Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 101837 12 pageshttpdxdoiorg1011552013101837

Research ArticleAutomated Visual Inspection of Ship Hull Surfaces Using theWavelet Transform

Carlos Fernaacutendez-Isla Pedro J Navarro and Pedro Mariacutea Alcover

Universidad Politecnica de Cartagena Campus Muralla del Mar 30202 Cartagena Spain

Correspondence should be addressed to Carlos Fernandez-Isla carlosfernandezupctes

Received 22 February 2013 Revised 29 April 2013 Accepted 6 May 2013

Academic Editor Wen-Jer Chang

Copyright copy 2013 Carlos Fernandez-Isla et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Anewonline visual inspection technique is proposed based on awavelet reconstruction schemeover images obtained from the hullThis type of visual inspection to detect defects in hull surfaces is commonly carried out at shipyards by human inspectors before thehull repair task starts We propose the use of Shannon entropy for automatic selection of the band for image reconstruction whichprovides a low decomposition level thus avoiding excessive degradation of the image allowing more precise defect segmentationThe proposed method here is capable of on-line assisting to a robotic system to perform grit blasting operations over damage areasof ship hulls This solution allows a reliable and cost-effective operation for hull grit spot blasting A prototype of the automatedblasting system has been developed and tested in the Spanish NAVANTIA shipyards

1 Introduction

Main shipsrsquo maintenance care consists of periodical (every4-5 years) hull treatment which includes blasting worksblasting consists in projecting a high-pressure jet of abrasivematter (typically water or grit) onto a surface to removeadherences or rust tracesThe object of this task is tomaintainhull integrity guarantee navigational safety conditions andassure that the surface offers little resistance to the waterin order to reduce fuel consumption That object can beachieved by grit blasting [1] or ultra-high pressure waterjetting [2] In most cases these techniques are applied usingmanual or semiautomated procedures with the help of robo-tized devices [3] In either case defects are detected by meansof human operators this is therefore a subjective task andhence vulnerable to cumulative operator fatigue and highlydependent on the experience of the personnel performingthe task Figure 1 shows a view of shiprsquos hulls under repair atNAVANTIArsquos shipyards

From an operational point of view there are two workingmodes full blasting and spot blasting Full blasting consists ofblasting the entire hull of the ship while spot blasting consistsof blasting numerous isolated areas where corrosion has beenobserved Spot blasting is the most demanded operation dueto cost saving reasons This second working mode demands

very precise information about position size and shape ofdamaged portions of the hull to make robotic devices [3ndash5]to achieve maximum efficiency

This paper proposes a computer vision algorithm whichequips a machine vision system (see Figure 2) capable forprecisely detecting defects in ship hulls which is simpleenough to be implemented in such a way as to meet the real-time requirements for the application

Because of the textured appearance of the hullrsquos surfaceunder inspection (see Figures 1(c) and 1(d)) we have usedthe wavelet transform and the developed computer visionalgorithm includes an image reconstruction approach basedon automatic selection of the optimal wavelet transformresolution level using Shannon entropy

2 Defect Detection in Textured Surfaces

Texture is a very important characteristic when identifyingdefects or flaws as it provides important information fordefect detection In fact the task of detecting defects has beenlargely seen as a texture analysis problem Figure 3 showsseveral texture images from ship hull surfaces

In his review Xie [6] classified texture analysis techniquesfor defect detection in four categories statistical approaches

2 Mathematical Problems in Engineering

(a) Shaped hull (b) Flat hull

(c) Damaged portions (d) Detail visual appearance

Figure 1 Shiprsquos hulls at a repair yard

Wirelessaccess point

CPU

Interface tocontrol sys

PCI b

us

Optic fiberto IEEE 1394

converter

Framegrabber

AnalogIO

Optic fiberIEEE 1394

to optic fiberconverter

Camera

Distance from camera to hull

Primarymechanical

system

U

DR

L

Secondarymechanical

system

Hull surface

Cleaninghead

Seconmech

syst

Cleaninhead

PROFIBUS

Figure 2 Machine vision system for hull blasting

structural approaches filter based approaches and modelbased approaches In his review of fabric defect detectionsimilarly Kumar [7] classified the proposed solutions intothree categories statistical spectral and model based In hisreview of automated defect detection in fabric Ngan et al[8] classified defect detection techniques in textured fabricinto nonmotif-based andmotif-based approachesThemotif-based approach [9] uses the symmetry property of motifs tocalculate the energy of moving subtraction and its varianceamong different motifs Many defect detection methodsusually use clustering techniques which are mainly based ontexture feature extraction and texture classifications Thesefeatures are collated using methods such as cooccurrence

matrix [10] Fourier transform [11] Gabor transform [12] orthe wavelet transform [13]

Spectral-approach methods for texture analysis charac-terize the frequency contents of a texture imagemdashFouriertransformmdashor provide spatial-frequency analysismdashGaborfilters wavelets A two-dimensional spectrum of a visualtexture frequently contains information about the periodicityand directionality of the texture pattern For example atexture with a coarse appearance analysed from the spectralpoint of view shows high-frequency components while atexture with a fine appearance shows low-frequency compo-nents The analytical methods based on Fourier transformshow good results in texture patterns with high regularity

Mathematical Problems in Engineering 3

Figure 3 Texture images from shipsrsquo hull surface

andor directionality but they are limited by a lack ofspatial localization In this field Gabor filters provide betterspatial localization although their utility in natural texturesis limited because there is no single filter resolution thatcan localize a structure The wavelet transform has someadvantages over the Gabor transform such as the fact thatthe variation of the spatial resolution makes it possible torepresent the textures in the appropriate scale as well as tochoose from a wide range of wavelet functions

3 The Wavelet Transform for Defect Detection

The suitability of wavelet transforms for use in image analysisis well established a representation in terms of the frequencycontent of local regions over a range of scales provides an idealframework for the analysis of image features which in generalare of different size and can often be characterised by theirfrequency domain properties [14] This makes the wavelettransform an attractive option when attempting defect detec-tion in textured products as reported by Truchetet and Lali-gant [15] in his review of industrial applications of wavelet-based image processing He reported different uses of waveletanalysis in successful machine vision applications detectingdefects for manufacturing applications for the productionof furniture textiles integrated circuits and so forth fromtheir wavelet transformation and vector quantization-relatedproperties of the associated wavelet coefficients printingdefect identification and classification (applied to printeddecoration and tampon printed images) by analysing thefractal properties of a textured image online inspection ofthe loom under construction using a specific class of the2D discrete wavelet transform (DWT) called the multiscalewavelet representation with the objectives of attenuating thebackground texture and accentuating the defects online fab-ric inspection device performing an independent componentanalysis on a subband decomposition provided by a 2-levelDWT in order to increase the defect detection rate

The review of the literature shows two categories of defectdetection methods based on wavelet transform The firstcategory includes direct thresholdingmethods [10 11] whosedesign is based on the fact that texture background can beattenuated by the wavelet decomposition If we remove thetexture pattern from real texture it is feasible to use existingdefect detecting techniques for nontexture images suchas thresholding techniques [16] Textural features extractedfrom wavelet-decomposed images are another categorywhich is widely used for defect detection [17 18] Featuresextracted from the texture patterns are used as featurevectors to feed a classifier (Bayer Euclidean distance NeuralNetworks or Support Vector Machines) which has unavoid-able drawbacks when dealing with the vast image data

obtained during inspection tasks For instance proximity-based methods tend to be computationally expensive andthere is no straightforward way of defining a meaningfulstopping criterion for data fusion (or division) Often thelearning-based classifiers need to be trained by the nondefectfeatures which is a troublesome and usually time consumingprocedure thus limiting its real-time applications [10] Forthis reason we have focused on direct thresholding methodsThe use of direct thresholding presents amain challenge howto select the decomposition level On the other hand directthresholding presents two main drawbacks (1) an excessivewavelet decomposition level produces a fusion of defects withthe texture pattern and (2) a wrong reconstruction schemeproduces false positives when defects are detected

The work presented here is based on the authorsrsquo researchon previous works [10 19] and addresses abovementioneddrawbacks by a new approach based on Shannon Entropycalculation Its main contribution is the formulation of anovel use of the normalized Shannon Entropy calculatedon the different detail subimages to determine the optimaldecomposition level in textures with low directionality Forthis purpose we propose to calculate the optimal decomposi-tion level as the maximum of the ratio between the entropyof the approximation subimage and the total entropy as thesum of entropies calculated for every subimage

31 Wavelet Decomposition For an image 119891(119909 119910) of size119872times119873 pixels each level of wavelet decomposition is obtainedby applying two filters a low-pass filter (L) and a high-pass filter (H) The different combinations of these filtersproduce four images that are here denotedwith the subscriptsLL LH HL and HH In the first decomposition level foursubimages or bands are produced one smooth image alsocalled approximation 119891(1)LL (119909 119910) that represents an approxi-mation of the original image 119891(119909 119910) and three detail subim-ages 119891(1)LH (119909 119910) 119891(1)HL (119909 119910) and 119891(1)HH (119909 119910) which representthe horizontal vertical and diagonal details respectivelyWith this notation 119891(0)LL (119909 119910) represents the original image119891(119909 119910) and 119891

(119895)

LL (119909 119910) represent the approximation image inthe decomposition level 119895 From each decomposition level119891(119895)

LL (119909 119910) we obtain four subimages designated here as119891(119895+1)

LL (119909 119910) 119891(119895+1)

LH (119909 119910) 119891(119895+1)

HL (119909 119910) and119891(119895+1)

HH (119909 119910) whichtogether form the decomposition level 119895 + 1 The pyramidalgorithm to obtain 119891

(119895)

LL (119909 119910) 119891(119895)

LH (119909 119910) 119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910) as well as the calculation of the inverse transformcan be found in [20] We will designate 119865(119909 119910) = 119882minus1[119891

(119895)

LL ]

as the inverse wavelet transform of a subimage 119891(119895)LL from theresolution level 119895 to level 0

4 Mathematical Problems in Engineering

(a)

LL LH

HL HH

(b)

LL LH

HL HH

(c)

LL LH

HL HH

(d)

Figure 4 Decomposition of an image from a damaged hull using Haar wavelet with two coefficients at three decomposition levels (a)original image (b) first decomposition level (c) second decomposition level and (d) third decomposition level

