Comparison of Global Histogram Methods for 2D and 3D Entropy Based Image Segmentation

Transcription

1 9th WSEAS Interntionl Conferene on EVOLUTIONARY COMPUTING (EC 8, Sofi, Bulgri, My 2-4, 28 Comrison of Glol Histogrm Methods for 2D nd 3D Entroy Bsed Imge Segmenttion GEORGI PETROV (, PANAYOT ILIEV (2, PLAMEN TZVETKOV (3 NBU, Sofi, Bulgri ( NBU, Sofi, Bulgri (2 TU-Sofi, Sofi, Bulgri (3 Astrt: - In this er we exlin two funtionl models for entroy sed imge segmenttion: using glol 2D nd 3D imge histogrms of grysle imges. We omre results otined y oth methods for different tye of imges suh s: iomedil nd miro ojets, digitl video reords nd nturl hotogrhs. Short introdution of multistge grdient 3D entroy segmenttion for texture nlysis is lso introdued. 2D nd 3D entroy segmented imges n e omined to hieve etter results in litions suh s digitl video dtses nd multimedi informtion retrievl frmeworks, miro ojet lssifition for mteril nlysis nd iomedil litions. Key-Words: - 2D, 3D glol entroy imge segmenttion Introdution Imge quisition nd roessing is eoming more nd more oulr in mny onsumer nd seilized eletroni systems tody. Sine se, medil nd militry litions re de-fto stndrd tehnologil fields where imge roessing is tking le, mny high seed systems were develoed to nlyze nd store ll these dt. Tody we hve new hllenges; there re mny new ommerilly ville multimedi rih litions; suh s internet imge dtses, digitl video nd video on demnd et. Mny new semnti sed models for video ontent were develoed. These systems need to nlyze visul ontent [] in multidimensionl nd dynmi environment. Here imge nd motion segmenttion tke n imortnt role in develoment of new ojet sed video omression nd user intertion models. In st five yers our reserh ws foused on develoment of new sttistilly sed models for motion imge sequenes segmenttion. Our model is well exlined in [2]. In this rtile we desrie two tyes of imge segmenttion using glol imge histogrm multistge entroy funtion. We desrie how 2D (grey level ixel roility distriution funtion nd 3D (joint ixel roility distriution funtion n e used for utomti nd otiml imge segmenttion in different litions suh s; nturl hotogrhy, miro ojets insetion systems nd digitl video reords for seurity litions. All of these litions need fst nd relile model for utomti imge nd motion segmenttion. Mny non seilized litions suh s onsumer digitl hotogrhy dt ses need more omlex roh to hieve relile feture nd ojet segmenttion. These litions use olor imges with higher stil resolution. Color sed model for imge segmenttion use oth 2D nd 3D multistge entroy funtions nd olor imge histogrms. 2 2D Entroy sed imge segmenttion Entroy funtion of 2D grey sle imge histogrms n e used for utomti imge segmenttion [3]. Sine 2D imge histogrms reresent only the roility distriution of single ixels inside n imge, segmented imges lose some imortnt stil dt (ojet edges nd surrounding rightness trnsition zones etween ojets nd kground. 2D entroy funtion n e used for fst segmenttion, ut ll imges need to e roessed with high ss or kground removl filter first. This is imortnt eseilly for mirosoi imges. In some ses of ojet retrievl these tehniques n e used for generl urose litions like; multimedi dt segmenttion nd motion detetion. 2. Entroy lultions All sttistil oertions re erformed on normlized imge histogrms (or PDF roility distriution funtions. For 8 it grey level imges we hve orresonding 2D normlized histogrm: P( 2 = {, 2,,,, } ( where P is normlized imge histogrm, - is roility to our orresonding ixel hving rightness, where =,,, ISBN: ISSN: 79-59

