ECE Department, NIT, Kurukshetra, Harayana, India

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1 ISSN : (P) ISSN : (Ol) Pfomac Evaluao of Coas Ehacm Tchqus fo Dgal Imags Vay Kuma, ma Basal, ECE Dpam, NIT, Kuusha, aayaa, Ida IJCST Vo l., Is s u, Ma c h Absac sogam qualzao (E) s wdly usd fo coas hacm dgal mags. owv, hs chqu s o vy wll sud o b mplmd cosum lcocs, such as lvso, bcaus h mhod ds o oduc ucssay vsual doao such as h sauao ffc. O of h soluos o ovcom hs wass s by psvg h ma bghss of h pu mag sd h oupu mag. Fo mpovg h coas dgal mags, sogam Equalzao (E) s o of h commo mhods usd fo coas hacm. Bu, hs chqu s o wll sud fo s mplmao cosum lcocs, as hs mhod wll oduc vsual doao such as sauao ffc. To ovcom hs wass h soluo s o psv h ma bghss of h pu mag sd h oupu mag. I hs pap h s a compaso of E wh Rcusvly Spaad ad Wghd sogam Equalzao (RSWE) ad Bghss Psvg Dyamc sogam Equalzao (BPDE). Th ssal da of RSWE s o sgm a pu hsogam o wo o mo sub-hsogams cusvly o modfy h sub-hsogams by mas of a wghg pocss basd o a omalzd pow law fuco, ad o pfom hsogam qualzao o h wghd sub-hsogams dpdly. RSIE (Rcusv Sub Imag sogam Equalzao) ad RMSE (Rcusv Ma Spaa sogam Equalzao) a som mhods smla o RSWE, bu hy do o cay ou h abov wghg pocss. W show ha compad o oh xs mhods, RSWE psvs h mag bghss mo accualy ad poducs mags wh b coas hacm. I wll hac h mag whou sv sd ffcs, ad a h sam m maa pu ma bghss. Compaso s do o h bass of dff paams l Imag Bghss Ma (IBM), Imag Coas Sadad Dvao (ICSD) ad Pa Sgal o Nos Rao (PSNR). Kywods Imag coas hacm, hsogam qualzao, bghss psvg hacm, hsogam pao. I. Ioduco Th hsogam of a dsc gay-lvl mag pss h fqucy of occuc of all gay-lvls h mag [8]. sogam qualzao s wdly usd fo coas hacm a vay of applcaos du o s smpl fuco ad ffcvss. I wos by flag h hsogam ad schg h dyamc ag of h gay-lvls by usg h cumulav dsy fuco of h mag. O dawbac of h hsogam qualzao s ha h bghss of a mag s chagd af h hsogam qualzao, hc o suabl fo cosum lcoc poducs, wh psvg h ogal bghss ad hacg coas a ssal o avod aoyg afacs. Bghss psvg b-hsogam qualzao (BBE) [], dvds h pu hsogam o wo subscos basd o h ma valu. Dualsc sub-mag hsogam qualzao (DSIE), whch has b poposd by Y.Wag, Q. Ch ad B. Zhag [], also spaas h pu hsogam o wo subscos, bu h spaao s basd o h mda valu. Ch ad Raml also hav poposd aoh mhod calld cusv ma-spaa hsogam qualzao (RMSE) [3]. RMSE cusvly dvds h hsogam o sval subscos basd o h local ma valus. Th umb of sub-scos s s by h us. Bghss psvg dyamc hsogam qualzao (BPDE) [], whch has b poposd by ad ad Ncholas, dvds h hsogam o sval subscos ad qualzs hm dpdly. owv, BPDE, h dvso of h hsogam s cad ou basd o h locaos of h local maxmums of h pu hsogam slf. I od o hac coas, psv bghss ad poduc aual loog, w hav sudd a w mhod calld Rcusvly Spaad ad Wghd sogam Equalzao (RSWE). Th ssal da of RSWE s o sgm a pu hsogam o wo o mo sub-hsogams cusvly, o modfy h sub-hsogams by mas of a wghg pocss basd o a omalzd pow law fuco, ad o pfom hsogam qualzao o h