Figure 4 shows the wavelet decomposition for three con-veniently scaled levels (119895 = 3) of a statistical texture patternmdashpainted surfacemdashwith corrosion defects the different subim-ages or bands are shown (named LL LH HL andHH)Thesewere obtained after applying the different coefficients of thewavelet filters More specifically the image in Figure 4(a) wasdecomposed through the application of theHaarwavelet withtwo coefficients At level 119895 images of size (1198732119895) times (1198722119895)pixels are obtained by iterative application of the pyramidalgorithm Note also that the subimages corresponding to thedifferent decomposition levels are produced by successivelyapplying the low-pass and high-pass filters and reducing therows and columns by a factor of two

4 Entropy-Based Method for theAutomatic Selection of the WaveletDecomposition Level

In image processing entropy has been used by many authorsas part of the algorithmic development procedure There

are examples of the use of entropy in the programmingof thresholding algorithms [21] and image segmenting [22]as a descriptor for texture classification [23] as one ofthe parameters selected by Haralick et al for applicationto gray level concurrence matrixes and used for texturecharacterization [24] as an element in characteristic vectorgroups used for classification by Bayesian techniques [25]neuronal networks [26] compact support vectors [27] andso forth

41 Automatic Selection of the Appropriate DecompositionLevel In this work we propose a novel approach for theautomatic selection of the appropriate decomposition levelby means of Shannon entropy The entropy function wasused to identify the resolution level that provides the mostinformation about defects in real textures For this pur-pose the intensity levels of the subimages of the wavelettransform were considered as random samples The conceptof information entropymdashShannon entropymdashdescribes howmuch randomness (or uncertainty) there is in a signal or animage in other words how much information is provided

Mathematical Problems in Engineering 5

119895 = 0 119895 = 1 119895 = 2 119895 = 3 119895 = 4

(a)

(b)

(c)

(d)

(e)

Figure 5 Approximation subimages (119891(119895)LL ) of four wavelet decomposition levels for different images ((a) H225 (b) H34 (c) H241 (d) H137and (e) H10) from portions of shiprsquos hulls

by the signal or image In terms of physics the greater theinformation entropy of the image is the higher its quality willbe [28]

Figure 5 shows how the texture pattern degrades as thedecomposition level increasesThis degradation is distributedamong the different decomposition levels depending on thetexture nature and can be quantified bymeans of the Shannonentropy

The Shannon entropy function [28 29] is calculatedaccording to the expression

119904 (119883) = minus119879

sum119894=1

119901 (119909119894) log119901 (119909119894) (1)

where 119883 = 1199091 1199092 119909119879 is a set of random variableswith 119879 outcomes and 119901(119909119894) is the probability of occurrenceassociated with 119909119894

For a 256-gray-level image of size 119873119905 pixels we definea set of random variables 119883 = 1199091 1199092 119909119894 119909256 asthe number of pixels in the image that have gray level 119894 Theprobability of this random variable 119909119894 is calculated as thenumber of occurrences hist[119909119894] divided by the total numberof pixels119873119905

119901 (119909119894) =hist [119909119894]

119873119905 (2)

6 Mathematical Problems in Engineering

To calculate the value of the Shannon entropy on theapproximation subimage (119891(119895)LL (119909 119910)) and on the horizont-al vertical and diagonal detail subimages (119891

(119895)

LH (119909 119910)

119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910)) in each decomposition level 119895 weobtain first the inverse wavelet transform of every subimageand then we apply (3)

119904119895

LL = 119904 [119882minus1 [119891(119895)

LL (119909 119910)]]

119904119895

LH = 119904 [119882minus1 [119891(119895)

LH (119909 119910)]]

119904119895

HL = 119904 [119882minus1 [119891(119895)

HL (119909 119910)]]

119904119895

HH = 119904 [119882minus1 [119891(119895)

HH (119909 119910)]]

(3)

The normalized entropy of each subimage for a decom-position level 119895 has been calculated as

119878119895119904 =1

119873119895

pixels

sum119909

sum119910

119904119895

LL (119909 119910)

119878119895

ℎ=

1

119873119895

pixels

sum119909

sum119910

119904119895

LH (119909 119910)

119878119895V =1

119873119895

pixels

sum119909

sum119910

119904119895

HL (119909 119910)

119878119895

119889=

1

119873119895

pixels

sum119909

sum119910

119904119895

HH (119909 119910)

(4)

where 119873119895

pixels is the number of pixels at each decompositionlevel 119895 Table 1 shows the values for Shannon entropy calcu-lated for images of Figure 5

Shannon entropy brings us information about theamount of texture pattern that remains after every decompo-sition level Considering (2) entropy provides ameasurementof the histogram distribution the higher the entropy thegreater the histogram uniformity that is a greater amountof texture pattern is contained in the image As the decom-position level increases the texture pattern is being removedthat is the information content decreases so the histogramdistribution gains uniformity An optimal reconstructionscheme would eliminate the texture pattern without loss ofdefect information To determine this optimal decompositionlevel we use a ratio 119877119895 (see (5)) between the entropy of theapproximation subimage and the sum of the entropies forall detail subimages so 119877119895 indicates how much informationabout the texture pattern is contained in decomposition level119895 Variations in this ratio allow detecting changes in theamount of information about the texture pattern between twoconsecutive decomposition levels

119877119895 =119878119895119904

119878119895119904 + 119878119895

ℎ+ 119878119895V + 119878119895

119889

119895 = 1 2 (5)

The goal is to find the optimal decomposition level whichprovides the maximum variation among two consecutive 119877119895

Table 1 Normalized entropies of four decomposition levels fortextures of Figure 5

Decomposition level 119895 119878 119895119904 119878119895

ℎ119878 119895119907 119878

119895

119889

H225

119895 = 1 000011 000008 000007 000004119895 = 2 000048 000042 000042 000037119895 = 3 000200 000172 000168 000179119895 = 4 000796 000750 000681 000716

H34

119895 = 1 000011 000007 000008 000006119895 = 2 000046 000038 000039 000038119895 = 3 000185 000179 000169 000186119895 = 4 000732 000750 000662 000698

H241

119895 = 1 000011 000007 000007 000005119895 = 2 000046 000038 000037 000036119895 = 3 000194 000159 000151 000164119895 = 4 000763 000669 000640 000643

H137

119895 = 1 000011 000007 000006 000004119895 = 2 000047 000028 000027 000031119895 = 3 000191 000127 000132 000118119895 = 4 000726 000593 000581 000524

H10

119895 = 1 000013 000004 000004 000002119895 = 2 000057 000035 000037 000025119895 = 3 000214 000190 000182 000140119895 = 4 000841 000711 000737 000665

values because this indicates that in decomposition level 119895the texture pattern still present in level 119895minus1has been removedkeeping useful information (defects)

For this purpose we define ADR119895 as the differencebetween two consecutive 119877119895 values (see (6)) The optimaldecomposition level 119869lowast is calculated as the value of 119895 forwhichADR119895 takes a maximum value This maximum value pointsout the greatest variation of information content among twoconsecutive decomposition levels which means that bothdecomposition levels are sufficiently separated in terms oftexture pattern information content and the decompositionprocess should end For decomposition levels 119895 lt 119869lowast ADR119895indicates that significant texture pattern information stillremains in the approximation subimage and the decom-position process should continue For decomposition levels119895 gt 119869lowast ADR119895 indicates that the approximation subimageis oversmoothed and the reconstruction result from suchsmooth approximation subimage will cause defect loss

ADR119895 = 0 119895 = 1

119877119895 minus 119877119895minus1 119895 = 2

119869lowast = argmax119895

(10038161003816100381610038161003816ADR119895

10038161003816100381610038161003816)

(6)

Table 2 shows values for 119877119895 coefficients at every imagedecomposition level (119895) for the different textures shown inFigure 5 together with the ADR119895 values

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

(a) Shaped hull (b) Flat hull

(c) Damaged portions (d) Detail visual appearance

Figure 1 Shiprsquos hulls at a repair yard

Wirelessaccess point

CPU

Interface tocontrol sys

PCI b

us

Optic fiberto IEEE 1394

converter

Framegrabber

AnalogIO

Optic fiberIEEE 1394

to optic fiberconverter

Camera

Distance from camera to hull

Primarymechanical

system

U

DR

L

Secondarymechanical

system

Hull surface

Cleaninghead

Seconmech

syst

Cleaninhead

PROFIBUS

Figure 2 Machine vision system for hull blasting

structural approaches filter based approaches and modelbased approaches In his review of fabric defect detectionsimilarly Kumar [7] classified the proposed solutions intothree categories statistical spectral and model based In hisreview of automated defect detection in fabric Ngan et al[8] classified defect detection techniques in textured fabricinto nonmotif-based andmotif-based approachesThemotif-based approach [9] uses the symmetry property of motifs tocalculate the energy of moving subtraction and its varianceamong different motifs Many defect detection methodsusually use clustering techniques which are mainly based ontexture feature extraction and texture classifications Thesefeatures are collated using methods such as cooccurrence

matrix [10] Fourier transform [11] Gabor transform [12] orthe wavelet transform [13]

Spectral-approach methods for texture analysis charac-terize the frequency contents of a texture imagemdashFouriertransformmdashor provide spatial-frequency analysismdashGaborfilters wavelets A two-dimensional spectrum of a visualtexture frequently contains information about the periodicityand directionality of the texture pattern For example atexture with a coarse appearance analysed from the spectralpoint of view shows high-frequency components while atexture with a fine appearance shows low-frequency compo-nents The analytical methods based on Fourier transformshow good results in texture patterns with high regularity

Mathematical Problems in Engineering 3

Figure 3 Texture images from shipsrsquo hull surface

andor directionality but they are limited by a lack ofspatial localization In this field Gabor filters provide betterspatial localization although their utility in natural texturesis limited because there is no single filter resolution thatcan localize a structure The wavelet transform has someadvantages over the Gabor transform such as the fact thatthe variation of the spatial resolution makes it possible torepresent the textures in the appropriate scale as well as tochoose from a wide range of wavelet functions

