# Log-Polar Space Convolution for Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2107.11943 · HTML: https://mlsanity.com/paper/2107.11943/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [R-FCN: Object Detection via Region-based Fully Convolutional Networks](https://mlsanity.com/paper/1605.06409/) (2016)
- [On the Relationship between Self-Attention and Convolutional Layers](https://mlsanity.com/paper/1911.03584/) (2019)
- [CE-Net: Context Encoder Network for 2D Medical Image Segmentation](https://mlsanity.com/paper/1903.02740/) (2019)
- [Understanding Convolution for Semantic Segmentation](https://mlsanity.com/paper/1702.08502/) (2017)
- [Drop an Octave: Reducing Spatial Redundancy in Convolutional Neural Networks with Octave Convolution](https://mlsanity.com/paper/1904.05049/) (2019)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Deformable Kernels: Adapting Effective Receptive Fields for Object Deformation](https://mlsanity.com/paper/1910.02940/) (2019)
- [Active Convolution: Learning the Shape of Convolution for Image Classification](https://mlsanity.com/paper/1703.09076/) (2017)
- [Optical Flow with Semantic Segmentation and Localized Layers](https://mlsanity.com/paper/1603.03911/) (2016)
- [Tree-structured Kronecker Convolutional Network for Semantic Segmentation](https://mlsanity.com/paper/1812.04945/) (2018)
- [POD: Practical Object Detection with Scale-Sensitive Network](https://mlsanity.com/paper/1909.02225/) (2019)
- [PSConv: Squeezing Feature Pyramid into One Compact Poly-Scale Convolutional Layer](https://mlsanity.com/paper/2007.06191/) (2020)

## Built on by (most cited first, 1 of 1)

- [Modelling Long Range Dependencies in ND: From Task-Specific to a General Purpose CNN](https://mlsanity.com/paper/2301.10540/) (2023)

## Abstract (arXiv)

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.