README.md

F-Conv

Code of "Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutions"
Paper link
Arxiv link
Supplementary Material

MinistExp\    : Code for the experiments on minist dataset
SRExp\        : Code for the experiments of image super resolution 
Supplementary Material.pdf: Supplementary Material

F-Convs are rotation equivariant convolutions with high representation accuracy, which can perform better on low-level computer vision tasks as comparsion with pervious rotation equivariant convolution methods.

Rotation symmetry on local features is an important structure characteristics of image, which can be hardly captured by commonly used CNN, as shown in the folliwing figure:

(a) is a typical input cartoon image. (b) and (c) are outputs of randomly initialized CNN and F-Conv, respectively, where the demarcated areas are zoomed in 5 times for easy observation.

From the figure, we can also observe that the proposed F-Conv is expected to better maintain the symmetry of local features underlying the image, which should be help for the computer vision tasks.

Besides the output of F-Conv can be more stable than output of CNN when the input is rotated, as shown in the following two figures.

CNN results:

F-Conv results:

Usage:

Detail usage can be found in the subfolders

Citation:

Qi Xie, Qian Zhao, Zongben Xu and Deyu Meng*. 
Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutions[J]. 
IEEE transactions on pattern analysis and machine intelligence, 2022.

BibTeX:

@article{xie2022FConv,
title={Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutions},
author={Xie, Qi and Zhao, Qian and Xu, Zongben and Meng, Deyu},
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
year={2022},
publisher={IEEE}
}