SINGLE IMAGE DE-HAZE UNDER NON-UNIFORM ILLUMINATION USING BRIGHT CHANNEL PRIOR

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1 SINGLE IMAGE DE-HAZE UNDER NON-UNIFORM ILLUMINATION USING BRIGHT CHANNEL PRIOR 1 XUEYANG FU, 1 QIN LIN, 1 WEI GUO, 2 XINGHAO DING, 3 YUE HUANG 1 Dpartmnt of Communication Enginring, Xiamn Univrsity, Xiamn, China 2 Prof., Dpartmnt of Communication Enginring, Xiamn Univrsity, Xiamn, China 3 Asstt Prof., Dpartmnt of Communication Enginring, Xiamn Univrsity, Xiamn, China 2 dxh@xmu.du.cn ABSTRACT Rcnt singl imag d-haz approachs assum th atmosphric light is th only illumination in on haz imag and us a globally constant to imag d-haz. Howvr, vry local pixls in an outdoor imag is actually undr th influnc of non-uniform illumination in ral world. Th accuracy of th nvironmntal illumination stimation has a grat influnc on th rsult, so th traditional haz imag modl is dfctiv and not conforms to th facts. In this papr, w rfin th haz imag modl undr th considration of nonuniform illumination, and thn w propos a nw prior calld bright channl prior to d-haz singl imag combining with th dark channl prior. Th bright channl prior, which inspird by th dark channl prior [1], is a statistic of haz-fr outdoor imags. Using this prior, w driv a mor accurat nvironmntal illumination stimating algorithm for singl imag d-haz. Our xprimnts prov th fasibility of th mthod w propos and outprform othr imag haz rmoval approachs. Kywords: Non-Uniform Illumination, Haz Imag Modl, Bright Channl Prior, Singl Imag D-haz 1. INTRODUCTION How to d-haz ffctivly has bcom a hot spot in rcnt yars and mad significant progrsss. Thr ar many xisting imag dhazing algorithms basd on th dichromatic atmosphric scattring modl [2]. Fattal [3] stimats th albdo of th scn and th mdium transmission basd on th assumption that th transmission and th surfac shading ar locally uncorrlatd. This approach may fail if th assumption is invalid. Tarl s approach [5] uss combinations of min, max, and mdian filtrs to nforc picwis constant, and us th stimat to obtain a contrast nhancd imag of th scn. But his approach only achivd satisfid rsult on vry low saturatd scns. Tan s approach [4] was maximizing th local contrast of th rstord imag to rciv a d-haz imag. H solvd th optimization problm by using mdian filtr. Howvr, mdian filtr cannot prsrv dg ffctivly and his rsults xisting halos in th rgion of txtur and angls. K.H [1] proposd th dark channl prior to stimat th transmission and using soft matting to obtain a good rsult. All approachs mntiond abov hav a common point that thy assum th airlight radianc is a uniqu and uniform illumination in on imag. Howvr, an outdoor imag is actually undr multipl and non-uniform illumination [11], and th accuracy of th nvironmntal illumination stimation has a grat influnc on th d-haz rsult. So it is too rstrictiv to us only on globally constant as th illumination. Motivatd with th mthod of Rtinx, th nvironmntal illumination in on imag should b accurat to vry local pixls and ultimatly can obtain an illumination imag [12], and liminating th illumination will improv th ffct of th rcovry gratly. In this papr, w first rviw and rfin th haz imag modl for non-uniform illumination. Thn w propos a nw prior calld bright channl prior which inspird by th dark channl prior to rmov haz. Through xprimnts on haz-fr outdoor imags, w discovr that in th most local patchs which not in dark rgions or covrd by dark objcts, som pixls hav high intnsitis in on color channl of th RGB. W us this prior to stimat th nvironmntal illumination mor accuratly in vry local pixls, and obtain a 1843

2 high quality of d-haz imag. Our contribution in this papr is th good prformanc on th rcovry of color, clarity and contrast by liminating th influnc of th nvironmntal illumination. This papr is organizd as follows: In sction 2, w first rviw th traditional haz imag modl, and thn rfin th modl for non-uniform illumination. In sction 3 w prsnt th nw prior calld bright channl prior and prov its xistnc with xprimnts. In sction 4 w us both bright channl prior and dark channl prior to d-haz imag. Exprimnt rsults ar dscribd in sction 5, and th work is concludd in sction 6. Sction 7 is th acknowldg. 