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We analyze the role of rotational equivariance in convolutional neuralnetworks (CNNs) applied to spherical images. We compare the performance of thegroup equivariant networks known as S2CNNs and standard non-equivariant CNNstrained with an increasing amount of data augmentation. The chosenarchitectures can be considered baseline references for the respective designparadigms. Our models are trained and evaluated on single or multiple itemsfrom the MNIST or FashionMNIST dataset projected onto the sphere. For the taskof image classification, which is inherently rotationally invariant, we findthat by considerably increasing the amount of data augmentation and the size ofthe networks, it is possible for the standard CNNs to reach at least the sameperformance as the equivariant network. In contrast, for the inherentlyequivariant task of semantic segmentation, the non-equivariant networks areconsistently outperformed by the equivariant networks with significantly fewerparameters. We also analyze and compare the inference latency and trainingtimes of the different networks, enabling detailed tradeoff considerationsbetween equivariant architectures and data augmentation for practical problems.The equivariant spherical networks used in the experiments are available athttps://github.com/JanEGerken/sem_seg_s2cnn .

Equivariance versus Augmentation for Spherical Images