Log-Polar Space Convolution for Convolutional Neural Networks

TL;DR

This paper introduces log-polar space convolution (LPSC), a novel convolution method that adaptively enlarges receptive fields using elliptical kernels and logarithmic divisions, improving feature extraction in CNNs.

Contribution

The paper proposes LPSC, a new convolution technique that encodes local spatial structures and expands receptive fields efficiently, compatible with existing CNN architectures.

Findings

LPSC enhances receptive fields without increasing parameters

LPSC improves performance across multiple tasks and datasets

LPSC can be implemented with standard convolution operations

Abstract

Convolutional neural networks use regular quadrilateral convolution kernels to extract features. Since the number of parameters increases quadratically with the size of the convolution kernel, many popular models use small convolution kernels, resulting in small local receptive fields in lower layers. This paper proposes a novel log-polar space convolution (LPSC) method, where the convolution kernel is elliptical and adaptively divides its local receptive field into different regions according to the relative directions and logarithmic distances. The local receptive field grows exponentially with the number of distance levels. Therefore, the proposed LPSC not only naturally encodes local spatial structures, but also greatly increases the single-layer receptive field while maintaining the number of parameters. We show that LPSC can be implemented with conventional convolution via log-polar space pooling and can be applied in any network architecture to replace conventional convolutions. Experiments on different tasks and datasets demonstrate the effectiveness of the proposed LPSC. Code is available at https://github.com/BingSu12/Log-Polar-Space-Convolution.