wghd sub-uhsogams dpdly. RSWE cosss of h moduls: (hsogam sgmao modul) spl a pu hsogam o wo o mo sub-hsogams cusvly basd o h ma o mda of h mag; (hsogam wghg modul) chag h sub hsogams hough a wghg pocss basd o a omalzd pow law fuco; (hsogam qualzao modul) lasly, qualz h wghd sub-hsogams dpdly. Rsuls of all h mhods a psd, dscussd ad compad wh E mhod h sco IV. Th sco V svs as h cocluso of hs wo. II. Pvous Wo Ths sco dscbs pvous wos h lau whch ma us of h E mhod wh h pupos of bghss psvg. W sa by dscbg h sogam Equalzao (E) mhod Sco II.A. Th E mhod was h bas fo h oh wo mhods, amly BBE ad DSIE. Ths mhods dcompos h pu mag o wo sub-mags whl RMSE, ME, DRSE, BPDE ad RSWE mhods dcompos h pu mag o mo ha wo sub-mags ad h qualz h hsogams of hs sub-mags dpdly. A. sogam Equalzao (E) X={X (,j)} do a gv mag composd of dsc gay lvls do as { X, X,..., X } wh X(,j) pss a sy of mag a h spaal locao (,j) ad X(, j) { X, X,..., X }.Th hsogam povds fomao fo h coas ad ovall sy dsbuo of a mag [8]. Th hsogam of a dgal mag wh gay lvls h ag [, -] s a fqucy dsbuo fuco dfd as ovall sy dsbuo of a mag. Fo a gv mag X, h pobably dsy fuco p (X) s dfd by: p( X ) = () Fo =,.., -, wh pss h umb of ms ha h lvl X appas h pu mag X ad s h oal umb of sampls h pu mag. Th cumulav dsy fuco s dfd as: Iaoal Joual of Compu Scc ad Tchology 3

2 IJCST Vo l., Is s u, Ma c h c( X ) = p( X j ) () Wh =, No ha c(x -) = by dfo. sogam qualzao s a schm ha maps h pu mag o h dyamc ag, (Xo, X-); by usg h cumulav dsy fuco as a asfom fuco. A asfom fuco f(x) s basd o h cumulav dsy fuco as: f( x) = X + ( X X) c( x) (3) E has a ffc of schg h dyamc ag of a gv hsogam sc E flas h dsy dsbuo of h mag. B. Bghss B-sogam Equalzao (BBE) I od o ovcom h dawbac oducd by h E mhod dscbd h pvous subsco, a bghss psvg B-E (BBE) mhod was poposd []. Th ssc of h BBE mhod s o dcompos h ogal mag o wo sub-mags, by usg h mag ma gay-lvl, ad h apply h E mhod o ach of h sub-mags. I [], s mahmacally show ha h BBE mhod poducs a oupu mag wh h valu of bghss (h ma gay-lvl) locad h mddl of h ma of h pu mag ad h mddl gay-lvl (.., /). X = { X (, j ) } do a gv mag composd of sy lvls dod as { X O, X I,.. ', X - },wh X (, j ) pss a sy of h mag a h spaal locao (, j ) ad X (, j ) {XO,X,, X - } ad Xm do h ma gay lvl of h mag X. Basd o h ma, h pu mag s dcomposd o wo sub mags X ad X as- X = X X (4) wh { (, ) (, ) m, (, ) } { (, ) (, ) m, (, ) } X = X j X j > X X j X (5) X = X j X j X X j X (6) Wh sub mag X s a s of { X, X, X,..., Xm} gay lvls ad h oh sub mag X s a s of { X, X,..., X } m+ m+ gay lvls. Pobably dsy fucos of h sub mag X ad X s - p ( X ) =, wh =,..,m. (7) p ( X ) =, wh = m+, m+..,-. (8) wh ad ps h spcv umbs of X gay lvl sub mag X, ad sub mag X, ad ad ps h oal umbs of pxls sub mags X ad X, spcvly. =, = m+ m = ad = = +. Th spcv cumulav dsy fucos fo sub mag X ad sub mag X a dfd as - c ( X ) p ( X ) = (9) j c ( X ) p ( X ) = () j 4 Iaoal Joual of Compu Scc ad Tchology wh C ( X m ) = ad C ( X - l ) = by dfo. Th asf fuco of ach sub mags s dfd by cumulav dsy fuco..