Rotation Equivariant Networks via Conic Convolution and the DFT

Benjamin Chidester, Minh N. Do, Jian Ma

Abstract: Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. In particular, to aid convolutional neural networks in learning rotation invariance, we consider a simple, efficient conic convolutional scheme that encodes rotational equivariance, along with a method for integrating the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) to encode global rotational invariance. We call our new method the Conic Convolution and DFT Network (CFNet). We evaluated the efficacy of CFNet as compared to a standard CNN and group-equivariant CNN (G-CNN) for several different image classification tasks and demonstrated improved performance, including classification accuracy, computational efficiency, and its robustness to hyperparameter selection. Taken together, we believe CFNet represents a new scheme that has the potential to improve many imaging analysis applications.

Keywords: deep learning, rotation equivariance, bioimaging analysis

TL;DR: We propose conic convolution and the 2D-DFT to encode rotation equivariance into an neural network.