Image Contrast Gain Control by Linear Neighbourhood Embedding

Transcription

1 Vsal nformaton Processng Laborator School of Compter Scence and nformaton Technolog The Unverst of Nottngham Techncal Report Report-VPLAB November 2005 mage Contrast Gan Control b Lnear Neghborhood Embeddng Jan Gan and Gopng Q School of Compter Scence and nformaton Technolog The Unverst of Nottngham 1

2 mage Contrast Gan Control b Lnear Neghborhood Embeddng Jan Gan and Gopng Q School of Compter Scence and nformaton Technolog The Unverst of Nottngham Abstract n ths paper we present a method that adaptvel comptes a contrast gan control map for the mage throgh the se of a novel technqe termed lnear neghborhood embeddng (LNE) whch frst comptes a locall lnear relaton for each pxel and ts neghbors and then embeds these relatons globall n the gan map mage. We borrow the thnk globall ft locall concept and comptatonal technqes from locall lnear embeddng (LLE) and compte the gan control mage n closed forms b solvng constraned optmzaton problems. We constran the gan map locall followng a gan contrast control mechansm smlar to that fond n the vsal cortex to ensre that weak local contrasts are boosted and strong local contrasts are compressed and propagate these local constrants globall followng the orgnal mage pxels locall lnear relatons. We have appled or technqe to compress hgh dnamc range mages for reprodcton n low dnamc range meda and to enhance ordnar dgtal photographs. Reslts demonstrate that or technqe s capable of preservng local detals whle avodng artfacts sch as halo 1. ntrodcton Toda dgtal cameras are bqtos. However when magng scenes contanng wde varatons of llmnaton ntenstes the pctre qalt often trns ot to be less than satsfactor and mage enhancement has to be appled to mprove the mage. Althogh the statons can be remeded b sng hgh dnamc range (HDR) magng technolog [4 21] where the so called HDR radance maps record the actal dnamc range of the scenes there s stll the problem of fathfll reprodcng the mage n conventonal low dnamc range (LDR) reprodcton meda sch as prnt paper and CRT. n ths paper we present a technolog that adaptvel comptes a contrast gan control mage for a gven mage throgh the se of a novel technqe termed lnear neghborhood embeddng (LNE). LNE comptes the gan map b solvng constraned optmzaton problems sng the concept and comptatonal technqes smlar to those of a recent hgh dmensonalt redcton method called local lnearl embeddng (LLE) [22]. We ntrodce the dea of thnk locall ft globall whch comptes the gan control mage at local and global scales smltaneosl. We show that or technolog can be appled to compress the dnamc range of HDR radance maps for vsalzaton n LDR reprodcton devces and to enhance low qalt ordnar LDR dgtal photographs. n secton 2 we brefl revew prevos work. n secton 3 we ntrodce or lnear neghborhood embeddng technolog for adaptvel comptng a contrast gan control mage for a gven mage. n secton 4 we present mplementaton detals. We present or reslts n secton 5 and conclde or presentaton n secton Prevos Work n the past several ears there has been tremendos nterest n hgh dnamc range magng from captrng [9 13] to storage [20] to dspla [ ]. Althogh new hgh dnamc range dspla devces are beng developed e.g. [19] the domnant reprodcton meda for HDR mages are tradtonal montors and prnt paper havng a lmted dnamc range between onl one to two orders of magntde. Therefore how to best compress the dnamc range of the HDR radance map so that the nformaton n the orgnal scene can be fathfll reprodced n LDR devces s one of the mportant techncal challenges n HDR magng workflow and a varet of HDR mage dspla technqes have appeared n the lteratre. Extensve revews can also be fond n prevos works sch as [ ]. There are manl two categores of technqes: global (spatall nvarant) and local (spatall varant). n a global method a nonlnear fncton T s sed to map each pxel of the npt mage (x ) ndependentl to form an otpt mage (x ) = T((x )). The ke to ths tpe of method s to fnd the approprate mappng fncton T whch can be some power fnctons [5 18] or mappng crves derved from the mage s hstogram [8]. The advantage of the global method s that t s comptatonal effcent bt t can destro local contrasts makng the 2