- ( ) ( ) f ( x) = X + X X c ( x) () o m o f( x) = Xm+ + X Xm+ c( x) () Basd o hs asfom fucos, h dcomposd sub mags a qualzd dpdly ad h composo of h sulg qualzd sub mags cosus h oupu of h BBE. Tha s fally xpssd as { (, )} ( ) ( ) ( ( )) ( ) ( ( )) ( ) Y = Y j = f X f X (3) f ( X ) = f X, j X, j X (4) f( X) = f X, j X, j X (5) As w ow ha c( x), c( x), so s asy o udsad ha f(x) qualzs h sub mag X ov h ag ( X, Xm ) whas f( X ) qualzs h sub mag X ov h ag (Xm+, X-). As a cosquc, h pu mag X s qualzd ov h dyamc ag (XO, X-) wh h cosa ha h sampls lss ha h pu ma a mappd o ( X, X m ) ad h sampls ga ha h ma a mappd o (Xm+, X-). C. Dualsc Sub-Imag sogam Equalzao (DSIE) Dualsc sub-mag hsogam qualzao (DSIE) [] also spaas h pu hsogam o wo subscos. Boh BBE ad DSIE a smla xcp ha DSIE chooss o spaa h hsogam basd o gay lvl wh cumulav pobably dsy qual o.5 sad of h ma as BBE,.. sad of dcomposg h mag basd o s ma gay lvl, h DSIE mhod dcomposs h mag amg a h maxmzao of h Shao's opy of h oupu mag. Suppos mag X s sgmd by a sco wh gay lvl of X = X, ad h wo sub-mags a X ad X, so w hav X = X X, - ISSN : (P) ISSN : (Ol) { (, ) (, ), (, ) } (, ) (, ), (, ) X = X j X j < X X j X { } (6) X = X j X j X X j X (7) Wh sub-mag X s composd by gay lvl of { X, X,..., X }, whl sub-mag X s composd by gay lvl of{ X, X+,..., X }. Th agggao of h ogal mag's gay lvl pobably dsbuo s dcomposd o p( X ) wh =, - ad p( X) wh =, + - cospodgly. Pobably dsy fucos, cumulav dsbuo fucos ad h asfom fucos a obad fom quao o. 7 o quao o.. Th sul of h dualsc sub-mag hsogam qualzao s obad af h wo qualzd sub mags a composd o o mag. Suppos Y s h Oupu mag, h- { (, )} ( ) ( ) ( ) ( (, )) (, ) ( ) (, ), Y = Y j = f X f X (8) { ( ) ( ) } f X = f X j X j X (9) f X = f X j X j X ()

3 ISSN : (P) ISSN : (Ol) ( ) ( ) ( ) ( ), X + X X c X, f X < X Y(, j) = X + X X c X ohws () D. Rcusv Ma - Spaa E Mhod (RMSE) I Rcusv ma-spaa hsogam qualzao (RMSE) [3] mhod, sad of dcomposg h mag oly oc, s poposd o pfom mag dcomposo cusvly, up o a scal, gag sub-mags. Af ha, ach o of hs sub-mags s dpdly hacd usg h sogam Equalzao (E) mhod. Wh = (o sub-mags a gad) ad =, h RMSE mhod s quval o h E ad BBE mhods, spcvly. I hs mhod, h psvao of h oupu mag cass as (spaao lvl) cass. E. Bghss Psvg Dyamc sogam Equalzao (BPDE) I BPDE [] mhod h ogal mag s dcomposd o mulpl sub mags accodg o h local maxma, h h dyamc hsogam qualzao s appld o ach sub mag ad fally, h sub mags a combd. I dvds h hsogam basd o h local maxma. I poducs h oupu mag wh h ma sy almos qual o h ma sy of h pu, hus fulfls h qum of maag h ma bghss of h mag. Ths mhod smoohs h pu hsogams wh o dmsoal Gaussa fl, ad h paos h smoohd hsogam basd o s local maxma. Af ha assgs w dyamc ag o ach pao. Th, h hsogam qualzao pocss s appld dpdly o hs paos, basd o hs w dyamc ag ad h oupu mag s omalzd o h pu ma bghss. F. Rcusv Spaad ad Wghd sogam Equalzao (RSWE) RSWE cosss of h moduls (s Fg. ): hsogam sgmao, hsogam