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)

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

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.

REFERENCES

Bissi, L., Baruffa. G., Placidi, P., Ricci, E., Scorzoni, A.,

2013. Automated defect detection in uniform and

structured fabrics using Gabor filters and PCA. Journal

of Visual Communication and Image Representation,

24, 838-845.

Bu, H. G., Wang, J., Huang, X. B., 2009. Fabric defect

detection based on multiple fractal features and support

vector data description. Engineering Applications of

Artificial Intelligence, 22(2), 224-235.

Bu, H.-G., Huang, X.-B., Wang, J., Chen, X., 2010.

Detection of fabric defects by auto-regressive spectral

analysis and support vector data description. Textile

Research Journal, 80(7), 579-589.

Chan, C., Pang, G., 2000. Fabric defect detection by Fourier

analysis. IEEE Transactions on Industry Applications,

36(5), 1267-1276.

Chen, J., Jain, A. K., 1988. A structural approach to identify

defects in textural images. In Proceedings of IEEE

International Conference on Systems, Man and

Cybernetics, Beijing.

de Andrade, R. M., Eduardo, A. C., 2011. Methodology for

automatic process of the fired ceramic tile‘s internal

defect using ir images and artificial neural network.

Journal of the Brazilian Society of Mechanical Sciences

and Engineering, 33(1), 67-73.

Dogandzic, A., Eua-anant, N., Zhang, B. H., 2005. Defect

detection using hidden Markov random fields. In AIP

Conference Proceedings, 760, 704-711.

Ghazini, M., Monadjemi, A., Jamshidi, K., 2009. Defect

detection of tiles using 2D wavelet transform and

statistical features. International Journal of Electrical,

Computer, Energetic, Electronic and Communication

Engineering, 3(1), 89-92.

Gururajan, A., Sari-Sarraf, H., Hequet, E. F., 2008.

Statistical approach to unsupervised defect detection

and multiscale localization in two texture images.

Optical Engineering, 47(2).

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

148

Han, Y., Shi, P., 2007. An adaptive level-selecting wavelet

transform for texture defect detection. Image and

Vision Computing, 25, 1239-1248.

Iivarinen, J., 2000. Surface defect detection with histogram-

based texture features. In Proc. SPIE 4197, Intelligent

Robots and Computer Vision XIX: Algorithms,

Techniques, and Active Vision.

Jia, H. B., Murphey, Y. L., Shi, J. J., Chang, T. S., 2014. An

intelligent real-time vision system for surface defect

detection. In Proceedings of the 17th International

Conference on Pattern Recognition, 239-242.

Jin, Y., Wang, Z. B., Zhu, L. Q., Yang, J. L., 2011. Research

on in-line glass defect inspection technology based on

Dual CCFL. Procedia Engineering, 15, 1797-1801.

Karimi, M. H., Asemani, D., 2014. Surface defect detection

in tiling industries using digital image processing

methods: Analysis and evaluation. ISA Transactions,

53, 834-844.

Kim, S. C., Kang, T. J., 2006. Automated defect detection

system using wavelet packet frame and Gaussian

mixture model. Journal of the Optical Society of

America A-Optics Image Science and Vision, 23(11),

2690-2701.

Kumar, A., 2008. Computer-vision-based fabric defect

detection: a survey. IEEE Transactions on Industrial

Electronics, 55(1), 348-363.

Latif-Amet, A., Ertüzün, A., Erçil, A., 2000. An efficient

method for texture defect detection: sub-band domain

co-occurrence matrices. Image and Vision Computing,

18, 543-553.

Li, Y. D., Ai, J. X., Sun C. Q., 2013. Online fabric defect

inspection using smart visual sensors. Sensors, 13(4),

4659-4673.

Lin, H. D., 2007. Automated visual inspection of ripple

defects using wavelet characteristic based multivariate

statistical approach. Image and Vision Computing,

25(11), 1785-1801.

Mak, K. L., Peng, P., Yiu, K. F. C., 2009. Fabric defect

detection using morphological filters. Image and Vision

Computing, 27, 1585-1592.

Mak, K. L., Peng, P., Yiu, K. F. C., 2013. Fabric defect

detection using multi-level tuned-matched Gabor

filters. Journal of Industrial and Management

Optimization, 8(2), 325-341.

Ngan, H. Y. T., Pang, G. K. H., Yung, N. H. C., 2011.

Automated fabric defect detection - A review. Image

and Vision Computing, 29, 442-458.

Ngan, H. Y. T., Pang, G. K. H., Yung, N. H. C., Ng, M. K.,

2005. Wavelet based methods on patterned fabric

defect detection. Pattern Recognition, 38, 559-576.

Nguyen, T. S., Begot, S., Duculty, F., Avila, M., 2011.

Free-form anisotropy: a new method for crack detection

on pavement surface images. In 18th IEEE

International Conference on Image Processing.

Raheja, J. L., Kumar, S., Chaudhary, A., 2013. Fabric

defect detection based on GLCM and Gabor filter: a

comparison. Journal for Light and Electron Optics,

124, 6469-6474.

Timm, F., Barth, E., 2011. Non-parametric texture defect

detection using Weibull features. In Proc. SPIE 7877,

Image Processing: Machine Vision Applications.

Tsai, D. M., Kuo, C. C., 2007. Defect detection in

inhomogeneously textured sputtered surfaces using 3D

Fourier image reconstruction. Machine Vision and

Applications, 18(6), 383-400.

Vaidelienė, G., Valantinas, J., Ražanskas, P., 2016 (to

appear). On the use of discrete wavelets in

implementing controllable defect detection system for

texture images. Information Technology and Control.

Valantinas, J., Kančelkis, D., Valantinas, R., Viščiūtė, G.,

2013. Improving space localization properties of the

discrete wavelet transform. Informatica, 24(4), 657-

674.

Wen, W., Xia, A., 1999. Verifying edges for visual inspection

purposes. Pattern Recognition Letters, 20, 315-328.

Xie, X., 2008. Review of recent advances in surface defect

detection using texture analysis techniques. Electronic

Letters on Computer Vision and Image Analysis, 7(3),

1-22.

Yuen, C. W. M., Wong, W. K., Qian, S. Q., Chan, L. K.,

Fung, E. H. K., 2009. A hybrid model using genetic

algorithm and neural network for classifying garment

defects. Expert Systems with Applications, 36,

2037-2047.

Zhao, X. F., Yang, J., Zhang, G. B., 2012. Glass defect

detection based on image processing. In 4th

International Conference on Software Technology and

Engineering, 155-159.

Wavelet-based Defect Detection System for Grey-level Texture Images

149