3 mage look washed ot. n a local method how a pxel s mapped wll depend on both the pxel vale and ts spatal context. Local methods are sgnfcantl more complex and can be ver dffclt to mplement n practce. Earler methods sch as [3] ntrodce halo artfacts mproved methods sch as [12] can redce the vsblt of halos and newer methods sch as [15 21] can avod halo artfacts. One tpe of sccessfl local methods that avod halo estmate edge preservng gan control mage. The ke observaton s that the gan map shold have sharp edges at the same ponts that the orgnal mage does thereb preventng halos [ ]. n [17] the athors compte a gan map sng the blateral flter and have acheved ver good reslts. n [15] the athors compte the gan map n the gradent doman that compresses strong edges and boosts weak edges. The redced low dnamc range mage s then retreved b solvng Posson s eqaton sng an approxmated solton whch acheves satsfactor reslts wth reasonable comptatonal cost. n [21] the athors ntrodce a method that comptes a gan map for mltscale sbband mages and the have sccessfll avoded halos that are often assocated wth mltscale methods. We have developed a method that comptes a gan map mage n the ntenst mage doman b solvng constraned optmzaton problems and we have appled the method to compress hgh dnamc range mage for dspla and to the enhancement of ordnar mages and have acheved good reslts. 3. Contrast Gan Control b LNE For a gven mage (x ) we seek a gan map mage G(x ) to prodce a new mage (x ) = (x ) + G(x ) for hgh dnamc range compresson and/or mage enhancement. Or basc dea s llstrated n Fgre 1 whch conssts of two steps; we frst compte a lnear relaton for each pxel and ts local neghbors n the orgnal mage and then embed these lnear relatons n the gan map mage. We sparsel constran the gan map mage locall b sng a contrast gan control mechansm smlar to that fond n the vsal cortex [25] and propagate these sparse local gan controls globall throghot the entre mage followng the locall lnear pxel neghborhood relatons of the orgnal mage. We compte the locall lnear relatons and solve the global embeddng problem b borrowng the comptatonal technqes of the thnk globall ft locall framework [22]. n fact as wll become clear later n the paper or work can be more accratel descrbed as thnk locall ft globall strateg Gan Map b Neghborhood Embeddng An mage (x ) can be regarded as a prodct of the srface reflectance mage R(x ) and llmnaton mage L(x ) [1] we can wrte (n logarthmc doman): ( ) x = Rx ( ) + Lx ( ) (1) (x ) ( v) w x (v) x = w x w v v 1 Compte lnear neghborhood relatonshp on the orgnal mage w x (v) G(x ) G( v) ( ) ( ) ( ) ( ) ( ) ( ) G x = w x w G v v 2 Map to embedded gan map Fgre 1: Schematc of lnear neghborhood embeddng (LNE) and ts applcaton to comptng the gan map mage. The locall lnear neghborhood relatons of the orgnal mage are sed to compte the gan map mage sbject to some approprate constrants. The largest varaton of the mage comes from the llmnaton mage snce real world reflectance mages are nlkel to have contrast greater than 100:1. The llmnaton mage tends to var slowl across the mage [2] and large ntenst varatons tend to mostl occr between regons rather than locall wthn a small area. f the mage can be separated nto the prodct of R and L then hgh dnamc range compresson can be acheved b compressng the llmnaton mage L onl. Ths wa the large contrast between brghtl llmnated regons and dark shadow areas can be redced whle the contrast cased b reflectance of local textre featres s preserved. However separatng the reflectance from the llmnaton s an ll-posed problem and t s almost mpossble to completel separate L from R. Assme that we can compte a gan map G(x ) for the mage (x ) to prodce a new mage (x ) for applcatons sch as hgh dnamc range compresson and/or mage enhancement we can wrte ( ) x = Rx ( ) + Lx ( ) + Gx ( ) (2) The gan map shold serve at least two objectves at a coarse scale t shold redce the hgh contrast between ver brghtl llmnated regons and dark shadow areas; and at a local scale t shold enhance or preserve the detals wthn local regons. As well as achevng these two objectves smltaneosl t mst avod ntrodcng artfacts sch as halo. Therefore G(x ) shold compress strong edges cased b llmnaton varatons (hgh dnamc range compresson) preserve or boost local edges (mage enhancement) and protect orgnal edge sgns (avodng halo). We have developed a thnk locall ft globall technolog to compte the gan map mage to acheve these goals smltaneosl based on followng ratonale. 3

