# Deep Learning Markov Random Field for Semantic Segmentation

arXiv: https://arxiv.org/abs/1606.07230 · HTML: https://mlsanity.com/paper/1606.07230/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2016.

## Built on by (most cited first, 27 of 27)

- [Exploring Cross-Image Pixel Contrast for Semantic Segmentation](https://mlsanity.com/paper/2101.11939/) (2021)
- [Rethinking Semantic Segmentation: A Prototype View](https://mlsanity.com/paper/2203.15102/) (2022)
- [Deep Dual-resolution Networks for Real-time and Accurate Semantic Segmentation of Road Scenes](https://mlsanity.com/paper/2101.06085/) (2021)
- [GMMSeg: Gaussian Mixture based Generative Semantic Segmentation Models](https://mlsanity.com/paper/2210.02025/) (2022)
- [Low-light Image Enhancement via Breaking Down the Darkness](https://mlsanity.com/paper/2111.15557/) (2021)
- [Mining Contextual Information Beyond Image for Semantic Segmentation](https://mlsanity.com/paper/2108.11819/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [Weakly Supervised Object Localization via Transformer with Implicit Spatial Calibration](https://mlsanity.com/paper/2207.10447/) (2022)
- [LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning](https://mlsanity.com/paper/2309.13556/) (2023)
- [Spatial Mixture-of-Experts](https://mlsanity.com/paper/2211.13491/) (2022)
- [MCIBI++: Soft Mining Contextual Information Beyond Image for Semantic Segmentation](https://mlsanity.com/paper/2209.04471/) (2022)
- [Graphical Modeling for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2104.13057/) (2021)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Transformer-Unet: Raw Image Processing with Unet](https://mlsanity.com/paper/2109.08417/) (2021)
- [Class-level Multiple Distributions Representation are Necessary for Semantic Segmentation](https://mlsanity.com/paper/2303.08029/) (2023)
- [Weaving Attention U-net: A Novel Hybrid CNN and Attention-based Method for Organs-at-risk Segmentation in Head and Neck CT Images](https://mlsanity.com/paper/2107.04847/) (2021)
- [Target Detection and Segmentation in Circular-Scan Synthetic-Aperture-Sonar Images using Semi-Supervised Convolutional Encoder-Decoders](https://mlsanity.com/paper/2101.03603/) (2021)
- [Dual Perceptual Loss for Single Image Super-Resolution Using ESRGAN](https://mlsanity.com/paper/2201.06383/) (2022)
- [The SAM2-to-SAM3 Gap in the Segment Anything Model Family: Why Prompt-Based Expertise Fails in Concept-Driven Image Segmentation](https://mlsanity.com/paper/2512.06032/) (2025)
- [Interpretable Small Training Set Image Segmentation Network Originated from Multi-Grid Variational Model](https://mlsanity.com/paper/2306.14097/) (2023)
- [PreCM: The Padding-based Rotation Equivariant Convolution Mode for Semantic Segmentation](https://mlsanity.com/paper/2411.01624/) (2024)
- [Shift-Memory Network for Temporal Scene Segmentation](https://mlsanity.com/paper/2202.08399/) (2022)
- [Joint Learning of Deep Texture and High-Frequency Features for Computer-Generated Image Detection](https://mlsanity.com/paper/2209.03322/) (2022)
- [Pseudo-Trilateral Adversarial Training for Domain Adaptive Traversability Prediction](https://mlsanity.com/paper/2306.14370/) (2023)
- [Scaling Neuro-symbolic Problem Solving: Solver-Free Learning of Constraints and Objectives](https://mlsanity.com/paper/2508.20978/) (2025)
- [Segmenting Low-Contrast XCTs of Concrete: An Unsupervised Approach](https://mlsanity.com/paper/2603.00127/) (2026)

## Abstract (arXiv)

Semantic segmentation tasks can be well modeled by Markov Random Field (MRF). This paper addresses semantic segmentation by incorporating high-order relations and mixture of label contexts into MRF. Unlike previous works that optimized MRFs using iterative algorithm, we solve MRF by proposing a Convolutional Neural Network (CNN), namely Deep Parsing Network (DPN), which enables deterministic end-to-end computation in a single forward pass. Specifically, DPN extends a contemporary CNN to model unary terms and additional layers are devised to approximate the mean field (MF) algorithm for pairwise terms. It has several appealing properties. First, different from the recent works that required many iterations of MF during back-propagation, DPN is able to achieve high performance by approximating one iteration of MF. Second, DPN represents various types of pairwise terms, making many existing models as its special cases. Furthermore, pairwise terms in DPN provide a unified framework to encode rich contextual information in high-dimensional data, such as images and videos. Third, DPN makes MF easier to be parallelized and speeded up, thus enabling efficient inference. DPN is thoroughly evaluated on standard semantic image/video segmentation benchmarks, where a single DPN model yields state-of-the-art segmentation accuracies on PASCAL VOC 2012, Cityscapes dataset and CamVid dataset.