Application of Shearlet transform to classification of surface defects for metals☆
Introduction
Surface quality control is one of the most important issues in metal industry. In recent years, computer vision based surface inspection systems have become the mainstream research. With the characteristics of non-contact and fast response, the systems have been widely used in modern manufacturing fields in order to obtain high-quality products. The inspection systems capture surface images of industrial products with CCD cameras under specific lighting conditions; then various algorithms of image processing are applied to the images, and surface defects are identified and classified using the algorithms for the defect detection and recognition. The algorithms are crucial for the inspection systems.
Recently, various algorithms for the defect detection and classification have been developed for the metal surface inspection systems. For example, an algorithm combined with discrete wavelet transform and morphological analysis was developed to detect corner cracks of steel billets from oxide scales [1]; Gabor filters were used to detect thin and corner cracks in raw steel block by minimizing the cost function of energy separation criteria of defect and defect-free regions [2]; defects of structural steel plates were detected using Discrete Fourier Transform Spectral Energy and Artificial Neural Networks [3]; an approach based on 3D profile data of steel slab surfaces was developed for an automated on-line crack detection system, and morphological image processing and logistic regression based statistical classification were integrated in the system [4]; a framework with multiple views was applied to detecting flaws in aluminum castings, and information gathered from multiple views of the scene was combined for the flaw detection [5]. Although the above methods achieved high detection rates of some defects, they were restricted to some specific products or defects, and classification rates of common defects were generally limited. There is a real need to develop algorithms for the detection and classification of common defects with wide-ranging versatility.
There are various defects generated by the same or different production lines of metals; the comprehensiveness and universality of the image features associated with the defects are essential to the classification of these defects. More information of images, including those retrieved from different scales and directions, can help improve the comprehensiveness and universality of the image features. The images are usually represented by low-level feature descriptors focusing on different types of information, such as color, texture, and shape [6]. Traditional methods for multi-scale signal analysis, such as Wavelet and Gabor transforms, are extensively applied to image processing applications. However, these methods fail to effectively extract the directional features due to their isotropic support and limited directional sensitivity. Multi-scale geometric analysis (MGA) is proposed to decompose images into different scales and directions [7]. The most common methods of MGA are Curvelet transform [8], [9] and Contourlet transform [9], [10]. Curvelet transform is not directly constructed in the discrete domain, but the implementation is more involved with less efficiency. Contourlet transform is a combination of a multi-scale and a directional filter bank in the discrete domain, and it has less clear directional features than Curvelet transform. Curvelet transform and Contourlet transform are both non-adaptive methods of MGA, which means that they cannot deal with images directly without information of image edges and contours. Except the non-adaptive methods, there are adaptive methods of MGA, which utilize known geometric information of an image to improve the approximation ability of the image transform. Bandelet transform is a major adaptive method of MGA [12], [13]. Compared with Curvelet transform and Contourlet transform, Bandelet transform not only has the characteristics of multi-scale analysis, time-frequency localization, directionality and anisotropy, but also offers particular properties of strict sampling and adaptability which are very important for image representation. However, Bandelet bases are regular functions with compact support, and the algorithm of searching the best Bandelet basis is very complicated [14].
Shearlet transform is a relatively new method of MGA [15], [16]. Compared with other methods of MGA, Shearlet transform can set up different direction numbers at different decomposition scales. Furthermore, Shearlet transform is optimal in approximating 2D smooth functions with discontinuities along C2-curves, and it yields nearly optimal approximation properties. So Shearlet transform is suitable to analyze image textures with complex background.
Kernel Locality Preserving Projections (KLPP) is introduced as a method of dimension reduction. Locality Preserving Projection (LPP) is a well-known dimensionality reduction method, which can project high-dimensional input data into a low-dimensional subspace by linear transformation [17], [18]. KLPP is the implementation of LPP in kernel space. Combined with Shearlet transform and KLPP, a feature descriptor called DST-KLPP is proposed in this article. Surface images of metals are decomposed into different scales and directions with Shearlet transform, and KLPP is employed to reduce redundant information and improve the operating efficiency. In order to test the generality and efficiency of the proposed method, sample images acquired from three different production lines were analyzed. Results of the proposed method were compared with the other methods.
The rest of the paper is organized as follows: Section 2 depicts the characteristics of surface images of metals, including the defects and some background information. Section 3 introduces three methods of MGA, which are Curvelet transform, Contourlet transform, and Shearlet transform. Section 4 describes the DST-KLPP method in detail. Experimental results with three typical metal surface images and discussions are presented in Section 5, followed by conclusions in Section 6.
Section snippets
Surface images of metals
As we know, there are three procedures of metal production, including continuous casting, hot rolling and cold rolling. In each procedure, metals are in different states, and have various defects with different features. In the paper, surface images of continuous casting slabs, hot rolled steels and aluminum sheets are used as samples because they represent three typical defect detection and classification problems to be resolved: 1) surfaces of the continuous casting slabs are very
Curvelet transform
Curvelet transform is developed on a basis of Ridgelet transform. For any a > 0, b ∈ R, and θ ∈ [0, 2π), 2D Ridgelet function ψa,b,θ(x1, x2) : R2 → R2 is defined as [23]:
Then, for 2D function f(x1, x2), continuous Ridgelet transform is defined as:
Continuous Ridgelet transform has a close connection with Radon transform which is defined as:
Thus, continuous Ridgelet transform can be written as:
Calculation of features
Many subbands are obtained by the decomposition of an image with Shearlet transform, and different subbands contain information of different scales and directions of the image. Features that can be calculated from the subbands include:
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Geometrical features—the geometrical features are used to represent the size and shape of an object. These features have been commonly used in a variety of pattern recognition problems. However, the geometrical features are not very useful for the images in this
Description of experiments
As described in Section 2, three surface image databases from different production lines of metals were used in the experiments to test the performance of the proposed method, including the continuous casting slabs, the hot rolled steels and the aluminum sheets. In the experiments, the number of images representing each defect is proportional to its frequency of occurring at the production lines. The odd numbers of samples were used for training, while the even numbers of samples were used for
Conclusions
An effective hybrid feature extraction method, DST-KLPP, is proposed and developed to take the advantages of both Shearlet transform and KLPP. DST-KLPP is applied to the classification of surface defects for 3 different types of metals. Experimental results show that DST-KLPP can produce higher classification rates than the traditional methods such as Gray Level Co-occurrence Matrix and Wavelet transform, and also outperforms the other MGA methods such as Curvelet transform and Contourlet
Acknowledgments
This work is sponsored by the National Science and Technology Support Program of China (Grant no. 2012BAB19B06), and Doctoral Fund of Ministry of Education of China (Grant no. 20120006110033).
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This paper has been recommended for acceptance by Prof. S. Todorovic.