Color Equivariant Network

Group equivariant convolutional neural networks have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale. Despite the improved interpretability, accuracy and generalizability afforded by these architectures, group equivariant networks have seen limited application in the context of perceptual quantities such as hue and saturation, even though their variation can lead to significant reductions in classification performance. In this paper, we introduce convolutional neural networks equivariant to variations in hue and saturation by design. To achieve this, we leverage the observation that hue and saturation transformations can be identified with the 2D rotation and 1D translation groups respectively. Our hue-, saturation-, and fully color-equivariant networks achieve equivariance to these perceptual transformations without an increase in network parameters. We demonstrate the utility of our networks on synthetic and real world datasets where color and lighting variations are commonplace.