The Four Color Theorem for Cell Instance Segmentation

TL;DR

This paper introduces a novel cell instance segmentation method based on the four-color theorem, transforming the problem into a constrained semantic segmentation task with improved accuracy and efficiency.

Contribution

It proposes a four-color encoding scheme inspired by the four-color theorem to distinguish adjacent cell instances, simplifying segmentation and enhancing performance.

Findings

Achieves state-of-the-art performance on multiple datasets.

Effectively distinguishes tightly touching cells.

Reduces computational complexity of instance differentiation.

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.