Adaptive Thresholding Based On Co-Occurrence Matrix Edge Information

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1 44 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER 27 Adative hresholdig Based O o-occurrece Matrix Edge Iformatio M. M. Mokji Faculty of Electrical Egieerig Uiversity of echology Malaysia, Malaysia musa@fke.utm.my S.A.R. Abu Bakar Faculty of Electrical Egieerig Uiversity of echology Malaysia, Malaysia syed@fke.utm.my Abstract I this aer, a adative thresholdig techique based o gray level co-occurrece matrix (GLM) is reseted to hadle images with fuzzy boudaries. As GLM cotais iformatio o the distributio of gray level trasitio frequecy ad edge iformatio, it is very useful for the comutatio of threshold value. Here the algorithm is desiged to have flexibility o the edge defiitio so that it ca hadle the object s fuzzy boudaries. By maiulatig iformatio i the GLM, a statistical feature is derived to act as the threshold value for the image segmetatio rocess. he roosed method is tested with the starfruit defect images. o demostrate the ability of the roosed method, exerimetal results are comared with three other thresholdig techiques. Idex erms o-occurrece matrix, etroy, thresholdig, edge magitude I. INRODUION hresholdig techiques are ofte used to segmet images cosistig of dark objects agaist bright backgrouds, or vice versa. It also offers data comressio ad fast data rocessig [1]. he simlest way is through a techique called global thresholdig, where oe threshold value is selected for the etire image, which is obtaied from the global iformatio. However, whe the backgroud has o-uiform illumiatio, a fixed (or global) threshold value will oorly segmet the image. hus, a local threshold value that chages dyamically over the image is eeded. his techique is called adative thresholdig. May works have bee doe to formulate the best techique for the adative thresholdig to accommodate image coditios such as o-uiform illumiatio, oisy image ad comlex backgroud [1-15]. Basically these techiques ca be divided ito regio-based ad edgebased thresholdig. Regio-based techique uses the whole image to extract the iformatio for the threshold value comutatio, while edge-based techique is based o the attributes alog the cotour betwee the object ad the backgroud. For regio-based techique, most of the early itroduced techiques are based o the image histogram. I 1979, Otsu [2] reseted a techique that cosidered the image histogram as havig a two gaussia distributio reresetig the object ad the backgroud. A threshold is selected to maximize the iter-class searatio o the basis of the class variaces. Usig the same two gaussia classes assumtio, Kittler ad Illigworth [3] selected a threshold value that miimized error i the Bayes sese. However, the shae of the image histogram is usually multi-modal istead of bimodal. Oe solutio for this roblem is by cosiderig the local statistic measure of the iut image [4]. hese statistics iclude the mea value of the gray level ad fuctio obtaied from the miimum ad maximum values of the gray level. Aart from that, a thresholdig techique, which is based o illumiatio-ideedet cotrast measure, is itroduced to segmet outdoor scee images [1]. he rimary idea of this method is to emloy oly the cotrast measure ad its threshold i a regio-wise iterolatio of the threshold for the adjacet regios. For the edge-based thresholdig techique, the idea of alyig the boudary based attributes is based o the fact that discrimiat features exist at the boudary betwee the object ad the backgroud [5]. hus, the edge-based thresholdig techique has become more oular for exloratio. Milgram [6] alied edge iformatio to segmet images by roosig suerslice method. I this method, the edge iformatio (gradiet) is itegrated with the recursive regio slittig techique. he suerslice method was also alied ad imroved i Refereces [5, 7]. For a more comlex aroach, a multiscale comutatio through wavelet trasform was itroduced. For examle, Zhoghua [8] extracted the edge iformatio o both of the coarse ad fie scale of the wavelet trasform to comute the threshold value. his is to make sure that the comutatio is less affected by oise. Usig almost the same idea, Zhag et. al [9] used the techique for the segmetatio of bright targets i a image. Aother aroach for the edge-based

