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.

翻译：深度拓扑数据分析（TDA）提供了一个原则性框架，用于捕获跨尺度持续存在的结构不变量（如连通性和环），这使其天然适用于异常分割（AS）。与基于阈值的二值化方法（在分布偏移下会产生脆弱的掩码）不同，TDA允许将异常表征为对全局结构的破坏，而非局部波动。我们提出了TopoOT，一个将多滤过持久性图（PDs）与测试时自适应（TTA）相结合的拓扑感知最优传输（OT）框架。我们的核心创新是最优传输链，它顺序地对齐跨阈值和跨滤过的持久性图，从而产生测地稳定性分数，用于识别在跨尺度上一致保持的特征。这些稳定性感知的伪标签监督一个轻量级头部，该头部通过OT一致性目标和对比目标在线训练，确保了在域偏移下的鲁棒自适应。在标准的2D和3D异常检测基准测试中，TopoOT实现了最先进的性能，在2D数据集上比最具竞争力的方法高出高达+24.1%的平均F1分数，在3D AS基准上高出+10.2%。