An intuitive multi-frequency feature representation for SO(3)-equivariant networks

TL;DR

This paper introduces a multi-frequency equivariant feature representation for 3D data that enhances the detail-capturing ability of SO(3)-equivariant networks, improving their performance in 3D vision tasks.

Contribution

It proposes a novel high-dimensional, multi-frequency feature representation that can be integrated with Vector Neuron networks to better capture 3D details.

Findings

Enhanced detail representation in 3D data

Improved performance of Vector Neuron networks

Demonstrated effectiveness on 3D vision tasks

Abstract

The usage of 3D vision algorithms, such as shape reconstruction, remains limited because they require inputs to be at a fixed canonical rotation. Recently, a simple equivariant network, Vector Neuron (VN) has been proposed that can be easily used with the state-of-the-art 3D neural network (NN) architectures. However, its performance is limited because it is designed to use only three-dimensional features, which is insufficient to capture the details present in 3D data. In this paper, we introduce an equivariant feature representation for mapping a 3D point to a high-dimensional feature space. Our feature can discern multiple frequencies present in 3D data, which is the key to designing an expressive feature for 3D vision tasks. Our representation can be used as an input to VNs, and the results demonstrate that with our feature representation, VN captures more details, overcoming the limitation raised in its original paper.