2 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER thresholdig is based o the co-occurrece matrix where distributio of grayscale trasitios together with the edge iformatio is embedded i the matrix [1]. From the co-occurrece matrix, several tyes of etroies such as global, local, joit ad relative etroy are comuted to determie the threshold value [1-15]. his techique is simle ad easy to use because the co-occurrece matrix itself already cotais most iformatio eeded for threshold value comutatio. However, most of the techiques do ot use the edge iformatio i the cooccurrece matrix effectively ad roduce oor result whe dealig with oisy, comlex backgroud ad fuzzy boudary images. hus, this aer is roosig a ew techique based o the co-occurrece matrix where statistical features will be defied from the edge iformatio to hadle images that have fuzzy boudaries betwee the object ad the backgroud of the image. II. GRAY LEVEL O-OURRENE MARIX co-occurrece matrix (GLM) has bee rove to be a very owerful tool for texture image segmetatio [16, 17]. GLM describe the frequecy of oe gray toe aearig i a secified satial liear relatioshi with aother gray toe withi the area of ivestigatio [18]. Here, the co-occurrece matrix is comuted based o two arameters, which are the relative distace betwee the ixel air d measured i ixel umber ad their relative orietatio φ. Normally, φ is quatized i four directios (horizotal:, diagoal: 45, vertical: 9 ad ati-diagoal: 135 ) [18]. hese orietatios are referred to the 4-adjacecy ixels at ( x + d,, ( x, y 1), ( x 1, ad ( x, y + 1). I ractice, for each d, the resultig values for the four directios are averaged out. o show how the comutatio is doe, for image I, let m rereset the gray level of ixels ( x, ad rereset the gray level of ixels ( x ± dφ1, y ± dφ2 ) with L level of gray toes where x M 1, y N 1 ad m, L 1. ( φ 1, φ2 ) is set to ( 1,) for horizotal directio, ( 1, 1) for diagoal directio, (,1) for vertical directio ad ( 1,1 ) for ati-diagoal directio. From these reresetatios, the gray level cooccurrece matrix m, for distace d ad directio φ ca be defied as M N = R P{ I( x, = m & I( x ± dφ, y ± dφ ) = } x= y= 1 2 where P {.} = 1 if the argumet is true ad otherwise, P {.} =. I words, for each of the itesity air ( m,, Equatio 1 couts the umber of the ixel air that occurred i the whole image I at relative distace d ad directio φ. Variable R i Equatio 1 ormalized (1) the comutatio. hus, GLM is actually reresets the robability of the ixel airs. As a examle, Figure 1 shows the GLM for d = 1, φ = ad M = N = L = 4 where the resultig GLM is atidiagoally symmetry. I = Figure 1. GLM I the classical aer [19], Haralick et. al have itroduced fourtee textural features from the GLM ad the i Referece [2] stated that oly six of the textural features are cosidered to be the most relevat. hose textural features are Eergy, Etroy, otrast, Variace, orrelatio ad Iverse Differece Momet. All these textural features are comuted based o the frequecy or reetitio of the ixel air, as it is the aaret iformatio cotais i the GLM. However, there is aother iformatio, which is alied for the comutatio of a few of the textural features. It ca be best described as a edge magitude defied as gray value differece of the ixel air. Iside the GLM, the edge magitude is ot show by the value of the matrix but the value of the edge magitude is determied by the ositio of the ixel air iside the GLM. Visually, the edge magitude icreases diagoally i the GLM as show by the bold arrows i Figure 2 (,) m 1 = 24 Figure 2. Edge magitude From Figure 2, the edge magitude is equal to zero alog the symmetrical lie where m = while the maximum value of the edge magitude are located at (l,) ad (, l) where l = L 1 is the maximum value of the gray toe of the image. Amog the six textural values defied from the GLM, oly the cotrast comutatio icludes the edge magitude iformatio as show i Equatio 2. his is why cotrast has the ability to measure coarseess of a image. For variace ad correlatio, almost similar iformatio is icluded. However, the edge iformatio is comuted based o the Symmetrical lie