wghg, ad hsogam qualzao. Th hsogam sgmao modul as h pu mag X, compus h pu hsogam (X) ad cusvly dvds h pu hsogam o wo o mo sub-hsogams. Th hsogam wghg modul modfs h sub-hsogams by usg a omalzd pow law fuco. asly, h hsogam qualzao modul us hsogam qualzao dvdually ov ach of h modfd sub-hsogams.. sogam Sgmao Modul Ths modul dcomposs hsogams h sam way as RMSE o RSIE dos. I dvds h pu hsogam (X) cusvly up o som spcfd cuso lvl, hus gag sub-hsogams. I fac, h modul poducs wo ds of sgmd suls. O s basd o h mas of h subhsogams ad h oh o s basd o h mdas of h sub-hsogams. Each algohm s dscbd blow. (a) Sgmao by Ma Cosd a sgmd hsogam ( X ) dfd ov a gay lvl ag [ Xl, X u] a a cuso lvl ( < ). Th ma X of h sub-hsogam s compud by (), M µ µ XM =. p( ) p( ) = l = l () Basd o h compud ma X M, h hsogam ( X ) s + h dvdd o wo sub-hsogams + + fo h x cuso lvl +, wh + a dfd ov X X l, M ad X +, X M u spcvly. (b) Sgmao by Mda CDF a h gay lvl Xl s c( l) = ml ad h CDF a h gay lvl Xu s c( u) = mu Th mda X D of h subhsogam ( X ) h sasfs c( X D) = ( ml + mu)/ I pacc, h mda X s calculad fom (3), D ml + mu XD = ag m l u c( ) (3) Now, h hsogam ( X ) s spl o wo sub-hsogams + + fo h x cuso lvl + by + usg X D. No ha + a dfd ov Xl, X D ad + [ XD +, Xu] spcvly. No ha + ad a dfd ov Xl, X D ad [ X +, X ] D u spcvly. Fg. : Th Fucoal Bloc Dagam of RSWE. sogam Wghg Modul Accodg o h spcfd cuso lvl, h hsogam sgmao modul has gad sub-hsogams, ( X ) ( ) wh s dfd ov h ag [ Xl, X ] u. Fo =, h hsogam wghg modul h modfs h PDF of h sub-hsogams ( X ) as follows: (a) Compu boh h hghs pobably p ma x ad h lows pobably p m by usg (4) ad (5), pmax = max p( ) (4) pm = m p( ) (5) (b) Fo ach sub-hsogam ( X ), compu a accumulav pobably valu α by usg (6). No ha h sum of allα s s qual o (f o (7)). α u = p( ) = l IJCST Vo l., Is s u, Ma c h (6) α = α + α+ α,, X = = (7) (c) Fo ach sub-hsogam ( X ), chag h cospodg ogal PDF p() o h wghd PDF pw( ) by usg pcompud valus (.., p ma x, p m ad α ) ad quao (8) α pw( ) pmax. ( p( ) pm pmax pm ) β, ( l u) = + (8) wh, β s a valu. Th dg of h ma bghss ad coas hacm of h oupu mag ca b Iaoal Joual of Compu Scc ad Tchology 5

4 IJCST Vo l., Is s u, Ma c h coolld by adjusg β. I s xpmally foud ha h oupu mag of sasfacoy qualy ca b obad, wh β s aoud pmax. XM XG /( Xmax Xm ), wh X max ad X m a h gas ad h las gay lvls of h pu mag X, spcvly. (d) Du o h abov PDF modfcao, h sum of all h valus p ( ) w fom = o - s o log o, so h modfd PDF ds o b omalzd. Th omalzao s do by usg (9). Th sula wghd ad omalzd PDF, calld pw( ) s h fowadd o h x hsogam qualzao modul. ISSN : (P) ISSN : (Ol) µ = l p ( l ) Tabl : Imag Bghss-Ma l= Tabl : Imag Coas Sadad-Dvao l σ = ( l µ ) p ( l ) l= p ( ) = p ( ) p ( j) (9) w w w 3. sogam Equalzao Modul Acually, h PDF pw( ) cosss of cuv sgms, wh h h cuv sgm ( ) s boudd by h sam ag Xl, X u as ha of h h sub-hsogam ( X ). Th as of h hsogam qualzao modul s h o spaaly qualz ach of all sub-hsogams by usg quaos (), (), ad (3). Th