-rod leuorletnduoc eql pue ']xaluoc lu,rodr-ue1 pur lurluds .rog Surlunocoe loJ sepoJ .Surpoc-ro1oc lueu -oddo ro3 seLUeqJS 'Surpoc roloc Äreur.rd3o ,(roeq1 rruelussnJr) atll sJUtl :seqt 8uo;e qJlJ)s pun ipoJ roloc e.Jo uorlou leLuro.] oql ,(o1due ,{e,tr lrcrldrur pue ôrlnlur u€ ur 'lleqs ; ,{yreelc cJoru sluoru -älr lcrlleroJql rtspq äql 1no Sulrq ol lrplo ul .,\\Jr \ Jo lurod tstleuortrulu pue 1ecrs,{qdoqcÄsd Ä1a:nd e rlo{ rloluesel loloJ ur sa,lrloedsrcd 1errs,(qdoqr -,(sd 1uc:e13rp Jo eurllno pcler^orqqe pue ,{: -olcnpollur ue epr.r.o.rd o1 ,{r1 11r,n 1 ;eldeqo srql u; l,erntcnlls [Ec -rs,{qd-oqcÄsd lurof eql Jo srseq eql uo pelrnrts -uoc eq (luepuadepur uor]llurunllr ere teql sapor 's:o1oc enbrun lo.I sepoJ 'ursrretueleru toJ sepoc ''3'e) serlredord urel:ec qlr,{\ sepoJ uec,\\oq (,secu;:ns yucrSolore, pue ,slttSll Iernteu, Jo ernlrnrts 1ecrs,{qd '.s}q8!1, .}o ernlJmts lecrsÄqd ''3'e) i,e:nlcnrts 1r:rrs,{qd 3ur,{lrepun cq} sr lr?q,tr (.sroloc lce tqo, lo luetussessu'seoue:eodde JoloJ .sploqseJql .seJns -eetu uotlBIIeJueJ loloo 'utsueruelclu ..3.e) i,o1 perreJer ore suorleler lecrSoloqcÄsd.Jo purl leq.tt :rJLllou P ouo ruo{ paqsrnSurlsrp oq ol suorlsenb Fur,trol -lo.l äql pue peplôe eq o1 slcadse yecrSolorsÄqdo.r -neu pus lucrSoloucluoueqd'lecrsÄqd Jo uorlElJuoO eq] s,{\ollu }l 'uorlelelrälur rreql Surpuels:epun ,roJ puu rlJJeesel loloo ur slêol eseql Burle;udcs ro-+ [oo] lngdleq ,{.relncryed p sl '(JJ9gZ.d .6g61 '1e 1e seddng) zluer; fq pecue,tpe sp .opoc loloc e.]o uorlou .tq1 'Surssecord lurneu 3o suorldr.rcsep pup sluir.rrJ^rtqJp leuorl.luni .;o uorlduJ\ep :rll 'uorldrrcsep lecrFoloueuoueqd eql .lucuruoJrluo lecrs^qd ä!l .Jo slcrds^e luêeler ,(11enldecjed ;o uorldrrcscp 1ucrs,(qd aq] :srsfleue pue uorlducsep Jo slêe[ luoloJJrp seqsrniurlsrp Ä1.rue1c euo,p q]r,u tluep ÄllnJs^seJcns rqÄpro uec suorlsanb qcng i,sleo8 leuoqcung slt Surns:nd ur3o e8eluêpu clul ue1s,{s Ipnsr^ aq} seop serluelnSer 1errs,{r-1d1o purl ]uq^A alucruuoJrlue slr o1 rusruuS:o eql 3o 3ur1d -noc e.,rrldepe ql.]o srulcl ur pczuelceleqJ cq uorl -dec:cd lolo3-+o sluetuêelqcu eql uec ,trog i,lndur ,{;osncs eql uo esodrur ue1s,(s yunldec.red oql sJop alntcnrls l€urelur Jo pull leq^A allqrqxc lueuruoj -l^uo eql Jo sälnteoJ 1ecrs.{qd jo Surpoc 1en1dec.r:ld oql seop scrpedord 1eq16 uotldec;edjo sanssr 1un1 -decuoc pue leuorlepuno.+ Jo setpnls :o3 iurp.re,ne.r Ä1.re1ncr1.red ecuorcs roloc selultr Ä3o1ouer-r-roucqcl puc,,(3o1ors,{qdorneu'slsÄqd 1o puclq enbrun s1 1 'peuleJuoc ete seJuctJs e,nrlru8oc eql qJrq,r qp.^\ 'sldeJJed snorcsuoc pue suolleorJls -se1c crlsrn8url ol uorlJnpsuull lelneu ruo{ .slêal 1o lnue3 eJrlue eql sesseduocue uorldec:ed .ro1ct -r 'secuelcs e,trlruSoc crllJo slJedse lulueurupulU olrrr suorlr8rlse,lut loJ lserelur crleur8rpe;ud ..1o plJl.l e uorldecred toloJ ep€ru oslu seq lnq ..uorlelr-resJr -der 1eue1ur, slr pue tplJo,!\ Iuulelxe, oql uoJ^\lec, uorlelel eql olur seurnbur lecrSolourelsrdo lo.] lä; -re1 luelrodur ue loloJ epeu ,{yuo lou seq loloJ.}o sscupecp.J-snuuf slqJ_ 'p1;o,n 1ecrsÄqd eq1 3o scrl.re -do.rd o1 fe,n 1n1,ney € ur perl e'te secuerredxe lolol suollrpuoc leurJou Jäpun eJuls .sclels ll?uorloue elrl 'leulelul ,{1el1ue eq louueo loloJ leql snot^qo sr lr'uorlruryep lnc-leel3,{ue lsrse: .e,rr1relqo. pue .e,tr1ceiqns, jo slderuoc eql q3nor11 .alntru e,trlcefqns eJo eq ot s:eedde 1 :ruc1s,{s lenst^ s rusl -ue3.ro eql 3o lcnpo-rd e eq ol sutäcs reqlcr lolo.J 'splro,r\ 1ecrs,(qd aq13o uorldr-rcsep lecr;leuroeF-or -rsÄqd e1o lred eq ol urocs ]ou sJop loloJ .eJurlsur ro3 e dt: r1s e>1r1u61 ',{11eor1e:ocqt tl qtr,{\ Icep o1 sldurepu :no o1 loedsc.r qlr,n orluru8rue lsou.l eql oq ol s;redde lolorJo elnqllllu eq1 sccuer:cdxe Iunsr^ Jo selnqrlte luereJJrp Äuuru eql iuonry uorlrnporlul l.7l pleJSnelN reuleu sroloJ uorlBurrunllJ puB lrofqo roJ opoJ IBnO B ol sapoJ uuBrussBrs ruorc :uopdoJJod JoloJ .zl 220 12. Color Perception: From Grassman Codes to a Dual Codc fbr spective dcvelopcd in the context of color constancy. This outl inc then serves as the background fbr thc discussion of some gencral topics, such as phcnorrenology and attr ibutes ofcolor. ancj conceptual problents, l ike the rneasurentent device conception ofcolorperception. Final ly, I shal l give the outl ines ofa new perspectivc orr color percept ion that is inspired by ethology. According to this perspectivc, which cor.rsiders the parsing of the sensory input in te r rns o f , e .g . , 'ob jec ts ' , . sur faces', and 'events' to be detcrmincd by an innately fixed categorization process. color is not regarded as sinrply rcpresenting a specif ic set ofphysical attr ibutes ofthe environntent, l ike surfäce spcctral ref lcctanccs, but rather is understood as part ofthe very fbrmat, as i t were, of the perccption inst inct that couples our perceptuo-motorial systcm as a whole to i ts environment. The cclebrated phenomena that shor.v the cl ialect ic relat ionship of l ight and object in color perception which in prcsentday computational approaches is rnisrepresented and ovcrideal ized as thc 'problern of color constancy' are, accorcling to this view, an inseparable part of our .förm of perc'aption, rather than a cor.r.rputational achievement of estimating natural surface ref'lectance functions on the basis of certain sensory inputs. I f the perceptual catcgories of ' i l lumination color ' and 'object color ' , which are thc mold inb which the internal coding of color is fitted, are internally constituted by a f-ew ,represcntat ive' physical features, then these physical characterist ics cor,r ld be instantiated by an otherrvise highly rcduced st imulus. Such 'minin.ral ' stirrruli would thcn sutfice to tr.igger internal perceptual achievements, l ikc the segregation oi ' ' ob jec t ' and ' i l l umina t ion ' in fb r lna t ion . whose cornplcxity fär excceds that of the triggering stir.nulus. Two problems of perceptual thcory, though related have to be dist inguished here (referr ing to two dif f-ercnt units of analysis, viz., the individual in a specif ic context and thc evolving species). The first is to understand the nature ofthe internal 'semantics' of the perceptual categories of , l ights' and 'objects' for a given organism. The seconcl problern refers to evolutionary processes during which the internal sernantics originated: what physical propcrt ies ofthe environment gavc r ise in evolut ionary history to the structure of thcse pcrceptual catcgorics' l This second pr-oblcrn is part of a general evolut ionary pcrspectir . ,e on thc univcrsal structure of color perception. as at lvancccl b, Shepard (1992; 1994) . 12.2 Elementaristic vs. Ecological Perspectives in Color Research In research on color perception \\ ,c can schcrnatical ly dist ingLrish tr.vo dif fbrent k incls o lthcoretical perspectives: an elementarist ic ps1'chophysical (and often neulophysiological) pcrspcctir . ,c lbcLrsing on ' front end' color coding. ancl a f irnct ional perspective emphasizing con.tplcx trrcrceptual achievements l ike color constancv or thc per.ccpl i o n o l ' s h a d o w s o l i l l u r t r i n r t i o n . The start ing points fbr the clcntentarist ic psychophysical perspective arc elentcntar-y achicr,crnents l ike color rnatching. color discrint ination etc. and their temporal and spatial cocl ing pfopcrt ies. Typical st imuli used l iere are dccontcxtualized colors, i .e., mere color ancl l ight patterns that are not embedded into a natural scene. I t is ucl l known that this perspcctivc provcd to be fiLritfir. for our understanding of elementary ncural color codes. On the other hand. the ft-rnct ional ist pefspcctivc which became int ir .nately connectcd u' i th a conrputat ional approach to color pcrception takes as i ts start ing point contplex achieventents ofthc I isual systcm, l ike color constancy. The corresponc.l inu stimuli are complex 'scenes' that are. phirsical ly described in terms of ' contplex achievcl lent-rclatcd concepts, i .e., in terms of 'surtace ' . 's1-rccular h igh l igh ts ' , ' shador ' " ,s ' , ' t ransparency ' c tc . Whereas thc elementarist ic psychophysicl l pcrspective only crnploys elcntentar-y spatio-tcntporal l ight patterns as such without r.elat ing thent to pcrceptual categorics or interpretat ions in tcnus of environrnental enti t ies. the contputat ional pcrspcct ive takes thc perccptual classit ' icat ion of the cnr., ironment, i .e., the f irrniturc of thc physical u,orld as perceived by thc organisnt, as gi len and attcrnpts to establ ish computational mechanisrus that al lou. propert ies olthe theorct ical ly predctenl inecl cnr, iOb jec t and I I lunr inu t iou C 'o lo rs uortJes txeu eql ur ourllno .,(ger.rq 11eqs I .,uorl -ernles, pue .sseulq8rrq, .,enq, 3o fxopoqlro ru-re1 roloc luerJno eql fq pelse88ns sr ueql uorlsenb pelDes pu€ Ier^rJ] ssol reJ e st roloc Jo selnqrJll€ 3o uorlsenb eql ecurs .Burpoc roloc Jo suorle8 -tlsêur roJ uott?^rlou pue lurod Burgels eql opl^ -o.rd ,,(11ensn ecue-reedde Joloc lnoqe suotlûJesqo lo rolor 3o secuereedde o1 pe>1ur1 .{llceripur fre,t fluo uoryo pue ,{11ee,u ,{1uo ere enrlcecls -red yecrSoloce u€ urqlr.{\ pue,{relueurelo ue urq}r.4A qloq rolor Jo Surpoc Ieurelur eql uo serroerlJ 'uortces [?urJ eql ur sserppB Ileqs I ]€q] icedse srql sr lI ']noqe atuoc.roloc lcefqo, ro.toloc uotteurtunllr,'.1cefqo, .,ece3tns, ery1 .serro8elec lenldecred frelueurale ,rtoq Jo rueyqord eror er{l qlr.& Aprcrldxe sieep snql Qoe;eql suorl€urqluoo ;o) se,rrlcedsred eseq] Jo reqlreN .(Buipes ,(1r1eer Ienur^ B ru ro uoercs JdJ e uo lcelqo uego >1urql) ldecred Surpuodserroc eql -rog .{ressaceu êe }ou ]nq ']uercrllns lou ,{1uo 1ou sr ,{1r1ue lecrsfqd eq1 Jo ecus]stxe oq] pue .aprcutos lou op .uouolu, pue ,1ceiqo, '.eJeJJns, ,uor1eururn11r, ,.{es Jo serro8 'ttlels^s,r\3r^-uerllo,\\xu141 crldo-orcru lel) eql : I.Z I .31.{ -e1ec lenldecred eql pur: lecrsfqd eq] lng .euors eql Jo uorldrrcsep 1ecrs.{qd eq} roJ Buruur8eq oql ruo{ lqBH ureql säsn pue peluer8 "ro3: seuo8 -e1ec lenldecred eseql se1e1 e,r,rlceds.red leuorlelnd -uoc eqt ?uerl reglo eqt uO .polcnrisuoc ere .1q8r1 pue lcefqo 'eoeJrns e>p1 ,serro8elec lenldecred Ä;elueruele ,&\oq Jo uelqord eql Bürssolppe lnc -r{lr.^ 'cle srsÄ1eur esrou-leu8rs ,Burrelp; ,uoltJnp -suer1 Ärosues e1r1 sessecord qlr.{\ sieep fluo e,tr1 -cedsred lecrsÄqdoqc,(sd .{.re1ueure1e oql .snql (.sueercs JUI uo su;e11ed lerodurel-orleds xeldruoc .s^ , I .Z I e:n8rg ur u,moqs se 'sure1s.{s 8ur,trer,r, uetllo,\\xel4 ,{leureu ,suo11 -eBrlsenur ;eyuewuedxe loj peÄoJdrue Ä;;urrclÄt snlereddego spuDl lueJoJJrp eql ur perorJrrr sr sârl -cedsred o,ri oseqlJo slurds lue;egglp eql) .1nc[1no eql go serro8elec lenldecred Bur,{oldrue ,{q lndur oql oqrrcsep ol puel seqceo;dde leuorlelnduroc eq1 seereq,tr 'selqerru,t lecrsfqd freiueurele Jo sru.rel ur pequcsep sr snlnurls oql elrloodsJed crlsr:e1 -uetuele eq1 go e8en8uel lecrleJooql eq1 u1 .lndur {rosuas Jq} uoü pätJnrlsuoJJr.q ot tr".ruo., -r^u0 paur ,r\olle ]uq] sldurepu ; se pFô\ Jt -r^uo orllJ -ceds:ed 1 Jo sr"uiol -;ed o1 rue ye.rodruel-r -red lecrsl 'c: ;u1nceds, -lelel-]ueu ,{11ucrs,{qd Surpuodsa I€nsr^ 0q1 sI se se)el -Lrro3 u qlt e,rrlceds.rer roloJ le.rn: InJIll.U 0q Ila,,!\ sr 1l ' ]e[p sr"rJo]]t -lenlx0][roi --redo-rd 3u uorJ€utu_il.I1 -e,terqcu ,{ -,{sd crlsr-u lenldec-red leuollcunJ -snJoJ êq 1ucrs,(qdoq lecrlelo0q] -rleujeqJS r UI SOr ,(q pecue,rl IesJ0Arun er jo 1-red sr ru LZZI{oreesäU roloJ ur se,rrlceds;e4 yecr8olocg .s^ Jrlsuelueureli1 Z.ZIsloloJ uc 2 2 2 1 2 . C l o l o r P c r c c p t i o n : F r o n r G r a s s m a n C o d c s t o a D u a l C ' o d e f o l O b j c c l l r r { I l l u n r i n a t i o p C o l o r s sornc ol-the conceptual intr icacics involved in the issues of asscssing attr ibutcs of color (withclut deal ing with thc many empir ical intr icacies in the complex phenomcnology of color appearances). 