Research Article Micro Surface Defect Detection Method for ...downloads.hindawi.com/journals/mpe/2013/429094.pdf · surface defect of silicon steel strip, a new detection method based

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 429094 13 pageshttpdxdoiorg1011552013429094

Research ArticleMicro Surface Defect Detection Method for Silicon Steel StripBased on Saliency Convex Active Contour Model

Kechen Song and Yunhui Yan

School of Mechanical Engineering amp Automation Northeastern University Shenyang Liaoning 110819 China

Correspondence should be addressed to Kechen Song unkechengmailcom

Received 20 September 2013 Accepted 22 November 2013

Academic Editor Gianluca Ranzi

Copyright copy 2013 K Song and Y Yan This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Accurate detection of surface defect is an indispensable section in steel surface inspection system In order to detect the microsurface defect of silicon steel strip a new detection method based on saliency convex active contour model is proposed In theproposed method visual saliency extraction is employed to suppress the clutter background for the purpose of highlighting thepotential objects The extracted saliency map is then exploited as a feature which is fused into a convex energy minimizationfunction of local-based active contour Meanwhile a numerical minimization algorithm is introduced to separate themicro surfacedefects from cluttered background Experimental results demonstrate that the proposed method presents good performance fordetecting micro surface defects including spot-defect and steel-pit-defect Even in the cluttered background the proposed methoddetects almost all of the microdefects without any false objects

1 Introduction

Silicon steel strip is a soft magnetic material that is mainlyused as core material in transformers and dynamos Thesurface quality of silicon steel strip directly affects the qualityandmagnetic properties of the final productTherefore accu-rate detection of surface defect has become an indispensablesection in steel industry In recent years the visual-basedinspection technology as a kind of noncontact inspectionmethod has become a research hotspot in the field of surfacedefect inspection In view of the characteristics of the realtime and easines to realize intelligently this technology hasbeen widely used in online real-time inspection of automaticproduction lines [1ndash3]

In order to detect the surface defects automatically a widevariety of methods have been developed in many applica-tions Caleb-Solly and Smith [4] described a reconfigurablesurface inspection system which involves using evolutionaryalgorithms to enable the user to interactively search thelocal space of image processing parameters and to evolvean optimum set based on the userrsquos visual evaluation Liet al [5] proposed a feature-preserving ldquosnake-projectionrdquo

method to detect the defect seam In addition Pan et al [6]exploited an engineering-driven rule-based detection (ERD)method for bleed detection in visual images which lie inthe low signal-to-noise ratio Yun et al [7] divided defectsinto two classes and respectively employed undecimatedwavelet transform and statistical approach to detect defectsMeanwhile Yun et al [8] developed the univariate dynamicencoding algorithm for searches (uDEAS) to detect thecracks Besides Bulnes et al [9] introduced the clusteringmethod to detect periodical defects Landstrom and Thurley[10] focused on automated detection of longitudinal cracksin steel slabs based on morphology theory Recently Zhanget al [11] exploited a target identification system based onadaptive genetic algorithm and feature saliency to detectsurface defects of copper strip

Despite the fact that the several methods mentionedabove have achieved moderate results in a certain singletype of defects it has not yet become a universal methodfor all of the surface defects Therefore it is necessary todevelop an appropriate detection method for micro surfacedefect of silicon steel strip Since the surface defects ofsilicon steel strip are small it is more difficult to detect

2 Mathematical Problems in Engineering

Camera

Movement direction

Light source

Silicon steel

Figure 1 Schematic of the image acquisition

these microobjects Furthermore the cluttered backgroundincreases the difficulty of detecting the defects in images

In recent years local energy functions based on activecontour have been introduced for object detection whichmakes it possible to detectmicro surface defect of silicon steelstrip in images with cluttered background In this work a newdetection method based on saliency convex active contourmodel (SCACM) is proposed to detect micro surface defectsof silicon steel strip In the proposed method visual saliencyextraction is employed to suppress the clutter backgroundThe extracted saliency map is exploited as a feature torepresent the pixels in the proposed model Then the abovefeature is fused into a convex energy minimization functionof local-based active contour Finally a fast and accuratenumerical minimization algorithm is introduced to separatethe micro surface defects from cluttered background

The rest of this paper is organized as follows Section 2presents the hardware configuration of image acquisition andthe analysis of micro surface defect Section 3 introduces theproposed saliency convex active contour model in detailThen Section 4 elaborates the experiments and discusses theexperimental results Finally Section 5 concludes the paper

2 Image Acquisition and Analysis of MicroSurface Defect

The hardware configuration of the image acquisition mainlyincludes two components light source and camera Thelayout of the acquisition equipment is shown in Figure 1 Thelight source provides the illumination to make the surfacedefects visible and helps to capture the surface defect imageswith camera Since the light-emitting diode (LED) has manyadvantages such as little power and longevity it is used toprovide stable illumination In this work the LED is made byCCS IncorporatedCompany of Japanwith themodel numberHLND-1200-SW2 In order to obtain themicro surface defectimage an area scan CCD camera is used The camera usedhere is made by Basler of Germany with the model numberacA640-90uc It has a resolution of 658 times 492 pixels withframe rate 90 fps and color image In this work the capturedcolor image is resized as 640 times 480 pixels for the purpose

of calculating expediently for defect detection In additiona 55mm focal length lens is installed on the camera