2 9th WSEAS Interntionl Conferene on EVOLUTIONARY COMPUTING (EC 8, Sofi, Bulgri, My 2-4, 28 Now we lulte imge entroy H using disrete histogrm P. H i= ( P ( 2 H ( A = i log i (2 H ( B = i log i (3 i= H ( A H( B = log P( A log P( B (4 P( A P( B Where = vr from to A = vr from to B = vr from to { H, H } H ( P D = H (5 ( 2, After this we n find entroy mximum, mx H ( P ( 2 (6 Mximum of entroy funtion defines the rightness threshold vlue * for the imge (Fig.. nd Fig... funtion n rovide us the ossiilities to utomtilly threshold inut imge on 4 lyers. Algorithm is s follow:. Clulte * from H ( P ( 2, = vr from to 2. Divide histogrm in two equl histogrms P (2 nd P 2(2 if * mx = (7 if * > mx if * mx 2 = (8 if * < mx Where = vr from to 3. Clulte H ( P nd H ( P2 4. Clulte * for P (2 5. Clulte 2 * for P 2(2 6. Now we hve *, *, 2 * tht re mximum entroy funtions lulted for different P intervls. We use these vlues to threshold inut imge on 4 lyers (Fig. 2. nd Fig. 2.. Fig.., Grey sle imge (right nd its 2D PDF (left Fig.2., Multi threshold 4 lyers, using fixed vlues Fig.., BW imge (right lulted using threshold level defined y 2D entroy funtion (left 2.2 Multistge 2D entroy segmenttion Single stge 2D entroy funtion is fst nd utomti roh for threshold different tyes of imges. But in mny ses eseilly when we work with outdoor nd omlex imges this is not suffiient for otiml ojet segmenttion. Thus the multistge 2D entroy funtion n e used. Multistge entroy funtion [4] defers from single stge only y numer of itertions nd histogrm divisions y rt A nd B. Simle 4 stge entroy Fig.2., Multi threshold 4 lyer imge, using multistge 2D entroy (right nd its entroy (left This funtion n e used to rete imge ojet extrtion msk for multilyer ojet segmenttion. We n ontinue this lol entroy segmenttion using the sme roedure for ny new entroy region inside imge histogrm. Prtil limits for multi threshold to hieve etter imge segmenttion re 4, 8 nd 6 lyers. In se we hve motion imges, we n use this roedure for lulting resulting kground imge. ISBN: ISSN: 79-59

3 9th WSEAS Interntionl Conferene on EVOLUTIONARY COMPUTING (EC 8, Sofi, Bulgri, My 2-4, D Entroy sed imge segmenttion 2D entroy funtion is ommonly used for mny imge segmenttion litions. 2D entroy lks his roustness when multile imges with lrge vriety of grdient rightness etween eh other nd kground need to e segmented. Here 3D entroy funtion omes in sense. Before this we need to define nd lulte 3D imge histogrm P ( 3D, this tye of histogrm reresents the roility distriution of joint ixels (Fig. 3.. Using this histogrm we n lulte 3D entroy funtion (Fig. 3.. Finding its mximum we n threshold imge muh etter thn using 2D entroy. This tye of thresholding will rovide us informtion regrding two tyes of joint ixels: homogeneity zones (joint ixels hving the sme rightness nd non homogeneity (ojet surrounding res nd shdes. well filtered imges hve most of vlues groued round min digonl. Different uthors exmine zone C nd D sertely, ut we thing tht for most of stndrd litions we n tret B, C nd D s kground. Zones C nd D tke n imortnt role when multistge segmenttion is tking le. If we hve 3D normlized histogrm: P (3D = i,,,,,, i,,, j, j i, j, j,, i,, (9 We lulte imge 3D entroy funtion H 3 D( P ( 3 using disrete histogrm P ( 3D. 3D entroy is lulted for eh olumn nd row inside P ( 3D using method desried in setion (2.. After this we rete two 3D entroy funtions, first is lled grdient entroy funtion nd is resented y; Fig. 3, 3D imge histogrm (, 3D entroy funtion ( 3D entroy funtion is lulted s sum of ll entroy funtions lulted for 3D histogrm olumns nd rows. The mximum of this funtion n e found dividing 3D histogrm in to 4 serte regions; A, B, C, D (Fig. 4. Zones A nd B orresonds to ojet nd kground, nd zones C nd D orresonds to ojet shdes nd surrounding res rightness grdient. In most of ses 3D entroy mximum lys on the min digonl ssing through A nd B qudrnts. H 3D (3D H H = H And seond for rows; H3Dr (3D Hr Hr2 = Hr H2 H2 H2 Hr Hr2 Hr H H H Hr Hr2 Hr ( ( After this we need to find entroy mximum: mx ( H 3D( P( 3D + H3Dr( P(3 D / 2 (2 Fig. 4, 3D entroy mximum divide 3D imge histogrm in to 4 regions (A, B, C nd D This digonl lys n imortnt role in 3D histogrm, euse vlues lying on it reresent the roility to our different homogeneity zones inside of imge. If imges re noisy or very shded, their histogrm mximum n lie round min digonl. In most ses Some imlementtions my onsider 3D entroy funtion s simultneously lulted for eh one oint inside 3D histogrm. We refer to rete 3D entroy funtion s frtion of 2D olumns nd rows entroy. This kind of reresenttion gives us the right to mke imge segmenttion sed on entire 3D entroy (Fig. 5 nd on 3D grdient entroy, without hving the need to relulte 3D entroy eh time we need to mke segmenttion for homogeneity nd grdient zones. ISBN: ISSN: 79-59

