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

TL;DR

This paper introduces TopoOT, a novel test-time adaptation framework for anomaly segmentation that leverages topology-aware optimal transport to improve robustness and accuracy across domain shifts.

Contribution

It presents a new topology-aware optimal transport chaining method that aligns persistence diagrams for robust test-time adaptation in anomaly segmentation.

Findings

Achieves state-of-the-art results on 2D and 3D anomaly detection benchmarks.

Outperforms previous methods by up to +24.1% mean F1 on 2D datasets.

Demonstrates robustness under domain shift with topology-based pseudo-labels.

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.