combao of all sula sub-mags ow bcoms h fal oupu mag. Tabl 3: PSNR = l l log( ) / yj oj ll= III. Rsuls ad Dscussos I hs sco w compa h pfomac of all algohms accodg o h paams () Imag Bghss ma, () Imag Coas sadad Dvao, () Pa Sgal o Nos Rao (PSNR). Ths h quaos a fd fom h Mul hsogam qualzao mhods fo coas hacm ad bghss [4]. Th suls show Tabl-I xhb h bghss psvg capabls of vaous mhods cosdd hs pap. By obsvg h absolu dffc bw h valu of bghss h ogal mags ad h pocssd mags (.., h bghss psvao), w sa ha: ) h mags poducd by RSWE mhod s b psvg h bghss; ) Ev hough RSWE mhod o always h bs bghss psvg os, h sulg bghss s always vy clos o h bghss of h ogal mags h abl s show as a gy shadd aa. Apa fom hs mhod, BPDE s also clos o h mag ma bghss. If w aalys h suls Tabl II; by obsvg h coas valus, w fd ha: ) RSWE mhod poducs ovall h bs mag coas hacm. I s show abl II gy shadd aa. ) Bsds hs mhod DSIE also poduc good suls fo mag coas hacm, 3) Th RMSE (=) mhod poducs lavly small mag coas hacm. Fally w aalys h daa psd Tabl III, whch shows h abls of vaous mhods o poduc aual loog mags. Fo h bs valu of PSNR should b as much as possbl. W obsv ha h mags pocssd by h BPDE mhod poduc h bs PSNR valus. Af ha RMSE (=) shows b sul. As w ow ha fo hgh PSNR h sgal should b as hgh as possbl ad os should b as small as possbl. Bu cas of coas hacm h os s h vaao of pxl valu ad f s vaao s lss h s o possbl o cas h coas of dgal mag. So BPDE v hough has hav bs PSNR, dos o poduc good coas. Moov, dos o psv bghss as wll. c wh ou am s o hac h coas h w ca glc h PSNR. (a) (b) (c) Fg. : Oupu RWSE Mhod o F6 Imag, (a) Ogal Imag of F6, (b) E Imag of F6, (c) RWSE Imag of F6 (a) (b) (c) Fg. 3: Oupu RWSE Mhod o Moo Imag, (a) Ogal Imag of Moo, (b) E Imag of Moo, (c) RWSE Imag of Moo Af aalysg h daa psd o Tabls 3 ad vsually obsvg som pocssd mags, w ca coclud ha: ) Th RSWE mhod poducs b mags coas ad also psv h bghss wh b qualy ha h oh mhods; ) owv, a b PSNR ca b obad by h BPDE mhod. Fg. (a) shows h ogal mag of F6 [], fg. (b) & (c) show h sul of E ad RWSE mhod. Fg. 3(a), 3(b) & 3(c) shows h ogal mag of MOTION, sul of E ad RWSE mhod spcvly. 6 Iaoal Joual of Compu Scc ad Tchology

5 ISSN : (P) ISSN : (Ol) IV. Coclusos Ths pap has psd a algohm fo coas hacm of dgal mags. I gal, s obsvd ha coas hacm ad hgh PSNR a wo coflcg qums. Th pfomacs of vaous algohms a compad accodg o h paams amly, Imag Bghss Ma, Imag Coas-Sadad Dvao ad PSNR. I s obsvd ha RWSE algohm poducs h bs mag coas hacm amog all whas DSIE ad RMSE a x wo algohms poducg good mag coas hacm. Th xpms showd ha BPDE ad RMSE a wll sud fo psvg h bghss of h pocssd mag ( lao o h ogal o) ad yld mags wh aual appaac, a h cos of coas hacm. owv, wh h ma objcv s o hac h coas of h mag ad psv s bghss, hus as show by h suls of Tabl I & III, RWSE s h bs mhod amog hos cosdd h ps sudy. Rfcs []. Y.-T. Km, Coas hacm usg bghss psvg b - hsogam qualzao, IEEE Tas. o Cosum lcocs, vol. 43, o., pp. -8, Fb []. Y. Wag, Q. Ch, B. Zhag, Imag hacm basd o qual aa dualsc sub-mag hsogam qualzao mhod, IEEE Tas. o Cosum Elcocs, vol. 45, o., pp , Fb [3]. S.