12.3 Attributes of Color The great variety of nuances of color appearances that natr"rral scenes off-er us can only be rrrade accessible for perceptual juclgments and l inguist ic concepts by processes of abstraction and categorization. Color tcrms gradually emerged in the process of cultural evoltLt ion. From Honrer's emphasis on forms of l ight, such as brightness, luster, and thc changcabil i ty of colors, to the subsequent and continuing intercst in the propcr color of objects ancl in color as such, thcre has been a cultural ly shaped progrcssiorr toward an increasingly abstract color vocabulary. Thus, the bui lding-up of a color terminology is a cultural achievcr.nent that fiom the very beginning of hur.nan culture rr irrors not only the signif icance of ccrtain biological ly important objects, but to an incrcaslng cxtent the invention and cultural role of colorat ion techniques and dyeing-processes. Our abstract color tcrms rnostly dcrive fion-r either concrcte objccts ( l ikc recl which in al l Indo-E,uropean languages scems to be dcrived fiom thc Sanskrit word fbr blood, rudhira, c.g., erythros, ruber, ruadh, rot. rougc, rosso) or fiom material propert ics, e.g., shining. glossy. spcckled, dul l , drab, resplendent (see Marty, 1879; Hochegger, 1884; Wactzoldt, 1909). OLrr conscious awareness is of objects and their rnaterial charactcr, whcreas color appearances only seem to bc a kind of medium we are reading through, as i t wcre, in the visual system's attempts to functional ly attain the biological ly signif icant object. Thcreforc cognit ive processes of sint i lar i ty classif icat ion arrd abstractrve catcgorization alc neccssary tbr a l inguist ic dcscript ion of color experienccs. This achicvement of an abstractivc categorization entai ls thc Janusfaccdness ofcolor with rcspect to i ts objectivc and subjective aspects, mirrorcd by the incoherencc of ' our evcryday concept of color, which hovers bctween two cluite difl'erent meanings of color, rramely (objectir . ,e) color patchcs and (subjectivc) color expcrienccs. Whereas propert ies of the blain ccrtainlv rcstr ict and prccletermine thc possiblc kinds o1'calcgorizlt ion ancl l inguist ic contprchcnsion olpcrccl-rtual expcr ie r rccs . thc rc i s to da tc no conrpc l l inq c r i dence tha t the coup l ing o1 'co lo r cxpcr icnccs to l in guist ic categories is in a spccif ic l iav prcclctermined by propert ic-s of intcnl lr l cot l ine (c1.. Frumkina , 1984; fo r a l tc rna t ivc v ie r rpo in ts see chaptel I and I I ) . Though thc basic pcrccl.rtual catcgories o1'bright ancl dark (r ihich lrarc bccomc rnetaphorical ly I inke.d tu sevcral cultural lv signifrcant dichotornies) nray ha.,,c inf luc-nccd l inguist ic categories. thcre ckrcs not sccl l to bc a l ' i red sct of natural l<inds 1br' l inguist ic color. conccpts. B io log ica l l y and l i rnc t ionu l l v c luc i l l l spcc ts o f the perceptuo-ntotorial systel l t clo not ntap in a natural ancl direct way to lan-r1uaqt. but l tavc to be ' rccOl ts t ruc lc ( l ' h ) e o r rsc i t l t t s c ( )sn i l i \ c t rc t i r i t r . Our l inguist ic -arip on color cxpcricnccs is basccl on a catcgorization ploccss that is pr. irnar. i ly shaped by contingcnt propcrt ics o1'thc cnvirontnent ( l i ke k inds o f b rokrg ica l l i , s ign i f i canr ob jcc rs and the avai labi l i ty of natural t lycs). b1, ' thc cultural contcxt ancl the cle-grce of l inguist ic abstraction achieved. Though therc havc bccn s* cr.al attcnrpts to show that this pl 'ocess ol 'catcgol izal ion is deter.mined by cer ta in in tc rna l p roper t i cs o l ' co lo r coding (e .g . , Rat l i f l . 1976) , no cor tv i r rc ins o idencc so fär could be provided tbr sr,rch a clarnr. I l ' thc construct ion of a color terrnirrolouy is I ' i r .st of 'al l a cLrltural achievcntent, i t clocs not contc as a sut.prise tha t sc ien t i f i c ins i -qh ts in to thc na turc o l ' in tc rna l color coding have sincc thc last ccnturv theniselves reciprocal ly inl lucncc-d thc uuy \\ 'e catcgorize and classify colors. Flnnt thc inve.nt ion ofthe 'basic color attr ibLrtes' huc. salr"rrat ion ancl brightness and thc ideas cln an irrternal oppuncnt or.gunization of color to color '-ordcl systcnts. l ikc thc Munsell or DIN systclt l (rr 'hich ar.c uscd l i rr inclustr ial processes that lcquirc stantlart ls anrl norrns fbr referr ing to colors). thc nuy u.c talk about color is continuously chanqins. -Ihcret irrc i t is hardly an exaggeration to sny that " 'color 'cl id not nrean to the Greeks I 'n,hat i l uteal ls to us" ( lr*, in. 1974, p . 1 ,1 ) . Co lor tcnns arc thc p roduc t o l 'a cu l tural ly shapecl abstraction process. "Thc Honreric '..3uur.rc,r uJ.lnlnzlô.rJrl Sunpurldu-rq Jpue-lJelicq Jrp s.rlJla,\\ 'Upq sctqJr-I ueirue [sep tr4toJJur_lrsoB e,rrlcelQcr Jrp ue qcrs ers up 'a8uarlî r_rorur.uo)Jlol eurJ JJqe lsr ars uJlrlJerleq JqJrtln)1r,u zuui eure sl? pnrH JJp lô crs Lreulro] .lt,!\ :urJs nz essuurairnlBu Jure 'ynelep qrnldsuV rrJurel lqruur SunrcparlD csJrC,, L suq sJr:^^qd.+o suorletodo pue sldecuoc ,(;elucue1e utol.] peluJp seuo8clec o1 fiurp;occe eueuroueqd lcnldoo'ted esled o] s1dure11r 3o o.rnluu crleluelqo-rd oqJ 'sltcpr Surpeclsrur puu ôtlrnpes lsotu eql Jo or,ro sr srrs,{qd ,{re1ueura1c.}o slruof oql Suolt: uor} -d:lo.red .Jo JJnlcu crl] Surtrls go du:1 Jrlb^rlpcrs,{qd eq] .{SoloqrÄsd lunldeo:ed .1o ,{:o1srq eql u1 ''(9 d 'zgg l 's^e rJ) uô) .)-c3ue'n:eddr: Surpuodse::oo oqt sesnPr ]trll lqSrl erp .]o r-erllrdo.rd c,trlcelqo ol sreJel ,(1uo 1r JJurs 'euo sno:ofiu ,{1e1r1duroc u 'lJ^e,lloq 'sr uorlciucsep e qJnS euo Ä.rr:1rq,re ,{1 -elc1du"roc u se 1r p.re8cr uec e,\\ ope q3nu lnoqlrm :ouo lBln]eu B eq ol utulJ lou saop,, sseulqir.rq pur: uorlelnles 'enq Jo 5^r.üJe1 ul secueleäddü .roloJ -JC) uolsr^rp e leql pelleurej eH 'suorlu,rcdo 1ucrs,(qd o1 ar1 8ucr:1s .ncq] utoi] sllnsal leql sldccunc :o1oo -1o norsroe;d luoreddu ur? JoJ sscuull:1rq.re 1ucr3o1 -or1c,(sd epull ol pa:.rc.1erd eq lnq suclqo.rd qcns .]o ere,ru sem 'zlloqu-rleg .1o lrdnd e 'seu) u( ',{al3 snoururnl elrl sJoulluedde ,{q pcsseu -lr,{\ cq utc su 'Äresseccu r-r }unoJJl? [Euorsueutlprq u lscel ]e '8ur:eg äJUrs u,roul llc.r\\ )-r s€ .slolo3 JlluuolrlJe l(U ueAE Jedo.rd uorldJJled loloc ueql esec ;eldurs e su p.t^recuocsrur e,trlcedslJd crl -sr1ecrs,{qd e tuo{ sr uorldecrcd Jolos urrllr,{\ tue(U -eAJlqoe yenldoo.red pooislcpun ,(pood ,trou o1 dn puu xe ldruoc ,{1q8rq e Sureq qorq,tr ,socuurecddr JrJtruolqJe;o Ä.roie1ec lenldec.rcd eql sl est:J Brrr -lsrJilur rJqlouV'sl()lo.r.lo,(lrsuelLrr -l() r)lods oq,{\ 'rcl qn g') pue' (,, t t at1 t1 :t r 13 ut.t p u ! 8,, ) sseulnl.lc.roJ .lo peelsur c)ocls oq,r 'lallr.l4 'g .C pue zle) tl-Ietll tuottlr? 'sJorllo ÄLrrLU ,(q pelcelc.r )-c./\\ uotJ -llrnlus.+o ldecuoo orp 'Lrrê lull[us u ul .leepr s]r ol rolos E Jo uorleurxo:dde eql Suunldeo uollelJ.l poppu ,(1o,tr1ru8oc u pue uorlcu.rlsqe e,rr'yru8ol u cc1 ol Lrorlulnles pêrorlroc aH '(9U 'tI ,Ll6I Jdunlg ',,It)uual.t)un Illqt.tllV slD lLl)tu ,rt,v, uauuo:1 Sutt8 -!lt!?5,,) Ä1e1e1duroc elnqrrllll roloJ u sl? .rrorll?.rn -Jes. pcssrLuslp'(g'd'116 1 Jdrurng',, uotDlD.ttr^q7. LtapLtdr)1lo''t .tap u;t8un8utp)g putt t1;t:181t11.t-.1..1 uor]3ellsqe 3ur1e1osr uu lo-] suollrpr-rof, Jrll puu ,(lrlrqe oql 1o urelqo.rd u eq o] selnqr-r1l1l .lolor.lo luelqord eqt pcrcptsuoc or-1,n '1dr-r-rnls puv .(0f cl '676 1 '3ur,reg) roloc 1o (,,llutt11ttq.r.1,, ) iurlr:r,r 3o ldccuoc (1eco:droe.r) eql pelle.Jr-rd ag .slrrdsu pcrsÄqd pue lunldco.red 1o cln-SLrrxrur l? su .1. -qle3olle uo rlelnJrs Jo ldocuo J oLIl pcl Jo t.r.r il-rr t.la H 'ccur?.lsur ioC leq] -]o Jlê\s c-ro,{\ a-lnlc-lelr1 ,{1.rur Jq] ur slolu,r Äur61 (selqurre,t lcnldoued :r:r.rql Äq peqr:csep eq ,(1e1e1duroo uuc soouu.rucddu .ro1o:r ]ttll ccueprlo se uc)e] ,{11cc.r.roour sr Surpoo .ro1or ,(:u1r-rcuele ;o Äouuorq orrl go lop,J erll eloull Jrll.ln l ) suorlErJdo I€Jts,{qd Ä.re1ueurc1o uro.q LleIpl sntll ciê\ sclnqulle -roloc Ä.re1ueruc1e eq1 .1qir1 :11rr1.r,, qll,{\ snlnurrts lq8rl e 3ur1n1rp uc Ä1rsLr:r1ur 1qir1 Sutsee;cur 'rl]Suelcle,u u 3urlce1cs -1o suorlr:.roilo 1ccrs,(qd Surpuodscloc eql uo.4 po,\u.p 'zllorl -ruleH.]o elu,{\ e q} ul 'ole,\\ sclnqUllr? ose q1 (;7 cl !t86 I lpur)Lunl-l oes Äcenbepcur lcrl] -]o cJrr:lp -r,to crlsrnSurl :o3) secucrredxe lol()3 .lo .iltlJluls leucmoueqd xelduror oql 3ur.{uldu,,rrop o'l stul.rou-lu secuellledd€ loloc JZrJelte.n:qr Ä1c1r:nbepc sclr, -qu]lu cseql l€rll pepr pcprn8srru lnq pJ/\reJJ.l .rll '(rsr d '2861 'scpls pue rlrozsÄ16) ..sseu lq8r.rq rrcql jo sselp:eie; snlnrurts orluLLroJrlcu e ttlol.:} sleJJlp snlnLurls 3rlllurolllJ s rlJtr_l,lt o1 ee;Sep eql .1o eplru oq o1 lueur8pnl e slu:ed qorq,t uollllsUeS [Pnb^lA u -+O e]nqtjllu ]LlJ., ;uotlt).ilttt)s ,.uo os pue 'e1d.rnd 'per ,no11eÄ 'uce;3 'cn1q Äq peloucp lrorlde:lred ioloo e .Jo olnqullu eql,. ;)ntl ('r-rorlducsep strlJ ur .csuelul. ldecuoc oql Jo .(trnitqLUe erll eloN) .lesuelur ssel lo c-tout cq o1 sreocldr snlnLurls uc,tri r qJrq^\ ol Surp.rocl: rrorJusues lul-lsr^ c .lo elnqllllu erll,. ..sr'.rirlr7,!).r17 :îJCutlücddu .ro1or iurcl.ros^Op lo+ uorll?Jr.]rsselc elelduroc puu enbrun'lu.ntluu e sc pepre8el ,(11enr-n srrlorq.,\\ 'sJlnqultl? -roloJ.lo uotlducsep.]o pul) 3ur,no1;tI aqt purJ e,,t uorlcbr -.recl .roloc uo r-)ooQlxol plupucls ll? lool J,\\.]l (ZZ' d'V tOI'rn^\rl ) ....rc,\\srn) o1 elqu uJeq euolll lel 'polelnLul(u c,\url .rJ,\Ju p1no,t ,{eql uorlscnb e sr .i,rolor sr tltrl1 . .sul.rrl ]ct-qsqe ur Iurr[] ol päu.n?ol 1e,{ 1or-r pllrl )o.1.tt) Jl-liru0H : -lrlJ u.+0 1: 'trr \\-rl ) ..sl 1ou plp ..ro :-l ll J.ltl+: lnoqn )lPl sLU.lolr pUI -snpul -to-+ rrlt rlrl 's -ruui.ro lu: -111;-r.rc1 pur rtll .+o uorl -o,irln:l a,r, -urarll i-rn Iuuiilur .+o :rsr:cl.tns t'l -lnr u Ilu.+( -uor.]tll.+J os e.rrrJpr \ -Por .ulloJ --rJlep sl u( sltlurollu 1e r.rollrR.rlsqr -.rn'll11r Jrll slrolqo 1uc -uo.il.\t-lJ ä ,(1 r.n:rtrr.rd PCSncl sr si 'i1r.rr1rn s, Jcl ol J.\llq u rrr cluttt .;o sltlclsr: 'sldoruor .lo l.s paxr_ i)ll:^lnn-UIl I -r.lruirs ,{11 iu.loJtq t.\ 1r':nldar.rrd ai:^ SlUIo(l '1r) ;-urpr -.rrlrprlcl ,, -rill 0l satu -r,\. ö-ulllJr 1un1dlr.roc1 -uzt.tt'l;-.rlur 1rr.r1sr.r,i1u ( r,r rlra fclns taa.roloJ.]o selnqullv I zIs.r0l0 ) u( 224 12. color Perceptio' : From Grassman codcs to a Dual code for obicct and bcen discr-rssed since the beginnings olperceptual thcory again and again. The conception ofthe perceptual system as a kind of rneasuring clcvice which 'inlorms' the organism about the physical input, along with the idea that elernentary physical variables, l ike intensity and wavelength of l ight, are connected with elementary pcrceptual variables, l ike brightness and color, is an important (mostly implici t ly employed) metaphoq which itself is a legacy of the way we scparated physical and psychological aspects in the phi losophical history ofthe f ield and which has governed our thinking in thc study of perception sincc. Along with Ihis meu.stu'entent device cont'eption ctf perception (cf., MaLLsfeld, 1993) comes the idea that there are atoms of perception, as it wcre, that are strongly t ied to these elementary physical variables: namely the sensations from which perceptions as somcthing ref-erring to the external world are constructed. Because of the dif f icult ies in keeping apart the physical and psychological aspects ofthe investigation of color and in not succumbing to the st imulus error, Katz ( 191 l , p. 29) remarked: , ,The most important rule for describing color phcnomcna is. what vagueness thcy have necds to be dcscribed as such; part icularly in this respect there is a dangeror-rs temptation to adultcrate the description by perspectivcs borrowecl frorn physics.", The problem ol how to deal theoretical ly with the complex phenomenology of color has not been squarely met by current theorics of color percept ion. This is not only test i f led by the vexing problcm of the dirnensional i ty of color codes: Since Hering. Katz, Gelb and others, indications have bcen accumulating that color appearances cannot be represented by a threc-dirnensional color code. As Niederöe (1996) r igorously showed, even in centcr-surround configurations the dimensional i ty of color codes must bc greater than three i f one is ' "Darf ich dic, r.vic mir scheint, rvichtigste Rcgel für clic Beschreibung von Farbplrärromerren nennen, so ist es diese: rvas an clen Farbphänornenen unbcstimn-rt ist. vcrlangt auch als solches beschriebcn zu rverdcn: geraclc in dieser BezichLrng ist dic Gefahrgrof3. dafJ die Bcschrcibr.rng durch dcr Physik cntlehnte Be_ trachtungsweisen verfälscht wird." I I lurr inatron ( ' t l lo ls wil l ing to accept the topological assuntptions which, at least implici t ly. unclerl ic alurost al l n-rodels of color coding. Though this tbrnral argunrcnt for the inappropriateness of t l rrce-cl intcnsional color codes is based on the tfacl i t ional I , ieu, orr center-surround st imuli , i t is consonant u, i th thc perspective to regard center-sLlrroLlltcl conl'iqLrrat lons as minimal st imuli lbr tr igger-in-u a dual coclc {br 'object ' and ' i l luminatior.r ' colors. 12.4 Early Color Coding and the Elementaristic Approach 12.4.1 Newton and Helmholtz's Approach to Color perception Newton regarc led co lo r l s l rn i r r t r i r rs ic l ) r ( ) l rc l . t \ ( ) r . disposit ion of l ight alonc and he t icd thc corrccDts of refi-angibility and color together. Ne*'ton firuntl thc basic fact of what wc cal l ntetunreri .stu l tantcly that there are l ights ( i .e.. u,avelcnuth contposit ions) that can be physical ly dif l -ercnt but arc perceptr"ral ly indist ingr-r ishablc ancl * 'as auare of the existence of extraspcctral l iues. l lc consiclcrccl (psychological ly simple) white l ight to bc plrvsical ly cornplex, namely composecl of al l cl i f l -ercnt l ights. One important insight of his is that thc encls of the spectrum have sontcthin-9 ir-r conlnon pcrceptual ly, which led hirn to provit le a ntctr ic ärr speci[r ing color mixturcs: his fhuous centcr-ot 'gravity principle. Newtot.r r .ncant his rnodel to bc more than just a pictorial rcprescntrt ion of l i is ideas; thc rnoclel is a quanti tat ir , ,e sche rnc to account fbr the results ofcolor nt ixture (antl in lnct i t is the f irst quanti tat ive ntodel in psvchophysics). Helmholtz startcd fion.r this ntodel u'ith sontc misunderstancl ings in thc begir.rninu t l tat uerc clari f ied by Maxwell and Grassrrann. Hclnrholtz' .s goal was to investigate thc naturc of ( in his lords) "tcrminal processes that are r-csponsiblc l i rr the dependcncy of visual expcrienccs on l isht st inrul i ." Hc devclopcd thc basic experinrcntal par.adigm for investigating basic principlcs of color perception, connectcd psychophvsical lindings with ncurophysiological conjectur-es and proviclcd the fundamentals of a theory of carlv color codinrr. T s l L^( tt a l br i r " t c l t l1 ( t a I l n A t f l i i rh hr TI t-l t qn p l l ta1 cil an gl ' l l l , be ( \ \ 'lll-+äsn eq Äeu s>1:uruc.r euros 'lueluoc s1 pLro,{eq ofi leqt suor1e1.t;d:elrr 1'ruc suorldmnssu luuollrppll lrJel o] peppc,\\ ueuo sr 1 äJurS 'o1c ,(tuelsuoo -roloJ .]o souoeql luuoll -elnduroc ':o1oc 3ur,(jrreds rol suels.