mlsanityData to 14 Oct 2026

Fence Theorem: Towards Dual-Objective Semantic-Structure Isolation in Preprocessing Phase for 3D Anomaly Detection

arXiv 2503.01100 ↗First posted 3 Mar 2025cs.CV cs.AIcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 20 of its 28 references that are in the map. First posted on arXiv 3 Mar 2025.

Builds on

20 of 28 references.

References · 20

  1. 2022Masked Autoencoders for Point Cloud Self-supervised Learningcited by 459
  2. 2021The MVTec 3D-AD Dataset for Unsupervised 3D Anomaly Detection and Localizationcited by 178
  3. 2023Deep Industrial Image Anomaly Detection: A Surveycited by 148
  4. 2023Multimodal Industrial Anomaly Detection via Hybrid Fusioncited by 139
  5. 2022Asymmetric Student-Teacher Networks for Industrial Anomaly Detectioncited by 117
  6. 2022Back to the Feature: Classical 3D Features are (Almost) All You Need for 3D Anomaly Detectioncited by 93
  7. 2023Complementary Pseudo Multimodal Feature for Point Cloud Anomaly Detectioncited by 75
  8. 2023Towards Scalable 3D Anomaly Detection and Localization: A Benchmark via 3D Anomaly Synthesis and A Self-Supervised Learning Networkcited by 67
  9. 2024R3D-AD: Reconstruction via Diffusion for 3D Anomaly Detectioncited by 45
  10. 2024PO3AD: Predicting Point Offsets toward Better 3D Point Cloud Anomaly Detectioncited by 30
  11. 2024Look Inside for More: Internal Spatial Modality Perception for 3D Anomaly Detectioncited by 30
  12. 2024PointAD: Comprehending 3D Anomalies from Points and Pixels for Zero-shot 3D Anomaly Detectioncited by 29
8 more
  1. 2024SplatPose & Detect: Pose-Agnostic 3D Anomaly Detectioncited by 25
  2. 2024Towards High-resolution 3D Anomaly Detection via Group-Level Feature Contrastive Learningcited by 25
  3. 2025Exploring the Potential of Encoder-free Architectures in 3D LMMscited by 16
  4. 2022Teacher-Student Network for 3D Point Cloud Anomaly Detection with Few Normal Samplescited by 12
  5. 2024Revisiting Multimodal Fusion for 3D Anomaly Detection from an Architectural Perspectivecited by 12
  6. 2024SplatPose+: Real-time Image-Based Pose-Agnostic 3D Anomaly Detectioncited by 11
  7. 2024Towards Zero-shot 3D Anomaly Localizationcited by 8
  8. 20243D-CSAD: Untrained 3D Anomaly Detection for Complex Manufacturing Surfacescited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025Examining the Source of Defects from a Mechanical Perspective for 3D Anomaly Detectioncited by 4
  2. 2025A Comprehensive Survey for Real-World Industrial Defect Detection: Challenges, Approaches, and Prospectscited by 2
  3. 2025The 1st International Workshop on Disentangled Representation Learning for Controllable Generation (DRL4Real): Methods and Resultscited by 0
  4. 2026Open-Set Supervised 3D Anomaly Detection: An Industrial Dataset and a Generalisable Framework for Unknown Defectscited by 0