Circular-Symmetric Correlation Layer

Despite the vast success of standard planar convolutional neural networks, they are not the most efficient choice for analyzing signals that lie on an arbitrarily curved manifold, such as a cylinder. The problem arises when one performs a planar projection of these signals and inevitably causes them to be distorted or broken where there is valuable information. We propose a Circular-symmetric Correlation Layer (CCL) based on the formalism of roto-translation equivariant correlation on the continuous group $S^1 \times \mathbb{R}$, and implement it efficiently using the well-known Fast Fourier Transform (FFT) algorithm. We showcase the performance analysis of a general network equipped with CCL on a popular autonomous driving dataset, nuScenes (Caesar et al., 2020), for semantic segmentation of 3D point clouds obtained from LiDAR sweeps from their $360^\circ-$panoramic projections. The PyTorch package implementation of CCL is provided online.