{s Itulsnpur 'Äroeql roloc-luauoddo sc rlJrls 'uorldecrcd ;o1oc Jo sJuoJql rir-1lo llrr.l() lnq uotst\ loloJ.lo ,{.rorql zlloqruleg-3unô eql 1o Ä1uo lou croJ eql sclntrts -'lro c 3u rpo c'Jo r c r o'lllT:';, ::ä::l-j3J]"r ", ol pureJal sepoJ roloc o1 pcsoddo se) -ro1oc ao sc -lnqupe cl3:rceds ol JeJel lou soop ursrJalut;letu lo.] epoJ uuerusselD e.+o uorlou eql 'êoq€ pauorluelu ,{peerp sV '(gl 'rlc '6961 ''1e 1c seddng i976.,1 'reiurporqc5 :tSgl'uueurssu:9) uorsrA loloJ 3o ,{.roeqt zlyoqLuleg-3unô-uol,4\eN eq} Jo oror 1ucrs,(qdoqc,{sd (,(1elnd) eq} eln}rlsuoc rlrsrraul -eleu Surluese:dcr sepoc uueussulD eseqJ 'saruereeddu loloc r{}r^\ parJrluepr eq uoql u?c s1qir1 crraureleur Jo sosselJ 'eceds ;o1ce,t srql ur (!ö "ö !rö) ö epoc roloc e,{q peqr:csep elu sluclu -ele 3sorl,tr 'eceds ;o1oc leuotsueutrp-aerql eJo uorl -decuoc Jrll ol spual qcrq,tr'eceds JolJeA lEJr leuors -uiturp-rärql ul :LloJ xJ^uoJ E ut slol()J luasudrl ,{11ecr;erunu ol elqrssod }r elrru s,{\el eseqJ 's,\\el uul?usserD eql q päquosep sr uorlducsep 1ecrs,{qd leuorsueurp-elrur.]ul äqlJo lno pelolf,€J ele sess€lJ ecuale,trnbe 1en1dacred,no11 uorldrrcsep 1ecrs,{qd cr-1l SuruesreoJ ol slunoure MerA Jo lurod lucrsÄqd u rrro{ rlrrrl,r 'slqill lerls{qd3o les ar{l uo sessel:t ecueye,tnbe slJnJlsuor snql ruels,(s lensrl oql .eceds :oloc EIJ ol speol t€rll (Z ,1,X) Surdduru oql pue sepoo roldeccr 1ucr3o1ors,(qd cq] lueserdcr ler{t s8urdder"u oq} ere eseql Suor"uy 'pclelol ,{1.reeur1 olü qrrq,{\ 'sepor qons go Äyruej eloq,tr n slsrye JrJLll lnq'rrrbrun ]ou st ll ',)1ro,) Ltunlltssnrg e peller eq III.{I ö Surddeur eq1 '*PUB 6 suorlu"redo lerrsÄqd oql o] lcedsol rllr.^\ rrotlclol scuonrSuoc e Eerorlele: 1ecr3o1oqc,{sd oqt sa)eui s \\ul uuctlr{serD Jrll 1o ,{trprlen lurrrrdr-ue eq1 '< ='* '@ ''l> elnl -cnr1s lecrsÄqdoqc,{sd erp p1er,{ o1 lce.relur Ä11ecu ''r. '@ ''l '' Jln].nlls 1rrrs,{qd erl'l'sllq.l_ ' (B)ö - (flö <+ B r r'q1 tlrll:^'rrud:^ .rotr.\ lce-r leuorsueurp-JoJrll eql olul (,{1:ueur1 "r'r) ,,{11r,lr -rqd;oruouroq <x '@ 'l> elnlf,lt-lls 1urrs,{r1cl r.rr1t1 -r1enb eql sdeul qcrq.,n slsrxe (iö':dl'rö)dl;-urcl -deur e ueql'(suorlnqrrlsrp,(8:euc luurpr:r.l 1u:1r:lds -Ilarll qtr,\\ peryrluepr slqFr1 go les oql :^r I r.lrll,\\) slq8r1 -1o ernl3nrls lccrs,{qd e,rr1r1r lunb crll .rl <*'@ '-l> Je.1 'csues 3ur,tro11tq eql Lu ulsr,t.ulrllJul lueserde: leq] sepoJ JeeutlJo r1dr.r1 c o1 osr.r so,rri snl] 'seqcleu clluluollcul 3o ssruenbrun orll puu Surqcleru roloo -1o,{ceuo:qor.t1 eql qlr \ .l.qlcn-ol. 's1q8t1 jo uorlecrldrllnu teleos prre uortrppu .rrpun pe,trescrd (1ua1xe c3.re1 e o1) sl ursr:euruloLu 'i-nrll B*1=V,r1 ,)@u=.)ov Plorl (,.s,uey uueusse:o,,) suorlele: 3ur.no11o.i JLIt uarll '(Y)'la + (Y)\'H - (Y)trrir\ q 'J t'\,,ilnlrtut .tol(),') ),ttttl)pn,. ) slqir1 eseqlJo rlrue ol .lsr,nlurod peppu sl (1)13 uollnqr.rt -srp Ä3reue qlr.u 3 lq8rl oures eql.Jr pur: (r1)tr;1 puu (1)vE suorlnqr:lsrp ,{8;eue 1u:lceds qtr.,$ .B V

''e'1'97q311 rtraunJau) s1q8r1 elqrqsrniurlsrpur Ä11en1dec-rad cre g pue V Jr leql sureut su.l.L '* ,{q pelouep 's1q3r1 ;o ,{1rsuc1ur iuriuuq:r puu '@ ,,(q pelouep '(serlrsucp ,(3:ouc 1u.t1tods Jo uorlrppe oq] ol Surpuodsa::oo) slq8r1 iursodurr -:cdns go suorle'redo 1ucrs,(qd eqt ,(q pe1re.11r:un ec1 ol punoJ sl ': Äq pelouop 'utsuerueJeur.lo t-lollule.l 1ecr3o1oqc,{sd eql plerg Iensr^ Ill?p oi-t.,\uorlJo rru ur pelucse;d sr c13ue lensr,r oZ lnoqn.]o ezls Jrll 3o Ä11ucrd,ft tq8rl -+o lods 11r:r"us u Jl :suortlpuor Sur,trer,r uregeJ ur s8urpurl lelueur:adxc oldurrs eruos uo peseq sr Äroaq1 z11oqtu1c1q-iuno1 oq1 sÄ{u.I s(uuutussBJS puB Äroaqa z11oqulag-8unoÄ rql Z.t.Zl '(soruu.rucddu .1o ,{lrlunbe ''o'r 'rusueruulelu q1r^\ s1tlcp ,{pro 1r) rolotJo ecueleeddu oql .{letuuu 'llu tll ssrlppu lou seop ,{.roaql srrll lEql loedsu euo sr äleql '-lJÄä.,\\nfi 'iurpor p.pr.\0-r( siurl-ln.. .roloJ J( -u.rr:cl 1u -rul1s lrl rql .roI (sP.ro.\\ r s,zllorFr -.rulJ J.r: aitr()s rll '(slr s.rqr lrE ur p ol Jtuä sril Jo r eq o1 I0 -.+o-.ralu; -l0J Jl.ll: -lrcl uor sPrrs arll lu..reJJII -rsiqd : pJ.lJprsl arlt lo 3. -.reci are -rsodurc -etUlltl pu110] u sldalro, .ro il.red qr Oql p epor lur r;-r ul !.1r JLI] rltr.\ ut) .r\Jt.' Iurrorsrr: 1reun3. -poLLr llr suorldru s.rol0 uo! < ='-I> ornlonlts lucrSoloqcÄsd eql pue 927qreo-rddy rrlsr.rutuJruolg aql pull 8urpo3.ro1o3,,tpeg y.71 226 12. Co lorPercept ion : FromGrass tnanCoc les toaDua l Codcf 'o rOb iec tand l l luminat ionColor .s does not rcpresent equali ty or inequali ty of color attr ibutes l ike hue, saturation. and brightness. Thc ratio of the length of two vcctor.s does not corrcspond to a rat io of brightnesses. and a l inc in Grassmann space does not neccssesari ly correspond to a constant hue. Thc Bezold-Brücke. sl t i t i ofhues under changes of intcnsit ies of l ights t locs not contradict propert ies of thc Grassntann structure. 5. The wcl l-known nonlinearit ies of neur.al coding do not cal l into questiori the val idity of thc l inear color representatior-r of the ( lrassmann theorl ' . F'irst of all. they do not ref-er only to thc Grassmann theory i tself ( the empir ical val icl i tv of whicl.r is a purely psychophysical questron). but to the Grassmann theory curtr neurophysiolo-uical l inking proposit ions. Secondly. evcn i f thc usr.ral l inking proposit ion discussed belou. is assumecl namely that two lights are r.r.rctar.ncric. i1' they result in the same number of photopirmcnl isomcrizations for cach of the three univanant types of receptors, any str ict ly monotonic transl irrmation of this process wil l preserve thc l inear representabi l i ty of the structure. 12.4.3 Opponent-ColorTheorv Sincc Leonardo da Vinci and. later. ( iocthc. Auber t and Mach ' red 'and 'g reen ' ! anc l 'b lue 'an t l 'ycl low' have bcen regarded as psycholo-uical l ,v basic and principlc colors. Gocthe, u'ho considered polari ty to bc one of thc basic principlc-s underlying color experienccs (fbr an account ol ' Goethch r.netatheorct ical principlcs on n'hich his approach to color is based, see Mausfeld. 199(r) provided central ideas and observations notabl ir on afterirnages, simultancous contrast and color.ecj shadows upon which opponcnt-color thcorv came to be based. For Hering, rvho took up central principles ol ' Goethe's approach, alrcady thc local color cocle is intr insical ly determined by thc entirc spatro-tentporal excitat ion of the rct ina. Phenorrrcnolosical lv Hering startcd f iom the observation that certain color experiences have the property of bcin-g unitary and that pairs of color experienccs that cxhibi t this property are perceptual ly inconrpatiblc. The L The Grassmann structure only ref'ers to l ights, and not to the color ofobjects. Though l ight is the r.nediun.r fbr asscssing the color of objccts, much morc complcx perccptual mechanisms arc involved whcn the st imulus consists of perceived objects and l ights. 2. The or.r ly psychological rclat ion involved in the Grassmann structure is metanterism. Thereforc only those formal propert ies ofthe vector space of equivalence classes of l ights can be given an empirical interpretatior.r that are based on thc relat ion of metamerism together with the two physical opcrations. These are only those that are invariant under l inear transfbrmations. Thus the vector space has no cmpir ical ly mcaningful scalar product, and Eucl idean distances between vectors cannot be intcrpretecl as color sirr i lar i t ies or indices of color discriminabil i ty. This can be easi ly secn fionr the fäct that the vector space distance betwecn two colors does not change whcn the same color is added to both of them; i f this third color is, fbr instance, a very bright one, the psychological distancc betwcen the colors wil l be reduced, however. Hou, to constrLlct a color space in which, in addit ion to the psychological relat ion of metamcrisr.r.r , other psychological relat ions l ike similari ty and discriminabil i ty are represented is st i l l an r.rnsolved problem of what Schrödingcr cal led highcr color metrics ("höhere Farhntetr ik"\. 3. The ideal izcd and theoretical relat ion of metarnerism which, for instance, implies str ict transit ivi ty of color matches can only be related to the cmpir ical relat ion of r.nctameric matchcs. i f (at least implici t ly) thc usual vector space topology is taken into account. Thus the Grassnrann structure nceds to be supplementcd by topological aspccts. Judgmental flr.Lctuations arc then taken to l ie within a ncighbourhood of the ' true'point, and small variat ions in the physical variables are assumed to lead to sr.nal l variat ions in the color appearancc (there are no jumps in color appearancc). Grassmann ( I 853, p. 72) and Schrödingcr (1920, p .4 l5 f . ) there fore cxp l i c i t l y inc luded cont inuity assun.rpt ions in their fbrmulations. 4. Thc Grassmann structLlre does not ref-er to color appearances (except for the dist inguishabil i tyindist inguishabil i ty aspect)! In part icular, i t tltrceperr eu ished c the b ipo l ycl lon ner l lcr ing dr n ious exp cocl ing th acter of ideas u,e G . E . M ü .lanreson I 972 ). r i mcntal tr inventcd The tcclt clctcrmini c l i sh co lo has to be u i th rcsJ Thus th is ncnt attr i t o f l igh ts theory to t ions cor-rr 12.4 .3 .1 As a ne-r thcorv ba honrogen lirpcs of 1 ond lqe l o l ' channr l lssoClate( 'u h i te -b l l fh is . ther ccpt of I hl pothesi thc rcspe ( I.lcLlfopnr gfccn eql colors thl ci thcr a L co lo r app t i r c va luc appcafan( c0rlrponel slql se.rnlsnlls ur-r8r-usselD luuolsuetrltp-Jtto plar^ secuolêrnbe uorlello3u€J leql uorlor,qsol eql sesodrlrr qorq^\ ']q8rl Surlurqrlrnb.t ctll .+o ectotlJ eqi.Jo luepuädepur cq slueulernsEJtll uolllllleottL?o letll lueluoirnbcr eq] q]t^\ op ol êtq sttotltpuoil rsrql'prllUlnl r.tu sJlnqrrlln.lo (ttlrqrltldutorut ptrc sslulrt?lr.tn ()l u()rlr[']pn t suot]cltttttssn eAtlull -1enb urelrec pepr,to.rd 'sepoc uuetusserg3o ,{1true-1 eq1 Suoruu uosor.lr cq Äldrurs ,{er-u scpoc }ueuoddo 1o scldr:1 'e,trlce ds-rad srq] ruor.+ letll tno surnl 11 (seuo leors,{qd q}r,t ,(r:1d-rcltrl rteq} pue suotl -u1er leorSolouoruoueqd 3o scrl:edord Stttrtlccttoc s\\pI pur? suolulel rrrlntrlnnb jo stuJ:l ttl"J t)\ttt() lecrsÄqdoqrÄsd Ä1e.rnd se pereptsuor c,Ill sopoJ 1lralroddo eql Jr pelse eq uec uollsct-lb Surprrodser -roJ v 0 :P().1 uunurssclD c ol "J'! 'srpor loldorr.l ,{reuud ot pe}plcr e:u .(eq} ,ttoq ISe o} lern}Eu sl lt 'srpoJ le-rnru sc {{1z)rq "Ö 't 71', '(1 'tyli 'öl lvtö sepoo lucuoddo 3o urclsÄs s sleprsttoc auo -]l sepoJ luauodd6 puB uusrüssBrc SupulelI z'E n'zl 'peltltrpu lJ(r \\Jutpr.l ltJIliJ(') -or{} puu ru8rperccl leluerut:edxe rql qllm ,(:e,t ,{er"u sepoo .]o urelsÄs e qJns Jo Sutuecut eql 'esJnoJ -]O 'seuo lre.rlsqp erolu .ro .sopoc lenldeo-rcd, uae,{\}eq uinl ur eleq puc '.rpor lucrs,{qdoqcÄsd, u 's \ .t|():r lcrneu. D.l() nirpr rtll t)l itrr.r.rrl:l Uee\\lirl 3ur1e1pce,r Äep lusse:d äq] ol uotleterd;etur slr rll,r 's:rBueqr snorJê ouo3:epun sutl sJpoc roloc Jo scdÄ1 Surpuodserroo eqt 1o Sutuccur eql 'Ä:oeql .roloc-lueuoddo 3o s8utuut8eq cLIt oruts 'clnlJn-rls uuerussnlD eql -]o srror]r?ledolsuotlelcr oql qll,^\ suorlelol eseq] -]o ,{e1dralr-rr eql Suture,ro8 s,tre1 e.trle}llunb eql qll^\ sleep Ärocql roloc-lueuoddo lecrsÄqdoqc.(sd Sutpuodser,ror eql'qsr,tto11a,{ iou qsrnlq lerpreu sreedde ,/ lnq] '(t,)zn puu 'qsrppei rou qstueerB reqllcu Surreedde ''J't 'utnu -qrpnbc uae:8-pe; ur ,(11ecrsÄqdoqoÄsd Suteq 7 sn1 -n(rlrls rql suciul.I ) v'tyl'f) orerl^\'{ z'l l} n selecrperd lucrioloqc,{sd eqt (setnqr-ute 1ecrs,(qd crsBq oql pln? Lusuelueletrt o] uolllppe ut) Jl€ pêlôLrr sLrorltler e,rr1e11nnb lcrluässi rtll stule] leors,(qdorlcÄsd Ä1e.rnd ut (ute8t uotletou erües eq] 3ursnl i qö pue i '6 sepoc ]ueuoddo Jrlüurortlc Jo s-rred 3o uorlcnpollur eql s,\\ollc uotltpuoc sttll (',{1o,u1ccdse.r'lueuodtuor qsruee-r8 pu€ tlsrppär t Sututuluoo seoutt.ttt:tclcltt r()loJ ol puoclsr.uo.r oluJIEI e.ru' '1).1() \.1ttlt'\.\tl -e8eu pue e,trlrsod 'uorlrppt u1) 'o:luurt.lcddu .tolof, elrq,{\ e ro ',lro11eÄ enbrun c 'cn19 enbtun r .l.tlll:) o1 "e'r 'qsruee:8 :or-r qsrppo.r lJqlreu e.rc lDql s-lolo.) o1 spuodse::oJ'0 : n '6] "e t 'utnuqrpnbt ur:l-rii- -per, e 'ecuelsul ro-l 'sepoJ (1ccr3o1ors,{qdo.rnctr) .rtlllutolqJ (),\\l Jtll .1o slttttlt.l otirz .r.rtllltlsl.l ..tll ,{q peurur:e1ep ole sroloJ enbrun 1nq1 srscqlocl{q 8trr1ur1 .rrlt .]o suueut [.q s.to1o,t atthrtrtt .1o tdrr -uoc 1crrs,{qdoqrÄsd eq} ot pcltle.r sr 'uotlt 'srtll ',{1e,tr1ccdser'sepoc roloc }uauoddo,IJtrlg-.ytl.