Equivariance versus Augmentation for Spherical Images

TL;DR

This paper compares rotational equivariance and data augmentation in CNNs for spherical images, showing equivariant networks excel in segmentation tasks while augmented non-equivariant CNNs can match equivariant performance in classification.

Contribution

It provides a comparative analysis of equivariant and non-equivariant CNNs on spherical images, highlighting their strengths and tradeoffs in different tasks.

Findings

Equivariant networks outperform non-equivariant ones in semantic segmentation.

With enough data augmentation, non-equivariant CNNs can match equivariant CNNs in classification.

Equivariant networks are more parameter-efficient for inherently equivariant tasks.

Abstract

We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems. The equivariant spherical networks used in the experiments are available at https://github.com/JanEGerken/sem_seg_s2cnn .