Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters
Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters
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发表时间：
2019-09
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通讯作者：
Wei Zhu;Qiang Qiu;Robert Calderbank;G. Sapiro;Xiuyuan Cheng
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作者：
Wei Zhu;Qiang Qiu;Robert Calderbank;G. Sapiro;Xiuyuan Cheng
将尺度信息显式编码到卷积神经网络（CNN）学习的表示中对于许多计算机视觉任务都是有益的，特别是在处理多尺度输入时。在本文中，我们研究了一种缩放-平移-等变（ST-等变）CNN，它具有跨空间和缩放群的联合卷积，这对于缩放-平移群ST的正则表示实现等变是充分和必要的。为了降低模型复杂度和计算负担，我们将卷积滤波器分解在两个预先固定的可分离基下，并将扩展截断到低频分量。截断滤波器扩展的另一个好处是改进的等变表示的变形鲁棒性，这是一个经过理论分析和经验验证的属性。数值实验表明，所提出的具有分解卷积滤波器的缩放-平移-等变网络（ScDCFNet）在多尺度图像分类中实现了显着提高的性能，并且在减小的模型大小下比常规CNN具有更好的可解释性。
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.