4 Becase hman vsal sstem s most senstve to local ntenst varatons then t s most mportant to preserve mabe even enhance local ntenst contrasts. However processng local contrasts wll have to be done at a global scale n the sense that when pttng locall processed regons together the whole mage shold preserve the orgnal scene s vsal ntegrt. Therefore we cannot process local regons ndependentl bt rather local regons contrasts shold be processed sch that the wll ft together globall. Eqall mportant the gan map shold protect the drectons of the ntenst changes across the whole mage to avod halo whch also reqres that local processng ft nto global relatons. Therefore the gan map mage mst be compted at local and global scales smltaneosl. Or method frst thnk locall t strategcall pcks a few local patches of the mage fnds the largest and the smallest ntenstes wthn each patch and processes the mn/max pxel pars accordng to a contrast gan control mechansm smlar to that fond n the vsal cortex. The processed mn/max pxel pars from these local patches are then ft globall to whole mage. To acheve sch thnk locall ft globall strateg we borrow the concept and comptatonal technqes smlar to those of the thnk globall ft locall framework locall lnear embeddng (LLE) [22]. At a coarse scale the regonal ntenst varatons wthn the mage ma be characterzed b locall lnear pxel relatons. One possble approach to characterzng the locall lnear spatal pxel relaton s to constrct a lnear model that reconstrcts the pxels from a lnear combnaton of ther neghbors. To bld sch model we can perform followng constraned optmzaton: Mnmzng 2 x (3) x v ( ) = ( ) ( ) ( ) E W x w v v Sbject to w v = 1 and w v = 0 f ( v) N v ( ) ( ) x x x where N x denotes a local neghborhood srronds the pxel at locaton (x ) w x ( v) s the weght whch qantfes the contrbton of the neghborhood pxel at locaton ( v) to reconstrctng the pxel at (x ). Note that the relaton s made local b settng the weghts of pxels otsde a local neghborhood of the pxel to zero. All weghts smmed to 1 to be nvarance to the absolte ntenst of the mage. The locall lnear spatal relaton at pxel locaton (x) n the orgnal mage s captred n the weght matrx W x = {w x ( v)}. These weght matrces shold also captre the spatal varatons of the gan map G becase from (2) t s clear that the gan map G shold follow the varatons of. Therefore we can constrct G b embeddng W x s n the gan map b solvng followng constraned optmzaton problem: Mnmzng 2 x (4) x v ( ) = ( ) ( ) ( ) E G G x w v G v Sbject to G(x ) = g = 1 2 where g s are pre-determned vales of the gan map at locaton (x ). Note that althogh the reconstrcton weght matrx for each pxel s compted from a local neghborhood n the orgnal mage and s ndependent of the weghts of other pxels the embeddng s a global operaton that coples all gan map pxels. Therefore G shold follow locall and globall as well. However becase the local weghts onl captre the lnear relatons the can onl captre the slow changng components of that shold reflect regonal varatons of the mage. Local scale processng can be realzed b settng the constrants locall. nformall we can vew (4) as globall fts the local constrants G(x ) to the whole mage globall. Clearl G wll be greatl dependent on the nmbers the locatons and the vales of the constrants G(x ) and settng the constrants s a crcal step n or algorthm Settng Constrants To get some nsght nto how the constrants shold be set t ma be helpfl to consder how the hman vsal sstem performs gan control. The vsal world s hgel complex and the vsal