One of the original micro surface defect images of siliconsteel strip is shown in Figure 2 As it could be seen inFigure 2(a) the original defect image represents an area of96 times 72mm2 in real silicon steel strip It is observed thatthe defect image contains two components the interestingmicrodefect object and the cluttered backgroundThe formeris to be detected while the latter is useless To illustratethe scale of microdefect object an area of 60 times 60 pixelsis cropped from original defect image The cropped arearepresents an area of 09 times 09mm2 in real silicon steelstrip which is shown in Figure 2(b) Then the defect areain Figure 2(c) is extracted from the cropped area FromFigure 2(c) we can see that the defect area consists of 6 times6 pixels that is the size of microdefect object is an areaof 90 times 90120583m2 in real silicon steel strip Obviously it isquite difficult to detect the microdefect object for most of thecurrent detection methods whose size of defect object is anarea of 05 times 05mm2

Furthermore the background of original microdefectimage is quite complex which is another difficult problemfor detecting the defect Despite the fact that the clutterbackground has certain characters of texture these charactersare more random than regular texture The surface plot ofFigure 2(a) is shown in Figure 3 As it could be seen inFigure 3 the clutter background has random distribution inthe whole image

In addition due to the surface roughness of silicon steelstrip the microdefect image contains some interference likenoise in clutter backgroundThis interference to some extentincreases the difficulty of detecting the defects in images

3 Saliency Convex Active Contour Model

In this section the proposed method is described in two sub-sections Firstly a saliency extraction approach is introducedin Section 31 for the purpose of highlighting the potentialobjects to get a saliency map Then the saliency map is fusedinto a convex energy minimization function in Section 32

31 Saliency Extraction Saliency extraction is an importantstep in machine vision which has been applied in manytasks including object detection and image segmentation Anexcellent saliency extraction method can well highlight thepotential objects to get a saliency map However most of thecurrent saliency methods often generate saliency maps thathave low resolution or poorly defined borders Furthermoresomemethodsmay generatemaps that have ill-defined objectboundaries

In order to avoid these drawbacks mentioned aboveAchanta et al [12] exploited a frequency-tuned approach toestimate center-surround contrast using color and luminancefeatures Although the frequency-tuned approach created fullresolution saliency maps with well-defined boundaries ofsalient objects it may fail to correctly highlight the salientregions in the presence of microsalient objects and complextextured background In this work the symmetric surround

Mathematical Problems in Engineering 3

96 mm

72 m

m

90120583m

09 mm

09 m

m90120583

m

(a) Original defect image

(c) Defect

(b) Cropped area

Figure 2 Sample image of micro surface defect

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Figure 3 Surface plot of the defect sample image in Figure 2

saliency [13] is employed to improve the frequency-tunedapproach

For an input image I the symmetric surround saliencyvalue 119878(119909 119910) is obtained as

119878 (119909 119910) =10038171003817100381710038171003817I120583(119909 119910) minus I

119891(119909 119910)

10038171003817100381710038171003817 (1)

where I119891(119909 119910) is the corresponding image Lab color space

vector value in the Gaussian blurred version (using anN timesNseparable binomial kernel) of the original image and sdot isthe 1198712norm Here the 119871

2norm is the Euclidean distance

In the Lab color space each pixel location is a [119871 119886 119887]119879

vector Different from the mean image feature vector of thefrequency-tuned approach [12] I

120583(119909 119910) is the average Lab

vector of the subimage whose center pixel is at position (119909 119910)as given by

I120583(119909 119910) =

1

119860

119909+1199090

sum

119894=119909minus1199090

119910+1199100

sum

119895=119910minus1199100

I (119894 119895) (2)

with offsets 1199090and 119910

0and area 119860 of the subimage computed

as

1199090= min (119909 119908 minus 119909)

1199100= min (119910 ℎ minus 119910)

119860 = (21199090+ 1) (2119910

0+ 1)

(3)

where 119908 and ℎ are width and height of an input imagerespectively

To illustrate the calculation procedure of the symmetricsurround saliency Figure 4 presents the schematic of thesaliency extraction for input defect image Firstly the originaldefect image (Figure 4(a)) is blurred byNtimesNGaussian filterwindow (N is set as 5) Then Lab color space images (ieFigures 4(c) and 4(d)) of original image (ie Figure 4(a)) andfilter image (ie Figure 4(b)) are obtained by converting colorspace from RGB to Lab Equation (2) is used to compute theLab average vector I

120583(119909 119910) Finally the symmetric surround

saliency value 119878(119909 119910) is obtained with (1)For the input defect image (Figure 4(a)) the obtained

saliency map and its surface plot are shown in Figure 5 Asit could be seen in Figure 5(a) the saliency map image bysaliency extraction is properly able to suppress the texturedbackground and amplify the difference between the inter-esting defect object and the textured background Moreoverin the surface plot image which is shown in Figure 5(b)the contrast between defect object and textured backgroundcould be obviously recognized as one peak in the image Thissurface plot image confirms that the symmetric surroundsaliency value is better than the intensity value for microsurface defect object in a textured background