3 The Wavelet Transform for Defect Detection

The suitability of wavelet transforms for use in image analysisis well established a representation in terms of the frequencycontent of local regions over a range of scales provides an idealframework for the analysis of image features which in generalare of different size and can often be characterised by theirfrequency domain properties [14] This makes the wavelettransform an attractive option when attempting defect detec-tion in textured products as reported by Truchetet and Lali-gant [15] in his review of industrial applications of wavelet-based image processing He reported different uses of waveletanalysis in successful machine vision applications detectingdefects for manufacturing applications for the productionof furniture textiles integrated circuits and so forth fromtheir wavelet transformation and vector quantization-relatedproperties of the associated wavelet coefficients printingdefect identification and classification (applied to printeddecoration and tampon printed images) by analysing thefractal properties of a textured image online inspection ofthe loom under construction using a specific class of the2D discrete wavelet transform (DWT) called the multiscalewavelet representation with the objectives of attenuating thebackground texture and accentuating the defects online fab-ric inspection device performing an independent componentanalysis on a subband decomposition provided by a 2-levelDWT in order to increase the defect detection rate

The review of the literature shows two categories of defectdetection methods based on wavelet transform The firstcategory includes direct thresholdingmethods [10 11] whosedesign is based on the fact that texture background can beattenuated by the wavelet decomposition If we remove thetexture pattern from real texture it is feasible to use existingdefect detecting techniques for nontexture images suchas thresholding techniques [16] Textural features extractedfrom wavelet-decomposed images are another categorywhich is widely used for defect detection [17 18] Featuresextracted from the texture patterns are used as featurevectors to feed a classifier (Bayer Euclidean distance NeuralNetworks or Support Vector Machines) which has unavoid-able drawbacks when dealing with the vast image data

obtained during inspection tasks For instance proximity-based methods tend to be computationally expensive andthere is no straightforward way of defining a meaningfulstopping criterion for data fusion (or division) Often thelearning-based classifiers need to be trained by the nondefectfeatures which is a troublesome and usually time consumingprocedure thus limiting its real-time applications [10] Forthis reason we have focused on direct thresholding methodsThe use of direct thresholding presents amain challenge howto select the decomposition level On the other hand directthresholding presents two main drawbacks (1) an excessivewavelet decomposition level produces a fusion of defects withthe texture pattern and (2) a wrong reconstruction schemeproduces false positives when defects are detected

The work presented here is based on the authorsrsquo researchon previous works [10 19] and addresses abovementioneddrawbacks by a new approach based on Shannon Entropycalculation Its main contribution is the formulation of anovel use of the normalized Shannon Entropy calculatedon the different detail subimages to determine the optimaldecomposition level in textures with low directionality Forthis purpose we propose to calculate the optimal decomposi-tion level as the maximum of the ratio between the entropyof the approximation subimage and the total entropy as thesum of entropies calculated for every subimage

31 Wavelet Decomposition For an image 119891(119909 119910) of size119872times119873 pixels each level of wavelet decomposition is obtainedby applying two filters a low-pass filter (L) and a high-pass filter (H) The different combinations of these filtersproduce four images that are here denotedwith the subscriptsLL LH HL and HH In the first decomposition level foursubimages or bands are produced one smooth image alsocalled approximation 119891(1)LL (119909 119910) that represents an approxi-mation of the original image 119891(119909 119910) and three detail subim-ages 119891(1)LH (119909 119910) 119891(1)HL (119909 119910) and 119891(1)HH (119909 119910) which representthe horizontal vertical and diagonal details respectivelyWith this notation 119891(0)LL (119909 119910) represents the original image119891(119909 119910) and 119891

(119895)

LL (119909 119910) represent the approximation image inthe decomposition level 119895 From each decomposition level119891(119895)

LL (119909 119910) we obtain four subimages designated here as119891(119895+1)

LL (119909 119910) 119891(119895+1)

LH (119909 119910) 119891(119895+1)

HL (119909 119910) and119891(119895+1)

HH (119909 119910) whichtogether form the decomposition level 119895 + 1 The pyramidalgorithm to obtain 119891

(119895)

LL (119909 119910) 119891(119895)

LH (119909 119910) 119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910) as well as the calculation of the inverse transformcan be found in [20] We will designate 119865(119909 119910) = 119882minus1[119891

(119895)

LL ]

as the inverse wavelet transform of a subimage 119891(119895)LL from theresolution level 119895 to level 0

4 Mathematical Problems in Engineering

(a)

LL LH

HL HH

(b)

LL LH

HL HH

(c)

LL LH

HL HH

(d)

Figure 4 Decomposition of an image from a damaged hull using Haar wavelet with two coefficients at three decomposition levels (a)original image (b) first decomposition level (c) second decomposition level and (d) third decomposition level

Figure 4 shows the wavelet decomposition for three con-veniently scaled levels (119895 = 3) of a statistical texture patternmdashpainted surfacemdashwith corrosion defects the different subim-ages or bands are shown (named LL LH HL andHH)Thesewere obtained after applying the different coefficients of thewavelet filters More specifically the image in Figure 4(a) wasdecomposed through the application of theHaarwavelet withtwo coefficients At level 119895 images of size (1198732119895) times (1198722119895)pixels are obtained by iterative application of the pyramidalgorithm Note also that the subimages corresponding to thedifferent decomposition levels are produced by successivelyapplying the low-pass and high-pass filters and reducing therows and columns by a factor of two

4 Entropy-Based Method for theAutomatic Selection of the WaveletDecomposition Level

In image processing entropy has been used by many authorsas part of the algorithmic development procedure There

are examples of the use of entropy in the programmingof thresholding algorithms [21] and image segmenting [22]as a descriptor for texture classification [23] as one ofthe parameters selected by Haralick et al for applicationto gray level concurrence matrixes and used for texturecharacterization [24] as an element in characteristic vectorgroups used for classification by Bayesian techniques [25]neuronal networks [26] compact support vectors [27] andso forth

41 Automatic Selection of the Appropriate DecompositionLevel In this work we propose a novel approach for theautomatic selection of the appropriate decomposition levelby means of Shannon entropy The entropy function wasused to identify the resolution level that provides the mostinformation about defects in real textures For this pur-pose the intensity levels of the subimages of the wavelettransform were considered as random samples The conceptof information entropymdashShannon entropymdashdescribes howmuch randomness (or uncertainty) there is in a signal or animage in other words how much information is provided

Mathematical Problems in Engineering 5

119895 = 0 119895 = 1 119895 = 2 119895 = 3 119895 = 4

(a)

(b)

(c)

(d)

(e)

Figure 5 Approximation subimages (119891(119895)LL ) of four wavelet decomposition levels for different images ((a) H225 (b) H34 (c) H241 (d) H137and (e) H10) from portions of shiprsquos hulls

by the signal or image In terms of physics the greater theinformation entropy of the image is the higher its quality willbe [28]

Figure 5 shows how the texture pattern degrades as thedecomposition level increasesThis degradation is distributedamong the different decomposition levels depending on thetexture nature and can be quantified bymeans of the Shannonentropy

The Shannon entropy function [28 29] is calculatedaccording to the expression

119904 (119883) = minus119879

sum119894=1

119901 (119909119894) log119901 (119909119894) (1)

where 119883 = 1199091 1199092 119909119879 is a set of random variableswith 119879 outcomes and 119901(119909119894) is the probability of occurrenceassociated with 119909119894

For a 256-gray-level image of size 119873119905 pixels we definea set of random variables 119883 = 1199091 1199092 119909119894 119909256 asthe number of pixels in the image that have gray level 119894 Theprobability of this random variable 119909119894 is calculated as thenumber of occurrences hist[119909119894] divided by the total numberof pixels119873119905

119901 (119909119894) =hist [119909119894]

119873119905 (2)

6 Mathematical Problems in Engineering

To calculate the value of the Shannon entropy on theapproximation subimage (119891(119895)LL (119909 119910)) and on the horizont-al vertical and diagonal detail subimages (119891

(119895)

LH (119909 119910)

119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910)) in each decomposition level 119895 weobtain first the inverse wavelet transform of every subimageand then we apply (3)

119904119895

LL = 119904 [119882minus1 [119891(119895)

LL (119909 119910)]]

119904119895

LH = 119904 [119882minus1 [119891(119895)

LH (119909 119910)]]

119904119895

HL = 119904 [119882minus1 [119891(119895)

HL (119909 119910)]]

119904119895

HH = 119904 [119882minus1 [119891(119895)

HH (119909 119910)]]

(3)

The normalized entropy of each subimage for a decom-position level 119895 has been calculated as

119878119895119904 =1

119873119895

pixels

sum119909

sum119910

119904119895

LL (119909 119910)

119878119895

ℎ=

1

119873119895

pixels

sum119909

sum119910

119904119895

LH (119909 119910)

119878119895V =1

119873119895

pixels

sum119909

sum119910

119904119895

HL (119909 119910)

119878119895

119889=

1

119873119895

pixels

sum119909

sum119910

119904119895

HH (119909 119910)

(4)

where 119873119895

pixels is the number of pixels at each decompositionlevel 119895 Table 1 shows the values for Shannon entropy calcu-lated for images of Figure 5

Shannon entropy brings us information about theamount of texture pattern that remains after every decompo-sition level Considering (2) entropy provides ameasurementof the histogram distribution the higher the entropy thegreater the histogram uniformity that is a greater amountof texture pattern is contained in the image As the decom-position level increases the texture pattern is being removedthat is the information content decreases so the histogramdistribution gains uniformity An optimal reconstructionscheme would eliminate the texture pattern without loss ofdefect information To determine this optimal decompositionlevel we use a ratio 119877119895 (see (5)) between the entropy of theapproximation subimage and the sum of the entropies forall detail subimages so 119877119895 indicates how much informationabout the texture pattern is contained in decomposition level119895 Variations in this ratio allow detecting changes in theamount of information about the texture pattern between twoconsecutive decomposition levels

119877119895 =119878119895119904

119878119895119904 + 119878119895

ℎ+ 119878119895V + 119878119895

119889

119895 = 1 2 (5)

The goal is to find the optimal decomposition level whichprovides the maximum variation among two consecutive 119877119895

Table 1 Normalized entropies of four decomposition levels fortextures of Figure 5

