**1. Introduction**

At present, machine vision–based surface inspection technology has been widely used in the detection and identification of surface defects of various industrial products due to its non-contact and real-time detection properties [1]. The machine vision–based detection method is to collect the image of the industrial product under the irradiation of the high-intensity light source and use the image processing and pattern recognition algorithm to analyze the surface image [2]. For different industrial products, one need consider defect image features of the products themselves and then adopt appropriate recognition methods.

In the production process of continuous casting slabs, defects often occur due to various factors like raw material, preprocessing technologies, etc. The defects will have a negative impact on the next rolling process, and severe defects will even lead to the scrapping of entire slabs [3,4]. The defect feature extraction method plays an important role in defect inspection, which is one of the hotspots in the research on surface defect recognition algorithms. The most important characteristic of surface defects of continuous casting slab are complex backgrounds, which make recognition difficult.

At present, research is more active on strip steel products with a simple background image [5–7]. However, the defect recognition of continuous casting slabs with complex backgrounds has received comparatively little attention. Wei SY et al. [3] extracted the shape feature values of the image to classify and recognition defects. Yun [8] proposed a surface defect recognition algorithm based on Gabor wavelet that can detect the fine cracks and angular cracks on the surface of the slabs by minimizing the cost function of the energy separation criterion for the defect area and the defect-free area. Pan E [9] proposed an engineering-driven rule-based detection (ERD) method according to the mechanism of deep longitudinal crack and transverse crack on slabs. Xu K et al. [10] used non-sampled wavelet to decompose the surface image by calculating the scale co-occurrence matrix and grayscale co-occurrence matrix, and used AdaBoosting classifier to identify cracks from water marks, slag marks, scales, and vibration marks. Subsequently, the author proposed combining the discrete shearlet transform (DST) and kernel local preservation projection (KLPP) algorithm to extract surface defect features [2]. Y. Ai utilized the combination of Contourlet transform and kernel local preservation projection (KLPP) algorithm to extract the defect features [1], then Xu K [11] improved the above method by introducing a texture feature. Si Yang [12] improved the local binary pattern and proposed a multi-block local binary pattern (MB-LBP) feature extraction method.

Of the above mentioned methods, the wavelet-based feature extraction (for example, references [1,2,8,10,11]) is the more effective and more studied technology. Although these methods have achieved some results, the recognition accuracy of surface defects of continuous casting slabs needs to be further improved with the increasingly strict quality requirements of users.

Discrete nonseparable shearlet transform (DNST) [13,14] is a new kind of wavelet-based method. It is a compactly supported shearlet transform with excellent localization properties in the spatial domain and excellent directional selectivity. DNST has been successfully introduced in the fields of compressed sensing magnetic resonance imaging [15,16]. According to defect images of continuous casting slabs with the scale and directionality traits, DNST was introduced into the surface defect feature extraction of continuous casting slabs. The gray-level co-occurrence matrix (GLCM) is an effective texture feature extraction method that can reflect the comprehensive information of the image gray in direction, adjacent pixel interval, and gray level variation [17]. Some defects images of continuous casting slabs also have texture traits, thus we consider introducing GLCM into the feature extraction of continuous casting slabs. Since the features extracted by DNST and GLCM are redundant, we use kernel spectral regression (KSR) [18,19] technology to remove redundant features. KSR is a kind of manifold learning dimensionality reduction technology, and it casts the problem of learning an embedding function into a regression framework that facilitates efficient computations. The proposed feature extraction approach is named discrete nonseparable shearlet transform gray-level co-occurrence matrix kernel spectral regression (DNST-GLCM-KSR), which combines multi-scale and multi-directional features of DNST with texture features of GLCM and uses KSR to remove redundant features. The DNST-GLCM-KSR approach can improve the defect recognition accuracy of continuous casting slabs and achieved better performance than traditional methods.

The novelty of our work lies in introducing DNST into the surface defect recognition of continuous casting slabs with the complex backgrounds, fusing GLCM texture features, and using a suitable dimensionality reduction algorithm KSR, which makes defect recognition easier and more effective. The rest of this paper is organized as follows. In Section 2, the surface defects information of continuous casting slabs is depicted. Section 3 introduces the basic principles of the DNST-GLCM-KSR feature extraction approach. The surface defect recognition algorithm is presented in Section 4. Section 5 describes the experimental results and discussions, followed by conclusions in Section 6.