Convert colorspace fromRGB to Lab

ComputeLab average

vector

Gaussian blur


(a) Original image

(b) Filter image

(c) Lab color space image of original image

(d) Lab color space image of filter image

I120583 =

L120583

a120583

b120583

[ [

If =

Lf

af

bf

[ [

S(x y) = I120583(x y) minus If(x y)

Figure 4 Schematic of the saliency extraction for the input defect image

(a) Saliency map

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(b) Surface plot of saliency map

Figure 5 Saliency map and its surface plot

32 Saliency Convex Active Contour Model The extractedsaliency map in Section 31 is exploited as a feature torepresent the pixels In view of the statistical information ofthe above feature this feature is fused into a convex energyminimization function of local-based active contour thatis the saliency convex active contour model (SCACM) isproposed

The energy function of local-based active contour is firstlydefined as

min119862

119864 (1198981 1198982 119862)

= int119862

119871 (119904 119862) d119904 + 120582intinside(119862)

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2d119909

+ 120582intoutside(119862)

1003816100381610038161003816119878 (119909) minus 11989821003816100381610038161003816

2d119909

(4)

where 119871(119904 119862) is the function with respect to the length ofcurve 119862 119904 is the integral variable for the length of curve 119862 120582is a fixed parameter 119878(119909) is saliency map and119898

1and119898

2are

two constants that approximate the image intensities insideand outside the contour 119862 respectively

1198981= mean (119878 isin (119909 isin Ω | 120601 (119909) lt 0 cap 119882

119896(119909))) (5)

1198982= mean (119878 isin (119909 isin Ω | 120601 (119909) gt 0 cap119882

119896(119909))) (6)

where 119882119896(119909) is a local Gaussian window with standard

deviation 120590 and size of the window is determined as (4120590 +1) times (4120590 + 1)

Equation (4) is usually handled with the level set method(LSM) where 119862 is represented by a level set function 120601


(a) Spot-defect image 1 (b) Spot-defect image 2

(c) Result of the SBM (d) Result of the SBM

(e) Result of the proposed SCACM (f) Result of the proposed SCACM

Figure 6 Results of the different methods for spot-defect image 1 and image 2

Therefore the LSM formulation of (4) is as follows

min120601

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla119867 (120601)1003816100381610038161003816

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

119867(120601) d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119867 (120601)) d119909(7)

where 120601 is level set function and119867(120601) is Heaviside functionAlthough the LSM is a successful numerical method to

solve (4) the level set minimization problem of (7) is anonconvex energy minimization problem This means thatthe final solution depends on the initial contour In otherwords a bad initial position can lead to a bad solution It

should be noted that the great watershed in optimization isnot between linearity and nonlinearity but between convexityand nonconvexity In order to find exact global solutions ofgeometric nonconvex problems Bresson et al [14] presenteda convex relaxation technique Recently Brown et al [15]proposed completely convex formulation of the Chan-Vesemodel Inspired by these methods mentioned above a newconvex active contour model based saliency is proposedEquation (7) is firstly reformulated as follows

min120601isin01

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla1206011003816100381610038161003816 + 120582 sdot int

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

120601 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 120601) d119909(8)


SDI 3

SDI 4

SDI 5

SDI 6

SDI 7

SDI 8

Original image SBM SCACM

Figure 7 Results of the different methods for spot-defect images (SDI 3simSDI 8)

In order to avoid any confusion with the LSM thenotation 120601 is changed into 119906 Function 119906 is constrained in[0 1] Equation (8) is reformulated as follows

min119906isin[01]

119864 (1198981 1198982 119906) = int |nabla119906| + 120582 sdot int

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

119906 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119906) d119909(9)

Minimizing (9) with respect to 119906 is equivalent to mini-mizing the saliency convex active contour model (SCACM)

min119906isin[01]

119864SCACM

(1198981 1198982 119906) = int |nabla119906| d119909 + 120582 sdot int 119903 sdot 119906 d119909

(10)


SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20

Original image SCACM Original image SCACM

Figure 8 Results of the SCACM for spot-defect images (SDI 9simSDI 20)

37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n

Label of the spot-defect image

Value of SBMAverage value of SBMAverage value of SCACM

(NFD

)

Figure 9 The NFD value of the two methods in spot-defect images(SDI 1simSDI 20)

where int |nabla119906|d119909 is the weighted total variation of function 119906and 119903 is defined as

119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)

In view of the fact that the numerical minimizationschemes of LSM are slow to converge to the minimizer a fastand accurate numerical minimization algorithm for (10) isintroduced in this work This algorithm is named the split

Bregman method which is proposed by Goldstein et al [16]A new vector function d is introduced as follows

min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909

such that d = nabla119906(12)

The constraint d = nabla119906 is enforced using the efficientBregman iteration approach [13] defined as

(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2

10038161003816100381610038161003816d minus nabla119906 minus b11989610038161003816100381610038161003816 d119909

119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)

The minimizing solution 119906119896+1 is characterized by the

optimality condition

120583Δ119906 = 120582 sdot 119903 + 120583 sdot div (d119896 minus b119896) 119906 isin [0 1] (14)

