Abstract: In this study, an efficient approach to inspect textural abnormalities of alloy steel metal surface based on Discrete Shearlet Transform (DST) and multilevel thresholding technique is proposed. Initially, the given metal surface is classified as defected or no defect surface by using DST energy features. As DST is a multiresolutional and multi directional analysis, the levels from 2 to 4 and directions from 2 to 64 are analyzed for classification. To segment or detect the defected surface, multilevel thresholding technique is applied. The proposed approach is evaluated by using 60 images with no defect to tiny or big defects. The experiment results imply that the multilevel thresholding method is effective to compute the threshold values for defect detection and outperforms other techniques such as Otsu and iterative thresholding.
INTRODUCTION
The Visual surface infection is treated as texture analysis problems in computer vision and image processing techniques. Over the years, extensive researches have been done for surface detection. A novel automated detection system of surface defects on spherical parts, by using laser and CCD measurements is proposed by Zhou et al. (2011). This automated detection system mainly focused on the techniques of measuring and identifying defects. The empirical mode decomposition algorithm is used to extract the possible defects in order to locate the surface defects initially. Canny edge detection is used for narrowing the search space of surface defects. Back propagation neural network is used as a classifier for detecting the defects.
A dissimilarity measure based on the optical flow technique for surface defect detection and aims at light-emitting diode wafer die inspection is proposed by Tsai et al. (2012). From an optical flow field, the dissimilarity measure of each pixel is derived. An automated visual inspection scheme for multi crystalline solar wafers using the mean shift technique is presented by Tsai et al. (2011). Mean shift technique is used to detect the defects in a complicated background. This technique is then applied on an entropy image for removing the noises and to detect free grain edges. A simple adaptive threshold method is used to identify the defected surface.
To extract a set of features that can effectively address the problem of defect detection on hot rolled steel surface by using machine learning algorithm is explained by Ghorai et al. (2012). Two types of features are extracted with two and three resolution levels. They are wavelet and contourlet features. SVM classifier is used for detecting the surface into normal or abnormal. A unified approach for defect detection is proposed by Choi and Kim (2012) for finding anomalies in surface images. This approach consists of global estimation and local refinement. Global estimation is used to estimate the defects roughly by applying a spectral based approach. Then refine the estimated regions locally based on the pixel intensity distribution which is derived from the defect and defect free regions.
An effective deblurring method is proposed by Wang et al. (2011) for surface defect detection on Gaussian blur images. Learned Partial Differential Equation (L-PDE) is applied for Gaussian blur images as a pre processing method. L-PDE model achieve much better results in comparison with the traditional image de-blurring methods. The detection of surface defects of the ceramic-glass based on digitized images is proposed by Ai and Zhu (2002). In order to gain the binary images threshold is used. Markov random field models are fitted to binary textures. This experiment is applied on the factory samples to verify the feasibility of this method.
A novel technique for detecting defects in fabric image based on the features extracted using a new multi resolution analysis tool called digital curvelet transform is proposed by Ni et al. (2013). The extracted features are direction features of curvelet coefficients and texture features based on GLCM of curvelet coefficients. K-nearest neighbor is used as a classifier for detecting the surface. A new method to detect the defect of texture images by using curvelet transform is presented by Moasheri and Azadinia (2011). The curvelet transform can easily detect defects in texture, like one-dimensional discontinuities or in two dimensional signal or function of image. The extracted features are energy and standard deviation of division sub-bands.
Multi scale geometric analysis is employed by Xu et al. (2013) to extract the statistical features of images in multiple scales and directions. Then, graph embedding algorithm is used to reduce the dimension of the extracted feature vector with higher dimension. In order to implement the proposed feature extraction method the grouping of curvelet transform and the kernel locality preserving projection algorithm is selected and for testing the validity of the method the samples from hot rolling production are used.
MATERIALS AND METHODS
The proposed system for the detection of defect in alloy steel is built based on DST and multilevel thresholding. In the following section, the background of DST and multilevel thresholding are briefly reviewed.
