Statistical Discriminator of Surface Defects on Hot Rolled Steel

D. Djukic, S. Spuzic, ‘<strong>Statistical</strong> <strong>Discriminator</strong> <strong>of</strong> <strong>Surface</strong> <strong>Defects</strong> on Hot Rolled Steel’,Proceedings <strong>of</strong> Image and Vision Computing New Zealand 2007, pp. 158–163, Hamilton,New Zealand, December 2007.<strong>Statistical</strong> discriminator <strong>of</strong> surface defects on hot rolledsteelD. Djukic 1 , S. Spuzic 21 IIST, College <strong>of</strong> Sciences, Massey University, Wellington, New Zealand.2 ITE, College <strong>of</strong> Sciences, Massey University, Wellington, New Zealand.Email: d.djukic@massey.ac.nzAbstractA statistical approach to defect detection and discrimination has been applied to the case <strong>of</strong> hot rolled steel. Theprobability distribution <strong>of</strong> pixel intensities has been estimated from a small set <strong>of</strong> images without defects, andthis distribution is used to select pixels with unlikely values as candidates for defects. Discrimination <strong>of</strong> truedefects from random noise pixels is achieved by a dynamical thresholding procedure, which tracks the behaviour<strong>of</strong> clusters <strong>of</strong> selected pixels for varying threshold level. Boundary levels <strong>of</strong> the dynamic threshold range aredetermined from the estimated probability distribution <strong>of</strong> the pixel intensities.Keywords: Steel rolling, <strong>Surface</strong> defect detection, Pixel statistics, Dynamical threshold1 IntroductionThe consumers <strong>of</strong> rolled steel persistently set everincreasingrequirements on product quality. An onlinediagnosis in manufacturing in general, andespecially in high volume fabrication <strong>of</strong> flat metallicproducts, substantially enhances total quality control.The purpose <strong>of</strong> an automated surface inspectionsystem is to detect and classify surface defects asearly as possible in the manufacturing process.Digital image analysis is increasingly used in surfaceinspection and discrimination <strong>of</strong> surface defects inhot, cold, and coated rolled steel products. Postfabricationinspection systems for metallic surfacesbased on image processing techniques have beenavailable for some time, but the recent development<strong>of</strong> electronics and information technology has enabledimplementation <strong>of</strong> on-line image analysis andautomated decision making, even in high ratemanufacturing processes, such as steel rolling andextrusion.<strong>Statistical</strong> approach to automated inspection <strong>of</strong> rolledmetallic products is a rich source <strong>of</strong> a variety <strong>of</strong>algorithms for defect discrimination. It appears that acombination <strong>of</strong> statistical pattern analyses, hard ands<strong>of</strong>t inference methods, with appropriate heuristicrules is a promising strategy to achieve an improvedreliability in defect detection.1.1 <strong>Defects</strong> on rolled steelIn this work, the problem <strong>of</strong> discriminating defectsrecorded in images <strong>of</strong> hot rolled steel taken in the nearinfra-red spectrum has been addressed. In particular,a statistical method for discrimination <strong>of</strong> defectscaused by rolled-in oxide scale has been conceivedand tested on samples collected in an industrial millfor manufacturing flat steel products.Figure 1-a: Typical oxide scale defect on hot rolledsteel surface (sample A)Two typical examples (samples A and B) <strong>of</strong> thesurface defect analysed in this work is shown in Fig.1-a and 1-b. This class <strong>of</strong> defects appears in theimages as a dark area <strong>of</strong> variable size and irregularshape, usually elongated in the rolling direction.2 Defect discrimination2.1 Pixel distribution estimationEven though the hot rolled steel surface appears to beflat and uniform at the macroscopic level relevant forobservation, there is a considerable variability in pixelintensities in the image <strong>of</strong> the surface underinspection. This variability may be explained by thenon-uniform reflection due to the surface topography158

