Surface Defect Edge Detection Based on Contourlet Transformation

2016 3 rd International Conference on Engineering Technology and Application (ICETA 2016) ISBN: 978-1-60595-383-0 Surface Defect Edge Detection Based on Contourlet Transformation Changle Li, Gangfeng Liu*, Yubin Liu & Jie Zhao State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang, China ABSTRACT: In order to preferably capture the surface defect edge information of strip steel, and provide more accurate data for subsequent defect analysis, this paper researches on the principle and implementation method of Contourlet transformation, analyzes the multi-directional and anisotropic characteristics, and proposes the image edge detection algorithm based on Contourlet transformation. This paper uses Laplacian Pyramid filter and directional filter for combination to realize Contourlet filter bank, and extracts the image edge information by the way of detecting the method of modulus maximum of Contourlet sub-band coefficient. The comparative experiments of the edge detection algorithm based on wavelet transformation and Sobel algorithm prove that the defect edge extracted by this algorithm is closer to the true edge of surface defect. Keywords: Contourlet transformation; edge detection; surface defect; image processing 1 INTRODUCTION *Corresponding author: liugangfeng@hit.edu.cn In the surface defect detection system of strip steel, the defect image edge detection is an important content and step, and also a necessary basis for the feature extraction, identification and classification and other subsequent treatment of the defects [1]. A variety of different shapes of defects are produced in the production process of strip steel [2], thus presenting higher requirements on the surface defect edge detection algorithm of strip steel. Obviously, the traditional edge detection algorithm based on the differential operator is unable to achieve the desired effect, and the image edge extracted by the image edge detection method based on wavelet transform is only a limited direction, and the surface defect edge direction of strip steel may be arbitrary. Therefore, the wavelet edge detection or edge detection based on the differential operator are unable to be the best approximation to the defect image edge [3-5]. In recent years, Contourlet transform has been widely used in the image processing field [6-8]. Contourlet transform is a true two-dimensional image sparse representation method, which can represent the image features of multi-resolution, localization, critical sampling, directionality and anisotropy. The two-dimensional wavelet extended from one- dimensional wavelet only has horizontal, vertical and diagonal directions. The lack of directionality makes the wavelet transform unable to take full advantage of the geometric features of the image itself, or represent two-dimensional linear or surface singular image to an optimal extent [9-11]. Thus, with respect to the wavelet transform, Contourlet transform can preferably capture the image edge information, and achieve better edge detection effect. 2 PRINCIPLE OF CONTOURLET TRANSFORM Contourlet transform was proposed by M. N. Do and Martin Vetterli in 2002 [12], which can effectively represents the important and complex geometrical structure in the visual information, and can also be called as pyramidal directional filter bank (PDFB). It uses Laplacian Pyramid filter for multi-resolution decomposition of the image to capture the singularity information, and uses directional filter bank (DFB) to combine with the singular points at the same direction as a coefficient. The schematic diagram of its transform is shown in Figure 1. Contourlet transform uses an elongated base structure to approximate the original image. This structure has a multi-scale, anisotropy, good directivity and other properties, which can represent a curve by the use of coefficients less than the wavelet. 101

diag(2,2) 0 k 2 l 1 l 1 l k l 1 diag(2,2 ) l 1 l 2 k 2 s (3) Where, k is the order label of DFB sub-band, and l is the number of layers of DFB decomposition. Q 0 Figure 1. Schematic diagram of Contourlet transform. X 2.1 LP transform The basic idea of LP is: firstly, to obtain a roughly estimated approximate image through low-pass filtering and sampling of the original image, and implement interpolation and filtering of the approximate image, and then calculate the difference from the original image, obtaining the decomposed band-pass component. The next level of decomposition is carried out in the low-pass approximate image, and multi-scale decomposition is completed by iteration. The decomposition filter H and synthesis filter G are normalized filter with symmetry. Assuming that the original image is represented