2. REFINING HAZE IMAGE MODEL FOR NON-UNIFORM ILLUMINATION Th traditional haz imag modl which widly usd in many imag d-haz approachs is calld th dichromatic atmosphric scattring modl [2]. This modl is a linar combination of attnuation L s and airlight L a : I = Ls + La βd βd = L ρ L (1 + ) (1) whr I is th obsrvd imag; β is th attnuation cofficint and can b sn as a constant; d is also known as th transmission widly dscribd in most imag dhazing approachs; L is th airlight radianc; ρ and d ar th scn albdo and dpth at th scn point. Th goal in imag dhazing is hop to dirctly stimat th tru scn albdo ρ. Although quation (1) is popular for its simplicity and has bn applid in many dhazing approachs, it is still not accurat nough and many qualitativ ffcts ar missing. In most imag dhazing algorithms, thy rgard L ρ as th final goal and considr th airlight is a constant in on imag. It is obviously not conform to rality. In th daytim, objcts ar actually undr non-uniform illumination. For instanc, th rflctd light by othr objcts surfac, lamplight and atmosphric particls scattrd light can b rgardd as diffrnt illuminations affct th scn point. In this sction, w will tak th non-uniform illumination into considration and rfin th haz imag modl. Figur 1 illustrats othr thr important visual ffcts du to light transport in scattring mdia bsids th attnuation and airlight in traditional modl. Firstly, light can travls in a straight lin to th obsrvr. Scondly, airlight also scattrs to th surfac and gts rflctd, lading to ffcts such as brightning of darkr rgions. Thirdly, rflctd light also scattrs to th obsrvr. This modl assums that th singl scattring is a common approximation in volumtric scattring and can b usd in haz condition. Figur 1. Thr Important Visual Effcts Whn Light Travls To Th Obsrvr Through Th Scattring Mdium. An objcts color valus may vary undr nonuniform illumination. So w add non-uniform illumination to quation (1), and th dirctly transmission of th light can b ignord for th scattring of particls in haz wathr. According to Figur 1, th attnuation L s and airlight L a ar rfind as: L l L Ls = + d L l La = (1 ) + (1 ) d dls d1 l d2 dso (1 ) ρ 2 2 ls d1 d5 d3 d L 4 r d d3 (2) whr L l is th radianc of th illumination; L r is th radianc of th rflctd light; d ls is th dpth btwn th illumination and th surfac; d so is th dpth btwn th surfac and th obsrvr; d 1 is th dpth btwn th illumination and th airlight scattring point; d 2 is th dpth btwn th airlight scattring point and th surfac; d 3 is th dpth btwn th surfac and th obsrvd light scattring point; d 4 is th dpth btwn th obsrvd light scattring point and th obsrvr; d 5 is th dpth btwn th obsrvd light scattring point and th illumination. W assum that th dpth btwn diffrnt illuminations and th camra in vry local pixls is narly qual in imaging systm. Th radianc of nvironmntal illumination, rspctivly, of th 1844

3 attnuation and th airlight is also approximatly qual in local pixls. For convninc, w dnot L rprsnts th nvironmntal illumination. Our final rfining haz imag modl is: I = L + L s a = L ρt+ L (1 t) (3) whr t is th nw transmission calld local transmission sinc th valu is rlatd to th nvironmntal illumination in our mthod. Equation (2) and (3) is mor accurat and clos to th objctiv fact for th considration of nonuniform illumination. Howvr, it is unralistic to stimat th illumination imag L dirctly with only on imag. It is an ill-posd problm to solv thr unknowns by on quation. In nxt sction, w will propos a nw prior calld bright channl prior to solv ths problms. 3. THE BRIGHT CHANNEL PRIOR Th bright channl prior w proposd is inspird by K.H s dark channl prior [1]. In his papr, h considrd that in most of th non-sky patchs, at last on color channl has vry low intnsity at som pixls in a haz-fr outdoor imag. In othr words, th pixls intnsitis in ths patchs will tnd to 0 aftr a minimum filtring. Th formula is: J dark ( x) = min ( min J ( y)) C ( RGB,, ) y Ω( x) C (4) whr J is th haz-fr outdoor imag; J c is a color channl of J ; Ω ( x) is local patch cntrd at x ; J dark is th dark channl of J. According to this prior, w gnrat an ida that an opposit prior of haz-fr outdoor imags should b xistnc and applicabl. W call this opposit prior th bright channl prior. Through obsrving haz-fr outdoors imags, w find that in th most local patchs which not covrd by dark objcts in haz-fr outdoor imags includ som pixls hav high intnsity valus in on color channl of th RGB. If w normaliz ths high valus, thy will tnd to 1. Th formula of bright channl is: J bright ( x) = max ( max J ( y)) C ( RGB,, ) y Ω( x) th symbols ar th sam maning as quation (4). W call J bright th bright channl of J. C (5) W choos 1000 haz-fr outdoor imags from intrnt to dmonstrat our ida is fasibility. Th imags w slct includ strt scns, cityscap scns, landscap scns, buildings and clos shot imags of flora and fauna. W dlt th dark objcts aras and us maximum filtring with a patch siz Svral haz-fr outdoor imags and thir bright channls ar shown in Figur 2. From th rsults, w can obsrv that all th outdoor imags in bright channls bcom mor whitly. It mans that most of th intnsitis ar almost tnd to 255 or qual to 255 aftr a maximum filtring opration. Figur 3 is th intnsity histogram ovr all 1000 bright channls and Figur 3 is th corrsponding cumulativ histogram. W can s that about 90% of th pixls hav high valus abov 240. Figur 3 is th avrag intnsity of ach bright channl. Figur 2. Top: Exampl Imags. Bottom: Thir Bright Channls. Figur 3. Statistics Of Th Bright Channl. (A) Histogram Of Th Intnsity Of Th Pixls In All Of Th Bright Channls (Each Bin Stands For 16 Intnsity Lvls). (B) Corrsponding Cumulativ Distribution. (C) Histogram Of Th Avrag Intnsity Of Each Bright Channl. This statistic is in lin with our ida about bright channl prior. Aftr analyz ths rsults, w mak 1845

4 a conclusion that th high intnsitis of th bright channl mainly from th sky, whit objcts and surfacs of colorful objcts. Sinc th intnsitis of th sky and whit objcts ar always high. Th surfac of colorful objcts has a good rflctanc, so th light intnsity from th rflction is also high. Our xprimnts vrify th corrctnss of th bright channl prior convincingly. In nxt sction w will us both bright channl prior and dark channl prior to stimat non-uniform nvironmntal illumination and liminat th influnc of both haz and nvironmntal illumination in singl haz imag. 4. IMAGE DE-HAZE USING PROPOSED PRIOR In this sction, w will utiliz th bright channl prior and dark channl prior to stimat vry local pixls non-uniform nvironmntal illumination and th local transmission. In th abov sction, w hav mntiond that in a haz-fr outdoor imag, th pixls intnsity is qual to 0 in dark channl and qual to 1 in bright channl aftr normalization. Th nvironmntal illumination L and th local transmission t can b sn as picwis constant in a local patch [14]. So w rwrit quation (3) in an idally situation. In dark channl, ρ = 0: dark Idark = L ρdark ( xytxy, ) (, ) + L (1 txy (, )) = L(1 txy (, )) In bright channl, ρ = 1: bright Ibright = L ρbright ( xytxy, ) (, ) + L (1 txy (, )) = L (6) (7) whr is th currnt pixl s coordinat; I dark and I bright ar th dark channl and th bright channl of a haz imag. Through xprimnts, w dmonstrat that both th dark channl and th bright channl can xist in on haz imag. According to th mthod of Rtinx [12], th illumination should hav th proprty of smooth, so w incras th patch siz of th maximum filtring to in this papr. W st th patch siz of th minimum filtring as A filtring opration calld guidd filtr [8] which proposd by K.H is usd to prsrv th dg and rfin both dark channl and bright channl. Th rsult is shown in Figur 4. It is asy to solv out L and t according to quation (6) and (7), th solution is: L = I bright Idark txy (, ) = 1 L (8) (9) Equation (8) and (9) is th stimation of nvironmntal illumination and local transmission. W us quation (3) to rconstruct th haz-fr imag combining quation (8) and (9), th solution is: Ixy (, ) L ρ = 1+ Lmax( txy (, ), t) 0 (10) whr t 0 is a lowr bound to avoid t clos to zro and a typical valu is 0.1. Equation (10) is th final rsult of vry pixl in th d-haz imag. Figur 4. Rsults Of Both Rfind Dark Channl And Bright Channl. (A) Original Haz Imag. (B) Th Dark Channl Map. (C) Th Bright Channl Map. 1846

