The Research of Histogram Enhancement Technique Based on Matlab Software

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1 Snsors & Transducrs 24 by IFSA Publishing, S. L. Th Rsarch of Histogram Enhancmnt Tchniqu Basd on Matlab Softwar Li Kai, 2 Zhang Y, Zhang Yu Xi an Radio & Tlvision Univrsity, 48# Wu Wi Crossroad, 72, China 2 Xi an Communication Institut, Wang Qu Zon, 76, China Tl.: poplstar@26.com Rcivd: 3 April 24 /Accptd: 3 July 24 /Publishd: 3 August 24 Abstract: Histogram nhancmnt tchniqu has bn widly applid as a typical pattrn in digital imag procssing. Th papr is basd on Matlab softwar, through th two ways of histogram qualization and histogram spcification tchnologis to dal with th darr imags, using two mthods of partial quilibrium and mapping histogram to transform th original histograms, thrby nhancd th imag information. Th rsults show that ths two inds of tchniqus both can significantly improv th imag quality and nhanc th imag fatur. Copyright 24 IFSA Publishing, S. L. Kywords: Imag procssing, Matlab, Histogram qualization, Histogram spcification, Imag nhancmnt.. Introduction Imag nhancmnt tchnology [, 2] is on common ways of digital imag procssing, it has bn widly usd in aviation, mdical, military tc. Through th nhancmnts of som charactristic information, maing th unshapd imags mor lgibl, or xpanding th faturs btwn diffrnt objcts, thus, amliorats th imag quality and satisfis th nd of human visual or som spcial analysis. Th imag nhancmnt tchnology includs histogram transform, imag smoothing, imag sharpning tc. [3]. A histogram is a statistical function btwn th gray scal and th gray frquncy, which rflcts th occurrnt tims or frquncy of diffrnt gray-scal lvls in on imag. Th histogram shown as a twodimnsional imag in visual [4], th valu of th abscissa rflcts all th gray-scal lvls, and th ordinat shows th occurrnt tims or frquncy of th whol gray-scal lvls. Th histogram nhancmnt tchniqu is a common way of imag nhancmnt tchnology. This papr mainly studis th histogram nhancmnt, with th mthod of obtaining and transforming th histogram distribution structurs as to nlarg th imag fatur information, improv th imag quality and achiv th purpos of imag nhancmnt. 2. Principl of Imag Enhancmnt Tchnology Using som spcial mthods to transform th imag information of original manuscript, mphasizing or bating som pculiar faturs to match th human visual, ar th principls of imag nhancmnt tchnology. During th procssing of imag nhancmnt, without considring th diffrncs in quality btwn th original and th procssd imags, th procssd imags ar not 7

2 ncssarily sam with th originals. As formula () shows: assuming that th gray valu of original imag in coordinat (x, y) is f(x, y), th postprocssd valu is g(x, y) so th procssing of imag nhancmnt can b xprssd as: ( x y) T[ f ( x y) ] g,,, () whr sign T dnots th diffrnt tchniqus of th procssing mthods. At th prsnt tim, th imag nhancmnt tchnology is dividd into two mainly catgoris: spatial domain nhancmnt tchnology [5] and frquncy domain nhancmnt tchnology [6]. 2.. Spatial Domain Enhancmnt Tchnology Spatial domain nhancmnt tchnology which blongs to th dirct imag nhancmnt tchnology is on of transformation mthods basd on imag pixl spac. It consists of gray lvl transformation, histogram transformation, nois limination smoothing and dg nhancmnt sharpning. 3. Histogram Equalization and Histogram Spcification Th histogram of digital imag procssing mainly rfrs to th gray-histogram, th mathmatical xprssion is: P ( r ) n n,, L-, (6) / In quation (6), sign n dnots th total numbrs of th pixls, sign r dnots th corrsponding gray lvl of, sign n dnots th occurrnt tims or frquncy of r, sign p(r ) dnots th probability of r. Th histogram can b dfind as anothr form: assuming that a continuous imag which dfind by Function D(x, y), Lt A mans th first contour surroundd ara, A mans th scond contour surroundd ara, whn th valus of corrsponding gray-lvl coms from D to D 2, th histogram can b dscribd as Fig Frquncy Domain Enhancmnt Tchnology Frquncy domain nhancmnt tchnology is a way to covrt imags from original spac to othr spac by a pculiar form. Procssing th imag in virtu of th uniqu charactrs in othr spac thn convrting thm bac to th original spac to display finally. In th frquncy domain, imag information is organizd according to th frquncy which is basd on th thory of Fourir transform [7, 8]. Two-dimnsional continuous Fourir transform: u, v) f ( x, y) j2π ( ux+ vy) dxdy, (2) Two-dimnsional invrs continuous Fourir transform: u, v) f ( x, y) j2π ( ux+ vy) dxdy, (3) Two-dimnsional discrt Fourir transform: m, n) i f ( i, ) j2π ( m i * n ), (4) Two-dimnsional invrs discrt Fourir transform: m, n) i f ( i, ) j 2π ( m i * n ), (5) H Fig.. Imag grayscal contour surroundd ara. ( D) ( D) A( D + ΔD) A d lim A( D), (7) ΔD ΔD dd For th discrt function, ΔD consquntly ( D) A( D) A( D +) H, (8) From th functions abov, histogram can rflct th charactristics of th probability and statistics. With th convrting of probability function, th structur of gray scal can b changd, so will nhanc th rquisit imag fatur. At prsnt, th common histogram transform tchniqu is dividd into two mainly catgoris: histogram qualization and histogram spcification. 3.. Histogram Equalization Histogram qualization is a way of convrting th structur of original histogram to th quilibrium ons with th gray-lvl transformation function. Thus, th dynamic rang of th gray-scal valus will incras, and th imag bcoms clar. Histogram qualization transform function as shown in Fig. 2, assum sign r and s dnot th 72

