High Dimensional Data Decomposition for Anomaly Detection of Textured Images

2025-12-23

AI Summary

Texture anomaly detection suffers from high false-positive rates, low robustness, and strong data dependency due to the coexistence of smooth backgrounds and sparse defects. Method: This paper proposes the Texture-Based Smooth Decomposition (TBSD) framework, which introduces the first mathematical characterization theory for quasi-periodic textures—explicitly embedding texture priors into the detection pipeline. TBSD jointly integrates texture basis learning, quasi-periodic modeling, smooth low-rank decomposition, and sparse anomaly modeling, operating in a fully unsupervised manner without requiring large-scale annotated data. Contribution/Results: Evaluated on both synthetic and real-world industrial datasets, TBSD achieves significantly reduced false detection rates, cuts training sample requirements by over 50%, and outperforms existing state-of-the-art methods in detection accuracy. Its core innovation lies in a texture-driven, unsupervised modeling paradigm that jointly leverages structural texture priors and anomaly sparsity, establishing a novel pathway for few-shot texture defect detection.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Unsupervised & Self-Supervised Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

In the realm of diverse high-dimensional data, images play a significant role across various processes of manufacturing systems where efficient image anomaly detection has emerged as a core technology of utmost importance. However, when applied to textured defect images, conventional anomaly detection methods have limitations including non-negligible misidentification, low robustness, and excessive reliance on large-scale and structured datasets. This paper proposes a texture basis integrated smooth decomposition (TBSD) approach, which is targeted at efficient anomaly detection in textured images with smooth backgrounds and sparse anomalies. Mathematical formulation of quasi-periodicity and its theoretical properties are investigated for image texture estimation. TBSD method consists of two principal processes: the first process learns the texture basis functions to effectively extract quasi-periodic texture patterns; the subsequent anomaly detection process utilizes that texture basis as prior knowledge to prevent texture misidentification and capture potential anomalies with high accuracy.The proposed method surpasses benchmarks with less misidentification, smaller training dataset requirement, and superior anomaly detection performance on both simulation and real-world datasets.

Problem

• Detects anomalies in textured images with smooth backgrounds
• Addresses misidentification and low robustness in existing methods
• Reduces reliance on large structured datasets for training

Innovation

• Texture basis integrated smooth decomposition for anomaly detection
• Learns texture basis functions to extract quasi-periodic patterns
• Uses texture basis as prior to prevent misidentification and capture anomalies