-D. Ch, A. Raml, Coas hacm usg cusv ma- spaa hsogam qualzao fo scalabl bghss psvao, IEEE Tas. o Cosum Elcocs, vol. 49, o. 4, pp. 3-39, Nov. 3. [4]. D. Mo,. Najma, J. Faco, A.A. Aaujo, Mul sogam Equalzao Mhods fo Coas Ehacm ad Bghss Psvg, IEEE Tas. O Cosum Elcocs, vol. 53, No. 3, Aug. 7. [5]. S.-D. Ch, A. Raml, Mmum ma bghss o bhsogam qualzao coas hacm, IEEE Tas. o Cosum Elcocs, vol. 49, o. 4, pp. 3-39, Nov. 3. [6]. Y.-T. Km, Coas hacm usg bghss psvg b - hsogam qualzao, IEEE Tas. o Cosum lcocs, vol. 43, o., pp. -8, Fb [7]. Y. Wag, Q. Ch, B. Zhag, Imag hacm basd o qual aa dualsc sub-mag hsogam qualzao mhod, IEEE Tas. o Cosum Elcocs, vol. 45, o., pp , Fb [8]. S.-D. Ch, A. Raml, Coas hacm usg cusv ma- spaa hsogam qualzao fo scalabl bghss psvao, IEEE Tas. o Cosum Elcocs, vol. 49, o. 4, pp. 3-39, 3. [9]. J.-C. Y, F.-J. Chag, S. Chag, A w co fo auomac mullvl hsholdg, IEEE Tas. o. Imag Pocssg, vol. 4, o. 3, pp , Ma []. G.. Pa, al., Imag Ehacm Mhod by Sauao ad Coas Impovm, IMID 7, Vol. 7, No., pp.39-4, 7. [].. Ibahm, N.S.P. Kog, Bghss psvg dyamc hsogam qualzao fo mag coas hacm, IEEE Tasacos o Cosum Elcocs, vol. 53, o. 4, pp , Nov. 7. []. N.S.P. Kog,. Ibahm, Colo Imag hacm usg bghss psvg dyamc hsogam qualzao, IJCST Vo l., Is s u, Ma c h IEEE Tas. O Cosum Elcocs, vol. 54 No. Nov. 8. [3]. Rajv Ramaah, Wsly E. Syd, Yougju Yoo, Ma S.Dw, Colo mag pocssg ppl, IEEE Sgal Pocssg Magaz, vol., o., pp , 5. [4]. R. Babu, I. V. M Ksha, Coas hacm of IRS-C ISS daa, IEEE Iaoal Goscc ad Rmo Ssg, 997 (IGARSS 97) Rmo Ssg A Scfc Vso fo Susaabl Dvlopm, vol. 4, pp , Aug [5]. M. uss, M. Echma, G. Schus, A. Kasagglos, Nw suls o ffc opmal mullvl mag hsholdg, IEEE Iaoal Cofc o Imag Pocssg, 6, pp [6]. K. Wogsog, K. Kayauaswa, F. Chvasuv, K. Djha, A. Sombooaw, Coas hacm usg mulpa hsogam qualzao wh bghss psvg, I Ccus ad Sysms, 998, IEEE APCCAS 998. Th 998 IEEE Asa-Pacfc Cofc o, pp , Chagma, Thalad, Nov [7]. M. Rabba, P. Jos, Dgal Imag Compsso Tchqus, sd.bllgham, WA, SA: Socy of Phoo- Opcal Isumao Egs (SPIE), 99. [8]. R. Gozalz, R. Woods, Dgal Imag Pocssg, d d. Pc all, Ja.. [9]. Imag Pocssg,[Ol] Avalabl : hp://.wpda.og/w/imag_pocssg, applcao of mag pocssg s a fom s. []. Imags",[Ol] Avalabl :hp://dcsa.ug.s/cvg/ dbmags/ g56.php. Vay Kuma cvd hs B.E ad M.Tch. dgs Elcocs ad Commucao Egg, fom h P. Rav Shaa Shula vsy ad Naoal Isu of Tcholoy, Kuusha (NIT KKR), Ida 6 ad 9, spcvly. s culy a Asssa Pofsso of h Dpam of Elcocs ad Commucao Egg a NIT KKR. s sach s cluds mag hacm, os duco, mag sgmao, 3D vsualzao, ad commucao. ma Basal cvd h B.Tch ad M.E. dgs Elcocs ad Commucao Egg, fom h Pujab Tchcal vsy, Jaladha ad Pajab vsy,chadgah, Ida 7 ad 9, spcvly. Sh s culy a Asssa Pofsso of h Dpam of Elcocs ad Commucao Egg a NIT KKR. Sh s sd dgal mag pocssg, dgal vdo sgal pocssg, mag daa fuso, opolcoc daa acquso ad pocssg. Iaoal Joual of Compu Scc ad Tchology 7