MathPhys-Guided Coarse-to-Fine Anomaly Synthesis with SQE-Driven Bi-Level Optimization for Anomaly Detection

2025-04-17

AI Summary

In industrial defect detection, the scarcity of real anomalous samples and the poor generalization of existing synthetic methods—due to their neglect of underlying physical mechanisms—pose significant challenges. To address this, we propose a physics-model-guided coarse-to-fine anomaly synthesis framework. Our method integrates mathematical-physical modeling of common defects (e.g., cracks, corrosion, deformation), partial differential equation (PDE)-based consistency constraints, wavelet-enhanced feature learning, and a boundary-cooperative module. We further introduce a novel Synthesis Quality Estimator (SQE) that drives a two-level optimization mechanism, jointly ensuring global structural plausibility and local detail fidelity. Evaluated on three major benchmarks—MVTec AD, VisA, and BTAD—our approach achieves state-of-the-art performance in both image-level and pixel-level AUROC, demonstrating substantial improvements in model generalization and detection robustness.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Anomaly detection is a crucial task in computer vision, yet collecting real-world defect images is inherently difficult due to the rarity and unpredictability of anomalies. Consequently, researchers have turned to synthetic methods for training data augmentation. However, existing synthetic strategies (e.g., naive cut-and-paste or inpainting) overlook the underlying physical causes of defects, leading to inconsistent, low-fidelity anomalies that hamper model generalization to real-world complexities. In this thesis, we introduced a novel pipeline that generates synthetic anomalies through Math-Physics model guidance, refines them via a Coarse-to-Fine approach and employs a bi-level optimization strategy with a Synthesis Quality Estimator(SQE). By incorporating physical modeling of cracks, corrosion, and deformation, our method produces realistic defect masks, which are subsequently enhanced in two phases. The first stage (npcF) enforces a PDE-based consistency to achieve a globally coherent anomaly structure, while the second stage (npcF++) further improves local fidelity using wavelet transforms and boundary synergy blocks. Additionally, we leverage SQE-driven weighting, ensuring that high-quality synthetic samples receive greater emphasis during training. To validate our approach, we conducted comprehensive experiments on three widely adopted industrial anomaly detection benchmarks: MVTec AD, VisA, and BTAD. Across these datasets, the proposed pipeline achieves state-of-the-art (SOTA) results in both image-AUROC and pixel-AUROC, confirming the effectiveness of our MaPhC2F and BiSQAD.

Problem

• Generating realistic synthetic anomalies for training data augmentation
• Addressing inconsistency in existing synthetic defect generation methods
• Improving anomaly detection model generalization with physics-guided synthesis

Innovation

• Math-Physics guided anomaly synthesis
• Coarse-to-Fine refinement approach
• SQE-driven bi-level optimization