and texture, by the changes in the ambient light, andby randomness in the conversion process from anoptical image to its digital representative. Because <strong>of</strong>this non-uniformity, it is not possible to select pixelscorresponding to a defect simply by classifying theirintensities, e.g. by a uniform thresholding operation.Figure 1-b: Typical oxide scale defect on hot rolledsteel surface (sample B)In the present work, the pixels in the image <strong>of</strong> theinspected surface are treated as realisations <strong>of</strong> arandom process described by a certain probabilitydistribution. The founding postulate <strong>of</strong> the methoddeveloped here is the fact that the probabilitydistributions <strong>of</strong> the pixels which represent the regular,flawless surface, and <strong>of</strong> the pixels which reperesentdefects, differ significantly to provide adequatefiltering criteria.Cumulative probability0.750.50.25Observed frequenciesNormal distributionWeibull distribution0.45 0.5 0.55Relative pixel intensityFigure 2: Pixel distribution estimationBefore defect discrimination can be performed, it isnecessary to determine the probability distribution <strong>of</strong>the pixel intensities in the images <strong>of</strong> the regularsurface. In this work, two cumulative distributionfunctions are tried: one based on Gaussian (normal),and another one based on Weibull distribution.1 1 I − µ( I)= + erf ( )2 2 2σP N(1)Wk⎛ I ⎞−⎜⎟⎝ λ ⎠P ( I ) = 1−e(2)Relevant functions are defined by equation (1) for thenormal distribution, and (2) for Weibull distribution.The parameters <strong>of</strong> these distributions, µ and σ , andk and λ respectively, are estimated from arelatively small number (50 in this case) <strong>of</strong> images <strong>of</strong>the regular, faultless, surface.Fig. 2 presents the observed cumulative frequency <strong>of</strong>the pixel intensities, together with the cumulativeprobability functions corresponding to the estimatednormal and Weibull distributions. It has been notedthat Weibull distribution shows better agreement withthe observed data, especially for low pixel intensities.2.2 Dynamical image thresholdingThe discrimination <strong>of</strong> defects in the image is achievedby selecting pixels and pixel clusters which do notbehave according to the estimated probabilitydistribution <strong>of</strong> the regular, faultless surface. Since theimage pixels are realisations <strong>of</strong> a random process,pixels with any intensity value are possible, howeverthey may be more or less likely. For thediscrimination <strong>of</strong> defects in the image it is notsufficient only to detect pixels with extremely lowprobability <strong>of</strong> appearance. Further decision needs tobe made on whether the selected pixels do indeedcorrespond to a true defect. Since typical scale roll-indefects are <strong>of</strong> certain size, the making <strong>of</strong> this decisionis directed by the size <strong>of</strong> clusters <strong>of</strong> selected pixels.From the estimated probability distribution functions,it is possible to deduce the quantile functions thatrelate pixel intensities to their correspondingcumulative probabilities. Selection <strong>of</strong> pixelsaccording to a certain probability level corresponds toa non-uniform thresholding, where the thresholdinglevel for each pixel is determined from the estimatedprobability distribution. In this process, a binaryvalued representative B xy(P)<strong>of</strong> the original image,Ixy, has been obtained, (3), where P is the givenprobability level, I is the intensity <strong>of</strong> the pixel atxycoordinates x and y in the original image, andq xy(P) is the corresponding quantile function.B⎧0( P)= ⎨⎩1IIxyxy≥ q< qxyxy( P)( P)xy(3)Reliable detection <strong>of</strong> defects requires resolving twoproblems: finding the correct probability level, andthe elimination <strong>of</strong> noise pixels.In addressing the first issue, one needs to establish thecorrect probability level for discrimination <strong>of</strong> pixels.159

The probability level at which the pixels are selected(discriminated) as pixels corresponding to a defect,depends on the actual defect, and also on theconditions under which the image is taken. Thus, thislevel ought not to be fixed in advance; it has to beallowed to change according to the imagecircumstances.The second problem, noise elimination, is related tothe fact that a pixel selected according to a fixedprobability threshold may also be a pixel that is not adeviation from the probability distribution, but is arealisation from its tail. A low probability fixedthreshold would eliminate the noise but it wouldsimultaneously hinder the detection <strong>of</strong> actual features<strong>of</strong> a real defect. A high probability fixed thresholdpollutes the defect contours, due to the increase innoise density.Both issues may be satisfactorily resolved throughdynamical thresholding. In dynamical thresholding,the probability level P changes, and the behaviour <strong>of</strong>the selected pixels i.e. the pixels with value 1 in(P) , is tracked by means <strong>of</strong> this change.B xyThe probability level is varied between two values,which need not be precisely determined, but roughlycorrespond to levels that allow the method todiscriminate pixels. The lower limit <strong>of</strong> the probabilitylevel <strong>of</strong> the moving threshold is that at which it isextremely unlikely that any <strong>of</strong> the pixels is selected asa candidate for defect. The upper limit <strong>of</strong> theprobability range is the level at which the number <strong>of</strong>selected pixels becomes