3 46 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER 27 curret ixel air ad the mea ixel value of the image rather tha based o the ixel air aloe. 2 ON = ( (2) = m= = m = Object i a image is visible if the boudary of the object is visible. Oe way of quatifyig the visibility of the object s boudary ca be doe by alyig the edge magitude comutatio. Normally, the object s boudary will have higher edge magitude value comare to the object regio itself ad the backgroud regio of the image. I GLM, istead of the ability of reresetig the edge magitude, the matrix ca be artitioed ito sub-regios where object, backgroud ad boudary of the object are laced i differet regio. hese regios are called GLM quadrats [22]. III. GLM QUADRANS Whe a threshold value is chose ad maed o the GLM, the threshold value artitios the GLM ito four quadrats as show i Figure 3. Quadrat A reresets gray level trasitio withi the object (dark area) while quadrat D reresets gray level trasitio withi the backgroud (bright area). he gray level trasitio betwee the object ad the backgroud or across the object s boudary is laced i quadrat B ad quadrat. hese four regios ca be further groued ito two classes, referred to as local quadrat ad joit quadrat. Local quadrat is referred to quadrat A ad D ad it is called local quadrat because the gray level trasitio arises withi the object or the backgroud of the image. he quadrat B ad is referred as joit quadrat because the gray level trasitio occurs betwee the object ad the backgroud of the image. (,) A B a result, two differet images with idetical image histogram will results similar threshold value [22]. he roblem is solved whe Pal ad Pal itroduced etroy based thresholdig based o GLM where correlatio of the ixel air is cosidered [13]. I their method, local etroy ( H LE ) is comuted withi the local quadrats. As there are two local quadrats i GLM (quadrat A ad D), two etroy values are comuted for each of the local quadrat as i Equatio 3 ad 4. H A ( ) = ( log( (3) m= = H ( ) = ( log( (4) D m= + 1 = + 1 he H LE is the derived by summig u the H A ( ) ad H D ( ). Based o the H LE, Pal ad Pal chose the threshold value as LE values secified by Equatio 6, which maximize the H LE defied by Equatio 5. H ( ) = H ( ) H ( ) (5) LE A + D = arg max H ( ) LE LE = (,1,..., ) (6) Alteratively, Pal ad Pal also derived etroy called joit etroy, H JE (Equatio 9) where it is a summatio of etroy i quadrat B (Equatio 7) ad etroy i quadrat (Equatio 8). H B ( ) = ( log( (7) m= = + 1 H ( ) = ( log( (8) H m= + 1 = ( ) = H ( ) H ( ) (9) JE B + m D Similar to local etroy, threshold value based o the joit etroy is selected whe maximum H is achieved. his is show i Equatio 1 where is the resultig threshold value. JE JE Figure 3. GLM quadrats As metioed i the Itroductio sectio, etroy as oe of the GLM feature is the oly feature alied to determie the threshold value [1-15]. Before etroy is quatified based o GLM, it is quatified based o gray level image histogram [23]. he drawback of this techique is lack of gray level correlatio iformatio. As = arg max H ( ) JE JE = (,1,..., ) (1) Aother etroy that ca be derived from the GLM quadrats is global etroy ( H ), which is simly defied as the sum of the local etroy ad the joit GE

4 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER etroy. he threshold value is the selected based o Equatio 11. = arg max H ( ) GE GE = (,1,..., ) (11) A exteded formulatio of the etroy, which is called relative etroy was also itroduced [22]. It is defied by Equatio 12 where, is GLM geerated m from the origial iut image ad geerated from the thresholded image. L 1 m= = h h is GLM J [{ };{ h }] = log (12) Relative etroy i Equatio 12 is actually a fuctio that measures the distace betwee the iut image ad the result image (thresholded image). Here, good thresholded image is the oe that tries to match the iut image. hus, the selected threshold value should be the gray value that miimizes the relative etroy as described i Equatio 13. = RE arg max J[{ };{ h }] (13) = (,1..., ) IV. PROPOSED HRESHOLDING EHNIQUE I the revious sectio, it was show how etroy i GLM is used for thresholdig. I this work, istead of etroy, iformatio based o edge magitude, which is foud i GLM cotrast quatificatio will be alied for the thresholdig rocess. Based o the edge magitude, a ew statistical feature reresetig the threshold value is comuted accordig to Equatio 14 as follow where 1 = η l l l m= = m+ l m= = m+ m + ( 2 (14) η = ( (15) ( i Equatio 14 gives iformatio o the frequecy of the ixel air ad o the other had, the edge comoet is rereseted by the rage of the two level summatio oeratios. his summatio rage forces the equatio to comute the threshold value withi a secific area