by f0, a low-pass sampling image obtained from the first layer of pyramid decomposition is f1, and the like, assuming that the decomposition layer is P, the formula of the iterative process is: p 1 f (, i j) h( m, n) f (2 i m,2 j n) p i m j n bp(, i j) fp 1(, i j) g( m, n) fp(, ) (2) 2 2 2.2 Directional filter bank The second step of Contourlet transform is the direction segmentation of spectrum. Do and Vetterli propose a construction method of directional filter bank based on Quincunx filter bank (QFB) [12], which avoids the modulation of the input signals in the method proposed by Bamberger and Smith, and simplifies directional decomposition. Its idea is to combine QFB with rotational image, thus obtaining wedge-shaped frequency division. The breakdown structure of the former two layers of DFB is shown in Figure 2. DFB starts from the third stage of decomposition. In order to obtain better frequency division, there is a need of resampling before filtering, and then the direction filtering and sampling. Resampling makes the whole link equivalent to a frequency response of a parallelogram filter and a decimator. A l layer of directional filter bank can be viewed as 2 t multi-channel filter banks, and the sampling matrix S is a diagonal matrix, which can be divided into an approximately horizontal and approximately perpendicular forms. Q 0 Figure 2. Decomposition of the former two layers of DFB. 3 SURFACE DEFECT EDGE DETECTION MEHTOD OF STRIP STEEL BASED ON CONTOURLET TRANSFORM For the specific issue of the surface defect image edge detection of strip steel, there are various types and complex shapes of defects to be detected. Based on such feature, this paper proposes a kind of surface defect image edge detection method of strip steel based on Contourlet transform. 3.1 Algorithm principle Contourlet transform is a double filter bank combined with Laplacian Pyramid filter and directional filter bank (DFB). In this article, assuming that the original image f0 carries out p layer of LP decomposition, l layer of DFB decomposition can be done on the corresponding 2 -p scale, and the matrix f can be used to represent the k-th directional sub-band coefficient matrix obtained from its decomposition. In this way, the matrix f contains the edge information of original image at this direction. However, the image edge has the features of direction and magnitude. Along with the direction of edge, the change of pixel gray is relatively smooth; perpendicular to the direction of edge, the change of pixel gray is relatively fierce. According to the characteristics of the image edge, when determining whether the point f (m,n) in the directional sub-band coefficient matrix is the image edge, there is a need to firstly solve the module value of this point - f (m,n), and compare it f with the module value of the adjacent points at the equivalent gradient direction of the image edge represented by the sub-band at this direction, in order to determine whether this point (m, n) is the point of image edge and complete the image edge detection. 102

Next, 4 layers of DFB decomposition can be implemented on 2 -p scale, in order to illustrate how to determine whether a certain point in the matrix f is the image edge at this direction. When l=4, the direction number of DFB decomposition is 2 4 =16. A plane can be divided into 16 sectors, which are respectively labeled as 0, 1,..., 15, as shown in Figure 3. 6 7 8 9 5 4 3 2 1 0 15 14 10 13 11 12 Figure 3. Schematic diagram of directional sub-band sector. The equivalent gradient directions of the image edge contained in the directional sub-band 1 and 9 are the directional sub-band 5 and 13. When determining whether the point (m, n) in the directional sub-band 1 and 9 is the point of image edge, there is only a need to compare it with the module value of adjacent points in the directional sub-band 5 and 13. If the point (m, n) is the local maximum value point of the module value, it is believed that this point is the image edge. 3.2 Algorithm description According to the above analysis and characteristics of Contourlet transform, this paper carries out Contourler transform for the image, and appropriately handles the threshold value of the directional sub-band coefficients obtained by transform, and uses the foregoing detection algorithm to obtain more ideal image edge. A brief description of the algorithm is as follows: To handle the original image by the use of Contourlet transform filter bank, and obtain the directional sub-band coefficient matrix f of each scale, and low-frequency sub-band coefficient matrix fp. (2) To assume that the low-frequency sub-band matrix fp=0, the directional sub-band matrix remains unchanged. (3) To process the threshold value of the matrix f, and