Discrete shearlet transform: The proposed surface defect detection is based on new multi-scale directional representations called the shearlet transform introduced by Easley et al. (2007). An NxN image consists of a finite sequence of values,
| (1) |
Thus the discrete analog of
| (2) |
The brackets in the equations
| (3) |
First, to compute:
| (4) |
In the discrete domain, at the resolution level j, the Laplacian pyramid algorithm is implemented in the time domain. This will accomplish the multi scale partition by decomposing faj-1 [n1, n2], 0≤n1, n2<Nj-1, into a low pass filtered image faj-1 [n1, n2], a quarter of the size of fdj-1 [n1, n2], and a high pass filtered image faj-1 [n1, n2]. Observe that the matrix faj-1 [n1, n2] has size NjxNj, where Nj = 2-2jN and f0a[n1, n2] = f[n1, n2] has size NxN. In particular:
| (5) |
Thus, fjd[n1, n2] are the discrete samples of a function fjd[x1, x2], whose Fourier transform is
| (6) |
| (7) |
After performing this change of co ordinates,
| (8) |
This expression shows that the different directional components are obtained by simply translating the window function W. The discrete samples gj[n1, n2] = gj(n1, n2) are the values of the DFT of fjd[n1, n2] on a pseudo-polar grid. That is, the samples in the frequency domain are taken not on a Cartesian grid, but along lines across the origin at various slopes. This has been recently referred to as the pseudo-polar grid. One may obtain the discrete Frequency values of fjd on the pseudo-polar grid by direct extraction using the Fast Fourier Trans-form (FFT) with complexity ON2 log N or by using the Pseudo-polar DFT (PDFT). In the proposed system, non-sub sampled version of DST in used.
Multilevel thresholding: The multilevel thresholding proposed by Papamarkas and Gatos (1994) includes three main stages. First, a hill-clustering technique is applied to the image histogram in order to approximately determine the peak locations of the histogram. Then the histogram segments between the peaks are approximated by rational function using a linear mini-max approximation algorithm. Finally, the application of the one dimensional golden search minimization algorithm gives the global minimum of each rational function which corresponds to a multi-threshold level. To clarify the approximation technique, let us consider that hill climbing method gives a total number of histogram peaks equal to P, where (Wn,G(Wn)), n = 1,…, P are the co ordinates of the peaks. This means that histogram has P-1 valleys which lie between the peaks. For the nth valley let:
| • | K be the total number of gray levels included |
| • | G(wk), k = 1,…, K, be the values of the histogram at the wk gray level |
| • | wk, k = 1,…, K, be the gray level values, with Wn≤wk≤Wn+1 |
For each valley, the LRA algorithm can fit the histogram points (wk, G(wk)), k = 1,…, K by a real rational function of the general form:
| (9) |
where, am and bm are the unknown coefficients, M and N are integers that define the degree of the polynomials A(w) and B(w). This approximation problem is solved by a well established linear programming approach based on the minimax criterion.
The rational function R(w) is real and continuous. To find its minimum in the region Wn, Wn+1, the one dimensional golden search algorithm is applied. The inputs of the golden search algorithm are only the limits of the interval. In this case, the limits are defined by the Wn and Wn+1 while the one dimensional function for each region is the real rational function R(w). To ensure that the golden search algorithm always converges to the global minimum, the following procedure are used:
| Step 1: | Find the minimum Rmin of R(w) |
| Step 2: | Define the function Y(w) according to the relation: |
| (10) |
| Step 3: | Find the minimum Ymin of Y(w) |
| Step 4: | If Ymin = Rmin, go to step 5; otherwise put Rmin = Ymin and go to step 2 |
| Step 5: | The global minimum solution is equal to Rmin. Terminate the procedure. |
The result of the above minimization procedure is the minimum value of R(w) and its position. The minimum is taken as a threshold value of the histogram.
PROPOSED SYSTEM
The proposed system to detect the surface defect in alloy steel mainly consists of two phases. The first step is the classification of the given surface into defected surface or not. The next step is the segmentation of the defected area in the given alloy steel surface. To avoid the unnecessary segmentation of no defect surface, the classification task is preceded before segmentation. Figure 1 shows the overall approach of the proposed system to detect the defects in alloy steel metal.
| Fig. 1: | Automated surface defect detection method in alloy steel material |
Texture is one of the most important characteristics in identifying defects in a metal surface. To analyze the texture of a surface, DST is used in the proposed approach. It is a multiresolutional and as well as multidirectional analysis. As the size and shape of the defect may vary, the DST is a good choice than multiresolutional analysis. Initially, the metal surface is decomposed by using DST at various scales and directions. Then the energies of each sub-band are extracted and used to represent the texture of the defect free metal surface. Textures are often characterized by mid and high frequencies, the energies in the high frequency sub-bands are considered in the proposed approach. The energy of each directional sub-band of the image I is calculated by using the formula in Eq. 11:
| (11) |
where, Ie(i, j) the pixel value of the eth sub-band and R, C is width and height of the sub-band, respectively. A predefined threshold is used to classify the metal surface into defected or non-defected.