i the GLM, which is a area restricted by m. his meas that the comutatio oly ivolves ixel air with the edge magitude greater tha or equals to. Figure 4 illustrates the comutatio area (shaded area) withi the GLM. By choosig a right value, the comutatio area will be o the object s boudary area. his area is differs from the GLM quadrats where the object s boudary area is laced i quadrat B ad. As the roosed techique comute the threshold value based o edge magitude, regios i the GLM are searated diagoally rather tha searatig it ito four differet rectagular as i the GLM quadrats. From Figure 4, It ca also be see that the comutatio area is oly assiged to the uer triagle of the GLM although area with edge magitude greater tha or equal to also exist at the lower triagle. he reaso is to reduce the comutatio burde as both areas at the uer ad lower triagles have similar values due to the symmetrical feature of the GLM. (,) m m Figure 4. hreshold comutatio area Symmetrical lie o illustrate the differece betwee the etroy based method ad the roosed method, Figure 5 shows three basic images ad its GLM maig. Brighter oits i the GLM rereset higher value of the GLM comoets or higher reetitio of the ixel air occurrece. Figure 5(a) is a two color image, Figure 5(b) shows a image with low blurred effect ad Figure 5(c) is a horizotal gradiet effect image where the image ixel value chages uiformly i the horizotal directio. I the etroy based method, the value is chose based o the most uiform or lowest radomess texture of the iut image i the joit quadrats [13]. Higher value of etroy cotributes to more uiform texture. hus, the resultig value for image i Figure 5(a) is equal to where white oits at the uer left, uer right ad lower left of its GLM maig were icluded i the comutatio. he thresholdig result is erfect where ixel value less tha or equals to zero becomes ad the rest becomes oe. For image i Figure 5(b), etroy based thresholdig results a threshold value equals to.92. Its thresholdig i Figure 6(b) shows a oor thresholdig. his is because the most uiform texture for the joit quadrats i the GLM is ear to the right ad bottom limit of the GLM. However, ixels value bouded by the joit quadrats have most values from to 1. hus, the resultig threshold value does ot recisely rereset the boudary s ixel values. Problem

5 48 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER 27 also occurred if the etroy based thresholdig is alied to the image i Figure 5(c) because the obtaied GLM cotaied oly ozero values maed diagoally o it. With this atter of GLM maig, for most gray values, etroy value comuted i the joit quadrats will be similar. hus the threshold value will be too low if the first maximum etroy is cosidered or the threshold value will be too high if the last maximum etroy is cosidered. Figure 6(c) shows the thresholdig results whe the first maximum etroy is cosidered. his is a oor thresholdig sice oly a small art of the image becomes dark. (a) (d) (b) (e) (a) (d) (c) (f) (b) (e) Figure 6: hresholdig results for image I Figure 5(a) to 5(c). (a)- (c) Results based o etroy method resectively, (d)-(f) Results based o the roosed techique. (c) Figure 5: Basic shaes ad their GLM maig. (a) wo color image, (b) Blurred image, (c) Gradiet image, (d)-(f) resective GLM maig for image (a)-(c) As for the roosed techique, the comutatio area is deeds o the edge magitude rather tha the GLM quadrats. I the roosed techique, oly the comutatio area is referred to the GLM while the threshold value comutatio is totally based o the gray values of the iut image (first order statistic feature). his is varyig with the etroy based techique where both the comutatio area ad the threshold value comutatio are based o the GLM ixel air reetitio (secod order statistic feature). hus a more recise reresetatio of the ixel values o the boudary of the (f) object ca be achieved by the roosed techique. Back to the three basic images i Figure 5, better thresholdig results as show i Figure 6 are obtaied by the roosed techique. For the image i Figure 5(a), the roosed techique oly icludes the GLM uer right white oit i its comutatio area. he, the average of the gray value cotaied i the comutatio area is comuted. his meas that, average of gray value ad 1 is comuted, which results a threshold value equals to.5. Previously, the etroy based techique results the threshold value