提出预处理新理论，提升3D异常检测的语义一致性与准确性。
Fence Theorem: Towards Dual-Objective Semantic-Structure Isolation in Preprocessing Phase for 3D Anomaly Detection
- 构建双目标语义-结构隔离框架，分两阶段实现语义分离与空间约束。
- 在Anomaly-ShapeNet和Real3D-AD上验证，细粒度语义对齐可显著提升点级检测准确率。
- 适用于需要高精度3D异常检测的工业质检、自动驾驶等场景。
3D异常检测虽重要但困难，因缺乏统一的预处理设计理论基础。本文提出Fence定理，将预处理形式化为双目标语义隔离器：(1) 尽可能消除跨语义干扰；(2) 在可行范围内将异常判断限定于对齐的语义空间，从而建立语义内可比性。任何预处理方法均通过语义分割与空间约束两阶段实现此目标。通过系统分解，我们以定性分析、定量研究与数学证明三重证据，将现有方法理论化纳入该定理。基于该定理，我们实现Patch3D，包含切块与匹配模块，用于分割语义空间并整合相似部分，同时独立建模各空间内的正常特征。在Anomaly-ShapeNet与Real3D-AD不同设置下的实验表明，预处理中逐步精细化的语义对齐能直接提升点级异常检测准确率，为定理因果逻辑提供逆向验证。
原文摘要 · Abstract (English)
3D anomaly detection (AD) is prominent but difficult due to lacking a unified theoretical foundation for preprocessing design. We establish the Fence Theorem, formalizing preprocessing as a dual-objective semantic isolator: (1) mitigating cross-semantic interference to the greatest extent feasible and (2) confining anomaly judgments to aligned semantic spaces wherever viable, thereby establishing intra-semantic comparability. Any preprocessing approach achieves this goal through a two-stage process of Emantic-Division and Spatial-Constraints stage. Through systematic deconstruction, we theoretically and experimentally subsume existing preprocessing methods under this theorem via tripartite evidence: qualitative analyses, quantitative studies, and mathematical proofs. Guided by the Fence Theorem, we implement Patch3D, consisting of Patch-Cutting and Patch-Matching modules, to segment semantic spaces and consolidate similar ones while independently modeling normal features within each space. Experiments on Anomaly-ShapeNet and Real3D-AD with different settings demonstrate that progressively finer-grained semantic alignment in preprocessing directly enhances point-level AD accuracy, providing inverse validation of the theorem's causal logic.
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