Title: TopoOT: Topology-Aware Optimal Transport for Test-Time Anomaly Segmentation
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Deep Topological Data Analysis, Optimal Transport, Test Time Traning, Anomly segmentation

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 threshold-based 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 with test-time adaptation (TTA). Our key innovation is Optimal Transport Chaining, which sequentially aligns persistence diagrams (PDs) across thresholds and filtrations, yielding geodesic stability scores that identify features consistently preserved across scales. These stability-aware 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 anomaly segmentation benchmarks.