\\. pln: .,no11eÄ-en1q,',lrccr8-per, etll tltr,lt prlllrrosslr .rq \\O pur i qO.; '0 Äq e:eq pepuop'slf,uucLlr-l(, sed,{1 ee.rql ru,ro.J ol Äe,m ct3toecls JLtlos tll le,\al ptro -cäs u le pcurquoc e.re s;o1d:r:lc.t ,{:uutt.td.yu sld.,(1 eerql eql ruorS Sutireule snlnurrls stroeueiotttotl u ro1 sleu8rs roloo eql lEql seluls ,{lltorstrq ,t.urrt1t -ro1oc-lueuoddo,{.rocqt 1urr3o1ors,{qdo-rlrrtl tr s5' salnqlrDV roloJ-luruoddo Supuasa.rdag sapoJ roloJ l't't'Zl 'lq8rljo lods c18urs r: go ,{1uo Stttlststtttl sttotl -ern8rluoc ol src;cr ]eqt pelelnluro.l :rq o1 {.roet1t roloc-lueuoddo .+o uorsrê u s,{\ollu puu slqitl .1t, les eq].+o clnlsnrls ä^rlrppu JLII L[]]^\ se]nqlJ]]tl ]Llitr -oddo.;o slueruSpni sJurquroJ enbtuq:lo1 slqt sntll 'elnqul]e sseuuccrS-sseuper oq1 t'r1 lccdse.t t11r,t urnuqrpnbc ol roloc eql 3ur.rq ot peppc eq ot stttl 1eq1 ueo,r8 prepuuls rt Jo tunoure eql ,{q .ro1ot rlsrp -poJ u ur sseuper Jo lutloruu eql Jo uolll?UILLLtJIJP eql s,\\olle uorlellecuuJ loloJ Jr) rrtbrtrtl.rrl :rt11 '(LZ6l) reu{cnrg Äq pcsn pue 8ur.rep1 Äq polrc.rut se,\\ leql'uorlellccuEO -to1ot'rrtbruq.1.1l lulttrtu -rratlxe ur: pc,{o1due ,{11ecr1crrrc1s,{s otl,$ '(ZL6l 'qf,r^rnH pue uosaruul ees) q3r^.n1H puc uosotutll ,{q Ä1}ucca: erotu pue 'srcr-lto pue r0ll!ll,\l :l D Äq pedolo,tep -requn-+ pue dn ue)tt ere.,\\ sllrpr srH -roloc Jo ernlonlls luueuoueqd Jql .:lo .latJlr -reqc lueuoddo ue qcns uo poseq sc,lr ]lltll ;-utpor loloJ Jo ]unocoe lucr]eroeql e slulutt.totlxe srroltr -e8ur -yt'r qllec,\\ B qy,m ;eqle8ol pcdolerep 3ur.rr;1 'sseulrelq/sseulrrl.,\\ pue'sseuenlq/ssou,\\ollr^ 'sscuee:STsseuper :slted lueuoddo ro -n:1odrq cql 3le sälnqu]le Joloc roJ rue1s,{s oleurp.rooJ peqsrni -urlsrp e olulllsuoo leql selnqu]lt lenldccrcd ea.rqt rql'rlqrte -qrrlxe tBr[] .....4,,.-^ -rLill 1)rrrJY ullll.lJJ ]eLl ,(11r,lrr;i-o1or -rtr:1-or1cd, sl .PoJ .lol .1o srlch:rur r(-rorq1 -rog po.lolor prr ilclutou r (966 I ple. srLl r.lrlrl.\\ .+o lulloJJr srlclr rur.rcl -prsuoJ or illurriolor puu.rnlq. 'rqtJoo '- -do.r .ruaurl -.lo.lsuu.l] J lullr.ru.\ru1-l 1u:rurirdol .ll'Jr.rerrru: -sU sl Iullsl-t 0rll . 1r:oriolorsr o1 tncl '(u0 .1o ,i1rpr1e.r rqt o1 ,,r1 ',r.r()oql uu -Lill .rlt.lo -por leine -Jn.us UUe soop stqir ].lrqs e)J11, -c.r.ror i1r r.rr JUll e -0.l.lol lou Jr-ll 'ssJru .ro1or.1o i s.roloJ r LZZqreorddy rrlsuutuoiuelg eqt pue 8urpo;.ro1o3 ,(peg y 71 228 12. Color Perception: From Grassman Codes to a Dual Codc fbr Obiect ancl I l lunt ination C'olors implies the condit ion of scalar invariance (of unique colors), i .c., the closurc of thc class of unique colors under change of intensity. Furtherrnore, the additive complerrcnt of-, say, unique green must be unique recl. i .e., each unique grcen can be made achromatic by an addit ion of uniquc red. A corrcsponding rigorous measurement theorctic analysis of the rclation of prirnary and opponent codes was given by Krantz (see Suppes et al. , 1989, chap. l5). This result could also have been stated in such a way that under the above condit ions a system ofopponent codes can be achieved from a tlxed Grassmann code by linear transformations. The operation of color cancel lat ion then yields a l inear representation in the vector spacc derived from the three-dimensional Grassmann structure of metameric color matching, i .e. Q, g ( l ) I ' r . : - , c r . , ' Q i ( l ) Q' r,( l) - (P,(A) Q" ,n , (1 ) I , : , . r . , c . . , . tp , ( l ) which, under the above assumptions, ncatly cor.rnects primary and opponent-color coding ( in thc expcrimental si tuation of a single small l ight spot in an otherwise dark visual f ield). A re-coding of primary color codes into opponent-color channels can be understood as a decorrelation of reccptor signals that proves to have intercsting fbrmal properties fiom the perspcctive of efficient and reliable infbrmation transmission in the visual system (Buchsbaum and Gottschalk. r e83) . However, the simplicity and beauty of thc exactly defined version of opponent-color theory characterized above is in conflict with empirioal evidencc. For instance, observations have been reported that a rrixture of unique green and uniqlre red appears yel lowish a rnixture of uniquc yel low ancl unique blue appears rcddish desaturating a spectral uniclue blr.re makes i t appcar redclish a unique white is not intensity irrvariant. Because of this and other cmpir ical results, the conccpts o f 'opponent co lo r ' , ' compler rcn tary color ' . ancl (successive or simultaneous) 'contrast color ' do not coincidc. nor do the cotrcepts ol ' ' un ique co lo r ' and ' in tens i ty invar ian t co lo r ' . Up to now, attempts to formulate a clear-cut uncl empir ical ly adequatc theory of opponenr-color coding have met with l i t t le success. Thcre is no coherent and empir ical ly satisfying thcory to account for our introspcctive obsenations that give r ise to thc intuit ion about an opponencv of color coding. The f ield of correspontl irrg rescarclr is rather strewn with highly expcriment-speci l ' ic models of opponent coding that are harcl ly cornpatible with each other. There are several othcr attentpts at ntoclelling second or higher-order chror-natic rnechanisms based not on color cancel lat ion but i trsteacl on other kinds of psychological relat ions. uhich suqgest the existence ofa grcat variety ofhi-qhcr-ordcr color mechanisms. For instance. Krauskopl. Wi l l iams ane l Hee lcy (1982) i rnes t r : l l e . l e l r lnucs in chromatic thresholcls in chromatical l l ' moclulated f ields and fbund 'cardinal direct ions' in color space corresponding to a lurninancc channel. a red-grcen channel and an S-cone axis. thc last being clearly dist inct f iorr the axis definin-q thc ser of colors that wcre in equi l ibr iunt fbr the r.cd-grccn channel. 12 .4 .4 Re la t ingPsychophys ica tand Neurophysiological Color Codes The color codes considered so lar are based on only two psychological relat ions. nantely ntetameric matches and color cancel lat ion (though thc r.notivation that leads to singling out tlrc-se psychological relat ions refers to a much r icher sct of observations). Now the qucstion arises rvhcthcr the purely psychophysical color codes obtaincd fiorr color rnatchcs and color canccl lat iou lcchnlques can bc interpreted in terms of ncural coi lcs. i .c.. neural mechanisrns. Current neurophysiological thcories ol ' color vision assume two major stages o1' thc prinrarv encocl ing of color: the f lrst stage refcr-s 1o thc uctir ' i ty of three types of univariant rcceptors. thc scconcl sttrge to the subsequent irrtcgration and r.corganization of this act ivi ty by cel ls lvi th spcctr.alh and spatial ly-opponerlt response characterist ics. Th corre psycl cocic r t a n I. * t of c r rclat i i ca l i a l co , preta l l l v l ! rng p th is g Th appei relatc nratcl Fig. I l :i (,t)d+ (v)d - (rev)d (v)dt - (v+r)o1 (s)d - (v)d Yn(7)'ArYt'h f = 'J tlt ttl !u 'u ld sopor .rtllor lsr:11 :3'31 'lirj yp(y) rA('f)\t J lll !u 'u lu € 8=V I a PO,) U U t) LLI S t^ t1 J 1-\ tusua(tEtaul V B sacl,{1 -rrldarer luerie,\run :alp.1o lndyrll 1 n : t t E r.t 1 o t s :it1 d r.t.t n a 1t1 suuä] ur äpoJ leJneu 3ur;xroclserlo:t uoJ s.rltlnul Jueur?leLu lo-] epoJ 1r::ls,tqdoqrÄs^d :r11] s:rtu1:r.r lPLllJuo st /lloqul.aH l.lurs i.luJrts.r()l()ir illll.rrlLll) lselccr8 rql peq seLl leql uorlsodorcl 8Lrr1ur1 :rq1 'Ältrcrldxe 1no pe 11eds 1ou ,{11errsn c.rr,l dui srql a8pr:q o1 pelôur eq o] êuq tcqt .:^uorllsodo.rcl iur -Iurl, orlt',(13urp.roccy erurl.rrd rlf,.rres..r rolsl,\ ul poleuuoc ,(1dr"urs eje ,opo3. rulcl :rq1 .}t'r suorlul:r-rd -relur luereJlrp eseql'Ä11ens61 .roqto .q1 uo s:)por Iu -lncu.lo sulrol ur sopoc osaql.]o suorlr'l1o.rd.rr1ur 1r'nr -3o1ors,{qdorncrr crll puu 'puerl ouo crll uo sr-rollul..l lecrSoloqcÄsd o1 ,{pro reJer }üql sapor .lolol .lo suorlou 1errs,{qdoqc.{sd e.,lr lulr tuun [-r uec.t 1oq chrii1ecr3o1 e 'Jêe,r\orl 'sr .rle qJ'ôoqu p.ssnrsrp sJpo:) .roloJ.]o sedÄ1 o,u1 Jrll (]1 (suol1u1:r-r 1r,)rri;-o1oqr,{stl ot lcedser qll,\\ ' e r) Ä11urrsÄr1doqr,{scl puoclsulor ol uclel c:e Surpocua lernau Jo sciuls o,lr1 osrr11 ,'-_\ (; ^JUrUOIlf,rJl pUC S\\UI s,UUCurSsBll) lD)ti'Itldoq),isd u8rpured oZ o{l ul sapoJ roloJ Jrssg f1,r.rlsucs lurlceds eqt eru (y)!A pue 'V tq8ll eql .lo suortcunJ ,{8:eue 1e.rlceds eql sr (y)vA e.req,tt t c l-J vp (v)'^ (v)frl [ -vp (v)A (v)]f f e g = v ' "J :sr sepoo .roldcccr ,{leurrd pr-r€ sapoJ uuurusserD 3ur1eler roJ pelôur uortrsodo;d 3ur1ur1 eq1 'scpoc ,{reuud yerneu;o uorleurqtuoc un?J -rec e uro{ llnse; }eq} sepoJ lerneu r.rp.ro req8Lq se pele"rd:e1ur uäql ere sepoJ roloo-lLreuoddo leors,(qd -oqcÄs6 'sroldece; go sed,{1 ccrq} .}o 1nd1no sqi ozrJelc€Jerlc esues eu-ros ul lerp sepoc ro[o3 urBuec 1no a18urs uuc euo ursrJeureleru roJ sepoJ Srroult: ieql eepr eq] uo peseq sur.rel lrcrSolorsÄqdorneu ur uorlele;cl.lelur ue utslJoueleru 3o ldeouoo 1ects,{qd -oqc,{sd Ä1ernd eqt se,u8 pue sro}docer ,{reurrrd;o 6ZZqoeorddy lrlslretrre rlre lE aql pue 8utpo3 ro1o3 ,{1leg y'71 230 12. Color Perception: Frorr Grassrnan Codesto a Dual Cocle fbr Ob.jcct and I l lurr ination Color.s congenital dichromats. and not clue to cl iseasc) provide insight into the relat ion bctu,cc-n thc tuirand three-dimcnsional Cjrassmann spaccs ir l .olr ec. l and their neurophysiological basis. Thc cxpcrr_ mental study of uni lateral dichrorrrat isnt thercl irre has bcen considered of part icular interest lbr oLrr. attempts to understand the early codins ofcolor. (von H ippc l , 1880; MacLeoc l and Lenn ie , 19761 Alpern e t a l . . 1983) . What experimental results can bc expectccl. r f therc are, for instance, no shortwar,,e rcccptors (tr i_ tanopia) and i f thus thc inptrt g, is lacking,.) Thc Young-Hclmholtz theory and starrclard opponcnt_ color theory assLu.ne that only son.rc of thc hi-gher order codes dcpend on g, and thus that thc blue_ yellow channel gr, g is missing. Accordins to the standard interpretat ion of thc youn-q-Hc-lnrholtz theory (which l inks thc Grassntann theorv r i . i th color appearanccs) one ntiuht cttn-jectur.c thut a uni lateral tr i tanopic subject shoulcl, u. i th his tr i_ tanopic eye, sec thc spectrum as .recl ' . .gre,ctr.anr1 'yel low' and combinations thereofl ncithcr .bluc. nor 'wh i te 'shou ld be seen. and thcre shou ld bc . , green that looks more saturated than any ercen attainable by the normal eyc. Accordins to thc, stanclard version ofopponcnt-color theorv thc loss o f the 'ye l lo rv -b luc 'channe l shoLr lc l r .esu l t in scc_ ing 'white' . ' recl ' and 'grcen' as for thc normal eye, while the mixture of red and greerr *.oulcl bc achromatic. Both predict ions arc irr conl l ict r i i t l r the experimental results: a uni lateral tr . i lanope secs thc entire spcctrum on the slrortwav.c siclc of thc neutral point between ,1210 nnt ancl -550 nnr as bluc, i .e., he matches i t to ,18_5 490 nm in his nor. mal eye. The colors he sees in thc spcctrurm arc recl white and blue with only a sntal l antount olycl low and no green at al l . Thus i t secms that cen_ tral elements in thc I inkin-e proposit ions of thc Young-Helrnholtz thcory and opponerrt-color the_ ory are utterly wrong: "thosc central mcchanisms ivhicl i . in thc nrtrrnal observer, correspond to blucness (ancl r i .c assulrrc, have heavy dependence on the outtr-rut of the short-wave cones) are most act ivc incleed in the tr i tanopc." (Alpcrn et al. . 1983. p. 6c)l) This and other results support thc conjecturc that the psychophysical ly obsenecl threc-cl intcnsional_ ity of color matches in the 2o-paracl isnr cannot bc distr ibutions fbr cach of the thrce types of reccp_ tors. . In this way <p,(A) can be identi f led with J Ê().) Vi(),) d),. and psychophysical color space rs associated with a corresponding three_din.rcn_ sional sensor space. Figure 12.2 juxtaposes the basic elemcnts ofneural and psychophysical color codcs in the experirnental si tuation of a small l ight in an otherwise dark visual f ield. Whether this l inking proposit ion is empir ical ly adequate, is st i l l a matter of dispute, since there rs confl ict ing empir ical evidcnce f iom various sources. notably. variabi l i ty within cone types, violat ions of the persistency rule (ntctameric lights rcmain metarneric if both viewcd in a clif_ f'erent contcxt; see below) for wontcn with an addit ional cone typc and fbr sub.jccts with nor_ mal color visiorr. Psychophysicists as well as neurophysiologists theretbre cal led ir .r to question the val idity of a l ink_ rng propctsitictn as simple as the one stated above. To quote two examples: ".. . evidence for the variabi l i ty among cones is enough to raise serious doubts as to whcther tr ichromatic matches arc determined at the reccptor lcvel: the cones probably are dist in_ guishing rel iably bctwecn the n-ratched f ietds. . . . it seems to rre that we still cio not havc a satis_ factory physiological basis for tr ichrontacy; but we can say that under some conditions at least trichromacy rests on a neural (ancl not a recep_ tora l ) t r i var iance. " (MacLeoc l 1936, 109/ l l l ) "Evidcnce is accumulating to suggcst that thc idca. that individuals with normal color visictn have only thrce spectral ly dif ferent cone pho_ toreceptors. is also inval id. . . . tr ichromacy of normal vision has i ts origin at a level of the visual pathrvay beyoncl that of thc cone pig_ ments, l ikely beyoncl t l rc receptors., ' (Neitz et a l . , 1993. p . 