# Contour-Aware Equipotential Learning for Semantic Segmentation

arXiv: https://arxiv.org/abs/2210.00223 · HTML: https://mlsanity.com/paper/2210.00223/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 1 Oct 2022.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [PointRend: Image Segmentation as Rendering](https://mlsanity.com/paper/1912.08193/) (2019)
- [Panoptic-DeepLab](https://mlsanity.com/paper/1910.04751/) (2019)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (2019)
- [Boundary IoU: Improving Object-Centric Image Segmentation Evaluation](https://mlsanity.com/paper/2103.16562/) (2021)
- [Gated-SCNN: Gated Shape CNNs for Semantic Segmentation](https://mlsanity.com/paper/1907.05740/) (2019)
- [Learning a Discriminative Feature Network for Semantic Segmentation](https://mlsanity.com/paper/1804.09337/) (2018)
- [Improving Semantic Segmentation via Decoupled Body and Edge Supervision](https://mlsanity.com/paper/2007.10035/) (2020)
- [SegFix: Model-Agnostic Boundary Refinement for Segmentation](https://mlsanity.com/paper/2007.04269/) (2020)
- [InverseForm: A Loss Function for Structured Boundary-Aware Segmentation](https://mlsanity.com/paper/2104.02745/) (2021)
- [Inductive Bias of Deep Convolutional Networks through Pooling Geometry](https://mlsanity.com/paper/1605.06743/) (2016)
- [Shape-Aware Organ Segmentation by Predicting Signed Distance Maps](https://mlsanity.com/paper/1912.03849/) (2019)
- [Active Boundary Loss for Semantic Segmentation](https://mlsanity.com/paper/2102.02696/) (2021)
- [Efficient Segmentation: Learning Downsampling Near Semantic Boundaries](https://mlsanity.com/paper/1907.07156/) (2019)
- [Devil is in the Edges: Learning Semantic Boundaries from Noisy Annotations](https://mlsanity.com/paper/1904.07934/) (2019)
- [Simultaneous Edge Alignment and Learning](https://mlsanity.com/paper/1808.01992/) (2018)

## Built on by (most cited first, 6 of 6)

- [Semi-supervised Semantic Segmentation with Multi-Constraint Consistency Learning](https://mlsanity.com/paper/2503.17914/) (2025)
- [Neural Rendering and Its Hardware Acceleration: A Review](https://mlsanity.com/paper/2402.00028/) (2024)
- [Fine-grained Background Representation for Weakly Supervised Semantic Segmentation](https://mlsanity.com/paper/2406.15755/) (2024)
- [A Deep Semantic Segmentation Network with Semantic and Contextual Refinements](https://mlsanity.com/paper/2412.08671/) (2024)
- [VPNeXt -- Rethinking Dense Decoding for Plain Vision Transformer](https://mlsanity.com/paper/2502.16654/) (2025)
- [Make It Up: Fake Images, Real Gains in Generalized Few-shot Semantic Segmentation](https://mlsanity.com/paper/2603.27206/) (2026)

## Abstract (arXiv)

With increasing demands for high-quality semantic segmentation in the industry, hard-distinguishing semantic boundaries have posed a significant threat to existing solutions. Inspired by real-life experience, i.e., combining varied observations contributes to higher visual recognition confidence, we present the equipotential learning (EPL) method. This novel module transfers the predicted/ground-truth semantic labels to a self-defined potential domain to learn and infer decision boundaries along customized directions. The conversion to the potential domain is implemented via a lightweight differentiable anisotropic convolution without incurring any parameter overhead. Besides, the designed two loss functions, the point loss and the equipotential line loss implement anisotropic field regression and category-level contour learning, respectively, enhancing prediction consistencies in the inter/intra-class boundary areas. More importantly, EPL is agnostic to network architectures, and thus it can be plugged into most existing segmentation models. This paper is the first attempt to address the boundary segmentation problem with field regression and contour learning. Meaningful performance improvements on Pascal Voc 2012 and Cityscapes demonstrate that the proposed EPL module can benefit the off-the-shelf fully convolutional network models when recognizing semantic boundary areas. Besides, intensive comparisons and analysis show the favorable merits of EPL for distinguishing semantically-similar and irregular-shaped categories.