equals to. For the blurred image i Figure 5(b) where most of the high values i the GLM are located ear the right ad bottom limit of the GLM, the roosed techique also results a better reresetatio of the boudary s ixel value. hus, a better threshold value is also obtaied. Based o the roosed techique, most of the GLM elemets cotaied i the joit quadrat are also icluded i the roosed techique comutatio area. By averagig all ivolve gray values i the comutatio area, threshold value equals to.57 is obtaied. By alyig this threshold value, a less corruted images is obtaied as show i Figure 6(e). For the last image as i the Figure 5(c), the roosed techique has overcome the roblem faced by the etroy based techique. If the etroy based techique oly cotaied oly certai GLM elemets i the joit

6 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER quadrats for ay gray levels value, the roosed techique icludes the etire GLM elemets i its comutatio area. hus, average value of the gray values gives a good threshold value where the iut image is segmeted evely with bright ad dark ixel as show i Figure 6(f). Aother arameter icluded i the threshold value formulatio is η, defied as the total umber of ixel airs withi the GLM with the edge magitude higher tha or equal to. Dividig the formulatio with η traslates the value to have a similar fuctio with the image gray value. his rocess is also called ormalizatio where the value is laced withi to L 1. Back to Equatio 1, ormalizatio is also alied i the GLM comutatio by dividig the formulatio with R. I the roosed techique, the GLM ormalizatio with R is igored ad relaced with the ormalizatio based o η i Equatio 14. hus, GLM used i Equatio 14 ( ( ) is ot ormalized. Relacig the ormalizatio fuctio is doe because the summatio rage i Equatio 14 has bee altered based o the shaded regio i Figure 4 while the summatio rage for GLM i Equatio 1 is the whole GLM. By adotig the ormalizatio i the Equatio 14, the thresholdig rocess ca be alied straight from the value. his circumstace gives a advatage to the roosed techique comared to the other co-occurrece matrix based thresholdig techiques [1-12] where a oliear trasformatio from the comuted arameter from the GLM is required rior to the thresholdig rocess. he oliear trasformatio is doe by selectig a gray value as a threshold value that maximizes or miimizes the arameter (Equatio 6, 1, 11, 13). he most sigificat feature i the roosed techique is its flexibility, which is deoted by variables d ad. his flexibility gives the ability to hadle either solid or fuzzy edges where wider ixel distace is occuied by the edges. Here, by chagig the value of d (relative distace betwee the ixel air) ad (edge magitude) will chage the sesitivity of the edge defiitio i the thresholdig rocess. he greater the fuzziess of the edges eed higher d ad. I revious work, such flexibility is also described i Referece [15]. However, the edge detectio rocess ad selectio of the suitable threshold value is doe searately while i this work, both rocesses are combied i oe equatio. I Referece [15], flexibility i its edge detectio rocess is ossible as it uses the Lalacia oerator where the outut deeds o the selected stadard deviatio (σ ). Figure 7 illustrates the results of the thresholdig rocess o starfruit ski with various values of d ad. he urose of the thresholdig rocess i this work is to segmet the defect area o the starfruit ski. he starfruit ski image is chose because defects o its surface have fuzzy edges as i Figure 7. he defect i the image is ot roerly segmeted whe the distace betwee the ixel air ad the edge magitude is too small (Figure 7(b) & 7(c)). he best segmetatio result is achieved whe d ad are set to 3 ad 5 resectively (Figure 7(e)) where edge is defied with wider ixel ad higher edge magitude. However, whe is set at a very high value (Figure 7(f)), o defect is segmeted. his is because i this case, ( usually has a zero value ad causes the threshold value to become ifiity. (a) (b) (c) (d) (e) (f) Figure 7. Segmetatio, (a) origial image, (b) d=1 =1, (c) d=2 =2, (d) d=2 =3, (e) d=3 =5, (f) d=3 =12. V. EXPERIMENAL RESULS Our method has bee tested with 5 starfruit defect images. hese images cotaied fuzzy edges, ueve light cocetratio ad comlex backgroud. Figure 9 shows the thresholdig results of our method o these images. For comariso, the results by Otsu method [2], Etroy based