122) Other intcresting empir ical f incl ings contc f iom expenments with people who cxhibit uni lateral dichromatism. Thcse rarc cases al low dichoptic color matches and comparisons betwcen the two eyes by color-naming techniques that uncler cer_ tain assurrpt ions (e.g., that their color sensations in the dichromatic eye are the same as those of attr trl. d a l1 Wh colr al s' co l t n h e 'str: acht t lon und cho u h e SVSt irnp anal ther, betr, worl resp cern Ar psyc colo resei tlie tr n o t ' its h * hic c ip l i o f c taker quis l to l l t psyc roph' tory' pseu( phen physl ' ep l s physi appar in ne csoql olur Eu3urorrsrlo Jo epnlrllnlrl eql e,\Jec ol ,{\oq lnoqe Älurulrerun Iecrleroeql eql sJorJrru suorl -rpuoJ snlnrurls pue sdnlos lelueun-redxe ]uoJe-+pp p ,(1e r.rc,t ]uepunqe slql '(suorlrpuoc 8ur.uar,r. pur Er,relr-rr lulueur8pnf lrrereJJrp su lle,tl se slcedse 1e: -odurel puu lerledsgo suorlJerelur xelduroc êlôur ueut) qJlqM ) suoltenlrs lctueurr.rrdxr e ql .lo slrurrp erll Jo stJr-lJr pools.rrPun ,(1.rood :qr xq pc -pedlur sr r,rorldecled roloc.Jo slcodse 1u:odrucl pue lerleds Surleirlsêur slucrur:cdxc Äueu Jql .Jo uorl -Bnlene're,re,no11'suor]€nlrs snlnurls leluerur:ed -xe or3rceds q1^\ polerJosst eq Jeuu€ru pozr -ll?opr ue ur ueJ,]serluoc, puu.uouJnpur, '.uorl -e1depe, sLruet JLll :suorlenys lelucurrcdxc crleur -8rpe:ed Surpuodse:roc puu Buauoueqd urel:er ol perl ,(1e1urur1ur eru se,trlceds:ed eseql :slcaJJe lerodruel pur lerlrds roJ luuocJe o] pedolêep ueäq ôeq se,ulceds;ed Ierrleroeqt lerôoS 'Surpoc roloo Äpee;o scuocql ur lxcluocJo sl3qjc Jql slepolurüocce o1,{r1 o1 Iernleu srecddr: eJoJeJer{l }l ']xa}uoJ Jo suor}urJl] \ q]l,lr eSucq: urc sêlesueql soJuerredde roloc eql 'slxeluoJ lerodrucl pue lerlcds 3o r8uer cpr,{\ e lJ^o prll?^ eru uorlelloJuec -roloJ Jo s,r\uI a,rrlcgrlenb pue s,trel uueusser{) eqt }eq} perunsse sr 1r q8noql (curlor eqt uo lrdnd eq1 q8no-rqt pelcefo:d sr 1q8r11o ueeq e pul? poxrJ sr peoq s,]coiqns eqt ereq,\\ '1'71 e.rn8rg ur u,ltorls'suorlrpuoc Sur,trer,t uerlle.\\xel\ pellec-os repun perpnts ,(11e1ueur:edxe Ä11ucrdfi) plarJ I€nsr^ Irep äsr,r\reqlo ue ur 1q8r1 snoeueSouroq Äyyerodruel pue ,{11eqeds lleus e sr snlnulls eql oreq,{\ suol} -€nys leluerfiuadxs o1 po,uoJol ,{1uo c,teq I Jp.J oS lxeluoJ Isrodtuel puu luquds u! suolf uUBA roJ SulJunoJJV sepoJ roloJ ,{ruluetuelfl s'n'zl 'rrorJcnper ueql JOrllcJ rrorleJUrun Ärolcueldxs ol anp se,n sÄu,n1e lsoutle qJrq,,lr serJoeql cr -.+lluercs ;o lueurdole,rep oql Jo Junocce pollrlsuoo -srLu e uo slse; 1 'esro,tr ur rE 'slrodse lue\olJr or.ll rq lq8rur ]e{Ä\ }noQe uorlelncods ploq e ueqt orou ou ol slunoruu rüsruorlcnpcJorncu 'ure,rq Jql Jo scrs,{qd oLItJo pootsräpun ,{ltueserd sr el}lrl }eq,{\Jo 1qir1 cqt u1 'sedoq urolroJ uo peseq eq ot ruees uorl -dr:csap Jo slôal o,r\l cql ueo,&leq de8 1ecr3o1 e qt o8prrg o1 slureJlsuoJ lucrJrllns apr,rord s][nso] lt?Jr -rrdrue leql surrelc 's8urpurl 1ucr3o1ors,{r1clo:ncu ur puu suorlêresqo lecrsÄqdoqc,{sd ur qtoq }uo.rucldu ,rtou Älxelduroo eql uo,u8 'lô0,{\oLl ,{iolors{qcl -olneu o] oqrJ3se .{eqt .Ä1u8rp 1u:rrSolotrolsrd:r. req8rq arp o1 ,{uourrlsel sr siurpur-1 1r:criolors,,rqd -ollläu polulosr Ä11unbe Jo snuel ur uuaurouctltl lecrsÄqdoqc,{sd peltlosr lo-1 suorlr:ucldxe-opncsd coq pe uodn 11cc Ä1r1seq pr-re ses^od.nld,^.rol -cue1dxc, -rreql slns ll ueq,r sur.rel 1r:rriolursiqclo.r -ncu.Jo s JAIasuteql 1 rc,tll,(1 sno r-ro1ou s1s rio 1 oqr,tscr lunldecred leqt ^cuepuel eq1 'Ä3o1ors,{qdo.rncu o1 Jsoretul lucrSoloqcÄsd aurnuei Jo plol.l u prqsrnl.r -ulleJ seq lue1xe e3.re1 uo1 pull olor ollp slr r.ro r.rolul 1c,{ 1ou seq Ä8o1oqcÄsd 'e.reg eouerrs .roloJ .Io suere a3:u1 qlr.{\ aseo cq} .{prreuJO sr srrll s:rurlclrr -srp Jeqlo olur fu,nu urds sp1cr.;-qrls un?l.lcr rlrlrl.\\ Äq ,{cuepuel 1e8n3r:1uer r jo :e8uup oqt ,{.rotsrq slr ur seceJ Ä3o1oqr,{sd eJurs 'sLuelqord 1noq1,t 1ou sr uorlenls srql uorldeued .ro1oc-1o iiolor-1r,rsd .rqt loC plerJ orll ur seoroJ 8ur,rr'rp äqt ueäq rlr.ru.s..r Joloc Jo s8uruur8eq eql aJurs c.trt1 Surpor -ro1or 3o Ä8o1clrs,{qdorneu oql pue sepor 1r:rrsÄqdoqr,{sd u:.1\\ltq uorlelJJ e(ll putlslJprrrr ol sltltrr:llV 'l).rtt.t.rl -slp eq uec srs,{1eue .+o sll^Jl o,\\l rsJrll ol trlclsl.r r-l lr,^\ r.rot lpluer.to ptte s r snqdr u,r u I s.1.1u.11i\ | | l p').1() \\ pcrSoyorsÄqdorneu putr lecrsÄqdoq:rÄsd u:rr,t1lc, Ä.rupunoq d.rcqs e eq ]ouuuJ prrl? lor-l sl J.lJrll q8noq1 '(suorncu.lo lôol crlt urqt ;er1to srs,iluur: Jo lrun u o1 urel:ad ,(eur qcrq,n) uorlr:lueurolclurr 1ecr3o1ors.(qdorneu uo elulnoeds o,\\ ucJ tuolsis eql jo .cr3o1, crstq aqt Jo repr uu êurl e,\\ urll,\\ ,{1uo e curs 'IS€l leorsÄqdor-1r,{sd .ro lucrioloq:r -Äsd e lsoure.ro-+ pue ls.rr-] sr sorietu:ts iur,tl.rcpun 3ql lec^cl oJ srusrueqoeu ltrnou lnocssr suorl -uynoeds uo Surryequrc lr-rorllr,r 's)sut s1r iur,l.rrqlr rog s,{oldure ure1s,{s lensrÄ ell 1eq1 ,serielr:.r1s. ]Jllrlsqe qlr,{\ pue scrsÄqd puu ,{;-o1ou:tuou:r11cl ;o ,{e1drc1n eqt qy.{\ sleep scrsÄqd-oqr,{sd '.ro1or go Surpoc le]ncu eqtJo e[l]nurur tql pun i11.r1s (s 1u -nsr^ eqlJo e-rnlJelrrlcre IeJllJu Jrll rl]l,\\ slui)p -lolo:) uo e,trlcedsred lecrSoyors,{qdo:nlu u suJ.rllA\ (EOS 'd '8861 ''lu 1o urrdly) .. slr-rrur -8rdo1oqd .+o lêel eql lt .{leraur torrslusrur} -tlJeu lPrluäJ.lo lJ^Jl Jql ln ru()l):,1.r1-;o s:.r.r;-.-P ee.rql .{yuo ol uorlt}rurl p cq lsnrLl J-lJrlf.. : :^rolde Je-roloqd .1o sccl,{1 eeJql-+o ecuä]srxe eqi ol ^û\ eldurrs e ur pJlncll.ltlrl Jq l, -luu tuql u! p .1t) lr .1.\\ Iurlr. -eqt illt .]o 1r l-lll -.lotl su erlt . saäs Lllt.rt rql luur. -ees ssol JLll Uaa.l uaq ,enl PUÜ -l.u Ele r[]r \, zllor :)rl1 -enl -l C I-lr: -lu0 eql _r.11 ) .+l T :91( .lolo .ill11 e.ro-+ -l.tJ( pr.\l -o,\\ (: ttaqruorddy rrlsuelrramalE eql pue 8urpo3 ro1o3 ,{peg y 71 / - ) I 12. Color Perception: FromGrassntan Codes to a Dual Coclefbr Objcct and I l lulnination C.olors which are considered as .basic' and those which arc considcrecl as sidc-eflects. The Young-Maxwel l-Helmholtz_Grassrnann thc_ ory describes the transduction of l ight into a psy_ chophysical or neural code ancl togethcr with the l inking proposit ion proposcs a reccptoral mecha_ nisrn that accounts fbr the Grassmann laws. Since metarnerisnt is the only psychological relat ion rnvolvecl the thcory cloes not refer to color appear_ ances. However, color appcarances are oftcn tacrt_ ly associated with the equivalence classes of metameric l ights. In this case the theory becomes a local l t-utot l i ,r .1ic, account of color appearances. It then has to deal with the problent that at one location of a visual scene the sarre tr iple of Grassmann codes/rcccptor outputs can give r ise to clvite di//erent color appearanccs if the temporal or spatial contcxt is variecl. The cxistencrof a sur_ round changes thc color appcarances in character_ ist ic ways and produccs new appearances, e.g., bror.vn, that cannot be observed in a dark .r,.rouid (see chapter l0). From a locally-atomistic perspective these are secondary eflbcts, to be treatecl under the headine of'context 'efTects. On the othcr han4 they could i lso show that the basic mechlnisrns detcrr l ining color appcarances rn natural scenes can only be tappecl by'minirnal st imuli ' that are r icher than the 2I iehts rppropriatc lbr isolat irrg rcccptorr l trrrrs. luct iori For the elementarist ic perspective on color per_ ccption (as opposcd to a t irnct ional onc guiclet l by ecological physics) the cf l-ects of certain temooral r r r t l spu t ia l var ia t ions ( )n lhe loca l .o lu r rpp" , , r_ ance were considered an important chal lenge. To l surpr is rng cx len t . lhc yor rng_Hc lmho l tz t rad i_ t ion, however., was successful in developing an extension ofthc theory that could at least in nrin_ ciple incorporate an important class of thcs" cffccts. The f irst systernatic investigations into mecha_ n i :ms respons ib le lo r lhesc var ia t ions wcrc Der_ l t r r r t red by l -ec l r i le r {1g40) . The cornp le r r , .n tun charactcr ofaftcrirnages lecl Fechner to the iclea oi. a t ir ing ol physiological processes (basecl on an arralogy with a " loss of tcnsion, ' , , I /er lu.rt an Spunnkrc(i") by which,,al l phenomena conccrninu r f ie r i rn i rgcs r r rd rdapt r t ion can be r .e t l r rce . l tu . "n l si t ivi ty processcs in the eye, ' Fechner, 1g40. p. 430)' . This intuit ion lcacl I lelntholtz to his concept of "fat igue of rcceptors.. ("Ernrt iduttgst lr t ,o_ ric "), which was given a ntore prccise lirrnr bv von Kries' "cocff icient schernc" l " l t r t t . . / / i: i t , r r t . , t r r . 11 _. 1. Because the young-tJeln.rholtz thcorv took us bas ic un i ts o f ana lys is s i r ru le l t {h t spo ts in r r . l l r k surround, i t had to postulate aclcl i t ional rncch"_ nisms to accoLlnt fbr thc et lects of spatial antl tcnr_ poral context. For opponcnt_color.theorv on lhc other hand i t was mrtre rraturl l to inctrr.nor. lr tc sPat ial and temporal ef lects, sincc i ts uncle r lyins intr,_ it ions were hisbrical ly rootccl in phenonrerra thar dcpend on variat ions of ' tcntporal and spatial con_ texts (Hering attr ibuted a ntuch ntore basic rolc 1., contrast and adaptation than I lelntholtz cl icl) . Ttr theoretical ly deal with thc situation of a sinqlc iso_ lated l ight in a dark surround only becanrc:possi_ ble aftcr the invention of ' the color cancel lat ion techn ique wh ich accord ing to I3 rückner (19271 uas a l rcady used by Her ing . In the fol lowing sections, I shal l br iel. ly outl inc how the Young-Helrnholtz theory ancl a rur. iant ol. opponent-color thcory deal with ten.rporal antl spa_ tial contexts in tcrms of appropriatc cotlcs (or code transfbrmations ). 12.4.5.1 The yon Kries CoefTicient Scheme Helmholtz took up Feclrner,s intuit ions lnd crlnjectured that "the fat iguing of the or-uan ol-r, ision modif ies the sensation of thc . just_scnse,cl l ight approxinately in a way as i f thc objcct i , , ,c interxity ofthe l ight is reducecl to a certain f iact ion of i ts m a g n i t u d e . " ( H e h r h o l t z , l 9 l l , V o i . 2 . p 2 0 0 ) , . This perspective al lotvs any ef-fects of adaptation to bc translated back to physics ancl to dcscribc thern as y' 'only thc ef lect ive physical st inrulus had changed. I I t ) t t p sl ( e l a l l l s t pr c ( E, I S 111 ca IZ ( is Kr o f pr( ' "durch die man cl ic ganze lJrschcinun-r dcr. Nachbilder auf ein Spiel l ,on Enrpfincl l ichkcir dcs Alrgcs reduciren kann" ' ". . . dic lrn-nüdung clcr Sehncn,cnsrrbstanz t l ie Enrpfindung ncu einfal lenclcn Lichtes unsc-l i ihr in denr Vcrhälhis bceinträchtigt, als rvr ire cl ic otrlckt ive Intensität dieses Lichtes unt c. incr.r trcst i inrrtcn Bruchteil ihrer Grölle verntincler.l..' Ä1rpr1e,r äqt teql lrp.+ eqlJo erc^\e scÄ\ Äpec.r1e ser,r; :5 lq8rl eutos .{q peldupu-c.rd uo1 'Cl xr.rleur leuo8ulp e ' e l 'srcquinu eerql .{q eÄe eql ro.,r uotltsodo:d 3ur1ur1 3ur,uo11o3 oql .1o poquosop Ä1e1e1druoo sruorleLuroJsuurl srq] seuoc Äyprlen eq] ol slunotue eueqos luarol.J.JeoJ set.t) cql .Jo suorlJtrn3 ,{1,r.r1sues 1u:1cec{s eq} ol lrcdser uô ttll u:qt 'a,{: prldepe-1:ep eqt ro-} prlL:t^ sr rtll,4A h,l xulntrl f ^ [ u ,{q "i |srnln^ snlnrull\ -r-r1 iurpuoclsc.uor eql Jo uorllrluro-]su€r1 :eeur1 e .{q vp (t)rn (v)'a j : Yp (Y )rA (Y )\ 3 I <J B = v pequcsop cq 'Äroeq] srq] ot Surproroe 'uuc reqlouu ,{1eueu ',{roeql zt1oqru1.:g-8unô cql :^ezl o1 uorleldepe Jo olels euo urol.I uorusullrl eqJ -lclcurutlJ 1eq1 uorlrsodo.rd 8ur1ut1 ctlt .JI ',\\oN uf,lr-urullslq r J\lt\Jlqo rrp : rrr lqrlr;-irn s Jlp zulllsclnsr srp }li)rlillpt .r:rp irrnrrraq: pcq slllllrurls rqr.lrsep 01 p ruo r1r:1clupu.1o ',(002 d'i sI.l() r-rorlJul-I -rsualrrr a,\rlJi tqitl pesuosrrnrsr,r 1o uui -Uol puu sllc ipoJ .lo) s.lpo -r,lds 1-rue lror l() lutlr.lu.\ e I :Iil1lno igor.r (/a6t) jrul: uo|llrll0Jrrcl -rssod auuro -osr :r1;-urs c.1 ([ (PlP z]lo ol .lo.r JlsPq -uor lnrluds 1 IPrll llueruorr; -nlur iur,t1.ro1 -ucls rlt:-urcht: lll rro ,{.roor -ttlJl pull l1]rl' -l]tlJil.tr luuo I.nrp u rrr sto sr: 1o01 Ä.r0; ' ( ,, :l t)su)lu)r ruo,r i(q nuo.y -(Drlt\^Eu ttPl.u -rrof, srrl 0l z (,.ziess1e1r 1euorgodo16,, ) e1n: Älr1euorlrodo.rd <J'B * 1> = <S'V i. l> € <l'B> = <s'v> pue <J'cl @ 8> = <S'J @ V> e <J'C> = <S'J> pue <J'8> = <S'V> :(se,(e qtoq urc,rleq seqJl€ru 'Ä1tuc.tc.gtp peldupe seÄo Llloq ' 3'e) uorleldcpE )t.tptLtLLtltr^n Jo osllo eql lo.I oslr änr] oq lsnru stql a,{e eq} go uorluldepeJo ä]llls luelsuoJ Äuu:o-1 prlê uteurcr lsnut s^\€l,{1ueeur1 uuelusserl) eq]'o;olurequnjl S lqirl SurlduPe-a:d ,{ue .roj <s'B> = <s'v> € g: v : (c 1nr,{cuelsts Jed',, zl D s' z ua I î lsr ad,, ) uolleldepc lJpun pêreserd eq lsnttt s1q8t1 jo sosselo Jlrcul -elel\ :,rollo.] secuenbesuoo p:crs,(qdoqcÄsd 1ue1 -Jodrur-+o.rcqutnu e uorlrsodord 3urryrr1 slql [uoJC '(Älsnoeuelynrurs sed,{} ro}dcrel ocrql lle roJ uorlpuor .