# The Four Color Theorem for Cell Instance Segmentation

arXiv: https://arxiv.org/abs/2506.09724 · HTML: https://mlsanity.com/paper/2506.09724/

## Key facts

- Cited by 3 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 11 Jun 2025.

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

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Panoptic Segmentation](https://mlsanity.com/paper/1801.00868/) (2018)
- [HoVer-Net: Simultaneous Segmentation and Classification of Nuclei in Multi-Tissue Histology Images](https://mlsanity.com/paper/1812.06499/) (2018)
- [Cell Detection with Star-convex Polygons](https://mlsanity.com/paper/1806.03535/) (2018)
- [Understanding Convolution for Semantic Segmentation](https://mlsanity.com/paper/1702.08502/) (2017)
- [Rethinking Semantic Segmentation: A Prototype View](https://mlsanity.com/paper/2203.15102/) (2022)
- [PanNuke Dataset Extension, Insights and Baselines](https://mlsanity.com/paper/2003.10778/) (2020)
- [CellViT: Vision Transformers for Precise Cell Segmentation and Classification](https://mlsanity.com/paper/2306.15350/) (2023)
- [InceptionNeXt: When Inception Meets ConvNeXt](https://mlsanity.com/paper/2303.16900/) (2023)
- [DCAN: Deep Contour-Aware Networks for Accurate Gland Segmentation](https://mlsanity.com/paper/1604.02677/) (2016)
- [Micro-Net: A unified model for segmentation of various objects in microscopy images](https://mlsanity.com/paper/1804.08145/) (2018)
- [SeMask: Semantically Masked Transformers for Semantic Segmentation](https://mlsanity.com/paper/2112.12782/) (2021)
- [CIA-Net: Robust Nuclei Instance Segmentation with Contour-aware Information Aggregation](https://mlsanity.com/paper/1903.05358/) (2019)
- [MSRF-Net: A Multi-Scale Residual Fusion Network for Biomedical Image Segmentation](https://mlsanity.com/paper/2105.07451/) (2021)
- [Attention-Based Transformers for Instance Segmentation of Cells in Microstructures](https://mlsanity.com/paper/2011.09763/) (2020)
- [CPP-Net: Context-aware Polygon Proposal Network for Nucleus Segmentation](https://mlsanity.com/paper/2102.06867/) (2021)
- [Deep Semi-supervised Knowledge Distillation for Overlapping Cervical Cell Instance Segmentation](https://mlsanity.com/paper/2007.10787/) (2020)
- [GP-NeRF: Generalized Perception NeRF for Context-Aware 3D Scene Understanding](https://mlsanity.com/paper/2311.11863/) (2023)
- [DoNet: Deep De-overlapping Network for Cytology Instance Segmentation](https://mlsanity.com/paper/2303.14373/) (2023)
- [TransNuSeg: A Lightweight Multi-Task Transformer for Nuclei Segmentation](https://mlsanity.com/paper/2307.08051/) (2023)
- [DAWN: Domain-Adaptive Weakly Supervised Nuclei Segmentation via Cross-Task Interactions](https://mlsanity.com/paper/2404.14956/) (2024)
- [SEINE: Structure Encoding and Interaction Network for Nuclei Instance Segmentation](https://mlsanity.com/paper/2401.09773/) (2024)
- [Category Prompt Mamba Network for Nuclei Segmentation and Classification](https://mlsanity.com/paper/2503.10422/) (2025)
- [RepSNet: A Nucleus Instance Segmentation model based on Boundary Regression and Structural Re-parameterization](https://mlsanity.com/paper/2505.05073/) (2025)

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

- [Cell Instance Segmentation: The Devil Is in the Boundaries](https://mlsanity.com/paper/2510.09848/) (2025)
- [Disco: Densely-overlapping Cell Instance Segmentation via Adjacency-aware Collaborative Coloring](https://mlsanity.com/paper/2602.05420/) (2026)
- [NuNext: Reframing Nucleus Detection as Next-Point Detection](https://mlsanity.com/paper/2603.07098/) (2026)

## Abstract (arXiv)

Cell instance segmentation is critical to analyzing biomedical images, yet accurately distinguishing tightly touching cells remains a persistent challenge. Existing instance segmentation frameworks, including detection-based, contour-based, and distance mapping-based approaches, have made significant progress, but balancing model performance with computational efficiency remains an open problem. In this paper, we propose a novel cell instance segmentation method inspired by the four-color theorem. By conceptualizing cells as countries and tissues as oceans, we introduce a four-color encoding scheme that ensures adjacent instances receive distinct labels. This reformulation transforms instance segmentation into a constrained semantic segmentation problem with only four predicted classes, substantially simplifying the instance differentiation process. To solve the training instability caused by the non-uniqueness of four-color encoding, we design an asymptotic training strategy and encoding transformation method. Extensive experiments on various modes demonstrate our approach achieves state-of-the-art performance. The code is available at https://github.com/zhangye-zoe/FCIS.