method [12] ad Yu Li method [15] are also illustrated. Otsu thresholdig algorithm is oe of the most oular methods [13, 14, 2]. It is simle ad has bee show to erform well i geeral. hus, it is icluded i the results comariso although it is ot related to the GLM while the other two methods are desiged based o the GLM. For GLM based thresholdig, etroy based method is widely used. Pal ad Pal [13] used the GLM to defie secod-order etroies, amed local etroy ad joit etroy. he, hag et al. [14] came out with a ew feature where they reseted a algorithm based o the cocet of relative etroy. Relative etroy ca be used as a criterio to measure the mismatch betwee a image ad a thresholded bilevel image [12]. However, for comariso urose, local etroy ad joit etroy is chose as features for the etroy based method. Last but ot least, the Yu Li method is chose to be icluded i the result comariso because our method ad the method roosed by Yu Li has similarity i the edge detectio elemet i the thresholdig algorithm. Here, Yu Li defied the edge based o the Lalacia comutatio as rereseted by Equatio 16 ad alied joit etroy based

7 5 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER 27 comutatio to select the threshold value. As for our method, we set d = 3 ad = 5. 2 I( x, = I( x 1, + I( x + 1, + I( x, y 1) + I ( x, y + 1) 4I( x, (16) From Figure 9, it shows that our method rovides the best result i segmetig all the test samles comare to other methods. However, whe there is a eve light cocetratio (Figure 9(b)), all the methods gave accetable results. For ueve light cocetratio ad comlex backgroud images (Figure 9(c), 9(d) & 9(e)), the results are cotrary for Etroy based method, Yu Li method ad Otsu method. Etroy based method ad Yu Li method resulted i oor segmetatio because false edges form from the ueve light cocetratio ad comlex backgroud are also comuted i their algorithms. As for the Otsu method, the oor segmetatio is due to the object (defect) ad the backgroud does ot searate well i the image histogram. Otsu method assumes that images have two ormal distributios with similar variaces. he threshold value is selected by searatig the image histogram ito two classes such that its iter-class variace is maximized [21]. Ufortuately, the ueve light cocetratio ad comlex backgroud of the tested images cause the defects to become ivisible i the Otsu comutatio. For the five images i Figure 9, the image histogram searatio by Otsu method is show i Figure 8. he figure also shows the threshold value for our method, the etroy based method ad Yu Li method. For image with the ueve light cocetratio but without the comlex backgroud (Figure 9(a)), Otsu method recogized the darker side as object although it is ot the defect because the edges of the defects are very fuzzy where it ca ot be recogize i the image histogram. he etroy based method ad Yu Li method segmets the image better as they have edge elemet i their comutatio. For our method, where more flexibility for edge defiitio is icluded, defect image with fuzzy edges ca be segmeted roerly. VI. ONLUSION I this aer, a thresholdig techique has bee roosed based o the gray level co-occurrece matrix. he techique extracts the edge iformatio ad the gray level trasitio frequecy from the GLM to comute the threshold value. he algorithm is also desiged to have the flexibility over the edge defiitio. hus, it ca hadle image with fuzzy boudaries betwee the image s object ad backgroud. he roosed techique was tested with starfruit defect image ad result good segmetatio i order to idetify the area of the defect o the starfruit ski. he results were comared with three other techiques. It showed that segmetatio usig the roosed method gives the best result comared to the other method. Magitude Magitude Magitude Magitude Magitude Proosed method = 61 Etroy based = 66 Otsu = 73 Yu Li = 67 (a) Proosed method = 76 Etroy based =79 Otsu = 78 Yu Li = 79 (b) Proosed method = 66 Etroy based = 75 Otsu = 73 Yu Li =75 (c) Proosed method = 71 Etroy based = 8 Otsu =79 Yu Li = 79 (d) Proosed method =7 Etroy based =78 Otsu = 74 Yu Li =78 (e) Figure 8. Image histogram ad threshold value, (a) to (e) are lotted from image (a) to (e) i Figure 9 resectively. REFERENES [1] A. Shio, A Automatic hresholdig Algorithm Based O A Illumiatio-Ideedet otrast Measure, IEEE omuter Society oferece o omuter Visio ad Patter Recogitio, , 4-8 Jue 1989.