{rleuutÄs srt{t slll-}ln-+ l€gt lq8rl elqezrlul ,{11ecrs,{qd e ,{luesseceu lou sI eleq} q8noqt) .rolcp.I clur?s eql ,{q ro}docer srrll loJ ttl8rl 1o ,(1rsue1ur c^rlcoJJe eq] Suronper, pur? .rolreJ t ,{q Älr,rrysuos -ro}dece; Surcnpc-r, suotleredo eql jo Ä;1eruu-rÄs eql :^^\oqs Ä11oo.rrp uotlenbe l!3u eq1 '(V)rö ((S)ö)'d <1y1t6 , uorJuturoJsuerl e ,{q pcrnl -dec ,{1e1e1duroJ cq uuc V plerJ}sot e jo cruereeddu ioloc eql uo s lxcluof, Jo lcäJJe 0q1 leq] su€eul srq] sepoo roldeoe: ,{;erut.rdSo slulel ul (sleuueqo Surureurc: o,rl eq] 3o luepuodcpul eq ol polunssc sr y1r (5)rö1o:o) (g)dr.]o uortcunl e st!d) ereq.u L ( I -l YP (Y)A (S)rd {Y)'rf I YP (Y),\. (S)'d (1)v:l I o S'e = S'V '<0'g> = <0'v> rl}l.\\ per.Jrluepr eq ucJ g = v ''e l 'eprcuroJ rusrueqdosr put tLISI.reLUuleLtl j:o sldecuoc oql (uorlnqplstp Ä8:eue o.rez eqt sr 0 eroq,r\'0: J'S) punorrns lrpp llJo estJ orlt rojl '<l'g> = <s'v> :auaqclost pcllPO eq llr,\\ ,.rolor crLrüs orll, Iool B pue V splcr.Iisol eqt lurll ,{1.redo.rcl eql êeq qclq^\ <l'g> puu <s'v> Ilnutls qrns o,\r1'S ]xeluoc letleds ro 1u:odue1 ,(ue:o1 uorltrlou srqt esn 11eqs 1'Ä11e.teue8 a.ro4 '<S'B> puc <S'Vr> se uälu,{r rq III.\\ 'S }q8ll e Äq Sutldtpe-r.td .tc1-1t: pclueserd ere ]eq] B pue V rlnuus o,tr1 :peÄo1drLr.r rlllrurls är[] Jo uortl?zucl3€r€rlr eql :cr-l ([66 l) ä?roperN pue pls.Jsnet\ Jo uorllrtou eql csn llutls 1 'ued-rclunoc 1ecrs,{qdoqcÄsd s1 elc1nuuo.1 t1 's 1.r r ltl -rclunoJ 1nttsitldctqc,tsrl s1 sscrppe suorluirl:^e,r -ur lecrrrdrue Surpuodseloc crll .Jo ,,(uttu '(..î.tol -dace: jcr en8qe.1,, ) srscqlod,{q 1 n t t'3o 1 u r "^,i 4 r I ot t t ;t u e eq ol popuelur ,{11eur3r.ro su,tr 1 q8noql 'uorlelcleptp ssecord cql equcsep ,t1 -e1e1duoo o] eorJlns snql fd 'zd 'rd s:eqrunu rltl.L ( t'o) >rd (y)r,t rd - (y)ll 'e't 'ut:oj rer-[l Jou 1nq rpnyldLLrr': .rreql o3ueqc se,t:nc Ä1r,lrlrsues lerlocds 3rll ' c r 'JolJp.] luelsuoc r: Äq run;1oods JL[] lclo pecnpo.l oq ol peunb^sr sr rold:loor 3o adÄ1 rlJue Jo ,{}r'rrlrs -ues eqJ 's;oldec.lr 1o sod,(1 oe.Iqt eqt -Jo Surrtirlul lertuere.'Jrp e s€ oreq pep;tie; sr uorlt,l1dcpy 'roqrrlnu 1ue.r e ,{q epoo roldcrcl q3ec.Jo uorlecrldrllnru su prgursep ec1 (,{1a1ttu -rxo:dde) 'ed,(1 ;oldece; LlJr?c ro.J 'uec uotlulduptl .Jo tceJJe eql ]eql peunsse rutcqrs 1u,tt,tt.ffao.'t s;;r.rv r.1ô polleJ-os srql's:oldeca: Ä.reruud .1o s:rd,{1 oelql uo 8ut1cu 1o:1uol Ält,r.t1tsucr^ lt?Jtlrl .lo sr\ -cqtod,{q eqt uo peseg '(ZSS t) sru) uô ,{q pesod -o:d 1s.rrj se,tr uorleldepe lerodutel Jo slce.].1ä eql .ro.] lullocce o] uorlrnlul slql.Jo Iopotu lrcllclxe uy lual ttzqcuordcly rrtsueluatuoll rt[] pue 8urpo.; -to1o3 ,{1:tq y 71s.rol0.) rror a ) + 12. Color Pcrception: Frorn Grassntan Codes to a Dr-ral Clodefbr Ob.ject arrd I l l t rminrt ion Color.s of thesc lar.vs providcs another pclssibility fbr cst imating the cone spcctral sensit ivi t ies by transfbrming the 3x3 matrix M by B rMB into a cl iag_ onal rnatrix D of reals (dass ,,ttie Erntüdtnc,_ ver.suche die Möglichl,eit _tt tirrt,r ,lire,.ten Bestintmutg cler Clomponentcn bieten,,, von Kries. 1882, p . l0 t3 ) . The yon Kries t,oe.//it'ient st.hente is at the core of many approaches for deal ing r.vi th mechanisms of sensit ivi ty control, adaptation and color con_ stancy in psychophysics, neurophysiology (.mult i_ pl icat ive gain control ' ) and corrputat ional vision. In fact, ' the'psychophysical von Kries hypothcsis as well as the proport ional i ty rule spl i t up into a variety of diffbrent hypotheses dependent on the expcrrmental and theoretical paradigrn chosen. Von Kries' original ideas of inclucl ing adaptation_ al phenomena u,i thin thc yirung-Helmholtz theory primarily ref-er to aspects of temporal adaptation ('successive corrtrast ') . whereas thc irse of von Kries type transformations in contputat ional approaches to color perception primarily refers tcr effects of spatial contexts that rnirror chanses in thc prcvai l ing i l lumination ta typicrl .*rn,pl. i , tn rntcrprct the transfbrmation q,(A) (Ai(p(S)). qi(A) as a kind of normalization of the receptor codcs corresponding to a surface A under some i l lumi_ nation by the rcceptor codes of a white surfäcc under the same i l lunrination). Various psychophysical investigations into the von Kries hypothesis have been carr iccl out sincewith more or less negative results (cf. Wyszccki and Sti les, 1982. p. 129tT.). Many of the relevant experirnental studies have concentratecl on conse_ quences clf the von Kries hypothesis rather than orthc hypothesis i tsel l , notably the l inearity Iaws (Wyszeck i and St i les , 1982, p .43 l ) and among these thc proportionulitl, nrle. This rule has. under several cxpcrirnental paradignrs, been shown to i i i l (cf. Jameson and Hurvich, 1972). There is abundant evidence both in psychophysics and ncu_ rophysiology that therc arc many types and sites of adaptation in the visual system (cf. MacLeocl 1978; Walravcn and Valeton, 19g4; Walraven ct al. , l9c)0). For instancc, Ahn ancl Macleod ( 1993 ) found that chrornatic adaptation hacl diflbr_ ent effects on flicker photometry and irniquc yel_ low sett incs. Even in cases whcre a mult ipl icat i ," ,e von Kr. ics transformatiotr is suggested by the clata. thc coclli_ cients night not be eirsi ly identi f iablc u, i t l t a ccrtarn stage of neural processing. since a srnglc co_ eficient can comprise the cfti,cts .-f ,n,r,li tr.,rn.fbrmations at quite cl i f ferent stages. Ncrer:thclcss. the fai lure of ' the ' von Krics larvrproport ional i tv rule gave r isc to search fbr .addit ional ntecltanisnrs- (rn an attcmpt to preserve the basic spir i t ol-a l incar coeff icient law). notably'subtractive' ones. 12.4.5.2 The ..Two-process Interpretation', of Spatial and Temporal Eflects in Opponent-Color Theorv Thc etlects on color appearance of spatial antl temporal variat ions of 'context wcre at the origin oi. opponent-color thcory. Hcring fbcLrsecl on certairr spatial i r-rteractions of colors aucl corrcsponcl inu phenomcna tracl i t ional ly subsurnecl r-rnder the head ings ' l igh t induc t ion ' , . co lo r inc luc t ion . . 'simultaneous contrast ' etc. Thesc pltenor.r.rcrra o f le r I n r tu ra l s la r l i r rg po iu t lb r i r spu t i l r l l r t , r . i cn t ed relat ional point of vierv as aclr,anced bv Fechneq Mach, Hering. Katz. I3ühlcq Koflka. lnd Land to mention only a fer.v well-knou.rr niutles. According to this pcrspective, color is inhercntlv de tc r rn ined by fea turcs o f t l r c en t r rc r i sur r l :ecn t i . Both aspects, the preadaptal ional ancl the relat ion_ al one, are of ien couched in thc same languitse oladaptation, ancl i t is. in f trct. ottcrr dit f icult r ir t . , l t thern apart in experimental or thcorct ical *,ork. Within the frarnework of opponent-color. theorv an expl ici t mathematical rnoclcl to rccouut tbr. t l ic, eflects of adaptation and incluctiorr in terrtrs of opponent-color processing was proposecl b1,. Janreson and Hurvich (e.g.. l9i '2). This is thc socalled "tv,o-prot:es.r interpretuIiot1 ". n,hosc nrath_ cmatical core is a forr.nal schemc. rvhich. l ike the von Krics coefficicnt schcme. allotvs ibr tlifl'ercnt interpretations. Whereas the l inear versiorr of opporrott-colorthcory discussed in section 12.;1.3 ref-crs to a sin_ gle spot of light or.rly, thc ,,two-process intcrpr.ctat ion" also refers to thc efTect ofa (spatial) contcxt i r r wh ic l r a tes t l ighr i s secn unr l y ic lds l r r l l ) ' i r re version of opponent-color theory. When applicd to a system <p of l inear primary codes. thc ntodel can. fbr the scherul (). ( u herc ( spatia and 115 model othcr tr This ncl l t-cc basecl t as. uncl l lent co I lltents be'long ltcl t t c( aff inc f arc. thu There ruroclcl luL'l;gn; 9' *( l This ntr A S € c c l t o a , (r, .(J A cliscu MaLrst'el In the cal scht s t imu l i . ( l t)g-l ) . 1 rcceptor tiveancl cont ro l . ( be'car"rse in to e igh p l e ' i n t e r corl trast rr 'cl l as t leaci in a ing o f th acl i ieven tirnct ionr scc t lon I puu (pucl 'seu) uô ' 3'e) puno-r:ns pexr.J B ro.J plerJur eql ur suorlJUnJ rueurl ere q:o.; seldruexg plerJur eql -]o ecurrreddu aql ro.J apoo rolor e sr ((g)dr '(V)dt)q - (S'V)O ]r?ql qcns ecuds JolJê ieer Ieuorsuor-urp-xrs 0r{l uo uorlJun-+ pänlt^ ro}cô oluos purJ o} s}uE,\\ cuo 'Älosrcerd eJol 'epoo uuerusserD Sulpuods -clroo cql .+o q uorlJunJ clduns curos sr teq] pue '(J'B)o - (S'v)o <+ <l'g> = <s'v> 'e rplerJur eql Jo eJueleadde eql serntdec lurll C) apor roloc e puu ol epelu ueoq oleq ocuercs roloc ur sldr-uelle ,{ueur 'oro.,rcrcql 'sple l.+ur eueqdosr ur }lnser ,{eru aceds -ro}Jal leer leuorsuJunp-xls ur slolJel lueJeJJrp e3r-rrs 'enrl lou sr 'Jâa,roq 'esrêUoc eqJ .<J.B>:15.y1 ue{} '(r)ö - (s)ö pue (a)ö - (v)ö:r :aueqdosr aJe rlnurls o,rl cq] 'sJnlel -ö lecrluepr ôeq osle I pue S spunorrns o.\\1 eql jr pue ö epoc uueussl?rD r ot lcedse; qtr,{\ sänlê Ieiltuepr êr?q B pup v splerJur o.u] ev]-]l 'eslnoc JO '<I'g> pue <s'v> rlnurls qcns o,{\l rcprsuoJ ('splcrJur otnlosqe eqt elouep sÄe,ttye "' 'S 'V'Älqu8ueqc.relur .punorS -IJeq, pue lpunorrns, surat eql esn I 8ur,tro1yo.; cql ut) '<S'V> ^q G'z't -l '(S)rö '(y)!ö sepoc :o1oc Ä:erur:d eql Äq pczuolce:eqc qcee) g punorS -IJtq/punorrns e ur pätuese:d y pler;ur lurluec e 1o Surlsrsuoo snlnurls e otouep lleqs l 'ôoqe sV 'pooqroqqSreu sy o1 (s)req1o orlt pue lurod ,{;e,r srq] ol Surureued euo 'suorlrsodruoc 1u;1ceds rreq] ,{q pczuelce-reqc '.s1qir1, o,n1 (1see1 1r) uee.trleq uorlelcl crli Äq pcurluiclep sr -ro1oo '1urod qcee lE 'qJrq,{\ o1 Surp-rooce 'Joloc.Jo a,trlccds:cd pcseq -luersueJ] leuorleler € slrns lurp uorlu:n8r.;uoc snlnlurls -]o purl .leururru, u ;o3 e,trlcedsred peseq -luorsuerl e qJns ;o slcedse crseq etuos Ägrceds ol sclll pue sllnscl lecr.rrdr,uo pue seopl lt:cr]oloor{l Surpuodsc;roc uo pcseq sr lepollr 8ur,uo11og eq1 'rolor.+o Surpoc aql ro.+ ,uoqeurloJurl [prluosse eql epr,to:d sluersuerl 1e:odurel-orluds 1eq1 eapr aq1 3ur -1.roddns qcleosär roloc ur eJr-ropr^e eldue sr e:eq1 .,(rlaruuÄsy luaruaJJa(J-luauraJJuI puB lapolN luutro aql t's't'zl '9 2[ r-lollrrs ur a,trlccds-rcd perrdsur-.{3o1orllo pue lsrlErrollrun+ Surpnodse:roc eql ol ulnl Il€rls I 'sluorrrêerqf,1) lenldecred xelduoc Jo sruräl rn lrpoLu srqt 3o 3ur -pr?cl pclecrlsrqdos e'toru e ol ,{u,n lu.rnleu e ul puJl ll qlr,r\ palJcuuoc suorlêJosqo pcr:rdrue :^u llc.\\ sE I€rrleroeql 'pu€q rrqlo eql uO 'iurpor tsc.rtrrol pue tuo{ Jo surre} leuor}rp€r} ur uorlelr.rdrolur 1d -utrs e s,{\olle pueq euo eql uo '(sr-ror8:l-r lqirl olur eceds uorlelrcxe roldeca: aql suorlued y asnuJaq) lapol\l luDl)o eq] pelltJ 'eueqJs srrlJ 'lo.lttroJ ,{1,trlsucs -+o stusrueqcetu äArlcerlqns puu c,\ll -ecrldr1lnu qloq sale-rodroour pue s1r:uirs roldere.r ,{:erur:d jo epoc tsulluoc e uo pcseq sr leql'(t66 l) egreporN puu plaJsnel Äq pre,ttrol 1nd 'r1nurr1s punoJJns-JelLrec ursepoc roloJ loJ eursrlJs luJ -rleroaql e czlJelululls ill?qs I uorlcos lxeu eql rrl '(t661 : 166 1 ) egreper51 puü ple.l:^nc[\l ur punoJ eq u€3 slopolu cscrll .lo uolssllJsrp v '(V)'ö. (S)'1 i' t '= (S:f );'rJ :lolluoJ ,(1r,tr1rsues d,(1 serr; uô u ol pc -lceiqns sr y ged lelucLur-r3ur eql .{pro V O S V pur) eql Jo rlllrurls ur ]uq] scurnssP lopolLr srll.L ((s),ö _ (v)rö) .(s)rt ri r=!3: (s:v), r) '.1apour,, 1t u tt tu31 t nL1 aqt Suttunotslp,, GL6l) que,tr.r1u16 elll lepour srq] Jo slueu€A 1uu1-rodrur lerJ^Js J-rn olrql 'sêlosuaq] sepoc uuel-LlsserD lou 'snql '.-nl püe scpoc ,{rer-r,rud Jeeurl eql Jo suorlcunj eur.}.lu eJe Ieporu qcr,\lnH-uoseuref eql Jo sepoJ 'lrrou -oddo eql 'sepoc uuerusserDJo ssclJ eqt o1 iuoleq 1q8rl ;o lods snocucSoruoq eliurs D qtr,\\ sluaull -"redxe uorlellecuuJ-,roloo ruoi] pôlJop sopoJ lrretr -oclclo oqt'suorldtunssu Ä1ucaur1 Jlqulnrs li\pun'sl: -ereql'slueurrredxe uorlellecuuJ-.roloJ uo pJsuq sc,r\ ]eq] 'z'f.'v'zl uortces Jo lepoul lolor-tucll -oddo rueurl aql tuol-+ luere-]-+rp st läporrr sLll 'sleuuur-lJ (),\\l .rarllo oqt roJ suorlunbe snoSoleue prlcllll:^od lopou.r qcr^rlH-uosetrlef eqJ 'sraqrunu lerl ilc (S)/ puu (S)!) pnt 'rq3r1 3urldupu (Ä1lerodua1 -ro .{11r:r1r:ds) orll S put; s1qir1 peluese;d eq1 selouep V r.lrrl.\\ (s)r - (v)'ö .(s)'r t' r'3 - (s:v)''ö :rllro.] JllllttlaLl]s 3ur,mo11og elp ua,rr8 eq ',urelsXs urc:8-pr-r. oql .rol -trur leporu : ol perldclu rt: JUrl.lu uu sp 'l\oluoJ ( lr?ll -tl1.r.tci.telrtt s -urs Ll ol sle. .roIoJ-ltrotro( IuJ.lJ++lp -roJ rql r)rl 'qor -rl'lr,[u asor[.\ -os Jrll sr slr ,rq pe soclo, .+() sLu-reJ trr .rll .lo.+ lLlnoi i.rosrll .ro1or ').r().\\ IeJ llal ol llnrrJ. 1o :l;-uniur:1 -uorlula.l srll 'rrrJJs l0l1sr. ,tllua.requr s 'sau.tt:tu U \\o puu 'u\+.+o) ,ic1 pr.run.rp -1r:rr-ro i11ur; t'lu:rtutttt.rqd '.u()r'lJrlpul Jrll -riprilr iu r1'rLrodsel.r urlrl.ralJ uo l.) .1o urir.ro aql 1'ruu lurluds .tro S}Jil.IE I .,uor1u1a;d 'seU( .luiurl BJo lr. , s t-us lUnqtett ilr1uuorl-rodr 's s i I crl l.lJ.