# Surface Networks via General Covers

## TL;DR

This paper introduces a novel surface-to-image representation for sphere-type surfaces that enables the effective application of CNNs, achieving state-of-the-art results in shape analysis tasks.

## Contribution

It proposes a low distortion covering map for surface-to-image representation, facilitating deep learning on geometric data with improved accuracy.

## Key findings

- Achieves state-of-the-art results in shape retrieval and classification.
- Provides a low distortion, single-image surface representation.
- Enables effective CNN application to 3D surface data.

## Abstract

Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation we are able to quickly adapt successful CNN models to the surface setting. The surface-image representation is based on a covering map from the image domain to the surface. Namely, the map wraps around the surface several times, making sure that every part of the surface is well represented in the image. Differently from previous surface-to-image representations, we provide a low distortion coverage of all surface parts in a single image. Specifically, for the use case of learning spherical signals, our representation provides a low distortion alternative to several popular spherical parameterizations used in deep learning. We have used the surface-to-image representation to apply standard CNN architectures to 3D models as well as spherical signals. We show that our method achieves state of the art or comparable results on the tasks of shape retrieval, shape classification and semantic shape segmentation.