approximately equal to theexpected number <strong>of</strong> the selected pixels, i.e. when theobserved frequency <strong>of</strong> the event becomes comparableto the probability <strong>of</strong> that event. In the problem treatedin this work, it has been observed that these twoprobability levels differ by several orders <strong>of</strong>magnitude.indicating a possible presence <strong>of</strong> a defect. As theprobability grows with further increments, new pixelsjoin the nucleus, and the cluster area increases.However, some pixels do not form clusters, and theyremain isolated as the probability level increases.Such pixels are considered to be the noise.Eventually, as the probability level increases further,the number <strong>of</strong> noise pixels begins to increase rapidly,however, the growth <strong>of</strong> the pixel clusters indicatingthe presence <strong>of</strong> a defect ceases. In order to observethis behaviour, it is necessary to perform the variation<strong>of</strong> the probability level in several increments overseveral orders <strong>of</strong> magnitude. In practice, 12 to 15increments over 3 to 6 orders <strong>of</strong> magnitude are ampleto draw a conclusion on the behaviour <strong>of</strong> the selectedpixels. In a number <strong>of</strong> cases, using as few as 5 to 8increments has been sufficient for a successfuldiscrimination <strong>of</strong> defects.Figure 3-a: B xy(P)(Gaussian distribution),P = q( µ − 4σ) = 0.000032.3 Defect discriminationAs the probability level P changes from the lower tothe upper limit, the number <strong>of</strong> selected pixels inB xy(P) increases, where some <strong>of</strong> the pixels formclusters, and some appear and remain isolated. Sincethe isolated pixels represent a very small area on theinspected surface, in order to declare the presence <strong>of</strong> adefect, it is necessary to detect the presence <strong>of</strong> acluster <strong>of</strong> selected pixels.When the threshold is at the lower end <strong>of</strong> its range <strong>of</strong>values, only the pixels with extremely unlikely valuesare selected. In practice, this usually amounts to onlyone or two isolated pixels. At this stage, they are allaccepted as the candidates. As the probability levelpasses onto the next higher increment, more pixels areselected. Some <strong>of</strong> these newly selected pixels areadjacent to, or in the immediate vicinity <strong>of</strong>, thepreviously selected pixels. Such pixels form a cluster,Figure 3-b: B xy(P)(Gaussian distribution),P = q( µ − 4σ) = 0.00003Based on these observations, a pixel trackingprocedure for distinguishing defects from noise pixelshas been devised. The procedure is based on simpleheuristic rules:160

- Begin at such a low probability level that nopixels are selected.- Increase the probability level and mark thepixels as they appear.- Retain the pixels that form a cluster the size<strong>of</strong> which increases as the probability levelincreases.- Suppress isolated pixels that are distant fromany cluster, and that remain isolated after theprobability level has increased by more thanone order <strong>of</strong> magnitude.- Suppress isolated pixels that are near acluster, i.e. whose distance from a cluster isless than the size <strong>of</strong> that cluster, but that donot join it when the probability changes formore than 2 orders <strong>of</strong> magnitude.This procedure has enabled a robust and reliablediscrimination <strong>of</strong> defects in all tested cases.3 Experimental resultsThe procedure for defect discrimination described inthe previous section has been tested on a set <strong>of</strong> images<strong>of</strong> hot rolled steel, collected at New Zealand Steelproduction site at Glenbrook. The parameters <strong>of</strong> pixeldistributions have been estimated from a subset <strong>of</strong>images without defects, both for Gaussian and forWeibull distributions.In this section, the defect detection procedure hasbeen applied to two typical images, each showing alocal region with rolled-in oxide scale (Figs. 1-a and1-b). The detection procedure has been applied usingboth Gaussian and Weibull distributions. The process<strong>of</strong> surface defect discrimination is presented herevisually, by means <strong>of</strong> B xy(P)images. These are bilevel(black and white) images in which the selectedpixels are shown in black.Figure 4-b: B xy(P)(Gaussian distribution),P = q( µ − 2.5σ) = 0.006Figure 5-a: B xy(P)(Gaussian distribution),P = q( µ −1.5σ) = 0.07Figure 5-b: B xy(P)(Gaussian distribution),P = q( µ −1.5σ) = 0.07Figure 4-a: B xy(P)(Gaussian distribution),P = q( µ − 2.5σ) = 0.006In the case <strong>of</strong> Gaussian distribution, the thresholdlevels have been set directly from the distributionparameters µ and σ , and the correspondingprobability level has been computed using equation(1). This has been necessary, as, for very small161