\3 I -stru.rl ,rrtuttt -o:r :11;-Lils unrl-liJ r? rlll. -l.U3()J Jrll'r sar.r) uo\ a s.rolo.) rrr) Itzrlceo:ddy lrtsriulue[ro[A eq] pue 3urpo,1 lo1o3 Ä1.ruE y'71 236 12. Co lorPercept ion : FromGrassnranCodestoaDua l Code lbrOb jcc tand l l lunr inar ipn( 'o lo rs afl ine functions (e.g., Jameson and Hurvich, Walraven, Shevell , Larimcr) that take values in the three-dimensional rcal vector space. The Octant Model is an incremcntal ly l inear model consonant with scveral cmpir ical and theoret ical f indings on color coding. [ t assumes a contrast code @, for each channel i and predicts that between the inf ields of two such configurations a color match is obtained i f the respective contrast codes for the two st imuli coincide ( interestingly enough, ner.rrophysiological as well as psychophysical observations sl lggest that thc primary signals in thc ret ina result from contrast coding, whereas absolute brightness and color must bc approxirnately reconstructed by higher-order processes). The contrast code Q, is given by the dif l-crence Qi(A) Q,(S), which in rurn is subjected to a mult ipl icat ive surround-dependent transtbrmation p,-[S] (or, more prccisely, p,, [<p(S)]). The distinctive feature of the Octant Model is that these transforntations are allowed to be diflerent for incremcnts ( i .c., Q,(A) 0,(S) > 0) and decrements ( r .e . , Q i (A) Q i (S) < 0 ) : p ,_ [S ] + p1 [S ] . tn neurophysiological terms, thc sign of the responsc in each ofthe three color channels depends entirely on thc background, and the 'ON' and 'OFF' parts of cach channel are subjected to diflbrenr mult ipl icat ive gain controls. Thc result that incremental and dccremental st imuli arc proccssed diff-crently does not comc as a surprisc in view of both the phenomenological dist inct ion between aperture and surface rrodes of color perception. and the functional ist dist inct ion between i l luminat ion colors and object colors. AII incremcntal ly l inear models that assurne that rncremcntal and decremental stimuli were subjected to the same multiplicative surround-dependent transformation pi[S] imply a qual i tat ive law of ' increntenl-det'rement synmletr.tt let A be an incremcnt superimposed on a background S and A' anothcr increment on a background T such that the two inf ields are isophcne ( i .c., <S O A,S> = <T @ A',Tt); then the inf ields of the corresponding decremental st intul i ( i f thcy are physical ly real izable) r.nust also bc isophene ( i .e., <S eA,S> = <T O A',T>). I f , on the other hand. the principle of increment-decrement symmetry is violated fbr a certain viewing condit ion and judgmental mode, then 1br suclt a concl i t ion no inc rementa l l y l inear mode l w i th p , [S ] -p , [S ] can hold. A sinrplc phenomenon. cal lcd lrrrtr ir t tut((, ( 'otttrast phenomerr.ur (Niederöe and Maustclcl . 1996). already quali tat ively shorvs that incrcnrcnt-clccrcment symmetry cannot hold gencral lv. Furthcrmore, quanti tat ive expcriments of ours sltou that the r.nult ipl icat ive'gain control ' coefi ' ic ients dif f fr . indeed considerably fcrr irrclonents ancl dc'crcments (Mausfeld and Niederöc. 1992) This dit ' fbrence does not only show up bet* 'ccn pr.oltcr increments and proper decrentents. but belnccrr several octant boundarics: Heyer ( I 996) b) ' cxpl ici t ly extending the Octant ntodel to a subscqucnt stage of opponent coding u'as ablc to shorr cxper imenta l l y ' k inks ' o f un iquc b luc l ines in unique yel lcrw surrounds at several octant boundaries. The dif l 'erencc in processing bctu'een incr.cments and decrcments (or, r .r .rore gcneral lv. the coding propert ies dcscribcd bv thc Ocrant Modcl) could possibly be understood as rcsult ing l iorn the structure of the eler-ncntary pcrceptual calcgor. ics of 'object color ' and ' i l lunt ination color- ' . r i l i ic l . wi l l be addressed belo*,. The above presentation cont ' inecl i tself to thc abstract core ofbasic elententary color coclcs. Thc elcmentarist ic perspcctive on color cocl ing is. however, much more variegated ancl richcr ancl incorporates for instancc ntechanisnrs relatcd to cye-movements. f i l l ing-in processes. contr lst cocling etc. Nevertheless. therc are ntanv pltenortrcna that cannot bc easi ly accontrnoclated in thc clcr.nentarist ic pcrspective on color cocl ing (cl. Mausfeld and Niederöe, 1993, sec. 9) aucl nccessitate an addit ional and cl i f l 'erent approach to color perception. 12.5 Ecological and Computational Perspectives The clementarist ic perspective on color cocl ing proved to be immcnsely f iui t f i r l 1or our unclcrstanding of the primary transduction ancl neurophysiology of early color coding. Thc elerncntaris- , U3]qJulclull nz lsqtes ciulc Jserp lJqn uiepuos 'sclqJrl uepuJruLUoI rre8urprrJullv uep uô sep lultlünÖ lepo lllllsuelul eirlra,urf rlp leqn trlJru sun 1rq ainy sup ieSurp -uäUnV .tJp lr:ncrlJS Jtl:lltuul\ ueiurr;r1u.r15 :s.rr1r tlJlllp îPp l-tln u-lapuos 'uaqes utJq qots sc llopueq lJLlrlos slt uciunpl,::1s lop urneqls sup um lqorN., . 'tuals^s lensr^ aql Jo sepou Surssecord e,trltrur:d puu Ä,relueurele ol enp Ä1r.reLur.rd se ,{cuelsuoc JoloJ pelcpr)^uoc oq,\\ 'Sulrag ur punoJ aq ,{peerlu ueJ ,(cuBlsuoc loloc uo êrlcedsted leuorleldepu ue 3o lr.rrds ilseq aqJ sroldece: eql Jo qlpr,\\puec aql 01 êrleler peorq e:e erllods lueurunllt puu sJuelJeu:eJ 3r Äcuelsuoc Joloc ol norltrr-urxordde poo8 e p1er,{ eldrcur.rd ur plnoc Surlucse; e,rrl -depe ue qcns lolcp.] luepuedap-uorleururnllr uu Äq tndlno loldef,or eqlJo uorluzrletu;ou odfl-sell) uô e sr lueuruo:d lsotrl eql esoql JO 'uorleu -rrulllF orllJo soSueqcao slce.lJe eqt szrlellneu lEql sutsrueqoärl ,(:u1ucr-ue1e eydurs 1o eloJ oql sezrs -eqdrue ôrlJedsled lpuorleldepe eqJ'suotleurur -n11r 3urÄre,r lepun slrelqoJo lolo3 orllJo Sulpoc leurrlur oqt qlr,r\ Ieep ,{llesrleroärll ol seqreordde Jo spur) o,lrl qsrnSurtslp Ä11ecrler"ueqrs uec ê\ 'uorsl \ loloJ o1 saqceordde yeuorlelnduoJ snouEA pe;rdsur c,teq .{aqt eroq,lr !qrleoser ecueirllelur leroU -ure.Jo eruaS:aruo eq] ol enp esrn8 ,uau e ur pelJel -rnser ueeq e.teq slqSrsur aseql '(9961) sopru) lo (6261) qlog ul ''3'e 'e;nlure1ll orsselc cql ur purJ ulrr euo leqt slq8rsur Jo lêal eq] urell€ ororu eJUo ()l lloJJJ pue Jultl Jruos elrnb loot 1r lnqt luelxo ue qJns ol uorldec:cd roloc ol seqceo:dde lsrlBuorlcunJ xclduroc pcsse.rddns scrs,{qdoqc -,{sd pclueuo Ä11ecr3o1ors,{qdorneu put? cr}srrel -ueutele Jo setxopoql-ro Surlru,rord eql .{leteunl -r(Uun sJtunu u,rou)-lli,,lr naj e 1snI uotlueu o1 'predeq5 'uosqtC 'Ir,r\sunrg lleploH 'lelqng ,{q pccue,tpe pue pooqca uceq ueql ecurs seq ä^tl -ceds:ed lstleuorloun-] e oJ luctrr]truruoc s,3urre11 (.. s0^[es -rueql slcaiqo oqt lnoqp sn uto.Jul o1 lnq 'slcoiqo Ir?ur.1lxo eql uro{ \euoJ leql tqFr; rqr go Ärr -1enb ro ,(1rsua1ur o,lrlcedser Jql lnoqe sn lrrloJur o] lou sr 1se1 s'.e.{a eqt :s.{€r Jseqt Jo sueoru Xq slcefqo luuretxe ees o1 Ä1r1rqe ql lnq 'qrns se sÄe; 1q3r1 8ur,r.rec:ed Jo Je]]€ru E lou sr uorsl^,, :(g 'd '0261) 3ur:e 11 ,rq p:lsso.rdrr ,r1.rur1r u:rrc1 Äpeerlu peq e,trlcedsrod srrlJ slr.rlqo pur: 1q;-r1 1o Äe1d.relur oq] qlr.\\ uorlJeuuoJ Lrr slrrcrlrJ.\Jlqiu lcnldec:ed xelduoo q.lr,\\ sluep uorldrr.rrtl lolor lcql eepr Jrll tuor.] sllets puc uorldor-rocl .1o slmclsu lslleuorlJunJ ]unoJJr? olur sclul luql p:rclo1o.r:rp ue Jq seq c,tloedsrad cnrleulJllrl uu uorlclrr.rlcl Joloc o]ul suorleirlse,rur Jr-]rluolJs .;o itrruur;-oq oql eturs l€tll lrp..] eql pcpe.\ putl strs,iqdorl:r,rsd ur pelre,terd êeq sepntrle Surpuodsor.ro,l ,'(io1or -sÄqdorncu go eur ldros rp,{rer l r xnu ur o1 s :r r s,(t1cktr1 r -,(sd pecnpe.r sepeoop ,{uunr .rcr.; sl?rl sLl.raJuoi) 1ecr3o1ors,(qdolnou ol loedsel qll,,\\ rrotsl,\ .roloJ o1 qceo.rddu Jrlsulllueurole oql .Jo sself,ns Jrll ,, s 1t I ttut Is .to I().) Burtuo;';ur aqt /o adnqs 1nuctt1,tuttf 1n.rl.'t;xls ,'tt1t Sutttrttttls,t Illt.l l),)Lt-t))tr(, ) \'.1 /t/,)/.\.lr ltttt\t.t ,ttlJ.. :c1e1s (76'd 'EgOt) )leqrslloD puu rllnuclsrlltg uIoA lelrttlrs e ul ,,'tut1.tl)ad:' ;ttll .r,'t,to .t:j.r,'tu,t li) s'uotlttqt.rl\tf lu,t.t,tlltlt )lltutltt.t.)\'tlt t,t \t ,1.t,1 ttlt /it t1sn1 aql'uotst^.tolo,)lo4,, ]eql l.ll?ruc.r (9-19 cl '7961 1 ) s,,trolteg ^q per3rldr-uaxe aq Är:ur srq1. 'norldec:ed ;o uorldecuoo(-snu) eJl^op llrlrro.nts -eetu e ol squrnJJns 1r uorldecred.lo sluol-.;o s1r. d -su lsrleuorlcurq e1e;odrocur n1 s1dun11it -lolst,\ .roloJ uo e,trlceds.red f,rlsllllueurclJ uu rrJLlAA 'lqn-ll JuetueJour e Äq pacelde.r sr ry lqirl rlJuo.]l .n-ur?q:) ]ou scop secuereeddr toloc-]o u:cur:d erll lpql uorl -drunsse eq] ol luelêrnbe sr '(gg.,1, 1) :lolep.rrp puu p1eJsnet\ Äq,t :t n ut ot q :; t.r 1 .r'.t ntu t t r I p,'t 7,I1.)/.\? p.I I ui) 'uorldunsse stqt (lV)ö Äelu sn1ntur1sr.r1 iirr -puodse;roc oqlJo uorlrun3 u sy ly s1qir1 .1o ,{u.r.nr 1u:oduel-orleds u ,{q pe)ôä sr qJlq,\\ scrur:-ntoddt Joloo lo urelled eW luql cuussp uorldeucd rolnr o1 seqceordde lle ]sorule ':eyncrl.rcd uf iurpor roloc xeldr-uoc;o ,{roeqt Äue ;cr3 :^rsrq crlt srlnl -rlsuoc Ä:ocq] uueursserD eql tcrll 1rr.1 :lq1 eiu:r1 -l€qc lou seop srql l€ql 8ut.{€s lrloqtrm sooi 11 'sct-lJJs ll:r.ll1 -1eu ur uorldec:ed rolocgo surelqold ol lr pirJlxJ ol r^1due11e euogr Surpeelsrru ,{c,t snorrrurad u ur 'sr e.lrlceds:cd eJrllro cql ;eqlrX uorldac::rd .ro1o:r .1o s,uerp e.rrlreds;ed crls r.rcluettre J J iLU eln 1r rd I u:rr 1:l.r -oeq] eql ur ernlnl eql ur pellr-] eq ol JuultJl)l Jttros Äldrurs e-re ereql lpqt uuelu lou seop srql'souJrs xelduoc ur uorldecred loloc .jo stuclqo-rd qtr,t Ieep ol poddrnbe-11 'lelä,{\oq 'sr e,trtmdslcd rrl -: -(') -.1: il -lo -ts lJ utl -pr ol pu 'sl eq erl rlr sal arl (le eq -pr UI ,\\c 1Lt: -lt u-1, .to( .il le.] Iur, '(9 -u( uur -TI I Ltzsc,trlreds.rc4 yuuorlulnduro3 pue prr8oloog 9 31 238 12. Color Perccption: From Cirassman Codes to a Dual Codc fbr Objcct and I l lLrnrination C'olors E,xpl ici t accouuts f iom dit lbrent theorct ical pcr_ spec t rves werc g iven by lves (1912) and. laenscn (1914) who introduce the concept of lcvel, ancl later. among othcrs, by Helson, . ludd Land, Bri l l and West (e .g . , West and Br i l l . 1982) , Mac leod (1986) , and Fos ter and Nasc imento (1994) . Non-adaptational approaches to color constancy werc developed by Sällström, Buchsbaum, Bri l l" Maloney and Wandell , and D'Zmura and lverson Thesc approaches are expl ici t ly couchcd in terms o1'the computational goal of recovering from the sensory lnput a function that depends only on cer_ tain physical propert ies of objects, viz. character_ istics of sr-rrfäce reflectance. In the fol lowing I shal l very bricf ly sketch some of thc basic ideas of the adaptational ancl non_ adaptational approachcs using thc example of Land's Retinex scher.ne and of Malonev's alsor i thm rvhich is based on the l inear f iamewlrk approach. 12.5.1 The Problem of Approximate Color Constancy from a Computational point of View A strong local ly-atomist ic perspectivc on color perceptlon takes the color appearancc at cach locat ion Ä of the visual f ield to be dcternrined by the l ight pertaining to this very location. i .c.. b1, t l rc respective tr iple <p(A*) alonc. This al leeccl point_ to-point correlat ion of u,ar, 'clength crl lposit ion and color appcarance is in confl ict u, i th ntan-v ernpir ical phenomena. among t lrcm colorecl shacl_ ows and the phenomenon that colors oi 'objccts tend to remain fair ly constant unclcr cl tan-ucs ol '1he co lo r o f the i l l umina t ion . The formal corc of the problenr of color con_ stancy as viewcd front a cortrputational pcrsl-rcctivc is schematical ly shown in Figure 12.j . Thc vari_ ables involvcd are the spectral encrgv distr ibLrt ion E(),) of the i l lumination ancl t l ie spectral rcf lcctance function R(.r,), ; at a locatiorr .r o1'n sur_ face. The signal cor.ning to the cve is thc point-n. isc product of i l lumination and ref lectarrce. as i t u,crc It causes in each type i of photorcceptor.s a ncur.al signal. In this signal t l ie i l lumination contp()ncnl and the rcf lectance conlponent are contpletclv con_ fbunded. Nevcrtheless, the inter-nal reprcsentntion. i .c., thc percept of the (approxinrate lv) ' tnre ' color o f the sur face , rcqu i res a k ind o fc l i scn tans l ins o t ' the two componcnts. On the basis of local inl i l ._ mation ol a singlc posit ion .r this is. olcoursc. impossible, on logical grounds (analoeousl l , to thc impossibi l i ty of identi fying cach of the tactors f ir l a glven product of trvo nur-nbers). VisLral nrccha_ n isurs tha t accornp l i sh a ( la rge l i r ) i l l r rn r ina t io r r_ indepcndcnt pcrceptual asscssl lent ol-the color ol ' In r t und ' M c ilcc( VCfS lre ( \ d t c ple-t co lc rrh i , i ) i l t ta ob.1r a l o 12. i l , cr Wht pcfs t(') p con! I n obta t lon N4or proc be' d be t l cor1l othe t ivc Retir r i c n thc t ( und race! aVeri s ider I t ma l ly t ion . irl'er thc C rt'lirttrl L o/or todc Jl( ; t nu.. ' ) vtr ' t o, l , / .1 1 ' , t \ ,{ ri ,J- -6) .'\\ tlt , V' R \ r ' ( s(nst)rl inful \ \ /, -_,,,,,,,,, rr,r !,.ir, ) x R( ,L ,x ) Fig. 12.3: Thc ploblertr ol ' color constancy. -ird Äq poure"rlsuoc .{11.lo,n Ä1uo sr lerll lopou o selqeuê 1ecrs.{qd 3ur,{1-rcpun oq} loJ lepour leJr -s,{r1d :ueur1 IuuorsueLUrp-ellut.