Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translationequivariant (ST -equivariant) CNN with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve ST equivariant representations. To reduce the model complexity and computational burden, we decompose the convolutional filters under two pre-fixed separable bases and truncate the expansion to low-frequency components. A further benefit of the truncated filter expansion is the improved deformation robustness of the equivariant representation. Numerical experiments demonstrate that the proposed scaling-translation-equivariant networks with decomposed convolutional filters (ScDCFNet) achieves significantly improved performance in multiscale image classification and better interpretability than regular CNNs at a reduced model size.