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.

1. 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.
2
ITE, College of Sciences, Massey University, Wellington, New Zealand.
Email: d.djukic@massey.ac.nz
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
1 Introduction and tested on samples collected in an industrial mill
for manufacturing flat steel products.
The consumers of rolled steel persistently set ever-
increasing requirements on product quality. An on-
line 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. Post-
fabrication 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 Figure 1-a: Typical oxide scale defect on hot rolled
automated decision making, even in high rate steel surface (sample A)
manufacturing processes, such as steel rolling and Two typical examples (samples A and B) of the
extrusion. surface defect analysed in this work is shown in Fig.
Statistical approach to automated inspection of rolled 1-a and 1-b. This class of defects appears in the
metallic products is a rich source of a variety of images as a dark area of variable size and irregular
algorithms for defect discrimination. It appears that a shape, usually elongated in the rolling direction.
combination of statistical pattern analyses, hard and
soft inference methods, with appropriate heuristic 2 Defect discrimination
rules is a promising strategy to achieve an improved
reliability in defect detection.
2.1 Pixel distribution estimation
1.1 Defects on rolled steel Even though the hot rolled steel surface appears to be
flat and uniform at the macroscopic level relevant for
In this work, the problem of discriminating defects observation, there is a considerable variability in pixel
recorded in images of hot rolled steel taken in the near intensities in the image of the surface under
infra-red spectrum has been addressed. In particular, inspection. This variability may be explained by the
a statistical method for discrimination of defects non-uniform reflection due to the surface topography
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2. and texture, by the changes in the ambient light, and I 
k
− 
λ
by randomness in the conversion process from an P (I ) = 1 − e
W (2)
optical image to its digital representative. Because of
this non-uniformity, it is not possible to select pixels Relevant functions are defined by equation (1) for the
corresponding to a defect simply by classifying their normal distribution, and (2) for Weibull distribution.
intensities, e.g. by a uniform thresholding operation. 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 Dynamical image thresholding
The discrimination of defects in the image is achieved
by selecting pixels and pixel clusters which do not
Figure 1-b: Typical oxide scale defect on hot rolled behave according to the estimated probability
steel surface (sample B) distribution of the regular, faultless surface. Since the
In the present work, the pixels in the image of the image pixels are realisations of a random process,
inspected surface are treated as realisations of a pixels with any intensity value are possible, however
random process described by a certain probability they may be more or less likely. For the
distribution. The founding postulate of the method discrimination of defects in the image it is not
developed here is the fact that the probability sufficient only to detect pixels with extremely low
distributions of the pixels which represent the regular, probability of appearance. Further decision needs to
flawless surface, and of the pixels which reperesent be made on whether the selected pixels do indeed
defects, differ significantly to provide adequate correspond to a true defect. Since typical scale roll-in
filtering criteria. defects are of certain size, the making of this decision
is directed by the size of clusters of selected pixels.
From the estimated probability distribution functions,
Observed frequencies it is possible to deduce the quantile functions that
Normal distribution
Weibull distribution relate pixel intensities to their corresponding
0.75
cumulative probabilities. Selection of pixels
Cumulative probability
according to a certain probability level corresponds to
a non-uniform thresholding, where the thresholding
0.5
level for each pixel is determined from the estimated
probability distribution. In this process, a binary
0.25 valued representative Bxy (P ) of the original image,
I xy , has been obtained, (3), where P is the given
0.45 0.5 0.55 probability level, I xy is the intensity of the pixel at
Relative pixel intensity
coordinates x and y in the original image, and
Figure 2: Pixel distribution estimation q xy ( P ) is the corresponding quantile function.
Before defect discrimination can be performed, it is
necessary to determine the probability distribution of 0 I xy ≥ q xy ( P)
the pixel intensities in the images of the regular Bxy ( P ) =  (3)
surface. In this work, two cumulative distribution 1 I xy < q xy ( P)
functions are tried: one based on Gaussian (normal),
and another one based on Weibull distribution.
Reliable detection of defects requires resolving two
1 1 I −µ
PN ( I ) = + erf ( ) (1) problems: finding the correct probability level, and
2 2 2σ the elimination of noise pixels.
