# PreCM: The Padding-based Rotation Equivariant Convolution Mode for Semantic Segmentation

arXiv: https://arxiv.org/abs/2411.01624 · HTML: https://mlsanity.com/paper/2411.01624/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 56 references that are in the map.
- First posted on arXiv 3 Nov 2024.

## Builds on (most cited first, 30 of 30)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [RepVGG: Making VGG-style ConvNets Great Again](https://mlsanity.com/paper/2101.03697/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [BiSeNet V2: Bilateral Network with Guided Aggregation for Real-time Semantic Segmentation](https://mlsanity.com/paper/2004.02147/) (2020)
- [ENet: A Deep Neural Network Architecture for Real-Time Semantic Segmentation](https://mlsanity.com/paper/1606.02147/) (2016)
- [ClassMix: Segmentation-Based Data Augmentation for Semi-Supervised Learning](https://mlsanity.com/paper/2007.07936/) (2020)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [FloodNet: A High Resolution Aerial Imagery Dataset for Post Flood Scene Understanding](https://mlsanity.com/paper/2012.02951/) (2020)
- [Self-Ensembling with GAN-based Data Augmentation for Domain Adaptation in Semantic Segmentation](https://mlsanity.com/paper/1909.00589/) (2019)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networks](https://mlsanity.com/paper/1604.06318/) (2016)
- [Attentive Group Equivariant Convolutional Networks](https://mlsanity.com/paper/2002.03830/) (2020)
- [LEDNet: A Lightweight Encoder-Decoder Network for Real-Time Semantic Segmentation](https://mlsanity.com/paper/1905.02423/) (2019)
- [Deep Learning Markov Random Field for Semantic Segmentation](https://mlsanity.com/paper/1606.07230/) (2016)
- [RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Network](https://mlsanity.com/paper/2211.11812/) (2022)
- [Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration](https://mlsanity.com/paper/2312.15701/) (2023)
- [Deep Rotation Equivariant Network](https://mlsanity.com/paper/1705.08623/) (2017)
- [Rotation Equivariant Siamese Networks for Tracking](https://mlsanity.com/paper/2012.13078/) (2020)
- [Convolution with even-sized kernels and symmetric padding](https://mlsanity.com/paper/1903.08385/) (2019)
- [Random Forest with Learned Representations for Semantic Segmentation](https://mlsanity.com/paper/1901.07828/) (2019)
- [Deep Learning for 2D and 3D Rotatable Data: An Overview of Methods](https://mlsanity.com/paper/1910.14594/) (2019)

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

- [Geometric Causal Models](https://mlsanity.com/paper/2607.05153/) (2026)

## Abstract (arXiv)

Semantic segmentation is an important branch of image processing and computer vision. With the popularity of deep learning, various convolutional neural networks have been proposed for pixel-level classification and segmentation tasks. In practical scenarios, however, imaging angles are often arbitrary, encompassing instances such as water body images from remote sensing and capillary and polyp images in the medical domain, where prior orientation information is typically unavailable to guide these networks to extract more effective features. In this case, learning features from objects with diverse orientation information poses a significant challenge, as the majority of CNN-based semantic segmentation networks lack rotation equivariance to resist the disturbance from orientation information. To address this challenge, this paper first constructs a universal convolution-group framework aimed at more fully utilizing orientation information and equipping the network with rotation equivariance. Subsequently, we mathematically design a padding-based rotation equivariant convolution mode (PreCM), which is not only applicable to multi-scale images and convolutional kernels but can also serve as a replacement component for various types of convolutions, such as dilated convolutions, transposed convolutions, and asymmetric convolution. To quantitatively assess the impact of image rotation in semantic segmentation tasks, we also propose a new evaluation metric, Rotation Difference (RD). The replacement experiments related to six existing semantic segmentation networks on three datasets show that, the average Intersection Over Union (IOU) of their PreCM-based versions respectively improve 6.91%, 10.63%, 4.53%, 5.93%, 7.48%, 8.33% compared to their original versions in terms of random angle rotation. And the average RD values are decreased by 3.58%, 4.56%, 3.47%, 3.66%, 3.47%, 3.43% respectively.