用拓扑结构分析提升异常分割在测试时的适应能力，效果显著优于现有方法。
Test-Time Adaptation for Anomaly Segmentation via Topology-Aware Optimal Transport Chaining
- 通过最优传输链对多滤波持久性图进行逐级对齐，捕捉跨尺度稳定特征。
- 在2D和3D异常检测数据集上，平均F1得分提升最高达24.1%和10.2%。
- 适合需要强泛化能力的工业缺陷检测场景，尤其在分布偏移下表现优异。
深度拓扑数据分析（TDA）提供了一种捕捉连通性与循环等跨尺度结构不变性的原则性框架，天然适用于异常分割（AS）。与依赖阈值的二值化方法不同，该方法将异常视为全局结构破坏而非局部波动。本文提出拓扑感知最优传输（TopoOT）框架，融合多滤波持久性图（PDs）与测试时自适应（TTA）。核心创新为最优传输链（Optimal Transport Chaining），通过逐级对齐不同阈值与滤波下的持久性图，生成测地线稳定性分数，识别跨尺度一致保留的特征。这些稳定性伪标签用于监督轻量级头部在线训练，结合最优传输一致性与对比学习目标，确保在域偏移下的鲁棒适应。在标准2D与3D异常检测基准上，TopoOT达到最先进性能，2D数据集平均F1最高提升24.1%，3D AS基准提升10.2%。
原文摘要 · Abstract (English)
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.
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