Decomposition level 119895 119878 119895119904 119878119895

ℎ119878 119895119907 119878

119895

119889

H225

119895 = 1 000011 000008 000007 000004119895 = 2 000048 000042 000042 000037119895 = 3 000200 000172 000168 000179119895 = 4 000796 000750 000681 000716

H34

119895 = 1 000011 000007 000008 000006119895 = 2 000046 000038 000039 000038119895 = 3 000185 000179 000169 000186119895 = 4 000732 000750 000662 000698

H241

119895 = 1 000011 000007 000007 000005119895 = 2 000046 000038 000037 000036119895 = 3 000194 000159 000151 000164119895 = 4 000763 000669 000640 000643

H137

119895 = 1 000011 000007 000006 000004119895 = 2 000047 000028 000027 000031119895 = 3 000191 000127 000132 000118119895 = 4 000726 000593 000581 000524

H10

119895 = 1 000013 000004 000004 000002119895 = 2 000057 000035 000037 000025119895 = 3 000214 000190 000182 000140119895 = 4 000841 000711 000737 000665

values because this indicates that in decomposition level 119895the texture pattern still present in level 119895minus1has been removedkeeping useful information (defects)

For this purpose we define ADR119895 as the differencebetween two consecutive 119877119895 values (see (6)) The optimaldecomposition level 119869lowast is calculated as the value of 119895 forwhichADR119895 takes a maximum value This maximum value pointsout the greatest variation of information content among twoconsecutive decomposition levels which means that bothdecomposition levels are sufficiently separated in terms oftexture pattern information content and the decompositionprocess should end For decomposition levels 119895 lt 119869lowast ADR119895indicates that significant texture pattern information stillremains in the approximation subimage and the decom-position process should continue For decomposition levels119895 gt 119869lowast ADR119895 indicates that the approximation subimageis oversmoothed and the reconstruction result from suchsmooth approximation subimage will cause defect loss

ADR119895 = 0 119895 = 1

119877119895 minus 119877119895minus1 119895 = 2

119869lowast = argmax119895

(10038161003816100381610038161003816ADR119895

10038161003816100381610038161003816)

(6)

Table 2 shows values for 119877119895 coefficients at every imagedecomposition level (119895) for the different textures shown inFigure 5 together with the ADR119895 values

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Figure 3 Texture images from shipsrsquo hull surface

andor directionality but they are limited by a lack ofspatial localization In this field Gabor filters provide betterspatial localization although their utility in natural texturesis limited because there is no single filter resolution thatcan localize a structure The wavelet transform has someadvantages over the Gabor transform such as the fact thatthe variation of the spatial resolution makes it possible torepresent the textures in the appropriate scale as well as tochoose from a wide range of wavelet functions

3 The Wavelet Transform for Defect Detection

The suitability of wavelet transforms for use in image analysisis well established a representation in terms of the frequencycontent of local regions over a range of scales provides an idealframework for the analysis of image features which in generalare of different size and can often be characterised by theirfrequency domain properties [14] This makes the wavelettransform an attractive option when attempting defect detec-tion in textured products as reported by Truchetet and Lali-gant [15] in his review of industrial applications of wavelet-based image processing He reported different uses of waveletanalysis in successful machine vision applications detectingdefects for manufacturing applications for the productionof furniture textiles integrated circuits and so forth fromtheir wavelet transformation and vector quantization-relatedproperties of the associated wavelet coefficients printingdefect identification and classification (applied to printeddecoration and tampon printed images) by analysing thefractal properties of a textured image online inspection ofthe loom under construction using a specific class of the2D discrete wavelet transform (DWT) called the multiscalewavelet representation with the objectives of attenuating thebackground texture and accentuating the defects online fab-ric inspection device performing an independent componentanalysis on a subband decomposition provided by a 2-levelDWT in order to increase the defect detection rate

The review of the literature shows two categories of defectdetection methods based on wavelet transform The firstcategory includes direct thresholdingmethods [10 11] whosedesign is based on the fact that texture background can beattenuated by the wavelet decomposition If we remove thetexture pattern from real texture it is feasible to use existingdefect detecting techniques for nontexture images suchas thresholding techniques [16] Textural features extractedfrom wavelet-decomposed images are another categorywhich is widely used for defect detection [17 18] Featuresextracted from the texture patterns are used as featurevectors to feed a classifier (Bayer Euclidean distance NeuralNetworks or Support Vector Machines) which has unavoid-able drawbacks when dealing with the vast image data

obtained during inspection tasks For instance proximity-based methods tend to be computationally expensive andthere is no straightforward way of defining a meaningfulstopping criterion for data fusion (or division) Often thelearning-based classifiers need to be trained by the nondefectfeatures which is a troublesome and usually time consumingprocedure thus limiting its real-time applications [10] Forthis reason we have focused on direct thresholding methodsThe use of direct thresholding presents amain challenge howto select the decomposition level On the other hand directthresholding presents two main drawbacks (1) an excessivewavelet decomposition level produces a fusion of defects withthe texture pattern and (2) a wrong reconstruction schemeproduces false positives when defects are detected

The work presented here is based on the authorsrsquo researchon previous works [10 19] and addresses abovementioneddrawbacks by a new approach based on Shannon Entropycalculation Its main contribution is the formulation of anovel use of the normalized Shannon Entropy calculatedon the different detail subimages to determine the optimaldecomposition level in textures with low directionality Forthis purpose we propose to calculate the optimal decomposi-tion level as the maximum of the ratio between the entropyof the approximation subimage and the total entropy as thesum of entropies calculated for every subimage

31 Wavelet Decomposition For an image 119891(119909 119910) of size119872times119873 pixels each level of wavelet decomposition is obtainedby applying two filters a low-pass filter (L) and a high-pass filter (H) The different combinations of these filtersproduce four images that are here denotedwith the subscriptsLL LH HL and HH In the first decomposition level foursubimages or bands are produced one smooth image alsocalled approximation 119891(1)LL (119909 119910) that represents an approxi-mation of the original image 119891(119909 119910) and three detail subim-ages 119891(1)LH (119909 119910) 119891(1)HL (119909 119910) and 119891(1)HH (119909 119910) which representthe horizontal vertical and diagonal details respectivelyWith this notation 119891(0)LL (119909 119910) represents the original image119891(119909 119910) and 119891

(119895)

LL (119909 119910) represent the approximation image inthe decomposition level 119895 From each decomposition level119891(119895)

LL (119909 119910) we obtain four subimages designated here as119891(119895+1)

LL (119909 119910) 119891(119895+1)

LH (119909 119910) 119891(119895+1)

HL (119909 119910) and119891(119895+1)

HH (119909 119910) whichtogether form the decomposition level 119895 + 1 The pyramidalgorithm to obtain 119891

(119895)

LL (119909 119910) 119891(119895)

LH (119909 119910) 119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910) as well as the calculation of the inverse transformcan be found in [20] We will designate 119865(119909 119910) = 119882minus1[119891

(119895)

LL ]

as the inverse wavelet transform of a subimage 119891(119895)LL from theresolution level 119895 to level 0

4 Mathematical Problems in Engineering

(a)

LL LH

HL HH

(b)

LL LH

HL HH

(c)

LL LH

HL HH

(d)

Figure 4 Decomposition of an image from a damaged hull using Haar wavelet with two coefficients at three decomposition levels (a)original image (b) first decomposition level (c) second decomposition level and (d) third decomposition level

Figure 4 shows the wavelet decomposition for three con-veniently scaled levels (119895 = 3) of a statistical texture patternmdashpainted surfacemdashwith corrosion defects the different subim-ages or bands are shown (named LL LH HL andHH)Thesewere obtained after applying the different coefficients of thewavelet filters More specifically the image in Figure 4(a) wasdecomposed through the application of theHaarwavelet withtwo coefficients At level 119895 images of size (1198732119895) times (1198722119895)pixels are obtained by iterative application of the pyramidalgorithm Note also that the subimages corresponding to thedifferent decomposition levels are produced by successivelyapplying the low-pass and high-pass filters and reducing therows and columns by a factor of two

4 Entropy-Based Method for theAutomatic Selection of the WaveletDecomposition Level

In image processing entropy has been used by many authorsas part of the algorithmic development procedure There

are examples of the use of entropy in the programmingof thresholding algorithms [21] and image segmenting [22]as a descriptor for texture classification [23] as one ofthe parameters selected by Haralick et al for applicationto gray level concurrence matrixes and used for texturecharacterization [24] as an element in characteristic vectorgroups used for classification by Bayesian techniques [25]neuronal networks [26] compact support vectors [27] andso forth

41 Automatic Selection of the Appropriate DecompositionLevel In this work we propose a novel approach for theautomatic selection of the appropriate decomposition levelby means of Shannon entropy The entropy function wasused to identify the resolution level that provides the mostinformation about defects in real textures For this pur-pose the intensity levels of the subimages of the wavelettransform were considered as random samples The conceptof information entropymdashShannon entropymdashdescribes howmuch randomness (or uncertainty) there is in a signal or animage in other words how much information is provided

Mathematical Problems in Engineering 5

119895 = 0 119895 = 1 119895 = 2 119895 = 3 119895 = 4

(a)

(b)

(c)

(d)

(e)

Figure 5 Approximation subimages (119891(119895)LL ) of four wavelet decomposition levels for different images ((a) H225 (b) H34 (c) H241 (d) H137and (e) H10) from portions of shiprsquos hulls

by the signal or image In terms of physics the greater theinformation entropy of the image is the higher its quality willbe [28]

Figure 5 shows how the texture pattern degrades as thedecomposition level increasesThis degradation is distributedamong the different decomposition levels depending on thetexture nature and can be quantified bymeans of the Shannonentropy

The Shannon entropy function [28 29] is calculatedaccording to the expression

119904 (119883) = minus119879

sum119894=1

119901 (119909119894) log119901 (119909119894) (1)

where 119883 = 1199091 1199092 119909119879 is a set of random variableswith 119879 outcomes and 119901(119909119894) is the probability of occurrenceassociated with 119909119894

For a 256-gray-level image of size 119873119905 pixels we definea set of random variables 119883 = 1199091 1199092 119909119894 119909256 asthe number of pixels in the image that have gray level 119894 Theprobability of this random variable 119909119894 is calculated as thenumber of occurrences hist[119909119894] divided by the total numberof pixels119873119905