5 5. EXPERIMENTAL RESULTS In our xprimnts, w procss th original haz imags by MATLAB R2010b on a PC with a 2.60GHz Intl Pntium Dual Cor Procssor. Figur 5 shows our d-haz rsults. In th rsults, our proposd approach liminats th influnc of nvironmntal illumination, so th rcovry of color and contrast has a significant improvmnt. Th rstoration of clarity is also promotd sinc our local transmission is rlatd to th nvironmntal illumination and includs mor dtail information. Figur 6 and Figur 7 show th comparison of our d-haz rsults with Tarl s [5] and K.H s [1]. As can b sn, all th rcovry of th color, clarity and contrast in our rsults outprform th othrs. Th advantag of proposd approach is spcially apparnt in th long shot and dark rgion. Whil in ths rgions, both Tarl s and K.H s rsults ar dark and cannot s objcts clarly. As shown in Figur 6, th color of th tr and th carriag in th distanc is not clar in Tarl s and K.H s rsults. Whil in our rsults, th rcovry of ths rgions Figur 6. Comparison Of Th Rsult Of Train. (A) Original Haz Imags. (B) Tarl s Approach. (C) K.H s Approach. (D) Th Proposd Approach. (d) Figur 5. D-Haz Rsults. Top: Original Haz Imags. Bottom: D-Haz Imags. improvs markdly. Morovr, our mthod can also rduc th influnc of th halo which producd by som bright light sourcs, such as th light of th train s lamp shown in Figur 6. Figur 7. Comparison Of Th Rsult Of Road. (A) Original Haz Imags. (B) Tarl s Approach. (C) K.H s Approach. (D) Th Proposd Approach. Furthrmor, w us th contrast of th imag as an objctiv valuation to vrify th rsult by our approach has a grat improvmnt. Th contrast can b xprssd as: (d) n 1 max() i - min() i C = n max () i +min () i i= 1 (11) whr C is th avrag of contrast in vry 3 3 non-ovrlapping patch; max() i is th highst gray valu in th currnt patch, min() i is th lowst gray valu in th currnt patch; n is th total numbr of patchs. Tabl 1 shows th comparison of th contrast of diffrnt approachs in Figur 6 and Figur 7. From th statistical data in Tabl 1, w can s that th contrast of our rsult improvs obviously. This xprimnt dmonstrats th 1847

6 significant advantag in th contrast of d-haz rsults by our mthod. Tabl 1: Th contrast of diffrnt rsults in Figur 7 Contrast Original Tarl s K.H s Our imag rsult rsult rsult Train Road CONCLUSION In this papr, w rfin th haz imag modl and propos a nw prior which calld bright channl prior to rmov haz in imag. Th advantag of our mthod is stimating vry local pixls non-uniform illumination and local transmission. Th rcovry of th color, clarify and contrast improvs significantly. Sinc our proposd prior is inspird by th dark channl prior, it has a fw similar limitations as [1]. In som particular rgions, such as th sky or larg aras of dark objcts, may hav a littl ovr nhancmnt. W lav ths problms for furthr rsarch. 7. ACKNOWLEDGE Th work is supportd by National Natural Scin c Funding of China, NO , and Fundamntal Rsarch Funds for th Cntral Univ rsitis , th Natural Scinc Foundation of Fujian Provinc of China 2012J REFERENCES: [1] Kaiming H, Jian Sun, Xiaoou Tang, Signal Imag Haz Rmoval Using Dark Channl Prior, IEEE Confrnc on Computr Vision and Pattrn Rcognition, 2009, pp [2] Srinivasa G. Narasimhan, Shr K, NayarVision and Atmosphr, Intrnational Journal of Computr Vision, Vol. 48, No. 3, 2002, pp [3] R.Fattal, Singl imag d-hazing, ACM Transactions on Graphics, Vol. 27, No. 3, 2008, pp.1-9. [4] Robby T. Tan, Visibility in Bad Wathr from a Singl Imag, IEEE Confrnc on Computr Vision and Pattrn Rcognition, 2008, pp [5] J.P. Tarl and N. Hauti r, Fast Visibility Rstoration from a Singl Color or Gray Lvl Imag, IEEE Intrnational Confrnc on Computr Vision, [6] Arjan Gijsnij, Rui Lu and Tho Gvrs, Color Constancy for Multipl Light Sourcs, IEEE Transactions on Imag Procssing, Vol. 21, No , Fbruary [7] Srinivasa G. Narasimhan, Shr K. Nayar, Contrast Rstoration of Wathr Dgradd Imags, IEEE Transactions on Pattrn Analysis and Machin Intllignc, Vol. 25, No. 6, 2003, pp [8] Kaiming H, Jian Sun, and Xiaoou Tang, Guidd Imag Filtring, Th 11th Europan Confrnc on Computr Vision,2010. [9] McCartny, E, Optics of th atmosphr: scattring by molculs and particls, Nw York: Wily, [10] Middlton, W, Vision through th atmosphr, Toronto: Univrsity of Toronto Prss,1952 [11] Sun, B., Ramamoorthi, R., Narasimhan, S. G., and Nayar, S. K, A Practical Analytic Singl Scattring Modl for Ral Tim Rndring, ACM Transactions on Graphics, Vol. 24, No , pp [12] Kimml R, Elad M, Shakd D, t al, A Variational Framwork for Rtinx, Intrnational Journal of Computr Vision, Vol. 52, No. 1, 2003, pp [13] Srinivasa G. Narasimhan and Shr K. Nayar., Chromatic Framwork for Vision in Bad Wathr, IEEE Confrnc on Computr Vision and Pattrn Rcognition, 2000, pp [14] Kimml R, Elad M, Shakd D, t al, Baysian Dfogging, Intrnational journal of computr vision, Vol. 98,2012, pp [15] Wnbo Jin, Zngyuan Mi, Xiaotian Wu, Yu Huang, Xinghao Ding, Singl Imag D-haz Basd On a Nw Dark Channl Estimation Mthod, IEEE Intrnational Confrnc on Computr Scinc and Automation Enginring, 2012, pp