Wiersma, R.T. (TU Delft Computer Graphics and Visualisation)
Eisemann, E. (TU Delft Computer Graphics and Visualisation)
Hildebrandt, K.A. (TU Delft Computer Graphics and Visualisation)

2020-07-03

This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a rotational ambiguity, which prevents a uniform alignment of these kernels on the surface. We propose a network architecture for surfaces that consists of vector-valued, rotation-equivariant features. The equivariance property makes it possible to locally align features, which were computed in arbitrary coordinate systems, when aggregating features in a convolution layer. The resulting network is agnostic to the choices of coordinate systems for the tangent spaces on the surface. We implement our approach for triangle meshes. Based on circular harmonic functions, we introduce convolution filters for meshes that are rotation-equivariant at the discrete level. We evaluate the resulting networks on shape correspondence and shape classifications tasks and compare their performance to other approaches.

CNNs on surfaces
circular Harmonic Filters
geometric deep learning
rotation-equivariance
shape classification
shape correspondence
shape segmentation
surface networks

http://resolver.tudelft.nl/uuid:7179c2ed-fb1e-418b-a32b-11d73b7e55a3

https://doi.org/10.1145/3386569.3392437

0730-0301

ACM Transactions on Graphics, 39 (4)

Institutional Repository

journal article

© 2020 R.T. Wiersma, E. Eisemann, K.A. Hildebrandt