119901 (119909119894) =hist [119909119894]

119873119905 (2)

6 Mathematical Problems in Engineering

To calculate the value of the Shannon entropy on theapproximation subimage (119891(119895)LL (119909 119910)) and on the horizont-al vertical and diagonal detail subimages (119891

(119895)

LH (119909 119910)

119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910)) in each decomposition level 119895 weobtain first the inverse wavelet transform of every subimageand then we apply (3)

119904119895

LL = 119904 [119882minus1 [119891(119895)

LL (119909 119910)]]

119904119895

LH = 119904 [119882minus1 [119891(119895)

LH (119909 119910)]]

119904119895

HL = 119904 [119882minus1 [119891(119895)

HL (119909 119910)]]

119904119895

HH = 119904 [119882minus1 [119891(119895)

HH (119909 119910)]]

(3)

The normalized entropy of each subimage for a decom-position level 119895 has been calculated as

119878119895119904 =1

119873119895

pixels

sum119909

sum119910

119904119895

LL (119909 119910)

119878119895

ℎ=

1

119873119895

pixels

sum119909

sum119910

119904119895

LH (119909 119910)

119878119895V =1

119873119895

pixels

sum119909

sum119910

119904119895

HL (119909 119910)

119878119895

119889=

1

119873119895

pixels

sum119909

sum119910

119904119895

HH (119909 119910)

(4)

where 119873119895

pixels is the number of pixels at each decompositionlevel 119895 Table 1 shows the values for Shannon entropy calcu-lated for images of Figure 5

Shannon entropy brings us information about theamount of texture pattern that remains after every decompo-sition level Considering (2) entropy provides ameasurementof the histogram distribution the higher the entropy thegreater the histogram uniformity that is a greater amountof texture pattern is contained in the image As the decom-position level increases the texture pattern is being removedthat is the information content decreases so the histogramdistribution gains uniformity An optimal reconstructionscheme would eliminate the texture pattern without loss ofdefect information To determine this optimal decompositionlevel we use a ratio 119877119895 (see (5)) between the entropy of theapproximation subimage and the sum of the entropies forall detail subimages so 119877119895 indicates how much informationabout the texture pattern is contained in decomposition level119895 Variations in this ratio allow detecting changes in theamount of information about the texture pattern between twoconsecutive decomposition levels

119877119895 =119878119895119904

119878119895119904 + 119878119895

ℎ+ 119878119895V + 119878119895

119889

119895 = 1 2 (5)

The goal is to find the optimal decomposition level whichprovides the maximum variation among two consecutive 119877119895

Table 1 Normalized entropies of four decomposition levels fortextures of Figure 5

Decomposition level 119895 119878 119895119904 119878119895

ℎ119878 119895119907 119878

119895

119889

H225

119895 = 1 000011 000008 000007 000004119895 = 2 000048 000042 000042 000037119895 = 3 000200 000172 000168 000179119895 = 4 000796 000750 000681 000716

H34

119895 = 1 000011 000007 000008 000006119895 = 2 000046 000038 000039 000038119895 = 3 000185 000179 000169 000186119895 = 4 000732 000750 000662 000698

H241

119895 = 1 000011 000007 000007 000005119895 = 2 000046 000038 000037 000036119895 = 3 000194 000159 000151 000164119895 = 4 000763 000669 000640 000643

H137

119895 = 1 000011 000007 000006 000004119895 = 2 000047 000028 000027 000031119895 = 3 000191 000127 000132 000118119895 = 4 000726 000593 000581 000524

H10

119895 = 1 000013 000004 000004 000002119895 = 2 000057 000035 000037 000025119895 = 3 000214 000190 000182 000140119895 = 4 000841 000711 000737 000665

values because this indicates that in decomposition level 119895the texture pattern still present in level 119895minus1has been removedkeeping useful information (defects)

For this purpose we define ADR119895 as the differencebetween two consecutive 119877119895 values (see (6)) The optimaldecomposition level 119869lowast is calculated as the value of 119895 forwhichADR119895 takes a maximum value This maximum value pointsout the greatest variation of information content among twoconsecutive decomposition levels which means that bothdecomposition levels are sufficiently separated in terms oftexture pattern information content and the decompositionprocess should end For decomposition levels 119895 lt 119869lowast ADR119895indicates that significant texture pattern information stillremains in the approximation subimage and the decom-position process should continue For decomposition levels119895 gt 119869lowast ADR119895 indicates that the approximation subimageis oversmoothed and the reconstruction result from suchsmooth approximation subimage will cause defect loss

ADR119895 = 0 119895 = 1

119877119895 minus 119877119895minus1 119895 = 2

119869lowast = argmax119895

(10038161003816100381610038161003816ADR119895

10038161003816100381610038161003816)

(6)

Table 2 shows values for 119877119895 coefficients at every imagedecomposition level (119895) for the different textures shown inFigure 5 together with the ADR119895 values

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

(a)

LL LH

HL HH

(b)

LL LH

HL HH

(c)

LL LH

HL HH

(d)

Figure 4 Decomposition of an image from a damaged hull using Haar wavelet with two coefficients at three decomposition levels (a)original image (b) first decomposition level (c) second decomposition level and (d) third decomposition level

Figure 4 shows the wavelet decomposition for three con-veniently scaled levels (119895 = 3) of a statistical texture patternmdashpainted surfacemdashwith corrosion defects the different subim-ages or bands are shown (named LL LH HL andHH)Thesewere obtained after applying the different coefficients of thewavelet filters More specifically the image in Figure 4(a) wasdecomposed through the application of theHaarwavelet withtwo coefficients At level 119895 images of size (1198732119895) times (1198722119895)pixels are obtained by iterative application of the pyramidalgorithm Note also that the subimages corresponding to thedifferent decomposition levels are produced by successivelyapplying the low-pass and high-pass filters and reducing therows and columns by a factor of two

4 Entropy-Based Method for theAutomatic Selection of the WaveletDecomposition Level

In image processing entropy has been used by many authorsas part of the algorithmic development procedure There

are examples of the use of entropy in the programmingof thresholding algorithms [21] and image segmenting [22]as a descriptor for texture classification [23] as one ofthe parameters selected by Haralick et al for applicationto gray level concurrence matrixes and used for texturecharacterization [24] as an element in characteristic vectorgroups used for classification by Bayesian techniques [25]neuronal networks [26] compact support vectors [27] andso forth

41 Automatic Selection of the Appropriate DecompositionLevel In this work we propose a novel approach for theautomatic selection of the appropriate decomposition levelby means of Shannon entropy The entropy function wasused to identify the resolution level that provides the mostinformation about defects in real textures For this pur-pose the intensity levels of the subimages of the wavelettransform were considered as random samples The conceptof information entropymdashShannon entropymdashdescribes howmuch randomness (or uncertainty) there is in a signal or animage in other words how much information is provided

Mathematical Problems in Engineering 5

119895 = 0 119895 = 1 119895 = 2 119895 = 3 119895 = 4

(a)

(b)

(c)

(d)

(e)

Figure 5 Approximation subimages (119891(119895)LL ) of four wavelet decomposition levels for different images ((a) H225 (b) H34 (c) H241 (d) H137and (e) H10) from portions of shiprsquos hulls

by the signal or image In terms of physics the greater theinformation entropy of the image is the higher its quality willbe [28]

Figure 5 shows how the texture pattern degrades as thedecomposition level increasesThis degradation is distributedamong the different decomposition levels depending on thetexture nature and can be quantified bymeans of the Shannonentropy

The Shannon entropy function [28 29] is calculatedaccording to the expression

119904 (119883) = minus119879

sum119894=1

119901 (119909119894) log119901 (119909119894) (1)

where 119883 = 1199091 1199092 119909119879 is a set of random variableswith 119879 outcomes and 119901(119909119894) is the probability of occurrenceassociated with 119909119894

For a 256-gray-level image of size 119873119905 pixels we definea set of random variables 119883 = 1199091 1199092 119909119894 119909256 asthe number of pixels in the image that have gray level 119894 Theprobability of this random variable 119909119894 is calculated as thenumber of occurrences hist[119909119894] divided by the total numberof pixels119873119905

119901 (119909119894) =hist [119909119894]

119873119905 (2)

6 Mathematical Problems in Engineering

To calculate the value of the Shannon entropy on theapproximation subimage (119891(119895)LL (119909 119910)) and on the horizont-al vertical and diagonal detail subimages (119891

(119895)

LH (119909 119910)

119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910)) in each decomposition level 119895 weobtain first the inverse wavelet transform of every subimageand then we apply (3)

119904119895

LL = 119904 [119882minus1 [119891(119895)

LL (119909 119910)]]

119904119895

LH = 119904 [119882minus1 [119891(119895)

LH (119909 119910)]]

119904119895

HL = 119904 [119882minus1 [119891(119895)

HL (119909 119910)]]

119904119895

HH = 119904 [119882minus1 [119891(119895)

HH (119909 119910)]]

(3)

The normalized entropy of each subimage for a decom-position level 119895 has been calculated as

119878119895119904 =1

119873119895

pixels

sum119909

sum119910

119904119895

LL (119909 119910)

119878119895

ℎ=

1

119873119895

pixels

sum119909

sum119910

119904119895

LH (119909 119910)

119878119895V =1

119873119895

pixels

sum119909

sum119910

119904119895

HL (119909 119910)

119878119895

119889=

1

119873119895

pixels

sum119909

sum119910

119904119895

HH (119909 119910)

(4)

where 119873119895

pixels is the number of pixels at each decompositionlevel 119895 Table 1 shows the values for Shannon entropy calcu-lated for images of Figure 5

Shannon entropy brings us information about theamount of texture pattern that remains after every decompo-sition level Considering (2) entropy provides ameasurementof the histogram distribution the higher the entropy thegreater the histogram uniformity that is a greater amountof texture pattern is contained in the image As the decom-position level increases the texture pattern is being removedthat is the information content decreases so the histogramdistribution gains uniformity An optimal reconstructionscheme would eliminate the texture pattern without loss ofdefect information To determine this optimal decompositionlevel we use a ratio 119877119895 (see (5)) between the entropy of theapproximation subimage and the sum of the entropies forall detail subimages so 119877119895 indicates how much informationabout the texture pattern is contained in decomposition level119895 Variations in this ratio allow detecting changes in theamount of information about the texture pattern between twoconsecutive decomposition levels

