## 1 Introduction  
Surface defect detection plays an important role in quality enhancement in industrial product manufacturing. However, traditional defect detection is performed by human eyes, which yields low efficiency and high missing rate. Currently, vision-based automated defect detection has drawn much attention, which has important theoretical and practical value [1; 2; 3; 4]. In automatic surface inspection of steel sheet, segmentation of surface defect is a significant step, which generates a binary map to identify defects. In the past two decades, commonly-used segmentation methods can be classified into three categories: statistical-based methods, filter-based methods and model-based methods. Statistical-based methods, such as [PERSON]'s method [5], gray level co-occurrence matrix, local binary pattern, maximum entropy, region growing and morphological watersheds, are used to evaluate the spatial distribution of pixel intensities for segmentation. Filter-based methods, such as discrete Fouriertransform [6], discrete Gabor transform [7] and discrete wavelet transform [8; 9], apply a bank of filters to the image, in which the energies of the filters response are utilized as features to segment the defects. Model-based approaches obtain certain models with specific feature distributions or other attributes using diverse descriptors, for instance, level set, fuzzy theory, partial differential equations and texture patterns. Most recently, with the development of saliency detection technology, segmentation methods that use saliency map are gradually rising in the industrial defect inspection field. This method constructs a saliency map that highlights the defect regions standing out from the rest of the image, which provide the good foundation for segmentation. [PERSON] et al. [10] proposed saliency map construction method using Gaussian pyramid decomposition. Then segmentation is conducted with the saliency map. This model exhibits good performance for strip steel defect detection. [PERSON] et al. [11] devised a low-rank representation-based saliency detection model for textile fabric defect detection. [PERSON] et al. [12] also presented a novel saliency detection model, which obviously improve the accuracy of automated defect segmentation. These methods achieve good results on defect segmentation for a certain and homogeneous texture, but remain a challenging issue for segmentation with miscellaneous textures due to random disturbance. Specially, as the surface defect image of steel sheet has a low signal-to-noise ratio, low contrast between defect object and background, heterogeneous and scattered defect, cluttered and complicated background, these methods still lack of accuracy and suffer from limited adaptability and robustness in industrial practice. Usually, a defect-free surface in industrial products has consistent texture. The emergence of defects can be regarded as the foreground object superposed in the regular-texture background. As shown in Figure 1, a surface defect image of steel sheet \(I\) is decomposed into two parts: relatively homogeneous background image \(B\) and a defect foreground image \(F\) that is the desired image for the following segmentation. Inspired by the above analysis, an easy-to-implement method based on double low-rank and sparse decomposition (DLRSD) is proposed in this paper for surface defect segmentation. Considering double low-rank and sparse characteristics of surface defect image, combined with a local consistency constrain among spatially adjacent sub-regions by imposing Laplacian regularization, the feature matrix that form by \(I\) can be adaptively decomposed into foreground feature matrix that form by defect foreground image \(F\) and background feature matrix that form by background image \(B\) in a certain feature space, respectively. Specifically, the foreground image \(F\) is served as the source image for segmentation, which can better cope with the intra-class variations and background clutters, leading to a higher performance.