Statistical discriminator of surface defects on hot rolled steel

D. Djukic, S. Spuzic, ‘Statistical Discriminator of Surface Defects on Hot Rolled Steel’, Proceedings of Image and Vision Computing New Zealand 2007, pp. 158–163, Hamilton, New Zealand, December 2007. Statistical discriminator of surface defects on hot rolled steel D. Djukic1, S. Spuzic2 1 IIST, College of Sciences, Massey University, Wellington, New Zealand. ITE, College of Sciences, Massey University, Wellington, New Zealand. 2 Email: [email protected] Abstract A statistical approach to defect detection and discrimination has been applied to the case of hot rolled steel. The probability distribution of pixel intensities has been estimated from a small set of images without defects, and this distribution is used to select pixels with unlikely values as candidates for defects. Discrimination of true defects from random noise pixels is achieved by a dynamical thresholding procedure, which tracks the behaviour of clusters of selected pixels for varying threshold level. Boundary levels of the dynamic threshold range are determined from the estimated probability distribution of the pixel intensities. Keywords: Steel rolling, Surface defect detection, Pixel statistics, Dynamical threshold caused by rolled-in oxide scale has been conceived and tested on samples collected in an industrial mill for manufacturing flat steel products. 1 Introduction The consumers of rolled steel persistently set everincreasing requirements on product quality. An online diagnosis in manufacturing in general, and especially in high volume fabrication of flat metallic products, substantially enhances total quality control. The purpose of an automated surface inspection system is to detect and classify surface defects as early as possible in the manufacturing process. Digital image analysis is increasingly used in surface inspection and discrimination of surface defects in hot, cold, and coated rolled steel products. Postfabrication inspection systems for metallic surfaces based on image processing techniques have been available for some time, but the recent development of electronics and information technology has enabled implementation of on-line image analysis and automated decision making, even in high rate manufacturing processes, such as steel rolling and extrusion. Figure 1-a: Typical oxide scale defect on hot rolled steel surface (sample A) Two typical examples (samples A and B) of the surface defect analysed in this work is shown in Fig. 1-a and 1-b. This class of defects appears in the images as a dark area of variable size and irregular shape, usually elongated in the rolling direction. Statistical approach to automated inspection of rolled metallic products is a rich source of a variety of algorithms for defect discrimination. It appears that a combination of statistical pattern analyses, hard and soft inference methods, with appropriate heuristic rules is a promising strategy to achieve an improved reliability in defect detection. 1.1 2 Defect discrimination 2.1 Pixel distribution estimation Even though the hot rolled steel surface appears to be flat and uniform at the macroscopic level relevant for observation, there is a considerable variability in pixel intensities in the image of the surface under inspection. This variability may be explained by the non-uniform reflection due to the surface topography Defects on rolled steel In this work, the problem of discriminating defects recorded in images of hot rolled steel taken in the near infra-red spectrum has been addressed. In particular, a statistical method for discrimination of defects 158 and texture, by the changes in the ambient light, and by randomness in the conversion process from an optical image to its digital representative. Because of this non-uniformity, it is not possible to select pixels corresponding to a defect simply by classifying their intensities, e.g. by a uniform thresholding operation. PW ( I ) = 1 − e I  −  λ k (2) Relevant functions are defined by equation (1) for the normal distribution, and (2) for Weibull distribution. The parameters of these distributions, µ and σ , and k and λ respectively, are estimated from a relatively small number (50 in this case) of images of the regular, faultless, surface. Fig. 2 presents the observed cumulative frequency of the pixel intensities, together with the cumulative probability functions corresponding to the estimated normal and Weibull distributions. It has been noted that Weibull distribution shows better agreement with the observed data, especially for low pixel intensities. 2.2 The discrimination of defects in the image is achieved by selecting pixels and pixel clusters which do not behave according to the estimated probability distribution of the regular, faultless surface. Since the image pixels are realisations of a random process, pixels with any intensity value are possible, however they may be more or less likely. For the discrimination of defects in the image it is not sufficient only to detect pixels with extremely low probability of appearance. Further decision needs to be made on whether the selected pixels do indeed correspond to a true defect. Since typical scale roll-in defects are of certain size, the making of this decision is directed by the size of clusters of selected pixels. Figure 1-b: Typical oxide scale defect on hot rolled steel surface (sample B) In the present work, the pixels in the image of the inspected surface are treated as realisations of a random process described by a certain probability distribution. The founding postulate of the method developed here is the fact that the probability distributions of the pixels which represent the regular, flawless surface, and of the pixels which reperesent