sstem s constantl exposed to scenes of hge dnamc ranges. Apparentl the vsal sstem performs varos tpes of atomatc control to cope wth the hgh dnamc ranges and nos envronments to keep t wthn the optmal operatng range. At a global level there seems to be a gan control mechansm at the retna where the photoreceptors rapdl adapt to the ambent lght level. n comptatonal vson ths tpe of gan control s normall modeled b takng the log of the npt ntenst. t s wdel accepted that the logarthm of the lmnance s a (crde) approxmaton to the perceved brghtness. Therefore dsplang the log mage drectl shold gve reasonabl correct brghtness bt sch mage wll be lack of detals 1. t s also wdel accepted that hman vsal sstem s not ver senstve to absolte lmnance reach the retna bt rather responds to local 1 Logarthm tself ncrs no nformaton loss the detals are destroed b nmercal qantzaton. When the log mage s scaled down to wthn the dnamc range of the reprodcton devces pxels wth smlar vales wll be qantzed to the same level ths destrong detals. 4

5 Log() G Log() (e) Fgre 2. The orgnal hgh dnamc range sgnal wth a dnamc range of 6218 : 1. Logarthm of. The gan map where the * are the constraned ponts. The reslt sgnal = +. (e) Lnearl scale and to the same dnamc range of 10 : 1. t s seen that n the reslt sgnal local detals are well preserved (slghtl enhanced) n the low dnamc range mage. ntenst varatons. n the vsal cortex there are nerons that operate a gan control mechansm known as contrast gan control n whch moderatel low contrasts are boosted whle hgh contrasts are compressed [25]. These mportant propertes of the hman vsal sstem ma provde s wth some mportant cles to set the local constrants for eqaton (4) to acheve or goals. Frstl we shold set the constrants G(x ) sparel scattered across the mage to enable the embeddng process to enforce G to follow the varatons of ths protectng the vsal ntegrt of the orgnal mage. Secondl we shold set the vales of these constrants sch that the wll boost weak local contrasts and compress local hgh contrasts. n ths paper we se followng strateg to set the constrants: Constrants Settng Procedre ) Segment the mage nto coarse regons ) Wthn each segmented regon randoml pck nonoverlappng patches of certan sze (n ths paper 17x17 patch sze s sed other patch szes are possble). ) For each patch P fnd the smallest and the largest pxel wthn the patch x = arg max x ; x P ( max( p ) max( ) ) ( { ( ) ( ) }) p ( xmn( p ) mn( ) ) arg( mn { ( ); ( ) }) p = x x P and compte the patch s contrast as C( P) = ( xmax( p ) max( ) ) ( mn( ) mn( ) ) p x p (5) p v) Wthn each patch set two constrants for G one at (x max(p) max(p) ) and the other at (x mn(p) mn(p) ) accordng to β ( ( ) ) 0 mn( ) mn( ) ( C P (6) G x P max( ) max( ) ) ( ) P = G x P P = α C P α where α determne whch local contrasts are boosted or compressed. f the local contrasts are smaller than α then the are boosted and f the are greater than α then the are compressed (assmng 0 < β < 1). A smlar fncton was sed n [15] and [21] for gradent doman gan contrast control and sbband doman gan control. n all reslts presented n ths paper α s set to 0.3 tmes the average local patch contrast of the mage and β between From the above contrast settng procedre we can make followng observatons. The prpose of coarsel segmentng the mage s to dentf the strongest changes across mage regons. Becase the edges across these regons are so mportant n protectng the vsal ntegrt of the mage we do not want to set constrants across these strong edges rather we want to set constrants awa from these strong edges and prefer to fnd the gan map pxels for these strong edges throgh embeddng. For each local patch we onl fx two pxels for the gan map one at the smallest pxel s poston and the other at the largest pxel poston. Bascall we fx the smallest pxel and ncrease or decrease the largest pxel. Althogh we n effect assme that logarthm wll make the smallest pxel n each patch have the rght brghtness (gan map vale eqals zero) and set the gan map vale at the largest pxel poston these constrants are rather mld becase frstl onl two