If the output of the classification task is defected, then the segmentation algorithm starts to detect the defected area in the surface. Automatic thresholding is applied in various image segmentation applications successfully. The basic idea behind the automatic thresholding is to automatically select an optimal threshold value for separating background and foreground in an image based on gray level distribution of that image. The most commonly used thresholding technique is Otsu technique. The size of the defects may vary from tiny to big; the gray level distribution of the defected image may be unimodal to bimodal. In such a situation, the Otsu thresholding fails which needs other thresholding technique based on histogram modeling. In the proposed approach, multilevel thresholding technique is applied to segment or detect the defects in the alloy steel surface.
EXPERIMENTAL RESULTS
In the experiments, the performance of the proposed system is tested by using 50 alloy steel surfaces with no defects and 10 alloy steel surfaces having defects of varying size and shapes. The DST energy feature are computed using the technique described above in order to classify the given alloy steel surface. For better classification accuracy, the decomposition levels and directions of DST are varied and the energy features are computed. From the features of various levels and directions, the best set which distinguishes the alloy steel surfaces is identified based on the mean and standard deviation of the particular features. The decomposition level and directions used in the proposed classification approach is varied from 2 to 4 and 2 to 64 directions. Among these features, the best set of 4 level 2 directions is identified with 100% classification accuracy. The mean and standard deviation of the first 2 high frequency sub-bands of the above set is given in Table 1.
Figure 2 shows box plots of the DST energy features used for the classification of alloy steel surface. This box plot indicates that the median values of DST energy features of defected surface and no defect surface is different and hence the DST features are significant. After the classification, multilevel thresholding is applied to detect the defect in the given alloy steel surface. For each experiment, the performance matrices such as sensitivity, specificity, accuracy, positive predictive value and negative predictive value are computed and tabulated in Table 2.
| Table 1: | Mean and standard deviation values of DST features for alloy steel surfaces |
| Table 2: | Performance metrics of the proposed alloy steel defect detection method |
| Fig. 2: | Box plot for two high frequency sub-band DST energy features at 4 level 2 directions |
From the Table 2, it is noted that the proposed system is able to detect the surface defects with a sensitivity of 99.8% and specificity of 95.5%. The positive predictive value which shows how best the proposed approach can detect the defects in alloy steel is 99.9%
Figure 3 shows the input image, Otsu thresholding, iterative thresholding and multilevel thresholding images. The performance of the segmentation mainly depends on the value of the computed threshold. The threshold value computed by the multilevel thresholding technique clearly segments the defect compared with other two techniques. Experimental results show that the multilevel thresholding outperforms the Otsu and iterative thresholding techniques.
| Fig. 3(a-d): | (a) Input image, (b) Otsu thresholding, (c) Iterative thresholding and (d) Multilevel thresholding |
| Fig. 4(a-b): | (a) Input image and (b) Image histogram with threshold calculated by multilevel, Otsu and iterative thresholding techniques |
Figure 4 shows the threshold value obtained by the thresholding techniques. The proposed approach requires 1.69 sec to classify the given alloy steel surface and 0.07 sec to detect the defected area.
CONCLUSION
In this study, the classification and detection of the defects in alloy steel surface based on DST and multi-level thresholding is presented. The proposed method decomposes the images by various levels of DST with different directions. For each and every direction, the energy features are extracted for no defect and defected surfaces. Among these features, the best set, 4 level 2 directions is chosen which distinguish the alloy steel surfaces efficiently than other DST features. Then, the multilevel thresholding is applied to segment the defected region. Experimental results show that the proposed approach is able to detect the surface defects with a sensitivity of 99.8% and specificity of 95.5%.