Data augmentation with Mobius transformations

Abstract Data augmentation has led to substantial improvements in the performance and generalization of deep models, and remains a highly adaptable method to evolving model architectures and varying amounts of data—in particular, extremely scarce amounts of available training data. In this paper, we present a novel method of applying Möbius transformations to augment input images during training. Möbius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space. As a result, Möbius transformations can operate on the sample level and preserve data labels. We show that the inclusion of Möbius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes.