Wavelet-based Defect Detection System for Grey-level Texture
Images
Gintarė Vaidelienė and Jonas Valantinas
Kaunas University of Technology, Department of Applied Mathematics, Kaunas, Lithuania
Keywords: Texture Images, Defect Detection, Discrete Wavelets Transforms, Statistical Data Analysis, Automatic Visual
Inspection.
Abstract: In this study, a new wavelet-based approach (system) to the detection of defects in grey-level texture images
is presented. This new approach explores space localization properties of the discrete wavelet transform
(DWT) and generates statistically-based parameterized defect detection criteria. The introduced system’s
parameter provides the user with a possibility to control the percentage of both the actually defect-free images
detected as defective and/or the actually defective images detected as defect-free, in the class of texture images
under investigation. The developed defect detection system was implemented using discrete Haar and Le Gall
wavelet transforms. For the experimental part, samples of ceramic tiles, as well as glass samples, taken from
real factory environment, were used.
1 INTRODUCTION
Visual inspection presents an important part of
quality control in manufacturing. Traditionally,
product defects are detected by human eyes, but the
detection efficiency is low enough because of eye
fatigue. Also, the human visual inspection is more or
less subjective and highly depends on the experience
of human inspectors. Some studies indicate, that an
expert, in human visual inspection, typically finds
only (60-75) % of the significant defects (Ngan et al.,
2011). Therefore, an increased need to develop online
visual-based systems capable to enhance not only the
quality control but also the marketing of the products
is observed.
The defect detection systems are designed and
explored for various texture surfaces, such as steel
plates, weldment, ceramic tiles, fabric, etc., and are
oriented to detect defects like cracks, stains, broken
points and other. There are numerous publications
offering approaches to solve the problem (Ngan et al.,
2011; Karimi et al., 2014; Xie, 2008; Kumar, 2008).
Texture defect detection methods can be roughly
categorized into four classes (approaches): statistical
methods, structural methods, filtering methods and
model-based methods.
The statistical approach analyses the spatial
distribution values in texture images using various
representations, say, auto-correlation function, co-
occurrence matrices, histogram statistics (mean,
standard deviation, median, etc.), Weibull
distribution (Gururajan et al., 2008; Ghazini et al.,
2009; Lin et al., 2007; Latif-Amet et al., 2000;
Iivarinent, 2000; Timm et al., 2011), etc.
Filtering methods are based, mainly, on
mathematical (linear and non-linear) transforms and
on various filtering schemes. In particular, Fourier
transform, discrete wavelet transforms, filters (Gabor,
Sobel, Gaussian, etc.), neural networks, as well as and
genetic algorithms are explored (Han et al., 2007;
Ngan et al., 2005; Tsai et al., 2007; Chan et al., 2000;
Bissi et al., 2013; Mak et al., 2013; Raheja et al.
2013).
In model-based defect detection approach, a
model is selected to analyse the texture image, and the
model parameters are desired unknowns. The model-
based methods include autoregressive model, Markov
random fields, fractal model, etc. Despite the novelty
and originality of the ideas employed, the model-
based methods have limited areas of application (Bu
et al., 2009; Bu et al., 2010; Dogandzic et al., 2005).
The structural approach usually analyses spatial
arrangement of texture elements, explores
morphological operators and edge detection schemes,
hierarchical forms, and often leads to undesirable
time-consuming operations. On the other hand, the
structural methods perform well with very regular
Vaidelien
˙
e, G. and Valantinas, J.
Wavelet-based Defect Detection System for Grey-level Texture Images.
DOI: 10.5220/0005678901430149
In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 4: VISAPP, pages 143-149
ISBN: 978-989-758-175-5
Copyright
c
 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
143

Figure 1: The general scheme of the defect detection system for grey-level texture images.
texture, (Chen et al. 1988; Wen et al., 1999; Mak et
al., 2009).
Lately, some hybrid models that combine various
ideas mentioned above have appeared (Li et al., 2013;
Jia et al., 2014, Yuen et al., 2009; Kim et al., 2006).
In this paper, a novel wavelet-based defect
detection system for grey-level texture images is
proposed. This system can be used for an automated
visual inspection and quality control in a process of
serial production, to avoid the financial problems
caused by the selling decrements.
2 A NEW DEFECT DETECTION
SYSTEM FOR TEXTURE
IMAGES
The characteristic feature of the proposed defect
detection system is simultaneous application of
several different scanning filters (two-dimensional
wavelets) to the texture image under investigation.
The decision on the quality of the test texture image
is given depending on a priori prescribed percentage
of positive filtering results.
2.1 The General Scheme
The general scheme reflecting implementation of the
developed defect detection system for grey-level
texture images is presented in Fig. 1.
The whole defect detection process comprises five
steps, namely (Fig. 1): (1) evaluation of discrete
wavelet (DWT) spectra
j
Y for defect-free texture
images (contained in the training set)
j
X
(1,2,,)jr=  of size NN× (
2, N
n
Nn=∈
);
(2) task-oriented partitioning of the discrete DWT
spectrum
j
Y
({1,2,,})jr∈  into a finite number of
non-overlapping regions
12
(, )iiℜ
12
(, 0,1, ,)ii n=  ;
(3) statistical analysis of wavelet coefficients falling
into a particular region
12
(, )iiℜ
12
(, {0,1, ,})ii n∈  ;
(4) generation of parameterized defect detection
criteria (sigma intervals)
12
(, )
pp
IIii=
, for all
regions
12
(, )iiℜ
12
( , 0,1, , ; [0.10, 0.99])ii np=∈ ;
(5) testing a texture image
test
X
.
2.2 Partitioning of the Discrete Wavelet
Spectrum of an Image
Consider a texture image
12
[( , )]
X
Xm m=
12
(, {0,1,, 1}, 2,
n
mm N N∈−=
N
).n ∈ Let
12
[( , )]YYkk=
12
(, {0,1, , 1})kk N∈− be its two-
dimensional discrete wavelet (DWT) spectrum.
The partitioning of the DWT spectrum
12
[( , )]YYkk= into a finite number of non-
intersecting subsets (regions)
12
(, )iiℜ
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
144

12
(, {0,1, ,})ii n∈  is based on the following two
observations, namely (Fig. 2):
1. Indices
1
k and/or
2
k of any wavelet coefficient
1
(,0)Yk ,
2
(0, )Yk or
12
(, )Yk k
12
(, {1,2, , 1}kk N∈− ),
can be uniquely represented in the form
1
11
2
ni
kj
−
=+,
2
22
2
ni
kj
−
=+, where
12
,{1,2,,}ii n∈  ,
1
1
{0,1, , 2 1}
ni
j
−
∈−
and
2
2
{0,1, , 2 1}
ni
j
−
∈−
.
2. The numerical values of all wavelet
coefficients, falling into a particular region,
(0,0)ℜ ,
1
(,0)iℜ ,
2
(0, )iℜ or
12
(, )iiℜ
12
(, {1,2, ,})ii n=  , are
specified by pixel values of image blocks of size
22
nn
× ,
1
22
i
n
× ,
2
22
i
n
× and
12
22
i
i
× , respectively.
The latter image blocks cover the whole texture
image
X
. Also, for Haar wavelets, these smaller
image blocks do not overlap, whereas for higher order
wavelets (Le Gall, Daubechies D4, etc. (Valantinas et
al., 2013)) partial overlapping is observed.
Figure 2: Partitioning of the DWT spectrum Y into a finite
number of non-intersecting regions (N = 4).
2.3 Generating Statistically-based
Defect Detection Criteria
Suppose,
12
{, , , }
r
X
XX is a collection (training
set) of good samples, randomly selected from some
total population
X
of defect-free texture images of
size
NN× (2
n
N = ,
N
n ∈ ), and
12
{, , , }
r
YY Y is
the corresponding set of their DWT spectra. In
implementing defect detection criteria for texture
images, the following algorithmic steps are
performed:
1. For all
1, 2, ,
s
r=  , the averaged values of
wavelet coefficients, falling into the regions
12
(, )iiℜ
(
12
,{0,1,,}ii n∈  ), are found:
(0,0) | (0,0) |
ss
YY=
1
1
1
21
11
2
0
1
(,0) | ( ,0)|
2
ni
ss
ni
j
Yi Yk
−
−
−
=
=

2
2
2
21
22
2
0
1
(0, ) | (0, ) |
2
ni
ss
ni
j
Yi Yk
−
−
−
=
=

21
12
21
2121
12 1 2
2
00
1
(, ) | ( , )|.
2
ni ni
ss
ni i
jj
Yii Ykk
−−
−−
−−
==
=

2. For each region
12
(, )iiℜ (
12
,0,1,,ii n=  ), using
sample values
112 212 12
((,), (,), , (,)),
r
Yii Y ii Yii
and applying the statistical analysis methods, the
statistical hypothesis on the type of the distribution
(normal, lognormal, exponential, etc.) of the mean
value (random variable)
12
(, )Yii , representing
precisely the same region of the total population
X
,
is tested.
3. Depending on the type of the distribution of the
mean value
12
(, )Yii (
12
,{0,1,,}ii n∈  ) and a priori
prescribed probability
p (
[0.10, 0.99]p ∈
), the
corresponding sigma interval
12
(, )
pp
I
Iii= is found,
namely: (1) for the normal distribution
(~(,)YNm σ ), (, )
p
Imtmt σσ =−⋅ +⋅, where
1
0
(2)tp
−
=Φ and
0
()tΦ is the Laplace function;
(2) for the lognormal distribution
(~ln(,))YNm σ ,
(, )
tt
p
Imm σσ =⋅
, where
1
0
(2)tp
−
=Φ ; (3) for the
exponential distribution
(~())YE λ ,
[0, )
p
It σ =⋅
,
where
ln (1 )tp=− − and 1 σ
λ
= .
2.4 Testing Texture Images
Let
test
X
be a test texture image of size NN×
(2
n
N = ,
N
n ∈ ). Let
test
Y be its discrete wavelet
(DWT) spectrum. This spectrum is partitioned into a
finite number of non-intersecting regions
12
(, )iiℜ
12
(, 0,1, ,)ii n=…, and the mean values
12
(, )
test
Yii of
wavelet coefficients, falling into
12
(, )iiℜ , are
calculated.
Taking into consideration a priori prescribed
value of the system’s parameter (probability)
p , the
defect detection criteria (sigma intervals)
12
(, )
pp
I
Iii=
12
(, 0,1, ,)ii n=  are selected.
Wavelet-based Defect Detection System for Grey-level Texture Images
145

The test image
test
X
is assumed to be defect-free,
provided the number of mean values
12
(, )
test
Yii
12
(, {0,1, ,})ii n∈  , falling into the respective sigma
intervals
12
(, )
p
Iii, is not less than
2
(1)pn+ .
Otherwise,
test
X
is assumed to be defective.
By selecting the value of
p , we are given a
possibility to control the risk boundary, i.e. we can
increase (decrease) the percentage of actually defect-
free images detected as defective or that of actually
defective images detected as defect-free).
The overall performance of the proposed defect
detection system can be improved by exploring only
a properly chosen subset of sigma intervals
12
(, )
pp
I
Iii=
12
(, 0,1, ,)ii n=  . Say, if some grid-
lines are visible in texture images, the usage of
intervals
12
(, )
pp
IIii= , with
12
, {0, , 1,..., }ii mm n∈+
(1 )mn<≤ , may serve the purpose because it
excludes comparison of less than
2
m
neighbouring
pixels of the texture image, in both the vertical and
the horizontal directions.
3 EXPERIMENTAL ANALYSIS
RESULTS AND DISCUSSION
To evaluate performance of the proposed texture
defect detection system, two sets of texture images,
taken from factories of Lithuania, have been selected
and processed, namely: defect-free glass sheet images
of size 256×256 (100 samples; Fig. 3, a) and defective
glass sheet images of the same size (100 samples; Fig.
3, b), as well as ceramic tile images of size 256×256
(100 defect-free samples and 100 defective samples;
Fig. 4).
All experiments have been implemented on a
personal computer using MatLab. Computer
simulation was performed on a PC with CPU Intel
Core i5-4200 U CPU@2.36Hz, 8GB of memory.
The statistically-based texture defect detection
criteria have been prepared and presented in both the
Haar and the Le Gall wavelet domains.
For each class of texture images, five experiments
were carried out. For each experiment, 50 defect-free
texture images (out of 100) and 50 defective texture
images (out of 100) were selected at random.
Experimental analysis results are presented in Table 1
(glass sheet images) and Table 2 (ceramic tile
images), where: TP – the percentage of actually
defective images detected as defective; FP – the
percentage of actually defect-free images detected as
defective; TN – the percentage of actually defect-free
images detected as defect-free; FN – the percentage
of actually defective images detected as defect-free.
To summarize the results obtained, i.e. to evaluate
performance of the proposed texture defect detection
system (Section 2), some secondary system’s
performance parameters, widely used in this area,
were introduced, namely: Specificity = TN/(TN+FP),
Sensitivity = TP/(TP+FN) and Accuracy =
(TP+TN)/(TP+TN+FP+FN).
(a) (b)
Figure 3: Glass sheet samples: (a) defect-free images; (b) defective images.
(a) (b)
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146

Figure 4: Ceramic tile samples: (a) defect-free images; (b) defective images.
Table 1: Glass sheet classification results using discrete Haar and Le Gall wavelet transforms.
Probability,
p
Discrete Haar wavelet transform (percentage) Discrete Le Gall wavelet transform (percentage)
Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5 Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5
0.99
TP 100 100 98 98 96 96 92 92 96 92
FP 2 0 2 4 2 42 38 42 40 38
TN 98 100 98 96 98 58 62 58 60 62
FN 0 0 2 2 4 4 8 8 4 8
0.95
TP 100 100 98 98 96 96 90 88 94 86
FP 8 6 8 8 6 42 36 40 36 36
TN 92 94 92 92 94 58 64 60 64 64
FN 0 0 2 2 4 4 10 12 6 14
0.90
TP 100 100 98 98 96 86 80 86 84 82
FP 14 14 12 16 10 44 36 34 36 30
TN 86 86 88 84 90 56 64 66 64 70
FN 0 0 2 2 4 14 20 14 16 18
Table 2: Ceramic tile classification results using discrete Haar and Le Gall wavelet transforms.
Probability,
p
Discrete Haar wavelet transform (percentage) Discrete Le Gall wavelet transform (percentage)
Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5 Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5
0.99
TP 100 98 96 98 100 98 96 100 96 98
FP 2 2 8 4 2 26 16 16 22 22
TN 98 98 92 96 98 74 84 84 78 78
FN 0 2 4 2 0 2 4 0 4 2
0.95
TP 98 98 96 96 100 100 98 100 98 98
FP 2 0 10 4 6 38 36 36 40 44
TN 98 100 90 96 94 62 64 64 60 56
FN 2 2 4 4 0 0 2 0 2 2
0.90
TP 96 90 94 96 100 100 98 100 98 98
FP 4 6 10 6 6 40 34 34 38 40
TN 96 94 90 94 94 60 66 66 62 60
FN 4 10 6 4 0 0 2 0 2 2
Table 3: Performance of the defect detection system, p = 0.99.
Test image
Discrete Haar wavelet domain Discrete Le Gall wavelet domain
Specificity Sensitivity Accuracy Specificity Sensitivity Accuracy
Glass sheets 0.98 0.98 0.98 0.60 0.94 0.77
Ceramic tiles 0.97 0.98 0.96 0.80 0.98 0.89
Table 4: Performance of the defect detection system,
p
=
0.95.