probabilities, the numerical computation <strong>of</strong> thequantile function becomes unreliable.very low. As the probability level increases (Figs. 4-aand 4-b), clusters that show a tendency to increase inarea are formed. Eventually (Figs. 5-a and 5-b), thepixel clusters indicating the defects stop growing, butthe number <strong>of</strong> noise pixels begins to rise rapidly.Figure 6-a: B xy(P)(Weibull distribution),P = 0.00001Figure 7-b: B xy(P)(Weibull distribution),P = 0.01Figure 6-b: B xy(P)(Weibull distribution),P = 0.00001Figure 8-a: B xy(P)(Weibull distribution),P = 0.1Figure 7-a: B xy(P)(Weibull distribution),P = 0.01Figs. 3-a and 3-b, related to samples A and Brespectively, show selected pixels that are candidatesfor defect indicators; however the probability level isFigure 8-b: B xy(P)(Weibull distribution),P = 0.1162

In the case <strong>of</strong> Weibull distribution, the quantilefunction may be computed with adequate accuracy,and this function has been used to determine thethreshold levels from the desired probability levels.The behaviour <strong>of</strong> the selected pixels as the thresholdincreases is similar to the behaviour described in theprevious paragraph (Figs. 6-a and 6-b, Figs. 7-a and7-b, and Figs. 8-a and 8-b).When compared to Gaussian distribution,thresholding levels determined by Weibulldistribution tend to produce less noise pixels. Thisobservation is <strong>of</strong> particular importance for the range<strong>of</strong> probability levels in which the clustercorresponding to the defect shows growth, as thisenables reliable elimination <strong>of</strong> noise pixels. Thisadvantage <strong>of</strong> Weibull distribution has been expected,since the Weibull distribution shows a betterconcordance with the observed distribution <strong>of</strong> pixelintensities. In addition, when estimated Weibulldistribution is being used, the defect discriminationdecision may be reached in fewer increments.4 ConclusionIn this work, the problem <strong>of</strong> detection <strong>of</strong> scale roll-indefects in hot rolled steel has been solved using astatistical approach. The probability distribution <strong>of</strong>pixels <strong>of</strong> regular, faultless surface has been estimated.Two standard probability distribution functions,Gaussian and Weibull, have been tried, and Weibulldistribution has shown some superiority in this case.The estimated distributions are used in a process <strong>of</strong>dynamical non-uniform thresholding, through whichcandidate pixels are selected. The candidate pixelsare further classified into defects and noise, by means<strong>of</strong> tracking <strong>of</strong> the candidate pixels as the thresholdinglevel varies.The method described here has been applied on a set<strong>of</strong> test images collected in an industrial steel mill forhot rolling. The results obtained in this test showclear potential <strong>of</strong> this method for robust and reliabledetection <strong>of</strong> scale roll-in defects.Two significant improvements <strong>of</strong> the methodpresented here are under consideration. Oneimprovement would involve morphological andstatistical analysis <strong>of</strong> pixel clusters. The otherimprovement would involve estimating multivariatepixel statistics, which would result in a more definitecriterion for noise filtering. This method will also beextended to allow detection <strong>of</strong> other types <strong>of</strong> hotrolling defects.References[1] T. Sugimoto, T, Kawaguchi "Development<strong>of</strong> a <strong>Surface</strong> Defect Inspection System UsingRadiant Light from Steel Products in a HotRolling Line", IEEE Trans Inst. Meas.vol. 47no. 2, April 1998, pp 409-416[2] C. Fernandez, S. Fernandez, P. Campoy, R.Aracil "On-line texture analysis for flatproducts inspection. Neural netsimplementation", Proceedings <strong>of</strong> IECON'94., Sept. 1994, vol.2, pp 867 - 872[3] R.J. Montague, J. Watton, K.J. Brown "Amachine vision measurement <strong>of</strong> slab camberin hot strip rolling", Journal <strong>of</strong> MaterialsProcessing Technology 168 (2005) 172–180[4] H. Jia, Y. L. Murphey, J. Shi, T.-S. Chang"An Intelligent Real-time Vision System for<strong>Surface</strong> Defect Detection", Proceedings <strong>of</strong>ICPR’04, IEEE Computer Society, 2004[5] C. Fernandez; C. Platero; P. Campoy; R.Aracil "Vision system for on-line surfaceinspection in aluminum casting process"Proceedings <strong>of</strong> IECON '93, Nov. 1993,vol.3, pp 1854-1859[6] J. J. Haapamaki, S. M. Tamminen, J. J.Roning "Data mining methods in hot steelrolling for scale defect prediction"Proceedings <strong>of</strong> AIA 2005, Feb. 2005, pp 453-4645 AcknowledgementsThe authors are grateful to Mr. H. Nieborak, Mr. R.Kimber, Mr. N. Joveljic, and Mr. P. Bagshaw <strong>of</strong> theNew Zealand Steel, for their kind provision <strong>of</strong> thesample images, and for their enthusiasm,encouragement and interest in this work.163