pxels wthn a 17x17 wndow are fxed (n practce <0.1% pxels are sed as constrants) secondl these pxels are onl borrowed to constran the optmzaton and over 99.9 % of the pxels are fond throgh global embeddng. The gan map pxels wthn each local patch are not onl affected b the constrants of ts own patch bt are also nflenced b ALL constrants from dfferent patches therefore these locall set constrants wll propagate globall. n fact n the fnal gan map the pxels at the constrant postons can be replaced b averagng or majort votng ths removng the hard constrants ntall pt on for comptatonal prpose Algorthm Smmar The LNE gan map constrcton method and ts applcaton can be smmarzed n followng steps: 1 Compte the logarthm of the npt 2 Compte lnear pxel neghborhood relatons accordng to (3) 3 Set gan map constrants accordng to the constran settng procedre 4 Compte the gan map G accordng to (4) 5 Compte the otpt mage = + G and lnearl scale t to wthn the dnamc range of the reprodcton meda. The procedre of or method s llstrated n Fgre 2. 5

6 4. mplementaton mplementaton of the LNE gan map algorthm s relatvel straghtforward. Becase t s onl necessar to segment the mages nto coarse regons and accrate mage segmentaton s not necessar we frst down scale the orgnal mage b a factor of 4 n both dmensons and then se the mean shft robst comptatonal segmentaton method [23] to atomatcall segment the mage nto regons. Snce or man prpose s to dentf where the strong edges are lkel stated we then rescale the segmented mage nto fll resolton and prodce thck bondares where constrant pxels shold not be placed across. nsde each segmented regon we place a 17 x 17 wndow at non-overlappng postons and at each poston dentf the smallest and the largest pxels wthn the wndow and set the constrants for G at these mn and max locatons accordng to (6). To solve the constraned least sqares ft problem of (3) we follow the comptatonal method of LLE [22] b solvng a lnear sstem of eqatons. However snce n or case the data s 1-d and there wll alwas be more neghbors than npt dmensons the least sqares problem for fndng the weghts does not have a nqe solton. We follow the method of [22] b addng a reglarzaton term to the reconstrcton cost fncton to solve the problem. The comptatonal complext of ths step scales as O(mn 3 ) where m s the nmber of pxels and n s the neghborhood pxels (n = 8 n all or reslts) For the embeddng problem of (4) snce the cost fncton s qadratc and the constrants are lnear ths optmzaton problem elds a large sparse sstem of lnear eqatons whch ma be solved sng a nmber of standard methods. The embeddng step of LLE solve a smlar optmzaton problem bt nder dfferent constrants. Wthot specal optmzaton the complext of ths step scales as O(m 3 ) where m s the nmber of pxels. To speed p the comptaton there are several alternatve methods for solvng the embeddng problem sch as mltgrd solver [24 27] whch wll lead to a complext scales as O(m). For hgh dnamc range compresson lke all other methods n the lteratre we onl work on the lmnance channel and color of the mage s ntoched. After compressng the lmnance color s pt back to the mage n a wa smlar to those n [15]. For ordnar mage enhancement we also onl process the achromatc channel. 5. Reslts Hgh dnamc range mage compresson. We have appled or technqe to compress hgh dnamc range radance maps for dspla n low dnamc range devce. Fgre 3 shows the segmented regons the locatons of the constrant pxels the gan map mage the log mage and gan map modfed mage of the Memoral Chrch HDR radance map. Fgre 4 shows a comparson of or reslt wth those of three other recent hgh dnamc range compresson technqes for the Memoral Chrch mage. Fgre 3. Segmented regons and constrants. The thck black crves shows the regon bondares fond b the segmentaton algorthm where constrants shold not be placed across. Constrants postons are shown n dfferent colors wthn the regons. The gan map mage compted b LNE. The achromatc channel of the log mage n whch local detals s lost de to scalng. Reslt mage = +. Radance map cortes of Pal Debevec. Fgre 5 shows the segmented coarse regons and the locatons of the constrants sed for constrctng the gan map the gan map mage or reslt and the reslt of the gradent doman method [15] for the Belgm Hose mage. Fgre 6 shows more examples of or reslt as compared wth other methods n the lteratre. These reslts demonstrate that or technqe works effectve n compressng hgh dnamc range mage for dspla. t s seen that n all or reslts local detals are 6