Test image
Discrete Haar wavelet domain Discrete Le Gall wavelet domain
Specificity Sensitivity Accuracy Specificity Sensitivity Accuracy
Glass sheets 0.93 0.98 0.96 0.62 0.91 0.76
Ceramic tiles 0.97 0.98 0.96 0.61 0.99 0.80
Table 5: Performance of the defect detection system,
p
= 0.90.
Test image
Discrete Haar wavelet domain Discrete Le Gall wavelet domain
Specificity Sensitivity Accuracy Specificity Sensitivity Accuracy
Glass sheets 0.87 0.98 0.93 0.64 0.84 0.74
Ceramic tiles 0.94 0.95 0.94 0.63 0.99 0.81
The averaged values of the above secondary
performance parameters (covering all five
experiments), for both classes of texture images, are
presented in Tables 3, 4 and 5.
First of all, we notice that (Tables 3, 4 and 5),
nearly for all indicated values of the probability
p ,
the Haar wavelets perform better than the Le Gall
wavelets. The only exception, the sensitivity values
for the class of ceramic tiles: 0.98, for
p = 0.99, and
0.99, for
p ∈ {0.90, 0.95}. So, Le Gall wavelets
should be explored if one is interested in the selection
of high quality products (ceramic tiles), i.e. in
Wavelet-based Defect Detection System for Grey-level Texture Images
147

eliminating all defective tiles, even at the expense of
some defect-free tiles.
Secondly, let us observe that comparison of the
above results with analogous results obtained using
other approaches and other texture defect detection
schemes is complicated enough. The necessary
precondition is to use the same texture image
databases. Otherwise, the comparison is not impartial.
Despite this fact, some parallels can be drawn. For
instance, in reference (Jin et al., 2011), we found that
the glass defect inspection technology based on Dual
CCFL performs with success rate (accuracy) 0.99. In
(Zhao et al., 2012), the task-oriented application of
digital image processing leads to the averaged
accuracy 0.916, in the same class of texture images.
Segmentation-based classification of pavement tiles
(Nguyen et al., 2011) gives the accuracy 0.93. In (de
Andrade et. al., 2011), the authors explore infrared
images and artificial neural network, and the overall
accuracy is 0.926.
In connection with this, we here emphasize that
the texture defect detection rate (accuracy), obtained
in our experiments using discrete Haar wavelets, are
comparatively high, what allows us to state that the
developed defect detection system is worth attention
and can contribute to improving automated texture
inspection schemes in industry.
4 CONCLUSIONS
In this paper, a new wavelet-based defect detection
system for texture images is proposed. The proposed
system explores space localization properties of the
discrete wavelet (Haar, Le Gall, etc.) transform,
generates statistically-based texture defect detection
criteria and leaves space for controlling the risk.
The experimental analysis results, demonstrating
the use of the developed defect detection system for
the visual inspection of glass sheets, as well as
ceramic tiles, obtained from real factory environment,
showed that the averaged defect detection rate
(accuracy) of the system was high enough: 0.98 for
glass sheets, and 0.96, for ceramic tiles, provided the
discrete Haar wavelets are employed and the system’s
parameter
p = 0.99.
Based on our own experience, we here emphasize
that, for a particular class of texture images, diligent
and serious adaptation of the developed defect
detection system is necessary. In each case, not only
numerical values of the parameter
p but also various
task-oriented subsets of sigma intervals should be
looked through carefully.
Also, let us mention that the proposed defect
detection system has been applied to the inspection of
fabric scraps (textile images). The achieved defect
detection success rate (accuracy), on average, turned
out to be quite acceptable, i.e. 0.931 (Haar wavelet
domain), for
p = 0.975 (Vaidelienė et al., 2016).
Our nearest future work will focus on the analysis
of the potential relationship between the
mathematical measures (coarseness, directionality,
etc.), used to classify a given texture, and the choice
of the most appropriate subset of sigma intervals,
comprising the defect detection criterion (Section 2),
for the same texture. In parallels, we are to analyse
possibility and efficiency of the application of higher
order statistics (e.g. sample variance) to developing
wavelet-based texture defect detection criteria.
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