119877119895 =119878119895119904

119878119895119904 + 119878119895

ℎ+ 119878119895V + 119878119895

119889

119895 = 1 2 (5)

The goal is to find the optimal decomposition level whichprovides the maximum variation among two consecutive 119877119895

Table 1 Normalized entropies of four decomposition levels fortextures of Figure 5

Decomposition level 119895 119878 119895119904 119878119895

ℎ119878 119895119907 119878

119895

119889

H225

119895 = 1 000011 000008 000007 000004119895 = 2 000048 000042 000042 000037119895 = 3 000200 000172 000168 000179119895 = 4 000796 000750 000681 000716

H34

119895 = 1 000011 000007 000008 000006119895 = 2 000046 000038 000039 000038119895 = 3 000185 000179 000169 000186119895 = 4 000732 000750 000662 000698

H241

119895 = 1 000011 000007 000007 000005119895 = 2 000046 000038 000037 000036119895 = 3 000194 000159 000151 000164119895 = 4 000763 000669 000640 000643

H137

119895 = 1 000011 000007 000006 000004119895 = 2 000047 000028 000027 000031119895 = 3 000191 000127 000132 000118119895 = 4 000726 000593 000581 000524

H10

119895 = 1 000013 000004 000004 000002119895 = 2 000057 000035 000037 000025119895 = 3 000214 000190 000182 000140119895 = 4 000841 000711 000737 000665

values because this indicates that in decomposition level 119895the texture pattern still present in level 119895minus1has been removedkeeping useful information (defects)

For this purpose we define ADR119895 as the differencebetween two consecutive 119877119895 values (see (6)) The optimaldecomposition level 119869lowast is calculated as the value of 119895 forwhichADR119895 takes a maximum value This maximum value pointsout the greatest variation of information content among twoconsecutive decomposition levels which means that bothdecomposition levels are sufficiently separated in terms oftexture pattern information content and the decompositionprocess should end For decomposition levels 119895 lt 119869lowast ADR119895indicates that significant texture pattern information stillremains in the approximation subimage and the decom-position process should continue For decomposition levels119895 gt 119869lowast ADR119895 indicates that the approximation subimageis oversmoothed and the reconstruction result from suchsmooth approximation subimage will cause defect loss

ADR119895 = 0 119895 = 1

119877119895 minus 119877119895minus1 119895 = 2

119869lowast = argmax119895

(10038161003816100381610038161003816ADR119895

10038161003816100381610038161003816)

(6)

Table 2 shows values for 119877119895 coefficients at every imagedecomposition level (119895) for the different textures shown inFigure 5 together with the ADR119895 values

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

119895 = 0 119895 = 1 119895 = 2 119895 = 3 119895 = 4

(a)

(b)

(c)

(d)

(e)

Figure 5 Approximation subimages (119891(119895)LL ) of four wavelet decomposition levels for different images ((a) H225 (b) H34 (c) H241 (d) H137and (e) H10) from portions of shiprsquos hulls

by the signal or image In terms of physics the greater theinformation entropy of the image is the higher its quality willbe [28]

Figure 5 shows how the texture pattern degrades as thedecomposition level increasesThis degradation is distributedamong the different decomposition levels depending on thetexture nature and can be quantified bymeans of the Shannonentropy

The Shannon entropy function [28 29] is calculatedaccording to the expression

119904 (119883) = minus119879

sum119894=1

119901 (119909119894) log119901 (119909119894) (1)

where 119883 = 1199091 1199092 119909119879 is a set of random variableswith 119879 outcomes and 119901(119909119894) is the probability of occurrenceassociated with 119909119894

For a 256-gray-level image of size 119873119905 pixels we definea set of random variables 119883 = 1199091 1199092 119909119894 119909256 asthe number of pixels in the image that have gray level 119894 Theprobability of this random variable 119909119894 is calculated as thenumber of occurrences hist[119909119894] divided by the total numberof pixels119873119905

119901 (119909119894) =hist [119909119894]

119873119905 (2)

6 Mathematical Problems in Engineering

To calculate the value of the Shannon entropy on theapproximation subimage (119891(119895)LL (119909 119910)) and on the horizont-al vertical and diagonal detail subimages (119891

(119895)

LH (119909 119910)

119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910)) in each decomposition level 119895 weobtain first the inverse wavelet transform of every subimageand then we apply (3)

119904119895

LL = 119904 [119882minus1 [119891(119895)

LL (119909 119910)]]

119904119895

LH = 119904 [119882minus1 [119891(119895)

LH (119909 119910)]]

119904119895

HL = 119904 [119882minus1 [119891(119895)

HL (119909 119910)]]

119904119895

HH = 119904 [119882minus1 [119891(119895)

HH (119909 119910)]]

(3)

The normalized entropy of each subimage for a decom-position level 119895 has been calculated as

119878119895119904 =1

119873119895

pixels

sum119909

sum119910

119904119895

LL (119909 119910)

119878119895

ℎ=

1

119873119895

pixels

sum119909

sum119910

119904119895

LH (119909 119910)

119878119895V =1

119873119895

pixels

sum119909

sum119910

119904119895

HL (119909 119910)

119878119895

119889=

1

119873119895

pixels

sum119909

sum119910

119904119895

HH (119909 119910)

(4)

where 119873119895

pixels is the number of pixels at each decompositionlevel 119895 Table 1 shows the values for Shannon entropy calcu-lated for images of Figure 5

Shannon entropy brings us information about theamount of texture pattern that remains after every decompo-sition level Considering (2) entropy provides ameasurementof the histogram distribution the higher the entropy thegreater the histogram uniformity that is a greater amountof texture pattern is contained in the image As the decom-position level increases the texture pattern is being removedthat is the information content decreases so the histogramdistribution gains uniformity An optimal reconstructionscheme would eliminate the texture pattern without loss ofdefect information To determine this optimal decompositionlevel we use a ratio 119877119895 (see (5)) between the entropy of theapproximation subimage and the sum of the entropies forall detail subimages so 119877119895 indicates how much informationabout the texture pattern is contained in decomposition level119895 Variations in this ratio allow detecting changes in theamount of information about the texture pattern between twoconsecutive decomposition levels

119877119895 =119878119895119904

119878119895119904 + 119878119895

ℎ+ 119878119895V + 119878119895

119889

119895 = 1 2 (5)

The goal is to find the optimal decomposition level whichprovides the maximum variation among two consecutive 119877119895

Table 1 Normalized entropies of four decomposition levels fortextures of Figure 5

Decomposition level 119895 119878 119895119904 119878119895

ℎ119878 119895119907 119878

119895

119889

H225

119895 = 1 000011 000008 000007 000004119895 = 2 000048 000042 000042 000037119895 = 3 000200 000172 000168 000179119895 = 4 000796 000750 000681 000716

H34

119895 = 1 000011 000007 000008 000006119895 = 2 000046 000038 000039 000038119895 = 3 000185 000179 000169 000186119895 = 4 000732 000750 000662 000698

H241

119895 = 1 000011 000007 000007 000005119895 = 2 000046 000038 000037 000036119895 = 3 000194 000159 000151 000164119895 = 4 000763 000669 000640 000643

H137

119895 = 1 000011 000007 000006 000004119895 = 2 000047 000028 000027 000031119895 = 3 000191 000127 000132 000118119895 = 4 000726 000593 000581 000524

H10

119895 = 1 000013 000004 000004 000002119895 = 2 000057 000035 000037 000025119895 = 3 000214 000190 000182 000140119895 = 4 000841 000711 000737 000665

values because this indicates that in decomposition level 119895the texture pattern still present in level 119895minus1has been removedkeeping useful information (defects)

For this purpose we define ADR119895 as the differencebetween two consecutive 119877119895 values (see (6)) The optimaldecomposition level 119869lowast is calculated as the value of 119895 forwhichADR119895 takes a maximum value This maximum value pointsout the greatest variation of information content among twoconsecutive decomposition levels which means that bothdecomposition levels are sufficiently separated in terms oftexture pattern information content and the decompositionprocess should end For decomposition levels 119895 lt 119869lowast ADR119895indicates that significant texture pattern information stillremains in the approximation subimage and the decom-position process should continue For decomposition levels119895 gt 119869lowast ADR119895 indicates that the approximation subimageis oversmoothed and the reconstruction result from suchsmooth approximation subimage will cause defect loss

ADR119895 = 0 119895 = 1

119877119895 minus 119877119895minus1 119895 = 2

119869lowast = argmax119895

(10038161003816100381610038161003816ADR119895

10038161003816100381610038161003816)

(6)

Table 2 shows values for 119877119895 coefficients at every imagedecomposition level (119895) for the different textures shown inFigure 5 together with the ADR119895 values

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

To calculate the value of the Shannon entropy on theapproximation subimage (119891(119895)LL (119909 119910)) and on the horizont-al vertical and diagonal detail subimages (119891

(119895)

LH (119909 119910)

119891(119895)

HL (119909 119910) and119891(119895)

HH (119909 119910)) in each decomposition level 119895 weobtain first the inverse wavelet transform of every subimageand then we apply (3)

119904119895

LL = 119904 [119882minus1 [119891(119895)

LL (119909 119910)]]

119904119895

LH = 119904 [119882minus1 [119891(119895)

LH (119909 119910)]]

119904119895

HL = 119904 [119882minus1 [119891(119895)

HL (119909 119910)]]

119904119895

HH = 119904 [119882minus1 [119891(119895)

HH (119909 119910)]]

(3)

The normalized entropy of each subimage for a decom-position level 119895 has been calculated as

119878119895119904 =1

119873119895

pixels

sum119909

sum119910

119904119895

LL (119909 119910)

119878119895

ℎ=

1

119873119895

pixels

sum119909

sum119910

119904119895

LH (119909 119910)

119878119895V =1

119873119895

pixels

sum119909

sum119910

119904119895

HL (119909 119910)

119878119895

119889=

1

119873119895

pixels

sum119909

sum119910

119904119895

HH (119909 119910)