defects, differ significantly to provide adequate filtering criteria. From the estimated probability distribution functions, it is possible to deduce the quantile functions that relate pixel intensities to their corresponding cumulative probabilities. Selection of pixels according to a certain probability level corresponds to a non-uniform thresholding, where the thresholding level for each pixel is determined from the estimated probability distribution. In this process, a binary valued representative Bxy (P ) of the original image, Observed frequencies Normal distribution Weibull distribution Cumulative probability Dynamical image thresholding 0.75 0.5 0.25 I xy , has been obtained, (3), where P is the given 0.45 0.5 I xy is the intensity of the pixel at coordinates x and y in the original image, and q xy ( P ) is the corresponding quantile function. probability level, 0.55 Relative pixel intensity Figure 2: Pixel distribution estimation Before defect discrimination can be performed, it is necessary to determine the probability distribution of the pixel intensities in the images of the regular surface. In this work, two cumulative distribution functions are tried: one based on Gaussian (normal), and another one based on Weibull distribution. 1 1 I −µ PN ( I ) = + erf ( ) 2 2 2σ 0 I xy ≥ q xy ( P) Bxy ( P ) =  1 I xy < q xy ( P) (3) Reliable detection of defects requires resolving two problems: finding the correct probability level, and the elimination of noise pixels. (1) In addressing the first issue, one needs to establish the correct probability level for discrimination of pixels. 159 indicating a possible presence of a defect. As the probability grows with further increments, new pixels join the nucleus, and the cluster area increases. The probability level at which the pixels are selected (discriminated) as pixels corresponding to a defect, depends on the actual defect, and also on the conditions under which the image is taken. Thus, this level ought not to be fixed in advance; it has to be allowed to change according to the image circumstances. However, some pixels do not form clusters, and they remain isolated as the probability level increases. Such pixels are considered to be the noise. Eventually, as the probability level increases further, the number of noise pixels begins to increase rapidly, however, the growth of the pixel clusters indicating the presence of a defect ceases. In order to observe this behaviour, it is necessary to perform the variation of the probability level in several increments over several orders of magnitude. In practice, 12 to 15 increments over 3 to 6 orders of magnitude are ample to draw a conclusion on the behaviour of the selected pixels. In a number of cases, using as few as 5 to 8 increments has been sufficient for a successful discrimination of defects. The second problem, noise elimination, is related to the fact that a pixel selected according to a fixed probability threshold may also be a pixel that is not a deviation from the probability distribution, but is a realisation from its tail. A low probability fixed threshold would eliminate the noise but it would simultaneously hinder the detection of actual features of a real defect. A high probability fixed threshold pollutes the defect contours, due to the increase in noise density. Both issues may be satisfactorily resolved through dynamical thresholding. In dynamical thresholding, the probability level P changes, and the behaviour of the selected pixels i.e. the pixels with value 1 in Bxy (P ) , is tracked by means of this change. The probability level is varied between two values, which need not be precisely determined, but roughly correspond to levels that allow the method to discriminate pixels. The lower limit of the probability level of the moving threshold is that at which it is extremely unlikely that any of the pixels is selected as a candidate for defect. The upper limit of the probability range is the level at which the number of selected pixels becomes approximately equal to the expected number of the selected pixels, i.e. when the observed frequency of the event becomes comparable to the probability of that event. In the problem treated in this work, it has been observed that these two probability levels differ by several orders of magnitude. 2.3 Bxy (P ) (Gaussian distribution), P = q ( µ − 4σ ) = 0.00003 Figure 3-a: Defect discrimination As the probability level P changes from the lower to the upper limit, the number of selected pixels in Bxy (P ) increases, where some of the pixels form clusters, and some appear and remain isolated. Since the isolated pixels represent a very small area on the inspected surface, in order to declare the presence of a defect, it is necessary to detect the presence of a cluster of selected pixels. When the threshold is at the lower end of its range of values, only the pixels with extremely unlikely values are selected. In practice, this usually amounts to only one or two isolated pixels. At this stage, they are all accepted as the candidates. As the probability level passes onto the next higher increment, more pixels are selected. Some of these newly selected pixels are adjacent to, or in the immediate vicinity of, the previously selected pixels. Such pixels form a cluster, Figure 3-b: Bxy (P ) (Gaussian distribution), P = q ( µ − 4σ ) = 0.00003 Based on these observations, a pixel tracking procedure for distinguishing defects from noise pixels has been devised. The procedure is based on simple heuristic rules: 160 - Begin at such a low probability level that no pixels are selected. - Increase the probability level and mark the pixels as they appear. - Retain the pixels that form a cluster the size of which increases as the probability level increases. - Suppress isolated pixels that are distant from any cluster, and that remain isolated after the probability level has increased by more than one order of magnitude. - Suppress isolated pixels that are near a cluster, i.e. whose distance from a cluster is less than the size of that cluster, but that do not join it when the probability changes for more than 2 orders of magnitude. Bxy (P ) (Gaussian distribution), P = q ( µ − 2.5σ ) = 0.006 Figure 4-b: This procedure has enabled a robust and reliable discrimination of defects in all tested cases. 