4 9th WSEAS Interntionl Conferene on EVOLUTIONARY COMPUTING (EC 8, Sofi, Bulgri, My 2-4, 28 Fig. 5, Imge thresholding using 2D entroy funtion (, nd using 3D entroy funtion (. 3. Imge segmenttion using 3D grdient entroy Beuse 3D entroy is sed on 2D entroy lultion of single olumns nd rows we introdue new 3D grdient entroy funtion. This funtion exmines only the olumns of 3D histogrm, interreting vlues on min homogeneity digonl s zeros. This roh gives us owerful method to lulte entroy only of rightness trnsition zones. This tehnique give use the ower of lol dtive 2D entroy segmenttion method nd histogrm equliztion using glol 3D imge histogrm (Fig. 6. Fig. 7, Inut imge (, 3D grdient entroy (, nd 2D entroy ( ojet is lost. 3.2 Multistge 3D nd grdient entroy In setion 2.2 we exlined how multistge segmenttion msk n e lulted using P entroy sed histogrm division nd lol entroy definition. No onsiders we hve 3D entroy funtion lulted for P ( 3D. In setion 3 we define how simle BW threshold vlue n e lulted more reisely tking in ount joint ixel roility distriution. Nothing esier if we tret 3D histogrm qudrnt A nd B, C, D s we treted 2D histogrms P (2 nd P 2(2. In this se we will define P (3 nd P 2(3 histogrms (Fig. 7. Rememer to fill ll non trget histogrm qudrnts s filled with zeros. Thus the multistge 3D entroy funtion is lulted. Fig. 7, Multistge 3D entroy segmenttion Fig. 6, 3D imge grdient entroy (, imge segmented using 3D grdient entroy (, nd using stndrd 3D entroy ( 3D grdient entroy n hel us to find trget ojet even if we work with noisy imges hving d stil resolution nd ontrst (Fig. 7. 3D grdient multistge entroy is lulted y lulting entroy funtions for ll olumns of 3D histogrm, treting min digonl s filled with zeros. Differene etween 3D multistge entroy nd 3D grdient multistge entroy is shown on Fig. 8. Beuse grdient entroy nlyze nd grou only imge shding zones it n e used s stge efore imge texture nlysis. ISBN: ISSN: 79-59

5 9th WSEAS Interntionl Conferene on EVOLUTIONARY COMPUTING (EC 8, Sofi, Bulgri, My 2-4, 28 d informtion regrding imge glol shding, thus giving god kground for future texture nlysis nd roessing using glol histogrm methods. Comining results hieved y 2D multistge entroy nd 3D grdient entroy rovide vlule informtion regrding lrge nd smll ojet sttistil reresenttion. Multistge entroy imge 3D histogrms hve less dt to e omred, mking imge lssifition fster, thn using entire 3D histogrms. Comined imges re more similr to originl one (Fig. 9. e Fig. 9, Multidimensionl entroy imge omined from 2D multistge entroy nd 3D grdient entroy (, nd originl imge ( Fig. 8, Multistge entroy imge (, nd 3D entroy funtion ( nd histogrm (, 3D grdient entroy imge (d, nd its 3D entroy funtion (e, nd histogrm (f. Entire 3D entroy funtion trends to serte 3D histogrm minly inside min homogeneity digonl, mking esier to etter extrt imge homogeneity zones nd surrounding res (Fig. 8,. In oosite to this 3D grdient entroy serte 3D histogrm in to different ikes round homogeneity digonl (Fig. 8,e. 4 Comlex method for multidimensionl entroy sed imge segmenttion Aove we hve exlined two glol histogrm methods for 2D nd 3D entroy sed multistge imge segmenttion. These methods n e omined in to multidimensionl entroy imge. Results otined from 2D nd 3D multistge entroy give us good understnding out imge ojet lying in lrge stil res nd their edges nd surrounding res nd shdes. 3D grdient entroy multistge segmenttion give us the f The most imortnt in new model for omlex multidimensionl entroy sed imge segmenttion is tht we hve more informtion for stil imge regions ojets nd kground, inluding informtion out the rightness grdient inside them. Beuse 3D imge histogrms n e interreted in severl wys; min digonl homogeneity entroy, entire entroy nd 3D histogrm olumns entroy, we n extrt orresonding dt for eh one seleted re inside 3D histogrm se nd finding orresonding ojets inside grey sle imge. 5. Multidimensionl motion imge segmenttion using 3D multistge entroy funtion In mny ses imge informtion is non stti so or we need to segment imges otined in non fixed onditions. A onrete se desried here is how 3D multidimensionl imge entroy n hel us to hieve etter nd fster digitl video segmenttion. Suh segmenttion is imortnt for mny ontent nlysis ost roessing tehniques used in modern video nd imge dt se indexing nd summriztion systems. All these methods work on vetor se deling with ojets insted of imges. For relile motion sed imge segmenttion we use 3 sttistil riterions for digitl video key frme detetion: Kolmogorov, Pirson nd Comlex, our model is well exlined in [2]. Using 2D nd 3D multistge entroy imges we n fster the roess of motion detetion simultneously hieving ojet segmenttion nd sttistil lssifition, see setion 7. ISBN: ISSN: 79-59

