# A Novel Representation of Periodic Pattern and Its Application to Untrained Anomaly Detection

arXiv: https://arxiv.org/abs/2409.05389 · HTML: https://mlsanity.com/paper/2409.05389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [Real Time Fabric Defect Detection System on an Embedded DSP Platform](https://mlsanity.com/paper/1410.0371/) (2014)
- [Defect detection for patterned fabric images based on GHOG and low-rank decomposition](https://mlsanity.com/paper/1702.05555/) (2017)
- [3D-CSAD: Untrained 3D Anomaly Detection for Complex Manufacturing Surfaces](https://mlsanity.com/paper/2404.07748/) (2024)

## Built on by (most cited first, 1 of 1)

- [Single-Step Reconstruction-Free Anomaly Detection and Segmentation via Diffusion Models](https://mlsanity.com/paper/2508.04818/) (2025)

## Abstract (arXiv)

There are a variety of industrial products that possess periodic textures or surfaces, such as carbon fiber textiles and display panels. Traditional image-based quality inspection methods for these products require identifying the periodic patterns from normal images (without anomaly and noise) and subsequently detecting anomaly pixels with inconsistent appearances. However, it remains challenging to accurately extract the periodic pattern from a single image in the presence of unknown anomalies and measurement noise. To deal with this challenge, this paper proposes a novel self-representation of the periodic image defined on a set of continuous parameters. In this way, periodic pattern learning can be embedded into a joint optimization framework, which is named periodic-sparse decomposition, with simultaneously modeling the sparse anomalies and Gaussian noise. Finally, for the real-world industrial images that may not strictly satisfy the periodic assumption, we propose a novel pixel-level anomaly scoring strategy to enhance the performance of anomaly detection. Both simulated and real-world case studies demonstrate the effectiveness of the proposed methodology for periodic pattern learning and anomaly detection.