# Small Defects Detection of Galvanized Strip Steel via Schatten-p Norm-Based Low-Rank Tensor Decomposition

## TL;DR

A new method for detecting small defects on galvanized steel is simpler and more effective than deep learning, with potential use in other industries.

## Contribution

A Schatten-p norm-based low-rank tensor decomposition method for small defect detection in industrial settings.

## Key findings

- The proposed SLRTD method outperforms existing methods in detecting white-spot defects on galvanized steel.
- The method effectively separates defect images into low-rank background, sparse defect, and noise components.
- The approach is applicable to other industrial products like glass, fabric, and LCDs.

## Abstract

What are the main findings?
Compared with the deep learning method for surface defect detection, the proposed SLRTD-based detection method is simpler and more effective in a galvanized strip steel production line.

Compared with the deep learning method for surface defect detection, the proposed SLRTD-based detection method is simpler and more effective in a galvanized strip steel production line.

What is the implication of the main finding?
The proposed SLRTD-based detection method of surface defect can be applied for other industrial products, such as glass, fabric, LCD, and AMOLED.

The proposed SLRTD-based detection method of surface defect can be applied for other industrial products, such as glass, fabric, LCD, and AMOLED.

Accurate and efficient white-spot defects detection for the surface of galvanized strip steel is one of the most important guarantees for the quality of steel production. It is a fundamental but “hard” small target detection problem due to its small pixel occupation in low-contrast images. By fully exploiting the low-rank and sparse prior information of a surface defect image, a Schatten-p norm-based low-rank tensor decomposition (SLRTD) method is proposed to decompose the defect image into low-rank background, sparse defect, and random noise. Firstly, the original defect images are transformed into a new patch-based tensor mode through data reconstruction for mining valuable information of the defect image. Then, considering the over-shrinkage problem in the low-rank component estimation caused by a vanilla nuclear norm and a weighted nuclear norm, a nonlinear reweighting strategy based on a Schatten p-norm is incorporated to improve the decomposition performance. Finally, a solution framework is proposed via a well-designed alternating direction method of multipliers to obtain the white-spot defect target image by a simple segmenting algorithm. The white-spot defect dataset from a real-world galvanized strip steel production line is constructed, and the experimental results demonstrate that the proposed SLRTD method outperforms existing state-of-the-art methods qualitatively and quantitatively.