Circular-Symmetric Correlation Layer based on FFT
This addresses the problem of signal distortion in manifold analysis for researchers and practitioners in computer vision and signal processing, offering a domain-specific improvement.
The paper tackled the inefficiency of standard planar CNNs for analyzing signals on curved manifolds like cylinders by proposing a Circular-symmetric Correlation Layer (CCL) based on roto-translation equivariant correlation, implemented efficiently with FFT, and demonstrated its performance on recognition and classification tasks across various datasets.
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 various recognition and classification tasks and datasets. The PyTorch package implementation of CCL is provided online.