(4)

where 119873119895

pixels is the number of pixels at each decompositionlevel 119895 Table 1 shows the values for Shannon entropy calcu-lated for images of Figure 5

Shannon entropy brings us information about theamount of texture pattern that remains after every decompo-sition level Considering (2) entropy provides ameasurementof the histogram distribution the higher the entropy thegreater the histogram uniformity that is a greater amountof texture pattern is contained in the image As the decom-position level increases the texture pattern is being removedthat is the information content decreases so the histogramdistribution gains uniformity An optimal reconstructionscheme would eliminate the texture pattern without loss ofdefect information To determine this optimal decompositionlevel we use a ratio 119877119895 (see (5)) between the entropy of theapproximation subimage and the sum of the entropies forall detail subimages so 119877119895 indicates how much informationabout the texture pattern is contained in decomposition level119895 Variations in this ratio allow detecting changes in theamount of information about the texture pattern between twoconsecutive decomposition levels

119877119895 =119878119895119904

119878119895119904 + 119878119895

ℎ+ 119878119895V + 119878119895

119889

119895 = 1 2 (5)

The goal is to find the optimal decomposition level whichprovides the maximum variation among two consecutive 119877119895

Table 1 Normalized entropies of four decomposition levels fortextures of Figure 5

Decomposition level 119895 119878 119895119904 119878119895

ℎ119878 119895119907 119878

119895

119889

H225

119895 = 1 000011 000008 000007 000004119895 = 2 000048 000042 000042 000037119895 = 3 000200 000172 000168 000179119895 = 4 000796 000750 000681 000716

H34

119895 = 1 000011 000007 000008 000006119895 = 2 000046 000038 000039 000038119895 = 3 000185 000179 000169 000186119895 = 4 000732 000750 000662 000698

H241

119895 = 1 000011 000007 000007 000005119895 = 2 000046 000038 000037 000036119895 = 3 000194 000159 000151 000164119895 = 4 000763 000669 000640 000643

H137

119895 = 1 000011 000007 000006 000004119895 = 2 000047 000028 000027 000031119895 = 3 000191 000127 000132 000118119895 = 4 000726 000593 000581 000524

H10

119895 = 1 000013 000004 000004 000002119895 = 2 000057 000035 000037 000025119895 = 3 000214 000190 000182 000140119895 = 4 000841 000711 000737 000665

values because this indicates that in decomposition level 119895the texture pattern still present in level 119895minus1has been removedkeeping useful information (defects)

For this purpose we define ADR119895 as the differencebetween two consecutive 119877119895 values (see (6)) The optimaldecomposition level 119869lowast is calculated as the value of 119895 forwhichADR119895 takes a maximum value This maximum value pointsout the greatest variation of information content among twoconsecutive decomposition levels which means that bothdecomposition levels are sufficiently separated in terms oftexture pattern information content and the decompositionprocess should end For decomposition levels 119895 lt 119869lowast ADR119895indicates that significant texture pattern information stillremains in the approximation subimage and the decom-position process should continue For decomposition levels119895 gt 119869lowast ADR119895 indicates that the approximation subimageis oversmoothed and the reconstruction result from suchsmooth approximation subimage will cause defect loss

ADR119895 = 0 119895 = 1

119877119895 minus 119877119895minus1 119895 = 2

119869lowast = argmax119895

(10038161003816100381610038161003816ADR119895

10038161003816100381610038161003816)

(6)

Table 2 shows values for 119877119895 coefficients at every imagedecomposition level (119895) for the different textures shown inFigure 5 together with the ADR119895 values

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Subimage of size

(119909 119910)

119896

M

2j+1times

N

2j+1

sumsumF998400(x y) =1

9

2

i=0

2

j=0

F(x minus 1 + i y minus 1 + j)

Figure 6 Smoothing mask (119896 = 3) for the wavelet coefficients

Step 1 Compute Shannon Entropy 119878119895119878 119878119895ℎ 119878119895V and 119878

119895

119889

Step 2 Compute 119877119895 = 119878119895

119878(119878119895

119878+ 119878119895

ℎ+ 119878119895V + 119878

119895

119889) for 119895 = 1 2 3 119869

Step 3 Compute optimal decomposition level119869lowast = arg max119895ADR119895 119895 = 1 2 3 119869

Step 4 Compute 119865 = 119882minus1[119891(119869lowast

)

119871119871 ]Step 5 Compute 1198651015840 = 119898119896times119896[119865]Step 6 Binarize 1198651015840

Pseudocode 1 Pseudocode to implement the developed algorithm

Table 2 119877119895 ADR119895 and optimal decomposition level obtained fortexture images of Figure 5

Image Level (119895) 1 2 3 4 119869lowast

H225 119877119895 03785 02812 02778 02704 2ADR119895 0 00973 00035 00074

H34 119877119895 03460 02852 02576 02575 2ADR119895 0 00608 00276 00002

H241 119877119895 03626 02931 02899 02811 2ADR119895 0 00695 00032 00088

H137 119877119895 0388067 0353254 0336133 0299523 4ADR119895 0 0034813 0017121 0036610

H10 119877119895 0545018 0369480 0294868 0284585 2ADR119895 0 0175538 0074612 0010283

Once the optimal decomposition level is obtained theprocess ends with the production of the reconstructed imageusing (7)

119865 (119909 119910) = 119882minus1 [119891(119895)

LL (119909 119910)] (7)

42 Smoothing Mask To remove the noise running throughthe successive decomposition levels we applied average-based smoothing over image 119865(119909 119910) to obtain 1198651015840(119909 119910) asshown in (8)

1198651015840 (119909 119910) =1

1198962

119896minus1

sum119894=0

119896minus1

sum119895=0

119865(119909 minus lfloor119896

2rfloor + 119894 119910 minus lfloor

119896

2rfloor + 119895) (8)

where 119896 is the size of the smoothing mask (see Figure 6)

5 Results

51 Algorithm Implementation The proposed computervision algorithm was implemented as shown in thePseudocode 1 using the C++ programming languageThe mother wavelet used for decomposition was the Haarbase function with two coefficients applied up to a fourthdecomposition level A decomposition level higher than fourproduced the fusion between defects and background thusreducing the probability of defect detection

52 Implementation of the Computer Vision System Thecomputer vision system for visual inspection of ship hullsurfaces (Figure 2) has been implemented on a Pentiumcomputer with a Meteor II1394 card This card is connectedto the microprocessor via a PCI bus and is used as a frame-grabber For that purpose the card had a processing nodebased on the TMS320C80 DSP from Texas Instruments andthe Matrox NOA ASIC In addition the card had a firewireinputoutput bus (IEEE 1394) which enables it to control ahalf-inch digital colour camera (15 fps 1024 times 768 squarepixel) equipped with a wide-angle lens (f 42mm)

The software development environment used to imple-ment the system software modules was the Visual C++ pro-gramming language powered by the Matrox Imaging Libraryv90 The system also had a Siemens CP5611 card whichacted as a PROFIBUS-DP interface for connection withthe corresponding robotized blasting system A Honeywellsensor was used to measure the distance to the ship byultrasound with a range of 200ndash2000mm and an output of4ndash20mA User access to the computer vision system was by

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

Figure 7 Robotized blasting system

means of an industrial PDS (Mobic T8 from Siemens) anda wireless access point Among other functions the softwarethat has been developed allows the operator to (1) enter thesystem configuration parameters (2) visualize the detectedareas to blast for validation by the operator before blastingcommences and (3) calibrate the computer vision system

53 Validation Environment The proposed computer visionalgorithm was assessed at the NAVANTIA shipyard in Ferrol(Spain) on a robotized system used for automatic spotblastingThis operation accounts for 70 of all cleaning workcarried out at that shipyard The robotized system (Figure 7)consists of a mechanical structure divided into two partsprimary and secondary The primary structure holds thesecondary structure (XYZ table) which supports the cleaninghead and the computer vision system More informationregarding this system can be found in [5]

With the help of this platform 260 images of ship hullsrsquosurfaces (with and without defects) were taken similar tothose shown in Figure 3 In this way a cataloguewas compiledof typical surface defects as they appear before grit blasting

54 Metrics To conduct a quantitative analysis of the qualityof the proposed segmentation method we need to use thebest suitedmetrics to that purposeTheperformance of imagesegmentation methods has been assessed by such authorsas Zhang [30] and Sezgin and Sankur [16] They proposedvarious different metrics for measurement of the quality ofthe segmentation in a given method using parameters likeposition of the pixels area edges and so forth Out of theseone of the quantitative appraisal methods proposed by Sezginwas selected and examined Misclassification Error (ME)

ME represents the percentage of the background pixelsthat are incorrectly allocated to the object (ie to theforeground) or vice versa

ME = 1 minus

1003816100381610038161003816119861119875 cap 1198611198791003816100381610038161003816 +

1003816100381610038161003816119874119875 cap 1198741198791003816100381610038161003816

10038161003816100381610038161198611198751003816100381610038161003816 +

10038161003816100381610038161198741198751003816100381610038161003816

(9)

The error can be calculated by means of (9) where 119861119875(background pattern) and 119874119875 (object pattern) represent the

pattern image of the background and of the object takenas reference and 119861119879 (background test) and 119874119879 (object test)represent the image to be assessed In the event that the testimage coincides with the pattern image the classificationerror will be zero and therefore the performance of thesegmentation will be the maximum

The performance of the implemented algorithms isassessed according to the equation

120578 = 100 sdot (1 minusME) (10)

55 Algorithm Appraisal The proposed visual inspectionalgorithm (see Pseudocode 1) was applied to the above men-tioned catalogue that had been taken at the shipyard (somesamples are shown in column (a) of Figure 8) The Shannonentropy was calculated and normalized for four waveletdecomposition levels and the optimal 119869lowast level was calculated(6) Images were also processed applying algorithms pro-posed by Han and Shi [10] and Tsai and Chiang [19] Theresult was 3 sets of 260 reconstructed images in which thedefects have been isolated from texture To check the qualityof the defect detection algorithms we have concluded with abinarization stage For that purpose we have selected Kapurrsquosmethod [21] which belongs to the group of entropy-basedmethods as classified by Sezgin and Sankur [16] in his reviewof thresholding methods this has resulted in 3 sets of 260images (column (b) of Figure 8 shows some results obtainedwith the proposed algorithm column (c) of Figure 8 showssome results obtainedwith the Tsai algorithm and column (d)of Figure 8 shows some results obtainedwithHan algorithm)

