# Equivariant Multi-View Networks

## TL;DR

This paper introduces equivariant multi-view networks that perform joint reasoning over multiple views using group convolutions, improving 3D shape retrieval and scene classification by maintaining equivariance throughout the process.

## Contribution

It proposes a novel group convolutional approach for multi-view aggregation that preserves equivariance, outperforming traditional view pooling methods.

## Key findings

- Achieved state-of-the-art results in large-scale 3D shape retrieval.
- Demonstrated improved panoramic scene classification performance.
- Showed that equivariant reasoning enhances global descriptor quality.

## Abstract

Several popular approaches to 3D vision tasks process multiple views of the input independently with deep neural networks pre-trained on natural images, achieving view permutation invariance through a single round of pooling over all views. We argue that this operation discards important information and leads to subpar global descriptors. In this paper, we propose a group convolutional approach to multiple view aggregation where convolutions are performed over a discrete subgroup of the rotation group, enabling, thus, joint reasoning over all views in an equivariant (instead of invariant) fashion, up to the very last layer. We further develop this idea to operate on smaller discrete homogeneous spaces of the rotation group, where a polar view representation is used to maintain equivariance with only a fraction of the number of input views. We set the new state of the art in several large scale 3D shape retrieval tasks, and show additional applications to panoramic scene classification.