Test-Time Adaptation for Anomaly Segmentation via Topology-Aware Optimal Transport Chaining

2026-01-28

AI Summary

This work addresses the fragility of anomaly segmentation masks under distribution shift, which arises from local threshold-based binarization. To enhance robustness in detecting structural anomalies, the authors propose TopoOT, a framework that integrates deep topological data analysis with test-time adaptation. TopoOT models global topological disruptions induced by anomalies using multi-filter persistent homology and introduces an optimal transport chain mechanism to align persistence diagrams across scales, yielding geodesically stable pseudo-labels invariant to scale variations. The framework further incorporates contrastive learning with a lightweight online head for self-supervised adaptation. Evaluated on both 2D and 3D anomaly segmentation benchmarks, TopoOT achieves state-of-the-art performance, improving average F1 scores by 24.1% in 2D and 10.2% in 3D settings.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased binarisation, which produces brittle masks under distribution shift, TDA allows anomalies to be characterised as disruptions to global structure rather than local fluctuations. We introduce TopoOT, a topology-aware optimal transport (OT) framework that integrates multi-filtration persistence diagrams (PDs) with test-time adaptation (TTA). Our key innovation is Optimal Transport Chaining, which sequentially aligns PDs across thresholds and filtrations, yielding geodesic stability scores that identify features consistently preserved across scales. These stabilityaware pseudo-labels supervise a lightweight head trained online with OT-consistency and contrastive objectives, ensuring robust adaptation under domain shift. Across standard 2D and 3D anomaly detection benchmarks, TopoOT achieves state-of-the-art performance, outperforming the most competitive methods by up to +24.1% mean F1 on 2D datasets and +10.2% on 3D AS benchmarks.

Problem

• anomaly segmentation
• domain shift
• test-time adaptation
• topological data analysis
• distribution shift

Innovation

• Optimal Transport Chaining
• Topology-Aware
• Test-Time Adaptation
• Persistence Diagrams
• Anomaly Segmentation