The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately limiting their generalization performance. To address this limitation, we devise a method that endows CNNs with simultaneous equivariance with respect to translation, rotation, and scaling. Our approach defines a convolution-like operation and ensures equivariance based on our proposed scalable Fourier-Argand representation. The method maintains similar efficiency as a traditional network and hardly introduces any additional learnable parameters, since it does not face the computational issue that often occurs in group-convolution operators. We validate the efficacy of our approach in the image classification task, demonstrating its robustness and the generalization ability to both scaled and rotated inputs.

本文提出了一种方法，通过使用可缩放的傅里叶-阿甘德表示法和类似卷积的操作来实现卷积神经网络对于平移、旋转和缩放的同时等变性，并验证了该方法在图像分类任务方面的有效性和对缩放和旋转输入的泛化能力。

利用类似卷积实现网络的尺度和旋转等变性增强