In addressing the first issue, one needs to establish the
correct probability level for discrimination of pixels.
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3. The probability level at which the pixels are selected indicating a possible presence of a defect. As the
(discriminated) as pixels corresponding to a defect, probability grows with further increments, new pixels
depends on the actual defect, and also on the join the nucleus, and the cluster area increases.
conditions under which the image is taken. Thus, this
However, some pixels do not form clusters, and they
level ought not to be fixed in advance; it has to be
remain isolated as the probability level increases.
allowed to change according to the image
Such pixels are considered to be the noise.
circumstances.
Eventually, as the probability level increases further,
The second problem, noise elimination, is related to the number of noise pixels begins to increase rapidly,
the fact that a pixel selected according to a fixed however, the growth of the pixel clusters indicating
probability threshold may also be a pixel that is not a the presence of a defect ceases. In order to observe
deviation from the probability distribution, but is a this behaviour, it is necessary to perform the variation
realisation from its tail. A low probability fixed of the probability level in several increments over
threshold would eliminate the noise but it would several orders of magnitude. In practice, 12 to 15
simultaneously hinder the detection of actual features increments over 3 to 6 orders of magnitude are ample
of a real defect. A high probability fixed threshold to draw a conclusion on the behaviour of the selected
pollutes the defect contours, due to the increase in pixels. In a number of cases, using as few as 5 to 8
noise density. increments has been sufficient for a successful
discrimination of defects.
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
Figure 3-a: Bxy (P ) (Gaussian distribution),
to the probability of that event. In the problem treated P = q ( µ − 4σ ) = 0.00003
in this work, it has been observed that these two
probability levels differ by several orders of
magnitude.
2.3 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 Figure 3-b: Bxy (P ) (Gaussian distribution),
are selected. In practice, this usually amounts to only P = q ( µ − 4σ ) = 0.00003
one or two isolated pixels. At this stage, they are all
accepted as the candidates. As the probability level Based on these observations, a pixel tracking
passes onto the next higher increment, more pixels are procedure for distinguishing defects from noise pixels
selected. Some of these newly selected pixels are has been devised. The procedure is based on simple
adjacent to, or in the immediate vicinity of, the heuristic rules:
previously selected pixels. Such pixels form a cluster,
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4. - 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 Figure 4-b: Bxy (P ) (Gaussian distribution),
not join it when the probability changes for
more than 2 orders of magnitude.
P = q ( µ − 2.5σ ) = 0.006
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 Figure 5-a: Bxy (P ) (Gaussian distribution),
1-b). The detection procedure has been applied using
both Gaussian and Weibull distributions. The process P = q ( µ − 1.5σ ) = 0.07
of surface defect discrimination is presented here
visually, by means of Bxy (P ) images. These are bi-
level (black and white) images in which the selected
pixels are shown in black.
Figure 5-b: Bxy (P ) (Gaussian distribution),
P = q ( µ − 1.5σ ) = 0.07
In the case of Gaussian distribution, the threshold
Figure 4-a: Bxy (P ) (Gaussian distribution), levels have been set directly from the distribution
parameters µ and σ , and the corresponding
P = q ( µ − 2.5σ ) = 0.006 probability level has been computed using equation
(1). This has been necessary, as, for very small
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5. probabilities, the numerical computation of the very low. As the probability level increases (Figs. 4-a
quantile function becomes unreliable. 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.
Figure 6-a: Bxy (P ) (Weibull distribution),
P = 0.00001
Figure 7-b: Bxy ( P ) (Weibull distribution),
P = 0.01
Figure 6-b: Bxy ( P ) (Weibull distribution),
P = 0.00001
Figure 8-a: Bxy ( P ) (Weibull distribution),
P = 0 .1
Figure 7-a: Bxy ( P ) (Weibull distribution),
P = 0.01
Figs. 3-a and 3-b, related to samples A and B Figure 8-b: Bxy ( P ) (Weibull distribution),
respectively, show selected pixels that are candidates P = 0 .1
for defect indicators; however the probability level is
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464
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
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level varies.
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
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improvement would involve estimating multivariate
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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.
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