To apply the metrics described above human inspec-tors were needed to segment each of the catalogue imagesmanually (samples of these are shown in column (v) ofFigure 8) Table 3 shows the performance (120578) when sampletexture images of Figure 8 were segmented using the threealgorithms

As can be observed from above results the proposedentropy-based algorithm achieved better results than Tsaialgorithm and significantly better results thanHan algorithm

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

(a)

(b)

(c)

(d)

(e)

(f)

(i) (ii) (iii) (iv) (v)

(g)

Figure 8 Continued

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

(h)

(i)

(j)

(k)

(i) (ii) (iii) (iv) (v)

(l)

Figure 8 Columns column (i) shows texture images of portions of hulls column (ii) shows reconstructed images resulting from the proposedreconstruction scheme column (iii) shows reconstructed images resulting from Tsai algorithm column (iv) shows reconstructed imagesresulting from Han algorithm column (v) shows defects segmented by hand the ldquoground truthrdquo Image Rows (a) H225 (b) H34 (c) H241(d) H1 (e) H120 (f) H121 (g) H99 (h) H137 (i) H48 (j) H9 (k) H10 and (l) H11

In both cases the proposed algorithm obtains higher perfor-mance with low decomposition level

We have also analysed the behaviour of the proposedalgorithm as misclassification rates A set of 120 images wereprocessed by the proposed algorithm and also by Han andTsai algorithms Results were then analysed by a skilledblasting operator who assessed what portions of the shownhull surface would be blasted in real conditions at the repairyard Table 4 shows the average number of defect pointsclassified as Type I and Type II errors for 120 samples of the260-image set indicated above

As we can see the proposed algorithm produced betterresults as regards false positivesmdashthat is points marked asdefective when they are not (Type I error) This is essentiallybecause the operator tends to blast larger areas than neces-sary and moreover he is less able to control the cut-off of thegrit jet On the other hand the proposed algorithm identifiedsimilar false negatives (Type II error)This difference was notvery significant and is quite acceptable in view of the clearadvantage offered by the computer vision system equippedwith the proposed inspection algorithm as regards Type Ierrors

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

Table 3 120578 in defect segmentation of texture images of Figure 8

Entropybased 119869lowast Tsai 119869lowast Han 119869lowast

Defect samplesH225 9709 2 9451 4 214 4H34 9741 2 7452 2 343 4H241 9604 2 9517 4 9741 2H1 8650 3 8263 4 8469 4H20 9140 3 8922 4 9008 4H121 8936 4 8991 4 9023 4H99 8930 4 7376 4 9146 3H137 9394 4 8287 4 9426 3H48 9306 4 9397 4 6423 4Average ondefect samples 9268 311 8628 378 6866 356

Nondefect samplesH9 9830 2 7404 3 9961 4H10 9833 2 8085 4 4805 4H11 9822 2 8906 4 4865 4Average onnondefect samples 9828 200 8132 367 6544 400

Total Average 9548 256 8380 372 6705 378

Table 4 Automated inspection examined by a skilled blastingoperator

Entropy-basedalgorithm

Hanalgorithm

Tsaialgorithm

Type I error 68 92 111Type II error 09 11 07

6 Conclusions

This paper has presented a computer vision algorithm basedon the wavelet transform which brings a robust method fordetecting defects in ship hull surfaces To achieve this weused an image reconstruction approach based on automaticselection of the optimal wavelet transform resolution level bymeans of a novel use of the Shannon entropy calculated onthe different detail subimages

The algorithm has been incorporated to a computervision system that masters a robotized system for blastingship hulls making it possible to fully automate grit blastingoperation The results as regards reliability were very similarto those achieved with human workers while faster inspec-tion was provided (among 8 for flat surfaces in oil tankersand 15 for shaped hulls like frigates) and the consequencesof operator fatigue minimized

Acknowledgments

The work submitted here was carried out as a part of theprojects ViSel-TR (ref TIN2012-39279) and EXPLORE (ref

TIN2009-08572) funded by the Spanish National RampDampIPlan

References

[1] A Momber Blast Cleaning Technologies Springer Berlin Ger-many 2008

[2] P Le Calve ldquoQualification of paint systems after UHP waterjetting and understanding the phenonemon of ldquoblockingrdquo offlash rustingrdquo Journal of Protective Coatings and Linings vol 24no 8 pp 13ndash26 2007

[3] P J Navarro J Suardıaz C Fernandez P Alcover and RBorraz ldquoTeleoperated service robot for high quality shipmaintenancerdquo in Proceedings of the 8th IFAC InternationalWorkshop on Intelligent Manufacturing Systems vol 8 pp 152ndash157 Alicante Spain May 2007

[4] C Fernandez A Iborra B Alvarez J A Pastor and J MFernandez ldquoShip shape in Europe co-operative robots in theship repair industryrdquo IEEE Robotics and Automation Magazinevol 12 no 3 pp 65ndash77 2005

[5] A Iborra J A Pastor P JNavarro et al ldquoA cost-effective roboticsolution for the cleaning of ship hullsrdquoRobotica vol 28 pp 453ndash464 2010

[6] X Xie ldquoA review of recent advances in surface defect detectionusing texture analysis techniquesrdquo Electronic Letters on Com-puter Vision and Image Analysis vol 7 no 3 pp 1ndash22 2008

[7] A Kumar ldquoComputer-vision-based fabric defect detection asurveyrdquo IEEE Transactions on Industrial Electronics vol 55 no1 pp 348ndash363 2008

[8] H Y T Ngan G K H Pang and N H C Yung ldquoAutomatedfabric detect detection-A reviewrdquo Image and Vision Computingvol 29 pp 442ndash458 2011

[9] H Y T Ngan G K H Pang and N H C Yung ldquoPerformanceevaluation for motif-based patterned texture defect detectionrdquoIEEE Transactions on Automation Science and Engineering vol7 no 1 pp 58ndash72 2010

[10] YHan andP Shi ldquoAn adaptive level-selectingwavelet transformfor texture defect detectionrdquo Image and Vision Computing vol25 no 8 pp 1239ndash1248 2007

[11] D M Tsai and T Huang ldquoAutomated surface inspection forstatistical texturesrdquo Image and Vision Computing vol 21 pp307ndash323 2003

[12] A Kumar and G Pang ldquoDefect detection in textured materialsusingGabor filtersrdquo IEEE Transactions on Industry Applicationsvol 38 no 2 pp 425ndash440 2002

[13] H Y T Ngan G K H Pang S P Yung andM K Ng ldquoWaveletbased methods on patterned fabric defect detectionrdquo PatternRecognition vol 38 no 4 pp 559ndash576 2005

[14] S Mallat ldquoMultifrequency channel decompositions of imagesandwavelet modelsrdquo IEEE Transactions on Acoustics Speech andSignal Processing vol 37 no 12 pp 2091ndash2110 1989

[15] F Truchetet and O Laligant ldquoReview of industrial applicationsof wavelet and multiresolution-based signal and image pro-cessingrdquo Journal of Electronic Imaging vol 17 no 3 Article ID031102 pp 3ndash11 2008

[16] M Sezgin and B Sankur ldquoSurvey over image thresholdingtechniques and quantitative performance evaluationrdquo Journal ofElectronic Imaging vol 13 no 1 pp 146ndash168 2004

[17] W K Wong C W M Yuen D D Fan L K Chan and EH K Fung ldquoStitching defect detection and classification using

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

wavelet transform and BP neural networkrdquo Expert SystemsWithApplications vol 36 no 2 pp 3845ndash3856 2009

[18] H-D Lin ldquoAutomated visual inspection of ripple defects usingwavelet characteristic based multivariate statistical approachrdquoImage and Vision Computing vol 25 pp 1785ndash1801 2007

[19] D M Tsai and C H Chiang ldquoAutomatic band selection forwavelet reconstruction in the application of defect detectionrdquoImage and Vision Computing vol 21 no 5 pp 413ndash431 2003

[20] S G Mallat ldquoTheory for multiresolution signal decompositionthe wavelet representationrdquo IEEE Transactions on Pattern Anal-ysis and Machine Intelligence vol 11 no 7 pp 674ndash693 1989

[21] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[22] C Yan ldquoLocal entropy-based transition region extraction andthresholdingrdquo Pattern Recognition Letters vol 24 no 16 pp2935ndash2941 2003

[23] L Setia and H Burkhardt ldquoFeature selection for automaticimage annotationrdquo in Proceedings of the 28th DAGM Sympo-sium pp 294ndash303 Berlin Germany September 2006

[24] R M Haralick K Shanmugam and I Dinstein ldquoTexturefeatures for image classificationrdquo IEEE Transactions on SystemsMan and Cybernetics vol 3 pp 610ndash621 1973

[25] M Toews andT Arbel ldquoEntropy-of-likelihood feature selectionfor image correspondencerdquo in Proceedings of the 9th IEEEInternational Conference on Computer Vision vol 2 pp 1041ndash1047 Nice France October 2003

[26] E Avci ldquoAn expert system based on Wavelet Neural Network-Adaptive Norm Entropy for scale invariant texture classifica-tionrdquo Expert Systems with Applications vol 32 no 3 pp 919ndash926 2007

[27] F Harirchi P Radparvar H Abrishami Moghaddam FDehghan andM Giti ldquoTwo-level algorithm for MCs detectionin mammograms using Diverse-Adaboost-SVMrdquo in Proceed-ings of the 20th International Conference on Pattern Recognition(ICPR rsquo10) pp 269ndash272 Istanbul Turkey August 2010

[28] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 p 379ndash423 623ndash656 1948

[29] R R Coifman and M V Wickerhauser ldquoEntropy-based Algo-rithms for best basis selectionrdquo IEEE Transactions on Informa-tion Theory vol 38 no 2 pp 713ndash718 1992

[30] Y J Zhang ldquoA review of recent evaluation methods for imagesegmentationrdquo in Proceedings of the 6th International Sympo-sium on Signal Processing and its Applications pp 148ndash151 KualaLumpur Malaysia August 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of