1. Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters.
- Author
-
Wei Zhu, Qiang Qiu, Calderbank, Robert, Sapiro, Guillermo, and Xiuyuan Cheng
- Subjects
- *
CONVOLUTIONAL neural networks , *IMAGE recognition (Computer vision) , *COMPUTER vision - Abstract
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST -equivariant) CNN with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve equivariance for the regular representation of the scaling-translation group ST. 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, a property which is theoretically analyzed and empirically verified. Numerical experiments demonstrate that the proposed scaling-translation-equivariant network with decomposed convolutional filters (ScDCFNet) achieves significantly improved performance in multiscale image classification and better interpretability than regular CNNs at a reduced model size. [ABSTRACT FROM AUTHOR]
- Published
- 2022