6 9th WSEAS Interntionl Conferene on EVOLUTIONARY COMPUTING (EC 8, Sofi, Bulgri, My 2-4, Exerimentl results 3D imge entroy is glol method to sttistilly roess digitl imges roduing the similr results s sttistil mode filtrtion, histogrm strething nd lol 2D entroy definition. Imrovements n e signifint in imges tht hve lrge mount of low ss noise, suh s snned douments (Fig.. Fig., Imge segmented using 2D entroy funtion ( nd 3D grdient entroy (. Multistge entroy imroves video [6] motion segmenttion (Fig.. e Fig., Imroving motion segmenttion using multistge entroy. Originl sequene ( nd its orresonding 8, 4 nd 2 lyer entroy frmes re shown. Shows sttistil riterion lulted for originl d 8 it imge (, for 4 it entroy imge (, for 3 it entroy (d imge nd for it entroy imge (e. 4 Conlusion After this short overview on different tyes of imge entroy we n onlude tht entroy segmenttion lys n imortnt role in mss imge nlysis systems. In some simle ses when working with good nd filtered imges we n use single stge 2D entroy funtion. For etter region segmenttion in more shded imges we n use multistge 2D entroy funtion. For etter stil ojet segmenttion we definitely reommend the use of glol 3D entroy funtion nd its multistge vrint. In litions tht we use lrge imges hving different ontent (hotogrhs we reommend to use multidimensionl 2D nd 3D multistge nd grdient entroy funtion, roviding muh esier nd fster wy for region segmenttion. Entroy segmented imges n hel us to hieve etter nd fster motion segmenttion, when we need to roess long time video reords nd multimedi dt. Entroy segmenttion n e used in olor imges, ut in this se we need to onvert RGB dt formt to HSL olor se nd threding this 3D se with multidimensionl entroy funtion. Severl imrovements need to e done for roosed here 3D grdient entroy. The min rolem is how to hieve etter strtegy for sttistil imge rtifts removl simultneously with 3D entroy lultion. Referenes: [] Tzvetkov, P.; Petrov, G.,Iliev, P. Multidimensionl dynmi sene nlysis for video seurity litions IEEE Comuter Siene 26 Istnul, [2] Iliev, P.; Tzvetkov, P.; Petrov, G., Motion Detetion Using 3D Imge Histogrms Sequenes Anlysis IEEE Volume, Set. 25 Pge(s:596-6 [3] PUN. T. "A new method for grey level thresholding using the entroy of the histogrm", Signl Proessing, 98, [4] Iliev,P. Tzvetkov,P. Petrov,G. Digitl imge roessing using 3D entroy funtion, nlysis nd lssifition of miro ojets, 25 ISBN [5] G.Petrov, "Automti Imge Segmenttion using 2D Multistge Entroy", htt://instrumenttion.hit.g/pers [6] Mrk,L. G.,Althouse, "Trget detetion in multisetrl imges using the setrl o-ourrene mtrix nd entroy thresholding" Otil Engineering 34(7, (July 995 ISBN: ISSN: 79-59