A fast approximated solution is provided by a Gauss-Seidel iterative scheme that is for 119899 ge 0

120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895


(a) Steel-pit-defect image

1090807060504030201

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0806

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108

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(b) Surface plot of steel-pit-defect image

(c) Saliency map

1090807060504030201

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(d) Surface plot of saliency map

Figure 10 Saliency map and surface plot of the steel-pit-defect image

120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)

The minimizing solution d119896+1 is given by soft threshold

d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)

The main steps of the proposed SCACM scheme fordetecting micro surface defects in textured backgroundimages can be summarized as follows

Step 1 Calculate the saliency map for the input defect imageaccording to the method described in Section 31 (Figure 4)

Step 2 Initialize the local Gaussian window 119882119896(119909) The

standard deviation 120590 is set as 3 and the size of the windowis determined as (4120590 + 1) times (4120590 + 1)

Step 3 Calculate the initial values1198981198961and119898119896

2for1198981and119898

2

using (5) and (6) respectivelyMeanwhile calculate the initialvalues 119903119896 for 119903 using (11)

Step 4 Initialize the basic parameters of the Gauss-Seideliterative scheme Meanwhile solve (32) to obtain 119906119896+1

Step 5 Solve (16) to obtain d119896+1 Then solve (13) to obtainb119896+1

Step 6 If the inequality 119906119896+1 minus 119906119896 gt 120576 is true then end Ifnot consider 119899 = 119899 + 1 and update the values119898119896+1

1and119898119896+1

2

and then repeat the algorithm from Step 3


(a) Steel-pit-defect image 1 (b) Steel-pit-defect image 2



Figure 11 Results of the different methods for steel-pit-defect image 1 and image 2

Step 7 Check the final edges of curves if the edges arenonnull (ie existing defects) then they are displayed on theinput image Otherwise the input image does not have anydefects (ie the image can be deleted)

4 Experimental Results and Discussion

In this section we evaluate the performance of the proposedmethod for detecting micro surface defects including spot-defect and steel-pit-defect Meanwhile the proposed methodis compared with another method on the detection of microsurface defects

41 Implementation Details The important basic parametersof the proposed method are set as follows the size of the

Gaussian blur window in Section 31 is set as 5 times 5 thestandard deviation 120590 of local Gaussian window in Section 32is set as 3 120582 and 120583 are set as 10 and 1000 respectively More-over the split Bregmanmethod (SBM) which is proposed byGoldstein et al [16] is compared with the proposed methodfor detecting micro surface defectsThe performance of thesemethods mentioned above is evaluated by the followingperformance criteria the number of true detection (NTD)the number of false detection (NFD) and the number ofmissed detection (NMD) Furthermore the code of thesemethods is run in Matlab 710 (R2010a) software on Pentium(R) Dual-Core machine with 28GHz and 4GB of memoryand theWindows XP operating systemThe demo code of theproposed SCACM can be downloaded from our homepagehttpfacultyneueducnyunhyanSCACMhtml


SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7


Figure 12 Results of the different methods for steel-pit-defect images (SPDI 3simSPDI 7)

42 Spot-Defect Detection Spot-defect is one of the mostcommon defect types in micro surface defect of siliconsteel strip Therefore we firstly evaluate the performanceof the SBM and the proposed SCACM for detecting spot-defect Figure 6 illustrates the experimental results for the twomethods in spot-defect image 1 and image 2 As is shown inFigures 6(c) and 6(d) although the SBM can detect themicrosurface defects in the cluttered background SBM increasesthe number of false detection On the contrary in Figures6(e) and 6(f) the proposed SCACM not only detects all ofthemicro surface defects but also reduces the number of falsedetection

To further evaluate the performance of the two methodsin spot-defect images another eighteen spot-defect imagesare employed to evaluate the performance of the method

Here the spot-defect image is abbreviated as SDI forinstance spot-defect image 3 is abbreviated as SDI 3 Figure 7shows the experimental results for the two methods in spot-defect image 3 to image 8 (SDI 3simSDI 8) Obviously it isobserved that SBM detects too many false objects due tothe clutter background Although the proposed SCACMdetects two false objects in SDI 7 it detects almost all of themicrodefects without any false objects

Table 1 shows the performance criteria of detecting spot-defect (SDI 1simSDI 8) for the two methods in detail As itcould be seen in Table 1 the two methods almost have thesame number of true detection (NTD) while the NFD valueof SBM is far greater than the one of SCACM Moreoverexcept in the SDI 8 the twomethods do not have the numberof missed detection


SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n

Label of the steel-pit-defect image


(NFD

)

Figure 14 The NFD value of the two methods in steel-pit-defectimages (SPDI 1simSPDI 15)

Due to the fact that the SCACM presented better exper-imental performance than that of SBM Figure 8 only showsthe experimental results for SCACM in spot-defect image 9 toimage 20 (SDI 9simSDI 20) In addition Figure 9 illustrates theNFD value of the twomethods in spot-defect images (SDI 1simSDI 20) As is shown in Figure 9 the NFD average value ofSBM is 65 while theNFDaverage value of SCACM is only 05Therefore Figures 8 and 9 further confirmed the performanceof the proposed SCACM for detecting spot-defect

