  Convolutional Neural Networks (CNN) offer state of the art performance in
various computer vision tasks. Many of those tasks require different subtypes
of affine invariances (scale, rotational, translational) to image
transformations. Convolutional layers are translation equivariant by design,
but in their basic form lack invariances. In this work we investigate how best
to include rotational invariance in a CNN for image classification. Our
experiments show that networks trained with data augmentation alone can
classify rotated images nearly as well as in the normal unrotated case; this
increase in representational power comes only at the cost of training time. We
also compare data augmentation versus two modified CNN models for achieving
rotational invariance or equivariance, Spatial Transformer Networks and Group
Equivariant CNNs, finding no significant accuracy increase with these
specialized methods. In the case of data augmented networks, we also analyze
which layers help the network to encode the rotational invariance, which is
important for understanding its limitations and how to best retrain a network
with data augmentation to achieve invariance to rotation.