consider the issue of small edge, in order to reduce the impact on detection results. (4) To determine the threshold value. In order to eliminate pseudo-edge information caused by the gray unevenness and other factors, there is a need of threshold processing. Only the local maximum value that is greater than the specified threshold value can be deemed as a point of image edge. In determining the threshold value, there is also a need to consider the issue of small edge. The use of entire threshold value method has a greater impact on the detection result, and the determination method of self-adaptive local threshold value is designed; n n window is used to process the transform coefficients within the window, and solve the threshold value. The calculation formula is: n Ai, j i, j (4) 0 0 T T M Where, T threshold value; T0 initial threshold value; Ai,j coefficient of current window; α 0 proportionality coefficient; M number of pixel of current window. The window size and value of T0 and α 0 can be adjusted according to the actual situation, thus achieving a good threshold processing effect. In the edge detection algorithm designed in this paper, the processing result is more ideal when the window size is 16 16, T0=3.5, α 0 =0.98. (5) The comparison processing of modulus maximum can be given to each directional sub-band coefficient matrix, the coefficient of non-modulus maximum value point f is set as 0, and the matrix ob- tained by transform is the modulus maximum value matrix of each directional sub-band coefficient F. (6) Contourler inverse transform is given to the matrix F and fp, thus obtaining the edge image. After refine processing of the image obtained, removal of isolated points and pseudo edge points, an ideal edge image can be obtained. 4 EXPERIMENT AND ANALYSIS This paper firstly uses Sobel operator, Prewitt operator and Roberts operator commonly used in the gradient operator, Log operator and Canny operator commonly used in the edge detection, and the edge detection method based on wavelet transform to do an edge detection experiment for the scratching defect image that is the most common in the surface defect of strip steel, and compares them with the method proposed in this paper. In the experiment, the edge detection algorithm based on wavelet transform uses Haar wavelet to do 4 levels of wavelet decomposition. In the implementation of Contourlet transform algorithm, 9-7 biorthogonal filter with a better effect in image processing is used to achieve the process of LP decomposition. The directional filter bank is implemented by the use of 23-45 biorthogonal Quincunx filter bank. Similarly, 4 layers of LP decomposition are also used at the finest scale. The number of layers of DFB decomposition is also four. In the edge detection based on wavelet transform foregoing self-adaptive local threshold determination method is also used, and the processing result is ideal when the window size is 103

32 32, T0=5.2, α 0 =0.82. The edge detection processing results of these methods are shown in Figure 4. Figure 4(g-1) and Figure 4(h-1) are the partial enlarged drawings of the processing results of the wavelet algorithm and the processing result of the algorithm proposed in this paper. Figure 4. Scratching defect edge detection result. As can be seen from the experimental results, the traditional gradient operator obtains slightly different edge due to different templates of gradient solved by various operators. However, the gradient operator is more sensitive to the limited direction information, so the edge detection result leads to the missing of more information. Sobel operator and Prewitt operator are more sensitive to the edge at the vertical and horizontal edges, while Roberts operator is more sensitive to the edge information at the diagonal direction, resulting that the edge detection of the gradient operator misses more edge information at other directions, and the smoothness of its edge is worse. The effect of edge detection method based on Canny operator and Log operator is better than the result of gradient operator, but through observation of the images, a lot of wrong edge information exists in Figure 4(e). The defect edge information in the upper part of Figure 4(f) is incomplete, and part of the image edge is lost. The processing result of edge detection algorithm based on wavelet transform is better than the result of other algorithms, which is also the closest to the processing result of algorithm in this paper. However, through observation of the partial enlarged drawings of the processing result of wavelet algorithm in Figure 4(g-1) and Figure 4(h-1), due to the limited directionality of the wavelet decomposition (decomposition directions are horizontal, vertical and diagonal