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arXiv · 1909.11193

Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters

Wei Zhu·Qiang Qiu·Robert Calderbank·Guillermo Sapiro·Xiuyuan Cheng
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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.

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Wei Zhu, Qiang Qiu, Robert Calderbank, Guillermo Sapiro, Xiuyuan Cheng. 2019-09-24. Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters. https://arxiv.org/abs/1909.11193

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