43 Steel-Pit-Defect Detection Steel-pit-defect is anothercommon defect type in micro surface defect of silicon steelstripDifferent from the spot-defect the shape of the steel-pit-defect is like that of a strip line and the intensity of the steel-pit-defect is more bright Figure 10 presents the saliency mapand surface plot of the steel-pit-defect image As it could be

Table 1 The performance criteria of detecting spot-defect for twomethods

Image Method NTD NFD NMD

SDI 1 SBM 1 37 0SCACM 1 0 0

SDI 2 SBM 1 179 0SCACM 1 1 0







seen in Figure 10(c) the cluttered background is suppressedin the saliency map Furthermore as it could be seen inFigures 10(b) and 10(d) the difference between the interestingsteel-pit-defect object and the cluttered background is ampli-fied

Figure 11 shows the experimental results for the twomethods in steel-pit-defect image 1 and image 2 FromFigures 11(c) and 11(d) it is observed that SBM detects alarger number of false detection in the cluttered backgroundHowever in Figures 11(e) and 11(f) the proposed SCACMdetects all of the micro surface defects without any falsedetection


Table 2 The performance criteria of detecting steel-pit-defect fortwo methods


SPDI 1 SBM 2 16 0SCACM 2 0 0







In addition to further evaluate the performance of thetwo methods in steel-pit-defect images another thirteensteel-pit-defect images are employed to evaluate the perfor-mance of the method In this work the steel-pit-defect imageis abbreviated as SPDI for instance steel-pit-defect image 3 isabbreviated as SPDI 3 Figure 12 illustrates the experimentalresults for the two methods in steel-pit-defect image 3 toimage 7 (SPDI 3simSPDI 7) Due to the clutter backgroundSBM detects too many false objects However except thatthe SPDI 7 has a false object the proposed SCACM detectsalmost all of the microdefects without any false objectsTable 2 shows the performance criteria of detecting steel-pit-defect (SPDI 1simSPDI 7) for the two methods in detail Asexpected the two methods almost have the same NTD valuewhile the NFD value of SBM is far greater than the one ofSCACM Moreover the NMD value of SBM is 1 in SPDI 3and SPDI 7 respectively while the SCACMdoes not have anymissed detection

Similar to Section 42 Figure 13 only shows the exper-imental results for SCACM in steel-pit-defect image 8 toimage 15 (SPDI 8simSPDI 15) Furthermore Figure 14 illus-trates the NFD value of the two methods in steel-pit-defectimages (SPDI 1simSPDI 15) As is shown in Figure 14 the NFDaverage value of SBM is 22 while the NFD average value ofSCACM is only 05 As expected Figures 13 and 14 furtherconfirmed the performance of the proposed SCACM fordetecting steel-pit-defect

44 Discussion On the whole the proposed SCACMpresents good performance for detecting micro surfacedefects including spot-defect and steel-pit-defect Even in thecluttered background the SCACM detected almost all of themicrodefects without any false objects In addition we alsoinvestigated a different size of the Gaussian blur windowwhich was set as 3times3 As expected the 3times3window obtainedthe same experiment results as those of the 5 times 5 window

Therefore the Gaussian blur window can also be set as 3 times 3in this work

5 Conclusion

In this research a new detection method based on thesaliency convex active contour model is presented to detectthemicro surface defect of silicon steel strip In order to high-light the potential objects the visual saliency extraction isemployed to suppress the clutter background in the proposedmethod The extracted saliency map is then exploited as afeature which is fused into a convex energy minimizationfunction of local-based active contour The split Bregmannumerical minimization algorithm is introduced to separatethe micro surface defects from cluttered background More-over two typical micro surface defects of silicon steel stripthat is spot-defect and steel-pit-defect are used to evaluatethe performance of the proposed method Experimentalresults demonstrate that the proposed method presents goodperformance for detecting micro surface defects The pro-posed method detects almost all of the microdefects withoutany false objects even in the cluttered background

Future perspectives of this work include extension ofdefect type and classification of the micro surface defect

Acknowledgments

Thiswork is supported by theNational Natural Science Foun-dation of China (51374063) and the Fundamental ResearchFunds for the Central Universities (N120603003)

References

[1] C Eitzinger W Heidl E Lughofer et al ldquoAssessment ofthe influence of adaptive components in trainable surfaceinspection systemsrdquo Machine Vision and Applications vol 21no 5 pp 613ndash626 2010

[2] E Lughofer J E Smith M A Tahir et al ldquoHuman-machineinteraction issues in quality control based on online image clas-sificationrdquo IEEE Transactions on Systems Man and CyberneticsA vol 39 no 5 pp 960ndash971 2009

[3] K C Song and Y Y Yan ldquoA noise robust method based oncompleted local binary patterns for hot-rolled steel strip surfacedefectsrdquo Applied Surface Science vol 285 pp 858ndash864 2013

[4] P Caleb-Solly and J E Smith ldquoAdaptive surface inspection viainteractive evolutionrdquo Image and Vision Computing vol 25 no7 pp 1058ndash1072 2007

[5] J Li J Shi and T-S Chang ldquoOn-line seam detection inrolling processes using snake projection and discrete wavelettransformrdquo Journal of Manufacturing Science and Engineeringvol 129 no 5 pp 926ndash933 2007

