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.

本研究通过开发一种新的表面到图像表示方法，成功地在几何数据分析中应用了卷积神经网络，以达到在形状检索、形状分类和语义形状分割等任务上取得了最先进的结果或相当的结果的目标。