3 valu of gray-scal lvl which hav bn normalizd rspctivly. Whn rs it stands for blac, whil rs mans whit. Th gray transform function shown as: ( R) S T, (9) It satisfis th following two conditions: ) r, T(r) is monoton incrasing; 2) r, T(r). 4. Imag Enhancmnt Using Matlab Softwar This papr adopts th Matlab softwar to nhanc th imag information [9, ] by using histogram transform tchniqu. Convrt th original color imag (as Fig. 3 shows) into th gray on (as Fig.4 shows) firstly in ordr to facilitat th procssing. Fig. 5 is th original 256 gray-scal histogram of Fig. 4. Fig. 2. Histogram qualization transform function. Fig. 3. Original color imag []. Gt th histogram qualization transform function from formula (6), namly th imag gray cumulativ distribution function s : s n j T ( r ) p r ( rj ), () n j j 3.2. Histogram Spcification Histogram spcification is a way to transform th local histogram to th ons dsird, via a gray mapping function GnwF (Gold), which can chang th partial shap of original histogram by accntuating som spcial rang information slctivly. Th histogram spcification constitutiv of thr stps: ) Histogram spcification of original histogram: Fig. 4. Gray imag. t EH ( s) p ( s),,, M-, () s i s i i 2) Ascrtain th histogram whil qualizd: v i EH ( s ) p ( u ) j,,, -, (2) u j j u j 3) Projct th original spac into th nw qualizd ons, so as to achiv th purpos of imag nhancmnt. Fig. 5. Original 256 gray-scal histogram. 73

4 4.. Histogram Equalization Using Matlab Softwar As Fig. 5 shows that, th valus of gray-lvl mainly concntratd in btwn [, 2]. In ordr to nhanc th imag information bttr, [, 2] was chos to qualization so as to gt a clar sharpning imag fatur in th modifid imag. Th post-corrction 2 gray-lvl imag and th postqualization 2 gray-lvl imag ar showd as Fig.6 and Fig.7 rspctivly. Fig. 8 shows th post-corrction 2 gray-scal histogram of Fig. 6. And Fig. 9 shows th postqualization 2 gray-scal histogram of Fig. 7. Fig. 9. Post-qualization 2 gray-scal histogram 4.2. Histogram Spcification Using Matlab Softwar Histogram spcification can nhanc th whol visual ffcts of th imag. Fig. 5 shows that th valus of gray-lvl mainly concntratd in btwn [, 2], if it can b convrtd to th dsird histogram narly li Fig. 9, so will gt th nhancmnt of imag information. 5. Exprimntal Rsults and Analysis Fig. 6. Post-corrction 2 gray-scal imag. 5.. Analysis of Histogram Equalization As Fig. 6 shows, th post-corrction 2 grayscal imag has bn significantly improvd in darr dtails and incrasd th dynamic rang than th original on. Aftr qualization, th imag quality has improvd furthr, th brightnss distributd quilibrium and th ton bcom gntlr. Thr ar mor dtails can b distinguishd in visual in th cntr of th sunflowrs. As Fig. 9 shows, th valus of gray-lvl which concntratd in [, 2], bcom a balancd distribution comparativly. Th xprimntal rsults which ar consistnt with th imag displayd, achivd th aim of imag nhancmnt. Fig. 7. Post-qualization 2 gray-scal imag. Fig. 8. Post-corrction 2 gray-scal histogram. 5.2 Analysis of Histogram Spcification Fig. is th post-spcification 256 gray-scal imag which has mor rans and dtails xprssion than th post-qualization on as showd in Fig.7. Only corrctd th valus of [, 2] gray scal during th procss of histogram qualization, thus lost th brightnss imag information in th original imag. But in procss of histogram spcification, th whol imag information has bn rsrvd. All th mountains and trs which causd of baclighting ar visibl, du to xpnding th dynamic rang with th whol gray scals. Aftr post-qualization, th dtails of imag fatur nhancd, th brightnss bcoms uniform and th ton has a gntlr apparanc. 74