7 well preserved and n some case slghtl enhanced. Compared or method wth those state of the art shows that or method works eqall well. Vsall there are some dfferences amongst the reslts of dfferent technqes sch as the overall brghtness contrast and color of the mages however as has been ver well stated n [21] these dfferences shold not be over-nterpreted snce the ma change dependng on the detal mplementaton. enhanced more when the mage s scaled down to ft the reprodcton devce the end effect s that local small detals are relatvel enhanced whle large changes between regons are relatvel compressed. Fgre 7 shows a scanlne form the Belgm Hose mage n Fgre 5 whch perfectl llstrates the behavor of or technqe. Fgre 4. Or reslt. Reslt of gradent doman technqe [15]. Reslt of sbband technqe [21] Reslts of blateral flterng method [17]. Radance map cortes Pal Debevec. A ver mportant propert of or technqe s that t s completel free from halo artfacts snce t wll not reverse the edges. n fact the wa n whch or technqe works can be nderstood n ths wa: t enhances the contrasts everwhere n the mage bt enhances small contrasts more and large contrast less. Therefore the drectons of ntenst changes wll be protected whle the magntde of changes are ether boosted or attenated. Becase strong changes are enhanced relatvel less and weak changes are Fgre 5 Coarsel segmented regons and the constrants sed for constrctng the gan map. The gan map mage or reslt Reslt of gradent doman technqe. Radance map cortes of Raanan Fattal Dan Lschnsk and Mchael Werman. mage enhancement. Or technqe can be eqall appled to the enhancement of ordnar mages. Fgre 8 shows an example of applng or technqe to the 7

8 enhancement of an ordnar mage. As a comparson reslt of the gradent doman technqe s also shown. We see that or technqe works well. The two reslts are slghtl dfferent agan the dfferences shold not be over-nterpreted becase the ma change dependng on the detals of mplementaton. sng weghts compted sng LNE clearl follows the orgnal sgnal and preserves and enhances local detals those sng weghts from sqared dfference and normalzed correlaton clearl loss track of the sgnal and smear local detals. ' = + G G Fgre 7 A scanlne from the Belgm Hose mage all three sgnals are scaled to 0 ~ 255. t s seen that the gan map mage (bottom lne) strctl follows the changes of the orgnal mage (mddle lne). The reslt mage (top lne) and the orgnal mage (mddle lne) have exactl the same edge drectons. t s also seen that (top lne) has more local detals than (mddle lne) (e) (f) (g) (h) Fgre 6 more examples. Or reslts (e) and (g). Reslts of gradent doman technqe [15] and blateral flterng technqe [17] (f) and (h). Radance map cortes of Raanan Fattal Dan Lschnsk and Mchael Werman and Pal Debevec. t s nterestng to note that the colorzaton sng optmzaton work of [26] solves a smlar optmzaton as eq. (4). However the se the W s drectl compted sng the sqared dfference or normalzed correlaton of neghborng pxels rather than compted sng eq. (3). These drectl compted weghts are not stable for comptng the gan map mage becase the fal to captre the local changes of the mage. Fgre 9 shows a scanlne and ts processed reslts b sng gan maps constrcted weghts from eq. (3) and those from sqared dfference and normalzed correlaton. t s seen that whle the reslt Fgre 8 Orgnal mage The gan map mage Or reslt Reslt of gradent doman technqe [15]. mage data and gradent doman reslt cortes of Raanan Fattal Dan Lschnsk and Mchael Werman. 6. Concldng remarks n ths paper we have presented a novel technqe for comptng a contrast gan control mage for a gven mage. We ntrodce the dea of thnk locall ft globall to constrct the gan map mage to acheve local detal enhancement/preservaton and global vsal ntegrt protecton smltaneosl. We have developed technqes to compte the gan map mage n closed form b solvng 8

