# Sorted Convolutional Network for Achieving Continuous Rotational Invariance

arXiv: https://arxiv.org/abs/2305.14462 · HTML: https://mlsanity.com/paper/2305.14462/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networks](https://mlsanity.com/paper/1604.06318/) (2016)
- [RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Network](https://mlsanity.com/paper/2211.11812/) (2022)
- [LOOP Descriptor: Local Optimal Oriented Pattern](https://mlsanity.com/paper/1710.09317/) (2017)

## Abstract (arXiv)

The topic of achieving rotational invariance in convolutional neural networks (CNNs) has gained considerable attention recently, as this invariance is crucial for many computer vision tasks such as image classification and matching. In this letter, we propose a Sorting Convolution (SC) inspired by some hand-crafted features of texture images, which achieves continuous rotational invariance without requiring additional learnable parameters or data augmentation. Further, SC can directly replace the conventional convolution operations in a classic CNN model to achieve its rotational invariance. Based on MNIST-rot dataset, we first analyze the impact of convolutional kernel sizes, different sampling and sorting strategies on SC's rotational invariance, and compare our method with previous rotation-invariant CNN models. Then, we combine SC with VGG, ResNet and DenseNet, and conduct classification experiments on popular texture and remote sensing image datasets. Our results demonstrate that SC achieves the best performance in the aforementioned tasks.