Spherical convolutional networks have been introduced recently as tools to
learn powerful feature representations of 3D shapes. Spherical CNNs are
equivariant to 3D rotations making them ideally suited to applications where 3D
data may be observed in arbitrary orientations. In this paper we learn 2D image
embeddings with a similar equivariant structure: embedding the image of a 3D
object should commute with rotations of the object. We introduce a cross-domain
embedding from 2D images into a spherical CNN latent space. This embedding
encodes images with 3D shape properties and is equivariant to 3D rotations of
the observed object. The model is supervised only by target embeddings obtained
from a spherical CNN pretrained for 3D shape classification. We show that
learning a rich embedding for images with appropriate geometric structure is
sufficient for tackling varied applications, such as relative pose estimation
and novel view synthesis, without requiring additional task-specific
supervision.

本文介绍了一种基于球形卷积网络的 2D 图像嵌入学习方法，在不需要特定任务的监督下，利用其等变结构特征解决了姿态估计和新视角合成等应用。

跨域 3D 等变图像嵌入

Cross-Domain 3D Equivariant Image Embeddings

The success of convolutional networks in learning problems involving planar
signals such as images is due to their ability to exploit the translation
symmetry of the data distribution through weight sharing. Many areas of science
and egineering deal with signals with other symmetries, such as rotation
invariant data on the sphere. Examples include climate and weather science,
astrophysics, and chemistry. In this paper we present spherical convolutional
networks. These networks use convolutions on the sphere and rotation group,
which results in rotational weight sharing and rotation equivariance. Using a
synthetic spherical MNIST dataset, we show that spherical convolutional
networks are very effective at dealing with rotationally invariant
classification problems.

本文介绍了一种新的网络结构 —— 球面卷积网络，用于处理具有旋转不变性的分类问题，并通过在球面上进行卷积和旋转权重共享来实现旋转等变性。实验结果表明，球面卷积网络在处理类似于 MNIST 的数据集时具有很高的准确率。