5 Fig. shows th post-spcification 256 gray-scal histogram of Fig.. qualization mapping spac to transform during th procss of histogram spcification, has th sam distribution structur with th post-qualization on in valus of [,9] gray scal which compard with th Fig. 9. Fig. prsrvs th [2, 255] lvls brightnss ton information in original imag is th rason for th diffrncs btwn th two histograms in [9, 255] gray scal. So w can s all th dtails of imag without losing th data of th distant hills and trs that ar invisibl in original manuscript. Aftr histogram spcification th imag faturs distinct, and achiv th aim of imag nhancmnt. Fig.. Post-spcification 256 gray-scal imag. Fig. 3. Post-qualization 256 gray-scal histogram. Fig.. Post-spcification 256 gray-scal histogram. Th post-qualization 256 gray-scal imag displays as Fig. 2, which prsrvs th whol dtail information of th original imag in thory. And Fig.3 shows th post-qualization 256 gray-scal histogram of Fig.2. Fig. 2 shows th post-qualization 256 grayscal imag. It sms slightly darr ovrall th whol ton in Fig. by contrast with th Fig. 2, but thy hav th sam xprssion in visual ffct. Comparing with Fig. and Fig. 3, th two histograms display th narly idntical gray frquncy distribution, diffrncs only btwn [8, 22] lvls in which a lowr numrical data in brightnss proportion of Fig.. Th rason is that, nglcting th [2, 255] lvls brightnss ton information in original imag and using [, 2] lvls qualization mapping spac to transform during th procss of histogram spcification. By comparing th two mthods, w can s that, slcts [,2] lvls gray scal data to dispos in this papr can sav mor computational spac, and th xprimntal procss is ntirly rasonabl and fasibl. 6. Conclusions Fig. 2. Post-qualization 256 gray-scal imag. As Fig. shows, post-spcification 256 grayscal histogram which using [, 2] lvls This papr is basd on Matlab softwar, adopt two inds of ways: histogram qualization and histogram spcification tchnologis to nhanc th imag information. In histogram qualization procss, with th sparation tratmnt of th gray lvls which ar concntratd in darr part of th imag on purpos, imag quality has bn improvd significantly and accordd with human visual. During th procss of histogram spcification, projct th original histogram into th mapping on through th 75

6 global transformation of th histogram, and display th whol imag information which is rich in dtails and brightnss of th original manuscript, achiv th aim of imag nhancmnt. To sum up, th coalscnt two inds of tchniqus can improv th imag quality and nhanc th imag fatur significantly. Th xprimntal rsults and mthods in this papr can provid th rfrnc for th furthr study in rlatd rsarch too. And also can provid th rfrnc for th mchanical information tchnology ducation of Th Opn Univrsity of China, spcially for th taching and practic of Radio and Tlvision Univrsitis in th futur. Acnowldgmnts Th authors wish to acnowldg th supports providd by Xi an Radio & Tlvision Univrsity, China. Rfrncs []. R. Carla, V. M. Sacco, S. Baronti, Digital tchniqus for nois rduction in APT OAA satllit imags, in Procdings of th Intrnational Goscinc and Rmot Snsing Symposium on Rmot Snsing (IGARSS' 86), 986, Vol. 2, pp [2]. H. D. Chng, Y. H. Chn, Y. Sun, A novl fuzzy ntropy approach to imag nhancmnt and thrsholding, Signal Procssing, Vol. 75, Issu 3, 999, pp [3]. Rafal C. Gonzalz, Richard E. Woods, Digital imag procssing, Publishing Hous of Elctronics Industry, Bijing, 2. [4]. Milan Sona, Vaclav Hlavac, Rogr Blyl, Imag procssing, analysis, and machin vision, Popl's Posts and Tlcommunications Prss, Bijing, 23 [5]. A. M. Esicioglu, P. S. Fishr, Imag quality masurs and thir prformanc, IEEE Transactions on Communications, Vol. 43, Issu 2, 995, pp [6]. Yao Min, Digital imag procssing, China Machin Prss, Bijing, 22. [7]. Luo Hongwi, Rsarch of sismic imag nhancmnt mthod basd of improvd histogram, Ph.D. Thsis, orthast Univrsity, Hi Longjiang, 23, pp [8]. V. amias, Th fractional ordr Fourir transform and its application to quantum mchanics, Journal of th Institut of Mathmatics and Its Applications, Vol. 25, 98, pp [9].. Otsu, A thrshold slction mthod from graylvl histogram, IEEE Transactions on Systm, Man and Cybrntics, Vol. 9, Issu, 979, pp []. Zhang Fngd, MATLAB Digital Imag Procssing, China Machin Prss, Bijing, 22. []. Sunflowr, 24 Copyright, Intrnational Frquncy Snsor Association (IFSA) Publishing, S. L. All rights rsrvd. ( 76