9 constraned optmzaton problems. We have demonstrated that mage gan map constrcted b or method can be sed to compress hgh dnamc range mages and enhance ordnar mages wthot ntrodcng vsal artfacts. LNE Sqared Dfference Normalzed Correlaton Fgre 9 An orgnal mage scanlne () and the processed reslts sng gan maps constrcted from weghts compted n dfferent was. t clearl shows that sng sqared dfference or normalzed correlaton between neghborhood pxels to compte the local pxel relatons are nstable for comptng the gan map. References [1] T. Stockham mage processng n the context of a vsal model Proceedngs of the EEE vol. 60 pp [2] B. K. P. Horn Determnng lghtness from an mage Compter Graphcs and mage Processng vol. 3 pp [3] K. Ch et al "Spatall nonnform scalng fnctons for hgh contrast mages" n Proceedngs of Graphcs nterface'93 pp [4] J. Tmbln and H. E. Rshmeer "Tone reprodcton for realstc mages" EEE Compter Graphcs and Applcatons vol. 13 pp [5] C. Schlck "Qantzaton technqes for the vsalzaton of hgh dnamc range pctres" n Proceedngs of 5th Erographcs Workshop on Renderng Jne 1994 [6] Greg Ward. A contrast-based scale factor for lmnance dspla. n Graphcs Gems V pages Academc Press 1994 [7] J. A. Ferwerda S. N. Pattanak P. Shrle and D. P. Greenberg. " A model of vsal adaptaton for realstc mage snthess". Proceedngs of SGGRAPH 96 pp [8] G. Ward H. Rshmeer and C. Patko "A vsblt matchng tone reprodcton operator for hgh dnamc range scenes" EEE Trans on Vsalzaton and Compter Graphcs vol. 3 pp [9] P. E. Debevec and J. Malk "Recoverng hgh dnamc range radance maps from photographs" n Proceedngs of SGGRAPH'97 pp [10] D. J. Jobson Z. Rahman and G. A. Woodell A Mltscale Retnex for Brdgng the Gap between Color mages and the Hman Observaton of Scenes EEE Transactons on mage Processng Vol. 6 pp [11] S. N. Pattanak James A. Ferwerda Mark D. Farchld and Donald P. Greenberg "A Mltscale Model of Adaptaton and Spatal Vson for Realstc mage Dspla" Proceedngs of SGGRAPH'98 pp Orlando Jl 1998 [12] J. Tmbln J. K. Hodgns and B. K Genter "Two methods for dspla of hgh contrast mages" ACM Trans on Graphcs vol. 18 pp [13] T. Mtsnaga and S. K. Naar Hgh dnamc range magng: Spatall varng pxel exposres Proc. CVPR 2000 vol. 1 pp [14] J. DCarlo and B. Wandell Renderng hgh dnamc range mages Proc. SPE vol.3965 pp [15] R. Fattal D. Lschnsk and M. Werman "Gradent doman hgh dnamc range compresson" n Proceedngs of SGGRAPH 2002 pages [16] E. Renhard M. Stark. P. Shrle and J. Ferwerda "Photographc tone reprodcton for dgtal mages" n Proceedngs of SGGRAPH 2002 pages [17] F. Drand and J. Dorse "Fast blateral flterng for the dspla of hgh dnamc range mage" n Proceedngs of SGGRAPH 2002 pages [18] Mchael Ashkhmn. A tone mappng algorthm for hgh contrast mages n Renderng Technqes 02 (Proceedngs of the 13th Erographcs Workshop on Renderng) pages Jne [19] H. Seetzen W. Hedrch W. Sterzlnger G. Ward L. Whtehead M. Trentacoste A. Ghosh A. Vorozcovs Hgh dnamc range dspla sstems ACM Transactons on Graphcs (Sggraph 2004) 23(3): [20] G. Ward and M. Smmons Sbband encodng of hgh dnamc range mager Proceedngs of the 1st Smposm on Appled percepton n graphcs and vsalzaton Pages: [21] Y. L L. Sharan E. H. Adelson Compressng and compandng hgh dnamc range mages wth sbband archtectres ACM Transactons on Graphcs (TOG) 24(3) Proceedngs of SGGRAPH 2005 [22] L. K. Sal and S. T. Rowes Thnk Globall Ft Locall: Unspervsed Learnng of Low Dmensonal Manfolds The Jornal of Machne Learnng Research [23] D. Comanc P. Meer: Mean Shft: A Robst Approach toward Featre Space Analss EEE Trans. Pattern Analss Machne ntell. Vol. 24 No [24] W. H. Press S. A. Tekolsk et al. "Nmercal Recpes n C++ -- The Art of Scentfc Comptng" Cambrdge MA Cambrdge Unverst Press 2002 [25] D. J. Heeger Half-sqarng n responses of cat strate cells Vsal Neroscence 9: [26] A. Levn D. Lschnsk and Y. Wess Colorzaton sng optmzaton SGGRAPH 2004 [27] W. Hackbsch Mlt-grd Methods and Applcatons Sprnger Berln