3 Experimental results The procedure for defect discrimination described in the previous section has been tested on a set of images of hot rolled steel, collected at New Zealand Steel production site at Glenbrook. The parameters of pixel distributions have been estimated from a subset of images without defects, both for Gaussian and for Weibull distributions. In this section, the defect detection procedure has been applied to two typical images, each showing a local region with rolled-in oxide scale (Figs. 1-a and 1-b). The detection procedure has been applied using both Gaussian and Weibull distributions. The process of surface defect discrimination is presented here visually, by means of Bxy (P ) images. These are bi- Figure 5-a: Bxy (P ) (Gaussian distribution), P = q ( µ − 1.5σ ) = 0.07 level (black and white) images in which the selected pixels are shown in black. Bxy (P ) (Gaussian distribution), P = q ( µ − 1.5σ ) = 0.07 Figure 5-b: In the case of Gaussian distribution, the threshold levels have been set directly from the distribution parameters µ and σ , and the corresponding probability level has been computed using equation (1). This has been necessary, as, for very small Bxy (P ) (Gaussian distribution), P = q ( µ − 2.5σ ) = 0.006 Figure 4-a: 161 probabilities, the numerical computation of the quantile function becomes unreliable. Figure 6-a: very low. As the probability level increases (Figs. 4-a and 4-b), clusters that show a tendency to increase in area are formed. Eventually (Figs. 5-a and 5-b), the pixel clusters indicating the defects stop growing, but the number of noise pixels begins to rise rapidly. Bxy (P ) (Weibull distribution), P = 0.00001 Figure 6-b: Figure 7-b: Bxy ( P ) (Weibull distribution), P = 0.01 Figure 8-a: Bxy ( P ) (Weibull distribution), Bxy ( P ) (Weibull distribution), P = 0.00001 P = 0 .1 Figure 7-a: Bxy ( P ) (Weibull distribution), P = 0.01 Figure 8-b: Figs. 3-a and 3-b, related to samples A and B respectively, show selected pixels that are candidates for defect indicators; however the probability level is 162 Bxy ( P ) (Weibull distribution), P = 0 .1 In the case of Weibull distribution, the quantile function may be computed with adequate accuracy, and this function has been used to determine the threshold levels from the desired probability levels. The behaviour of the selected pixels as the threshold increases is similar to the behaviour described in the previous paragraph (Figs. 6-a and 6-b, Figs. 7-a and 7-b, and Figs. 8-a and 8-b). References [1] [2] When compared to Gaussian distribution, thresholding levels determined by Weibull distribution tend to produce less noise pixels. This observation is of particular importance for the range of probability levels in which the cluster corresponding to the defect shows growth, as this enables reliable elimination of noise pixels. This advantage of Weibull distribution has been expected, since the Weibull distribution shows a better concordance with the observed distribution of pixel intensities. In addition, when estimated Weibull distribution is being used, the defect discrimination decision may be reached in fewer increments. [3] [4] [5] 4 Conclusion In this work, the problem of detection of scale roll-in defects in hot rolled steel has been solved using a statistical approach. The probability distribution of pixels of regular, faultless surface has been estimated. Two standard probability distribution functions, Gaussian and Weibull, have been tried, and Weibull distribution has shown some superiority in this case. The estimated distributions are used in a process of dynamical non-uniform thresholding, through which candidate pixels are selected. The candidate pixels are further classified into defects and noise, by means of tracking of the candidate pixels as the thresholding level varies. [6] The method described here has been applied on a set of test images collected in an industrial steel mill for hot rolling. The results obtained in this test show clear potential of this method for robust and reliable detection of scale roll-in defects. Two significant improvements of the method presented here are under consideration. One improvement would involve morphological and statistical analysis of pixel clusters. The other improvement would involve estimating multivariate pixel statistics, which would result in a more definite criterion for noise filtering. This method will also be extended to allow detection of other types of hot rolling defects. 5 Acknowledgements The authors are grateful to Mr. H. Nieborak, Mr. R. Kimber, Mr. N. Joveljic, and Mr. P. Bagshaw of the New Zealand Steel, for their kind provision of the sample images, and for their enthusiasm, encouragement and interest in this work. 163 T. Sugimoto, T, Kawaguchi "Development of a Surface Defect Inspection System Using Radiant Light from Steel Products in a Hot Rolling Line", IEEE Trans Inst. Meas.vol. 47 no. 2, April 1998, pp 409-416 C. Fernandez, S. Fernandez, P. Campoy, R. Aracil "On-line texture analysis for flat products inspection. Neural nets implementation", Proceedings of IECON '94., Sept. 1994, vol.2, pp 867 - 872 R.J. Montague, J. Watton, K.J. 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