# Graph-Theoretic Consistency for Robust and Topology-Aware Semi-Supervised Histopathology Segmentation

arXiv: https://arxiv.org/abs/2509.22689 · HTML: https://mlsanity.com/paper/2509.22689/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 9 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest](https://mlsanity.com/paper/1603.00275/) (2016)
- [MILD-Net: Minimal Information Loss Dilated Network for Gland Instance Segmentation in Colon Histology Images](https://mlsanity.com/paper/1806.01963/) (2018)
- [Learning Disentangled Stain and Structural Representations for Semi-Supervised Histopathology Segmentation](https://mlsanity.com/paper/2507.03923/) (2025)
- [HDC: Hierarchical Distillation for Multi-level Noisy Consistency in Semi-Supervised Fetal Ultrasound Segmentation](https://mlsanity.com/paper/2504.09876/) (2025)

## Abstract (arXiv)

Semi-supervised semantic segmentation (SSSS) is vital in computational pathology, where dense annotations are costly and limited. Existing methods often rely on pixel-level consistency, which propagates noisy pseudo-labels and produces fragmented or topologically invalid masks. We propose Topology Graph Consistency (TGC), a framework that integrates graph-theoretic constraints by aligning Laplacian spectra, component counts, and adjacency statistics between prediction graphs and references. This enforces global topology and improves segmentation accuracy. Experiments on GlaS and CRAG demonstrate that TGC achieves state-of-the-art performance under 5-10% supervision and significantly narrows the gap to full supervision.