8 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER [2] N. Otsu, A hreshold Selectio Method from Gray-Level Histogram, IEEE ras. o System Ma yberetics, SM, vol. 9(I), , [3] J. Kittler ad J. Illigworth. Miimum Error hresholdig, IEEE rasactios o Patter Recogitio, vol. 19, No.1, , [4] M. akatoo, Gray scale Image Processig echology Alied to Vehicle Licece Number Recogitio System, Proceedig of It. Worksho o Idustrial Alicatios of Machie Visio ad Machie Itelligece, 76-79, [5] F.H.Y. ha, F.K. La Hui Zhu, Adative hresholdig By Variatioal Method, IEEE rasactios o Image Processig, vol. 7, o. 3, , March [6] D. L. Milgra Regio Extractio Usig overget Evidece, IEEE ras. o omuter Grahics ad Image Processig, vol. 11 o. 1, [7] S. D. Yaowitz ad A. M. Bruckstei, A New Method For Image Segmetatio, IEEE ras. o omuter. Visio, Grahic ad Image Processig, vol. 46, , [8] Zhoghua liu ad Qilog Wag, Edge Detectio Ad Automatic hreshold Based O Wavelet rasform I he VPPAW Keyhole Image Processig, IEEE oferece Record of the Idustry Alicatios oferece, vol. 2, , 8-12 Oct. 2. [9] Xiao-Pig Zhag ad M.D. Desai, Segmetatio Of Bright argets Usig Wavelets Ad Adative hresholdig, IEEE rasactios o Image Processig, vol. 1 o. 7, , July 21. [1] M.L.G. Althouse,.I. hag, Image Segmetatio By Local Etroy Methods, Proceedigs of the Iteratioal oferece o Image Processig, vol. 3, , [11] Y. Ebrahi Etroy based thresholdig of crossdissolved ultrasoud images, aadia oferece o Electrical ad omuter Egieerig, vol , 23. [12] Shug-Shig Lee, Shi-Ji Horg, Horg-Re sai, Etroy hresholdig Ad Its Parallel Algorithm O he Recofigurable Array Of Processors With Wider Bus Networks, IEEE rasactios o Image Processig, vol. 8 o. 9, , Set [13] N.R. Pal ad S.K. Pal, Etroy hresholdig, IEEE ras. o Sigal Processig, vol.16, , [14].I. hag, K. he, J. Wag, M.L.G. Althouse, A Relative Etroy-Based Aroach o Image hresholdig, IEEE ras. o Patter Recog., vol. 12, , [15] Yu Li,. Mohamed,.Y. Sue, A hreshlod Selectio Method Based O Multiscale Ad Graylevel o- Occurrece Matrix Aalysis, Proc. of Eighth Iteratioal oferece o Documet Aalysis ad Recogitio, vol. 2, , 25. [16] J. Weszka,. Dyer, A. Rosefeld, A omarative Study Of exture Measures For errai lassificatio, IEEE ras. o SM, vol. 6, o. 4, , Aril [17] R.W. oers,.a. Harlow, A heoretical omariso Of exture Algorithms, IEEE ras. o PAMI, vol. 2, , May 198. [18] A. Baraldi, F. Parmiggiai. A Ivestigatio Of he extural haracteristics Associated With GLM Matrix Statistical Parameters, IEEE ras. o Geosciece ad Remote Sesig, vol. 33, o. 2, , March 1995 [19] R. Haralick, K. Shamuga I. Distei, exture Features For Image lassificatio, IEEE rasactio o SM, vol. 3, o. 6, , [2] H. ia, S.K. La. Srikatha, Imlemetig Otsu's hresholdig Process Usig Area-ime Efficiet Logarithmic Aroximatio Uit, Proc. of the Iteratioal Symosium o ircuits ad Systems, vol. 4,. IV/21-IV/24, May 23. [21].H. hou,.. Huag, W.H. Li, F. hag, Learig o Biarize Documet Images Usig A Decisio ascade, IEEE Iteratioal of. o Image Processig, vol. 2,. II/518-II/521, Set. 25. [22].-I. hag, Y. Du, J. Wag, S.-M. Guo, P.D. houi, Survey ad comarative aalysis of etroy ad relative etroy thresholdig techiques, IEE Proceedigs-Visio, Image ad Sigal Processig, vol. 153, o. 6, , Dec. 26. [23] J.N. Kaur, P.K. Sahoo, A.K. Wog, A ew method for grey-level icture thresholdig usig the etroy of the histrogram, omuter Visio, Grahic ad Image Processig, vol. 29, , 1985.

9 52 JOURNAL OF OMPUERS, VOL. 2, NO. 8, OOBER 27 (a) (b) (c) (d) (e) Figure 9. Segmetatio results for starfruit defect image (a), (b), (c), (d) ad (e). From to row to fifth row: Origial image, roosed method, Otsu Method, Etroy based method ad Yu Li method.