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

TL;DR

The paper addresses the challenge of producing topologically valid segmentations in semi-supervised histopathology by moving beyond pixel-level consistency to region-graph topology. It introduces Topology Graph Consistency (TGC), a dual-network framework that converts segmentation outputs to region graphs and enforces global structure through a topology loss consisting of $L_{spec}$, $L_{conn}$, and $L_{adj}$ while retaining pixel-level supervision via DiceCE and pseudo-label exchange to reduce confirmation bias. Topology losses align Laplacian spectra, component counts, and adjacency statistics between predicted and reference graphs, promoting topology-aware segmentation. On GlaS and CRAG, TGC achieves state-of-the-art results under 5–10% supervision and narrows the gap to full supervision, with qualitative improvements in gland topology preservation.

Abstract

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.

Figures (1)

• Figure 1: Overview of the proposed TGC framework. Two networks $f(\theta_1), f(\theta_2)$ process labeled and unlabeled inputs, producing probability maps converted into graphs. Graph descriptors (spectrum, connectivity, adjacency) define the topology loss, complementing DiceCE supervision on labeled data and pseudo-label consistency on unlabeled data.