[6] E Pan L Ye J Shi and T-S Chang ldquoOn-line bleeds detectionin continuous casting processes using engineering-driven rule-based algorithmrdquo Journal of Manufacturing Science and Engi-neering vol 131 no 6 pp 0610081ndash0610089 2009

[7] J P Yun S Choi and SW Kim ldquoVision-based defect detectionof scale-covered steel billet surfacesrdquo Optical Engineering vol48 no 3 Article ID 037205 2009

[8] J P Yun S Choi J-WKim and SWKim ldquoAutomatic detectionof cracks in raw steel block using Gabor filter optimized by


univariate dynamic encoding algorithm for searches (uDEAS)rdquoNDT and E International vol 42 no 5 pp 389ndash397 2009

[9] F G Bulnes R Usamentiaga D F Garcıa and J MolledaldquoVision-based sensor for early detection of periodical defectsin web materialsrdquo Sensors vol 12 no 8 pp 10788ndash10809 2012

[10] A Landstrom and M J Thurley ldquoMorphology-based crackdetection for steel slabsrdquo IEEE Journal of Selected Topics in SignalProcessing vol 6 pp 866ndash875 2012

[11] X W Zhang W Li J Xi Z Zhang and X N Fan ldquoSurfacedefect target identification on copper strip based on adaptivegenetic algorithm and feature saliencyrdquoMathematical Problemsin Engineering vol 2013 Article ID 504895 10 pages 2013

[12] R Achanta S Hemami F Estrada and S SusstrunkldquoFrequency-tuned salient region detectionrdquo in Proceedingsof the the 27th IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo09) pp 1597ndash1604 Miami Fla USA 2009

[13] R Achanta and S Susstrunk ldquoSaliency detection using max-imum symmetric surroundrdquo in Proceedings of the 17th IEEEInternational Conference on Image Processing (ICIP rsquo10) pp2653ndash2656 Hong Kong China September 2010

[14] X Bresson S Esedoglu P Vandergheynst J-P Thiran and SOsher ldquoFast global minimization of the active contoursnakemodelrdquo Journal of Mathematical Imaging and Vision vol 28 no2 pp 151ndash167 2007

[15] E S Brown T F Chan and X Bresson ldquoCompletely convexformulation of the Chan-Vese image segmentation modelrdquoInternational Journal of Computer Vision vol 98 no 1 pp 103ndash121 2012

[16] T Goldstein X Bresson and S Osher ldquoGeometric applicationsof the split Bregman method segmentation and surface recon-structionrdquo Journal of Scientific Computing vol 45 no 1-3 pp272ndash293 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Camera

Movement direction

Light source

Silicon steel

Figure 1 Schematic of the image acquisition

these microobjects Furthermore the cluttered backgroundincreases the difficulty of detecting the defects in images

In recent years local energy functions based on activecontour have been introduced for object detection whichmakes it possible to detectmicro surface defect of silicon steelstrip in images with cluttered background In this work a newdetection method based on saliency convex active contourmodel (SCACM) is proposed to detect micro surface defectsof silicon steel strip In the proposed method visual saliencyextraction is employed to suppress the clutter backgroundThe extracted saliency map is exploited as a feature torepresent the pixels in the proposed model Then the abovefeature is fused into a convex energy minimization functionof local-based active contour Finally a fast and accuratenumerical minimization algorithm is introduced to separatethe micro surface defects from cluttered background

The rest of this paper is organized as follows Section 2presents the hardware configuration of image acquisition andthe analysis of micro surface defect Section 3 introduces theproposed saliency convex active contour model in detailThen Section 4 elaborates the experiments and discusses theexperimental results Finally Section 5 concludes the paper

2 Image Acquisition and Analysis of MicroSurface Defect

The hardware configuration of the image acquisition mainlyincludes two components light source and camera Thelayout of the acquisition equipment is shown in Figure 1 Thelight source provides the illumination to make the surfacedefects visible and helps to capture the surface defect imageswith camera Since the light-emitting diode (LED) has manyadvantages such as little power and longevity it is used toprovide stable illumination In this work the LED is made byCCS IncorporatedCompany of Japanwith themodel numberHLND-1200-SW2 In order to obtain themicro surface defectimage an area scan CCD camera is used The camera usedhere is made by Basler of Germany with the model numberacA640-90uc It has a resolution of 658 times 492 pixels withframe rate 90 fps and color image In this work the capturedcolor image is resized as 640 times 480 pixels for the purpose

of calculating expediently for defect detection In additiona 55mm focal length lens is installed on the camera

One of the original micro surface defect images of siliconsteel strip is shown in Figure 2 As it could be seen inFigure 2(a) the original defect image represents an area of96 times 72mm2 in real silicon steel strip It is observed thatthe defect image contains two components the interestingmicrodefect object and the cluttered backgroundThe formeris to be detected while the latter is useless To illustratethe scale of microdefect object an area of 60 times 60 pixelsis cropped from original defect image The cropped arearepresents an area of 09 times 09mm2 in real silicon steelstrip which is shown in Figure 2(b) Then the defect areain Figure 2(c) is extracted from the cropped area FromFigure 2(c) we can see that the defect area consists of 6 times6 pixels that is the size of microdefect object is an areaof 90 times 90120583m2 in real silicon steel strip Obviously it isquite difficult to detect the microdefect object for most of thecurrent detection methods whose size of defect object is anarea of 05 times 05mm2

