# gcDLSeg: Integrating Graph-cut into Deep Learning for Binary Semantic Segmentation

arXiv: https://arxiv.org/abs/2312.04713 · HTML: https://mlsanity.com/paper/2312.04713/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 68 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Segmenter: Transformer for Semantic Segmentation](https://mlsanity.com/paper/2105.05633/) (2021)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation](https://mlsanity.com/paper/2010.16061/) (2020)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Adversarial Examples for Semantic Segmentation and Object Detection](https://mlsanity.com/paper/1703.08603/) (2017)
- [Embracing Imperfect Datasets: A Review of Deep Learning Solutions for Medical Image Segmentation](https://mlsanity.com/paper/1908.10454/) (2019)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [On the Robustness of Semantic Segmentation Models to Adversarial Attacks](https://mlsanity.com/paper/1711.09856/) (2017)
- [DS-TransUNet:Dual Swin Transformer U-Net for Medical Image Segmentation](https://mlsanity.com/paper/2106.06716/) (2021)
- [On Regularized Losses for Weakly-supervised CNN Segmentation](https://mlsanity.com/paper/1803.09569/) (2018)
- [Normalized Cut Loss for Weakly-supervised CNN Segmentation](https://mlsanity.com/paper/1804.01346/) (2018)

## Built on by (most cited first, 3 of 3)

- [MOSAIC: A Multi-View 2.5D Organ Slice Selector with Cross-Attentional Reasoning for Anatomically-Aware CT Localization in Medical Organ Segmentation](https://mlsanity.com/paper/2505.10672/) (2025)
- [Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm](https://mlsanity.com/paper/2605.13402/) (2026)
- [DeepFlow: Two Convergent Differentiable Approaches for Pairwise Conditional Random Fields](https://mlsanity.com/paper/2610.16546/) (2026)

## Abstract (arXiv)

Binary semantic segmentation in computer vision is a fundamental problem. As a model-based segmentation method, the graph-cut approach was one of the most successful binary segmentation methods thanks to its global optimality guarantee of the solutions and its practical polynomial-time complexity. Recently, many deep learning (DL) based methods have been developed for this task and yielded remarkable performance, resulting in a paradigm shift in this field. To combine the strengths of both approaches, we propose in this study to integrate the graph-cut approach into a deep learning network for end-to-end learning. Unfortunately, backward propagation through the graph-cut module in the DL network is challenging due to the combinatorial nature of the graph-cut algorithm. To tackle this challenge, we propose a novel residual graph-cut loss and a quasi-residual connection, enabling the backward propagation of the gradients of the residual graph-cut loss for effective feature learning guided by the graph-cut segmentation model. In the inference phase, globally optimal segmentation is achieved with respect to the graph-cut energy defined on the optimized image features learned from DL networks. Experiments on the public AZH chronic wound data set and the pancreas cancer data set from the medical segmentation decathlon (MSD) demonstrated promising segmentation accuracy, and improved robustness against adversarial attacks.