directions), this method is only sensitive to the edge information at its decomposition direction, but fails to preferably express the edge on other directions. As a result, the edge information of detection result is also limited, and the smoothness of the image edge is not good. Through comparison between two partially enlarged drawings, with respect to the wavelet edge detection method, the edge detection method based on Contourlet transform can preferably approximate to the image edge due to multi-directionality and anisotropy of Contourlet transform, and the detection results of image edge obtained is smoother. Therefore, in the experiment of surface scratching defect of strip steel, the algorithm in this paper can preferably approximate to the image edge. In order to verify the effect of method proposed in this paper on other types of surface defect edge detection of strip steel, this paper tests the defects of corrosion and holes. The last experimental results show that, the edge detection method based on wavelet transform is the closest to the experimental results of the method proposed in this paper. Therefore, to verify the algorithm of corrosion and hole defects, this paper focuses on the comparison between the experimental results of these two kinds of methods, and also selects the traditional gradient operator --Sobel operator to do comparative experiments. The experimental results of two kinds of defects in Figure 5-6 show that, Sobel operator obtains limited information due to its inherent characteristics. As can 104

be seen from Figure 5, for the corrosion defect, the edge detection method based on wavelet transform is closer to the experimental result of the method proposed in this paper. For the hole defect in Figure 6, the wavelet method obviously misses the edge information of the hole, and the method proposed in this paper significantly detects more defect edge information. this paper. For the hole defect in Figure 6, the wavelet method obviously misses the edge information of the hole, and the method proposed in this paper significantly detects more defect edge information. Combined with these two groups of experiments, it fully proves that the surface defect edge detection method of strip steel based on Contourlet Transform can preferably detect the surface defect edge information of strip steel, and lay a good foundation for defect image segmentation of strip steel and identification of defect types. 5 CONCLUSION Figure 5. Corrosion defect edge detection result Contourlet transform is an analytical method of multi-scale, localization, directionality and anisotropy, which can preferably capture the image edge information, and obtain sparse representation of the image edge. Based on the characteristics of Contourlet transform, this paper designs the edge detection algorithm of surface defect image of strip steel based on Contourlet transform, and verifies that the image edge extracted by the algorithm is more smooth and approximate to the original image through contrast experiment, thus improving the performance of edge detection. The analysis and experiments verify that Contourlet transform has certain advantages in the image edge extraction. ACKNOWLEDGEMENT This paper is supported by National Science Technology Support Plan Projects (No.2015BAF10B02; No.2014BAF12B06; No.2014AA041601); State Natural Sciences Foundation (61473104); Independent Project of The State Key Laboratory of Technology and System of Robots (SKLRS201410B). REFERENCES Figure 6. Hole defect edge detection result. The experimental results of two kinds of defects in Figure 5-6 show that, Sobel operator obtains limited information due to its inherent characteristics. As can be seen from Figure 5, for the corrosion defect, the edge detection method based on wavelet transform is closer to the experimental result of the method proposed in [1] Singhka D.K.H., Neogi N., Mohanta D. 2014. Surface defect classification of steel strip based on machine vision. Computer and Communications Technologies (ICCCT), 2014 International Conference on. IEEE, pp: 1-5. [2] Hu H., Li Y., Liu M., et al. 2014. Classification of defects in steel strip surface based on multiclass support vector machine. Multimedia Tools & Applications, 69: 199-216. [3] Yu, Kunlin, Xie, Zhiyu. 2014. A fusion edge detection method based on improved Prewitt operator and wavelet transform. 2014 International Conference on Engineering Technology and Applications, ICETA 2014, 4: 289-294. [4] Jin Ruijin, Yin Junjun, Zhou Wei, Yang Jian. 2015. Edge detection in polarimetric SAR images based on the nonsubsampled contourlet transform. 2015 IEEE International Radar Conference, Radar Con 2015, 6: 319-323. 105

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