Furthermore the background of original microdefectimage is quite complex which is another difficult problemfor detecting the defect Despite the fact that the clutterbackground has certain characters of texture these charactersare more random than regular texture The surface plot ofFigure 2(a) is shown in Figure 3 As it could be seen inFigure 3 the clutter background has random distribution inthe whole image

In addition due to the surface roughness of silicon steelstrip the microdefect image contains some interference likenoise in clutter backgroundThis interference to some extentincreases the difficulty of detecting the defects in images

3 Saliency Convex Active Contour Model

In this section the proposed method is described in two sub-sections Firstly a saliency extraction approach is introducedin Section 31 for the purpose of highlighting the potentialobjects to get a saliency map Then the saliency map is fusedinto a convex energy minimization function in Section 32

31 Saliency Extraction Saliency extraction is an importantstep in machine vision which has been applied in manytasks including object detection and image segmentation Anexcellent saliency extraction method can well highlight thepotential objects to get a saliency map However most of thecurrent saliency methods often generate saliency maps thathave low resolution or poorly defined borders Furthermoresomemethodsmay generatemaps that have ill-defined objectboundaries

In order to avoid these drawbacks mentioned aboveAchanta et al [12] exploited a frequency-tuned approach toestimate center-surround contrast using color and luminancefeatures Although the frequency-tuned approach created fullresolution saliency maps with well-defined boundaries ofsalient objects it may fail to correctly highlight the salientregions in the presence of microsalient objects and complextextured background In this work the symmetric surround


96 mm

72 m

m

90120583m

09 mm

09 m

m90120583

m


(c) Defect

(b) Cropped area


1090807060504030201

01

0806

0402

0

108

0604

020




119878 (119909 119910) =10038171003817100381710038171003817I120583(119909 119910) minus I

119891(119909 119910)

10038171003817100381710038171003817 (1)








I120583(119909 119910) =

1

119860

119909+1199090

sum

119894=119909minus1199090

119910+1199100

sum

119895=119910minus1199100

I (119894 119895) (2)



as

1199090= min (119909 119908 minus 119909)

1199100= min (119910 ℎ minus 119910)

119860 = (21199090+ 1) (2119910

0+ 1)

(3)








ComputeLab average

vector

Gaussian blur


(a) Original image

(b) Filter image



I120583 =

L120583

a120583

b120583

[ [

If =

Lf

af

bf

[ [



(a) Saliency map

1090807060504030201

0

10908070605040302010

108

0604

020





min119862

119864 (1198981 1198982 119862)

= int119862

119871 (119904 119862) d119904 + 120582intinside(119862)

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2d119909

+ 120582intoutside(119862)

1003816100381610038161003816119878 (119909) minus 11989821003816100381610038161003816

2d119909

(4)


1and119898

2are



119896(119909))) (5)


119896(119909))) (6)










min120601

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla119867 (120601)1003816100381610038161003816

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

119867(120601) d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119867 (120601)) d119909(7)




min120601isin01

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla1206011003816100381610038161003816 + 120582 sdot int

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

120601 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 120601) d119909(8)


SDI 3

SDI 4

SDI 5

SDI 6

SDI 7

SDI 8




min119906isin[01]


1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

119906 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119906) d119909(9)


min119906isin[01]

119864SCACM


(10)


SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20



37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n



(NFD

)



119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)



min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909



(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2


119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)





120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895



1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










96 mm

72 m

m

90120583m

09 mm

09 m

m90120583

m


(c) Defect

(b) Cropped area


1090807060504030201

01

0806

0402

0

108

0604

020




119878 (119909 119910) =10038171003817100381710038171003817I120583(119909 119910) minus I

119891(119909 119910)

10038171003817100381710038171003817 (1)








I120583(119909 119910) =

1

119860

119909+1199090

sum

119894=119909minus1199090

119910+1199100

sum

119895=119910minus1199100

I (119894 119895) (2)



as

1199090= min (119909 119908 minus 119909)

1199100= min (119910 ℎ minus 119910)

119860 = (21199090+ 1) (2119910

0+ 1)

(3)








ComputeLab average

vector

Gaussian blur


(a) Original image

(b) Filter image



I120583 =

L120583

a120583

b120583

[ [

If =

Lf

af

bf

[ [



(a) Saliency map

1090807060504030201

0

10908070605040302010

108

0604

020





min119862

119864 (1198981 1198982 119862)

= int119862

119871 (119904 119862) d119904 + 120582intinside(119862)

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2d119909

+ 120582intoutside(119862)

1003816100381610038161003816119878 (119909) minus 11989821003816100381610038161003816

2d119909

(4)


1and119898

2are



119896(119909))) (5)


119896(119909))) (6)










min120601

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla119867 (120601)1003816100381610038161003816

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

119867(120601) d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119867 (120601)) d119909(7)




min120601isin01

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla1206011003816100381610038161003816 + 120582 sdot int

