MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentation

TL;DR

MATCH addresses topological errors in semi-supervised histopathology segmentation by enforcing dual-level topological consistency across MC dropout perturbations and temporal training snapshots. It introduces MATCH-Pair and MATCH-Global to robustly match topological structures across noisy persistence diagrams using a spatial-overlap–persistence–proximity similarity, without ground-truth correspondences. The framework yields stronger topology fidelity and robust segmentation on three histopathology datasets with limited labels, validated through comprehensive ablations and comparisons to state-of-the-art SSL methods. This approach enhances the clinical reliability of digital pathology readouts by preserving meaningful topological structures while maintaining pixel-level accuracy, and provides uncertainty maps as a by-product of the dual-consistency mechanism.

Abstract

In semi-supervised segmentation, capturing meaningful semantic structures from unlabeled data is essential. This is particularly challenging in histopathology image analysis, where objects are densely distributed. To address this issue, we propose a semi-supervised segmentation framework designed to robustly identify and preserve relevant topological features. Our method leverages multiple perturbed predictions obtained through stochastic dropouts and temporal training snapshots, enforcing topological consistency across these varied outputs. This consistency mechanism helps distinguish biologically meaningful structures from transient and noisy artifacts. A key challenge in this process is to accurately match the corresponding topological features across the predictions in the absence of ground truth. To overcome this, we introduce a novel matching strategy that integrates spatial overlap with global structural alignment, minimizing discrepancies among predictions. Extensive experiments demonstrate that our approach effectively reduces topological errors, resulting in more robust and accurate segmentations essential for reliable downstream analysis. Code is available at \href{https://github.com/Melon-Xu/MATCH}{https://github.com/Melon-Xu/MATCH}.

Figures (6)

• Figure 1: Intuition of the proposed framework. (a) Colored likelihood maps are coming from the MC dropout. Connected components consistently matched in at least three predictions retain identical colors across instances, indicating topological stability; components shown in grey fail to reach this consensus and are therefore treated as topologically transient. (b) Limitation of TopoSemiSeg xu2024semi, which relies on a fixed persistence threshold ($\phi=0.7$, red dashed line) and therefore overlooks less-persistent yet meaningful structures (e.g. the violet point). (c) Our method adaptively identifies relevant topological structures without the need for human-selected thresholds.
• Figure 2: Comparison of our matching with Betti Matching stucki2023topologically and Wasserstein Matching hu2019topology. We match two likelihood maps obtained from the same input histopathology patch. The birth critical points of the matched pairs are highlighted in the same color. Note that Wasserstein Matching gets most matches wrong, and Betti Matching also gets two matches wrong while pairing biologically unrelated features when lacking the guidance of the ground truth.
• Figure 3: Overview of the proposed MATCH framework with dual-level topological consistency. Note that the $\mathcal{L}_{\text{intra}}$ and $\mathcal{L}_{\text{temp}}$ are used to directly optimize the parameters of the student model.
• Figure 4: Pipeline of the MATCH-Pair algorithm between two persistence diagrams.
• Figure 5: Qualitative illustration of MC dropout predictions (after the model convergence). Top row: original patch, the four likelihood maps, and the final segmentation. Bottom row: ground-truth mask, corresponding error maps, and the pixel-wise variance (uncertainty) map.