# CyCNN: A Rotation Invariant CNN using Polar Mapping and Cylindrical Convolution Layers

arXiv: https://arxiv.org/abs/2007.10588 · HTML: https://mlsanity.com/paper/2007.10588/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2020.

## Built on by (most cited first, 15 of 15)

- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [RoRD: Rotation-Robust Descriptors and Orthographic Views for Local Feature Matching](https://mlsanity.com/paper/2103.08573/) (2021)
- [Rotation Equivariant Feature Image Pyramid Network for Object Detection in Optical Remote Sensing Imagery](https://mlsanity.com/paper/2106.00880/) (2021)
- [Learning Online Visual Invariances for Novel Objects via Supervised and Self-Supervised Training](https://mlsanity.com/paper/2110.01476/) (2021)
- [Foveation in the Era of Deep Learning](https://mlsanity.com/paper/2312.01450/) (2023)
- [RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2408.06110/) (2024)
- [Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries](https://mlsanity.com/paper/2210.06741/) (2022)
- [Circular-Symmetric Correlation Layer based on FFT](https://mlsanity.com/paper/2107.12480/) (2021)
- [Hand bone age estimation using divide and conquer strategy and lightweight convolutional neural networks](https://mlsanity.com/paper/2405.14986/) (2024)
- [GMR-Conv: An Efficient Rotation and Reflection Equivariant Convolution Kernel Using Gaussian Mixture Rings](https://mlsanity.com/paper/2504.02819/) (2025)
- [A Rotation Meanout Network with Invariance for Dermoscopy Image Classification and Retrieval](https://mlsanity.com/paper/2208.00627/) (2022)
- [Foveated Retinotopy Improves Classification and Localization in Convolutional Neural Networks](https://mlsanity.com/paper/2402.15480/) (2024)
- [Equivariant Imaging Biomarkers for Robust Unsupervised Segmentation of Histopathology](https://mlsanity.com/paper/2505.05689/) (2025)
- [Soft-Argmax for the Projective Plane via the Veronese Embedding](https://mlsanity.com/paper/2609.00521/) (2026)
- [Task-driven Processing with Coarse-to-Fine Glimpse-based Active Perception](https://mlsanity.com/paper/2609.09025/) (2026)

## Abstract (arXiv)

Deep Convolutional Neural Networks (CNNs) are empirically known to be invariant to moderate translation but not to rotation in image classification. This paper proposes a deep CNN model, called CyCNN, which exploits polar mapping of input images to convert rotation to translation. To deal with the cylindrical property of the polar coordinates, we replace convolution layers in conventional CNNs to cylindrical convolutional (CyConv) layers. A CyConv layer exploits the cylindrically sliding windows (CSW) mechanism that vertically extends the input-image receptive fields of boundary units in a convolutional layer. We evaluate CyCNN and conventional CNN models for classification tasks on rotated MNIST, CIFAR-10, and SVHN datasets. We show that if there is no data augmentation during training, CyCNN significantly improves classification accuracies when compared to conventional CNN models. Our implementation of CyCNN is publicly available on https://github.com/mcrl/CyCNN.