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

120601 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 120601) d119909(8)


SDI 3

SDI 4

SDI 5

SDI 6

SDI 7

SDI 8




min119906isin[01]


1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

119906 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119906) d119909(9)


min119906isin[01]

119864SCACM


(10)


SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20



37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n



(NFD

)



119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)



min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909



(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2


119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)





120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895



1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











ComputeLab average

vector

Gaussian blur


(a) Original image

(b) Filter image



I120583 =

L120583

a120583

b120583

[ [

If =

Lf

af

bf

[ [



(a) Saliency map

1090807060504030201

0

10908070605040302010

108

0604

020





min119862

119864 (1198981 1198982 119862)

= int119862

119871 (119904 119862) d119904 + 120582intinside(119862)

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2d119909

+ 120582intoutside(119862)

1003816100381610038161003816119878 (119909) minus 11989821003816100381610038161003816

2d119909

(4)


1and119898

2are



119896(119909))) (5)


119896(119909))) (6)










min120601

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla119867 (120601)1003816100381610038161003816

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

119867(120601) d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119867 (120601)) d119909(7)




min120601isin01

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla1206011003816100381610038161003816 + 120582 sdot int

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

120601 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 120601) d119909(8)


SDI 3

SDI 4

SDI 5

SDI 6

SDI 7

SDI 8




min119906isin[01]


1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

119906 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119906) d119909(9)


min119906isin[01]

119864SCACM


(10)


SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20



37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n



(NFD

)



119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)



min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909



(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2


119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)





120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895



1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















min120601

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla119867 (120601)1003816100381610038161003816

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

119867(120601) d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119867 (120601)) d119909(7)




min120601isin01

119864 (1198981 1198982 120601) = int

1003816100381610038161003816nabla1206011003816100381610038161003816 + 120582 sdot int

1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

120601 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 120601) d119909(8)


SDI 3

SDI 4

SDI 5

SDI 6

SDI 7

SDI 8




min119906isin[01]


1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

119906 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119906) d119909(9)


min119906isin[01]

119864SCACM


(10)


SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20



37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n



(NFD

)



119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)



min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909



(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2


119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)





120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895



1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SDI 3

SDI 4

SDI 5

SDI 6

SDI 7

SDI 8




min119906isin[01]


1003816100381610038161003816119878 (119909) minus 11989811003816100381610038161003816

2

119906 d119909

+ 120582 sdot int1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(1 minus 119906) d119909(9)


min119906isin[01]

119864SCACM


(10)


SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20



37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n



(NFD

)



119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)



min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909



(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2


119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)





120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895



1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SDI 9

SDI 10

SDI 11

SDI 12

SDI 13

SDI 14

SDI 15

SDI 16

SDI 17

SDI 18

SDI 19

SDI 20



37

179

80

34 3219 24 33

9884 91

48

9275

102

176

2849 16 8

65

050

20406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The n

umbe

r of f

alse

det

ectio

n



(NFD

)



119903 =1003816100381610038161003816119878 (119909) minus 1198981

1003816100381610038161003816

2

minus1003816100381610038161003816119878 (119909) minus 1198982

1003816100381610038161003816

2

(11)



min119906isin[01]d

119864SCACM

(1198981 1198982 119906) = int |d| + 120582 sdot 119903 sdot 119906 d119909



(119906119896+1

d119896+1) = min119906isin[01]d

int |d| + 120582 sdot 119903 sdot 119906 +120583

2


119896 ge 0

b119896+1 = b119896 + nabla119906119896+1 minus d119896+1(13)





120572119894119895= d119909119896119894minus1119895

minus d119909119896119894119895

minus b119909119896119894minus1119895

+ b119909119896119894119895

+ d119910119896119894119895minus1

minus d119910119896119894119895

minus b119910119896119894119895minus1

+ b119910119896119894119895



1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1090807060504030201

01

0806

0402

0

108

0604

020


(c) Saliency map

1090807060504030201

01

0806

0402

0

108

0604

020



120573119894119895=1

4(119906119896119899

119894minus1119895+ 119906119896119899

119894+1119895+ 119906119896119899

119894119895minus1+ 119906119896119899

119894119895+1minus120582

120583119903 + 120572119894119895)

119906119896+1119899+1

119894119895= max min 120573

119894119895 1 0

(15)


d119896+1 = nabla119906119896+1

+ b1198961003816100381610038161003816nabla119906119896+1 + b1198961003816100381610038161003816

max (10038161003816100381610038161003816nabla119906119896+1

+ b11989610038161003816100381610038161003816 minus 120583minus1 0) (16)






2for1198981and119898

2





1and119898119896+1

2













SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SPDI 3

SPDI 4

SPDI 5

SPDI 6

SPDI 7








SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SPDI 8

SPDI 9

SPDI 10

SPDI 11

SPDI 12

SPDI 13

SPDI 14

SPDI 15



1619

38

3128 28 26

18

23 26

10 18 12

25

14

22

0505

10152025303540

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The n

umbe

r of f

alse

det

ectio

n



(NFD

)







SDI 2 SBM 1 179 0SCACM 1 1 0























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra























5 Conclusion



Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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