The Four Color Theorem for Cell Instance Segmentation

Ye Zhang, Yu Zhou, Yifeng Wang, Jun Xiao, Ziyue Wang, Yongbing Zhang, Jianxu Chen
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:77194-77215, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhang25do, title = {The Four Color Theorem for Cell Instance Segmentation}, author = {Zhang, Ye and Zhou, Yu and Wang, Yifeng and Xiao, Jun and Wang, Ziyue and Zhang, Yongbing and Chen, Jianxu}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {77194--77215}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhang25do/zhang25do.pdf}, url = {https://proceedings.mlr.press/v267/zhang25do.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T The Four Color Theorem for Cell Instance Segmentation %A Ye Zhang %A Yu Zhou %A Yifeng Wang %A Jun Xiao %A Ziyue Wang %A Yongbing Zhang %A Jianxu Chen %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhang25do %I PMLR %P 77194--77215 %U https://proceedings.mlr.press/v267/zhang25do.html %V 267 %X 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.
APA
Zhang, Y., Zhou, Y., Wang, Y., Xiao, J., Wang, Z., Zhang, Y. & Chen, J.. (2025). The Four Color Theorem for Cell Instance Segmentation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:77194-77215 Available from https://proceedings.mlr.press/v267/zhang25do.html.

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