} e rlJns uo pes€B 'seJuelcoL+0J lfllJaos lelnleu -]o sle:^ e3:e1 -ro3 oJrrl?UB^ llElêo .]o 66 0 rr\o .roJ lunoJJü sr.rorlJUnl srseq tq;ite'Jirur)t\ul .roJ 'ecurs '11eu"rs Ä1qe1:uulel sr loJle Ienplsel cqI 'loporrr rBeurl :elncryed srql lo.J scJuelcelJOl äJp,J -,rns elqrssod 11e cle.rcLre8 o1 Äru,l uEJ uolleutqruoJ -uloull srqllo slq8rc,tr eql'peleptsuol scct;-]lns erll 1o lucpuedepur eq ol pue pexrJ petrtnsse sr suorl -JUnj srseq , 0q1 -]o qJee pue ,/ Jequnu erlJ suorl -)unl srsnq r/.lo uollcurqtuor.nrJutl u sc pessoldxr urql \r eJtrplrJ[1.1.r 1e.r1.r:cls e.]nllns qJuS suotl -oun+ srstq pelrrurl-,(ouenbe"r;1o las cllu-] pexrJ ü Jo uorluulqluoc lueurl e Äq peler,r-rrxo.rdde 11e,tr e;e suonJunl .l.luulJJUel ;cll.rrds r.'ruJ:ns Xunu prrr s1q8r1 ,1e:n1eu, -]o suollnquli-tp ,(8roue lurlccds cql 1eq1 ernlcefuor rrll o] pel ôeq säf,uelregel 1e:1cads JJp.J.rns ournrJolcp lurll sossecotd 1eors.(qd eqt olur suorlrirlsä^rrr sE llc^\ se s1q8rl pue seop.+llls lucr-rrdurc .]o slos ä8lu[ Jo scs,{1eue :uepr 3ur,no1 -loJ ortl uo pcseq ere ,{ruelsuoc roloc Jo slepour leuorletdupr:-uou .Jo sselc ]ueuruo,rd ]sollr eqJ ruqlrJo8lv s6,teuoluI,\l puB IroÄ,r,äruBJJ s6lepow rBaut-l aql z'I's'zl 'lueutrlrnllr etlros lcpun seJu8] -Jollcl cJr,.IJns elqrssod lle to1 sepoc uuelussllg 1o lnure8 cql ut uepprq uollr?lrr;oJur JuEulLu -n11r 3u11cu-rlxc lo.+ IJo,r\alue-rJ e pl.ro,lr uuupuo]\ e rol pesodord (066 t) qilsloC 'stur?urLullllr lulntuu ur sciueqc repun luerJêur ]solu[t? scceJlns leJn -lllu JoI ärB sorlur uolleltcxo euoc sJurs 'suor]8lel :o1oc lerleds yo Surpoc l3orrp e Äq pe,terqoe eq ,{uur sepoc luuuêur luuurrünlll leq} eJUeprAO pJplA -ord (7661) olu.LurcsrN pue lelsoJ 'Äe.r8-prur e sr ,1u:rs ärll Jo JJr.rr?lJJLl.1l e,lule ru eql luql l(l Jtlo)s Jrl] ur älqülrEAu c3P.+Jl-ls elrq.\\ e lcqll0 sr 0leql luql Jtunssc puu uollDZrlnuu(ru:d^l-seu) uo\ n uo pesuq oslu ert; teqt pedole,rcp ueoq êuq ,{cuelsuoc roloc ro.J srur1luo8p luuorleldepc -ror{to IBrä^cS ',{lesueluurr fruclsr-roc loloc uo qJrccser lecr.rrdure pue lecrlolooql lorptn] poleln -Lurls 'suorlelresqo leorrrdruc qym ocuultul lE pu€ ,t;olcejsrlesun f11ecr1e;oeq1 Surcq elrdssp'Äcuu1s -rroo roloc o1 qoeo.rddu luuorlelndr"uoc s.puu1 'seere uuupuot\l orll .lo s.poJ UUu[rssu.l1) Jrl] Jo uecrLr ouleuoe8 Jql t.ll Iuuort.lodo.rd Ä1rs.rr.trr eq ol petunssu e;c 'd sluclJr.+.+ioJ rrll J.rirrl.\\ -uorl -t?luJoJSuc-rl ad,(1-sor.r; uo,\ c ot irrrlr:rrnbr {11urLr --to.rt r-r ur{lrJo;lu xrurlol erll 'lurli snor.\qo sl ll ' asuclJelle.r Äe.r3-p r r-u u ol sptrocl:^ J-r.lot pi.lip r s -uoc ul?upuoL\ aql Jo cJlrulJagc.r 1r.rtr:ltls :ri;-r:.rr.rr: otl]-+r uorluurtunlll ur seiuurlo -rJ.\o luul.lu.\rrr (si:lul -llls puu slqir1 lnoqu suorldrurrssu ;-uo.r1s .rrpLrn) sr 1{ö)97'ö-l rpor.rolor snl.l. (iö).,),'ö ":r'r 'uEcnl 3uleuroei srql ol lroclso.r rlll,\\ pl.r.l ls.l Jql .Io apoJ loloo orll sJzrlurLuou puu ('ö)! uuirr.l Jl.l -letuoe8 Jql seltlnolur,(11r,lrrsr:c1 urqtr.rol-1t \irulil1 (eq] Jo uols.rc^ Jelul) eqJ sJpor uuuutssu-rr) ..\ll -ccdse; oql elouJp ucupirot\ Jt-ll.+o.r s.rlr1r:cl .r:rr1to 11: ,ro.1 tö 1e1 'Ä13urpuodsa.l.ro.) .\' uro.r1 iurtuo:r IqFII ctll .+o opoJ rnrculssu.l{) etlt .lo Jnlc\ rrl} icl ('tö ";ö "rö) -'ö 1c1 :s.lro11ol s) piclr.rrsil) icl 'sepoJ roloJ uuerusstlr)Jo sul-tJl ur 'uur r.rnplro.rd eql .{lsnoeuc3oruoq polllrrulnlll sr }lll1 r-rcl.lprrot\ poxl.] e Jo ,r pler.l 1sc1 ue,rri u .ro,1 :r.rnprro.rtl uorl -uzrlEtulou prru rrosr.ruduor e lclu-rrs u ,,ic1 p:lurtlqo e;u s:oleu8rsep JoloJ escql i-rorrll \rurli1 ul '(JuJls pexl.I ouo ulrllt.\\) iluulsuol .to1oc loeyed soun-rssr lr :srrollltlJ-l lnnldor.rlcl tt1 apoJ luetJelur-uollr?ulLunllr erl1 sall (rr'l.rr1mds.r:ld 1ut-torlulndruoc e ulo.r+ luJrlla.rrnLrc.r I st (r :^ui.lJq,,\\ ' :^i JUU.nraciclu .rol o J leJuuepr o1 puods:l:.rnJ stoluun-lsJp 1rn['rr (rr ( s.Jl)l -Jns Jo uorlernSr3uoo pcxt.+ u.ro.l ) uolluulu.ntlll ;o se8uuqc -ropLnl luuull.\ul :rilt s.ro'lur.lirslp 1r ploq iur,to11o.l rqt rlJrq.\\ loJ (srequnu 1o c1dr.r1 u'J'r) s.rolnui;-rscp .ro1o:r pulJ ol sr,n rlcecl.rdde s.puul 'pJlullorsrp .n1:rt:r1cl -tttoJ rq ()l sü(l lr.rcr.nunrllr.lrll ll)tll lr.1pt illl iq p,rtr:r -llof.tl sl?,^\ .1ttl:li.r\ stql r.rrr,r12 .\,1tt ! 1.\)l l).1lll)),rtl qcrq,r\ reluoqcs 1tuor1u1ndnro:r o1clur r su.l o srr()ls.lJ.\ lllloles p:B,rro.] lnd puul siurpurl srrl .ro.l 'lulloJll oJ'puel ul,\\p3 .+o stlollull:^tlottlJp,tllll.lptlol\. sttotttc8ur eql ot Jlip Iu,\r,\a.r r? lua.\\.rapull ,{ctrulsnoc Joloc -}o uclqo-rd orll oluI strorluii-rlsr.rtr1 ,iruu;suo3 roloJ ol qruo"rddy sspuE.I I'l's'zl 'euoJ:^ lcrlsl.\ Jrll .]o:^uolllt.rJ(lo Ilt -qo13 euros uo päseq eq ^lluJnbisuor lsltu.r s1.rrllo (tEZs:,r.r1cecls:a4 leuorlelnduo;1 pue lucr8oloog g 7; 240 12. Color Perception: From Grassman Codcs to a Dual Code for Ob.jcct ancJ I l luminatior.r ( 'olors ceptual considcrations -. Maloney (1985, 1992) proposed a mechanism that exploits the underlying physical regulari t ies. I ts goal is to cst imate from the sensory input a function that clepencls only on the surface spectral rcflectance function. For his algori thrn, Maloney assumes that for the case of three receptor types each light can be suff icicntly well approximated by a l inear combinat ion of three basic l ights, and each surface reflectance by a linear combination of two basic ref lectance functions, i .e., the vector space ofpermissiblc l ights has thc dirnension 3. the vector space of permissible ref lectances the dimension 2. Therefore the values of the Grassmann codes of the pcrmissible ref lectances under a f ixed permissible l ight come to l ie in a two-dirnensional l inear subspace of the three-dimensional Grassmann space. Maloney provided natural assumptions undcr which this subspace is characteristic fbr the i l lumination in the sense that the i l lumination can up to scalar mult ipl icat ion be determined f iom thc posit ion of this subspace with rospect to the (irassmann space. This in turn allows the clctermination up to scalar mult ipl icat ion of the rcflectances. For a set ofempirical rcflectances the system would have to determine (according to some distance measure) the best approximating l inear subspace in sensor space ( i fone chooses the Euclidean distance this task is accon.rpl ishcd by some kind of principle componcnt analysis). Maloneyh penetrating analyses into the mathematical structure that results from the interaction of lights, surfaces and propcrties ofthe eyc (together with assumptions of the visual system's task) can be considered an important accomplishmcnt for the conceptual clarification of the problem of color constancy. On empirical grounds, however, the gencral assumption that the visual systems's achicverrcnt is to obtain a function of the sensory input that clepends on R(.r.)"), but not on E(1"), wh ich on Maloney \ accoun l i s lun tarnount l ( ) recovering reflectances, does not seent to be appropriate. F-urthcrmore. to accollnt fbr empirical surfacc reflcctances which require (at least) thrce degrccs of frecdom in surfacc reflectance funct ions, the algori thm rcquircs fbur types of receptors. But even i f thc algori thm should not tcach us much about thc actual rncchtrnisms of huntan color pcrception, the underlying approach is certainly a whetstone to clari fy our basic concepts. Maloney\ approach particularly shows in a precise urathcntatical way, how strong the implications are that can be derived from ecological consiclerations about the'physical fr iendl iness' of our enr, ' i ronnrent. 12.5.2 Qualitative Observations on the Dialectic Relationship of Illumination and Object Color Plausible as computational approachcs of the kincl mentioned above are at first sight (proviclcd one restr icts attention to appropriate'scmi-ccoloqical. si tuations, such as a 'Mondrian rvorld'). these approaches have systcmatic drarvbacks lirnr a psychological point of view. The most gencral objection is that thc reduction of color perccption to estimating surface reflectances is. ll"ont thc point of view of perceptual psychology. nearlv as misleading as the local ly atonrist ic rvavclensthbased perspective. The claim that "tht, goul ol color vision is to rec'over the int,ut.iunt .\;l)e(,ttul refleclance of cthjecl.s (sutfitt.e,s) " (Poggio. lt)t)0. p. 147) amounts to a distal variant of the measure_ ment device conccption ofperception. Though the adaptive coupling of the organism to i ts environment takes strong advantage of physical regulari_ t ies of physical ref lectances, the clainr that the estimation of spectral ref lectancc functions is i , goal of color vision arnounts to unc-leresti tnatins constraints derived from its intcrnal .selnantic structure', as i t were, and irnputes to the visual system a goal that is not consonant with i ts actr.ral achievements. What is achieved is not an estiruation ofspectral reflectance l'unctions. but rathcr an abstractivc catcgorial descript ion ofthc .color of 'a perceived object ' , which is more stable than can be. expectcd on the basis of the local sensory input. i .e., the wavelength composit ion of the l i -qht conting f iont the ob.ject to the cye. In t lr is scrrse. thc perccpt 'color of an object ' sccuts to bc nturc strongly t ied to the spectral ref lectancc charactcr_ ist ics of the ob.jcct han to the rvar,clength contposit ion of the local sensory input. Thcre is. hoi is.er. no color constancy in thc str ict sense thi l t tro locations of the same spectral ref ' lcctarrce . look the sill.tle' t scel les appeari .juclgrni ception a lso oL nratic i kint i th nrinatic u i th in rurinatic appeari v ieu , in (Katz , tliflc-^rer t i t ' rn in due to t are ofte nolllen( structio tends t appropt this sit t cal lang perccpt i l lu rn in descrip Vagucrlr ln th t carcfirll that are (chrom p . 2 . l l ) ut tht' .s thc oth< colors i \ " H in r t niltn gst' posecl c " " lnner ( i cs icht hcrzrrstt gleichc-l Ciesicht: - "Farbt r olhand hindulcl ..ucrcs .lzlJsJtue[rllrusnz 3r-rrrlqrncltg ueircl-n',j .rep snu ucqJlneH uapue8e rgnulup LLrJr-rrc pun eqleJllelclO ucqcrllurfira iap snp ars qo slu 'uJurarlosra,, ueqluC ! eq [rêJ -ro 'Jo slule] ur poolstepun cq ,{le}äldruoc uec SurpoJ roloJ-]o selyodold ]uql uorld[rnsse ole -rrdo.rddrur eql suopueqc euoJr 'rêe,$o11 slqirsur lerrlo.rooq] requnJ epr^ord o1 esrr-uo;d lou op teql Ä8o1orlcuroueqd ur sesrcJexe JlJu,r oq o] tuees ssel ro cloru osoq] olrl suorldrJcsap leorSoloueuroueqd 'seArlJedsrcd leuorlrlnduroc .{ep-lucsord uro.rg 'o,r1 3rl1 uee,rleq uorlrsr-rrJl snonurluoJ puu uorlesuedruoc lerJJcd e ]seol ]u -1o ,{lrlrqrssod rq} solelrssoJeu ,{cuulsuoc lloloc .]o ]ueiueJrnbeJ êtldepe oql 'leqlo qJec nrol.+ po3rôrp Ä1e1e1duroc X11:crSoloueruoueLId ueeq êuq plnor seJurlueddu -rnolor .JO ,spllo,r\, o,\\t eseql aldrcur:d ur qSnoqJ :Älrrelrurs 1ec -rSoloueuroueqd ärlros llqrqxe eJrJlns uaeJS-JArlo ue pue 'ocuelsur ro3 '1q3r1 ueeJS r 'oloulequnj{ 'lJe le uorll?uttunllr elu-rudJs e 1o uorsse;dut oq1 êl?q ol aseec e,\\ leq] ur lerceds 3q ol suees uorlBrjrlunllr c]lq,r e (uorleuIrrr -nlll cql Jo ]uolussesse ue ro.+ scpoo uul]russelD .Jo Jsuullr?^ or{l olrl Surqlcruos esn 1q3rur urel -s,{s lensr^ eql lurl] e:nlcefuoc Jrl] o] esu sêr8 r{clq^\) euo alrq,r € ruo{ sä}rr^ep uor}eurtttnllr cql Jlor-Lr eq] IurJqs ol spuJt sroloJJo lnuu8 crll (,s1cefqo aqt.+o s.toloc, eqt ol sseccr poo3 c^ell o] puäl e,{\ q8noqt) ,uorJeurru -nllr llllrJou, -ropun ueql en8e,r e:our pue J^llourl -srp ssel eJr uroor eql ur slce{qo Jo sJoloJ cr[] ( lucuodr"uoc .roloJ uorleurrunllr, ruu puc ,]ueuodruoJ :oloc tcelQo, ue olur lndur ,{-rosr-rcs Jql ,osoduoJep, e,{\ ,\\orl ur utopeel.J eluos 'rrorluJlle Jo sgrqs q3no:ql 'sr elerlJ sesuo ,{ueu ur) uoqeurLunlll or{tJo toloc aqt pue (1p,tr .0111^\,) lcefqo eq.;o loloJ or{t qtoq.ees, uer e,r\ :lc,\Je sqo lnIOreJ u ur suorsserdur .1t'r spur>1 Furn8ulur esnore ueJ 'lqirt qsrppor e ,{q peleurunllr ltrool c ur lle,\\ Jll{rr e ,{'us 'suorlunls ,(epÄ.re,te ue,lg '(ozo r ) qteo .ro'(g76 1)sqcng'(lggt "3e) 8ur-reg ur punol aq ueJ uorlêlosqo Jelrurs ..'uolleurunllr Jrleur -o-rqr rapun sioloc Jo {llllqel snounc oqt,. palou ftLZ 'd 'l I6l ) zle) .,,'uorleururnllr rrleuo"rqr er{l ,.lsr rrJLIJS nz qJ.lnpurq a.roPuu Jrp rlJlllp sqre-{ .lutc,, oA\ pull ,.plrrs rrJPrmrl.lo\ seplr.lslrlf,rss{) sep llel Llcqlrs[lrp r-il erp 'rrrcliu,l.. .. rrJ-]JJrluu ru.rpl.1.l slqrlsJl) uclJlt[JnJlJq Srqrultunq ur .rr.'rr Jq]li.t 'ucrlrr:r1l- ,3unqcrzcg :epaf ur LtauJp Jrp 'uarlf,lts.le,\ rrrllrlsnz.rll JIJnlpureqrE,t qrrlqci.n,r uEtr plr^\ srplJ.+slrlrrs.r) uJlrltl.rn:lrq lculrorr \ilnlllr:nlr s.rur.r qlrrrl.t,ru(r1.. Äq Surleoc u pul? roloc ]Jolqo lulltrl? oqt.1o p.rsocl -u-toJ ole,tl .{eql gr su .recddc sloloJ,, '(.. urttn.rsiLutLu -4du.1LlqN4 utt udl.toLlJD,l uotr .t)rL.tt)ttt).t,)lu!H,.) ,.JeI{}o eq} purqoq euo eceds lenldelrecl ur s.ro1t'r:r 3ur1uco1,,;o elods (gy d'ZZOI) irlLlrlB -...reqlo Jql pLrrqoq 3uo plerJ lensr^ eLIJ Io uoun.)ol atut)s' ,)rlJ tt) uoos eq uec l8q1 s,roloc,, sr ueql peqr.lrsJp (!-l,z d 'Z IoA'1 161) zlloqurlcH'uorllturunrllr (rrluuroiLlt) iepur-l scouereedde :o1oc Jo.+ orlsuelJu.ruqJ J.m luql serlrrurlnccd leueuoueqd eql rqr-rrsep,{11n1r-rr,l:r o1 s1duelle ,{ueur pur3 e,,u är1ll?lo}rl Jrsslllt orlt ul 'uorlezrro8cleJ pue uorlJuJlsqu'ss:lu:niu.r 'eJrn4sul .rog Jo slcedse qlr,{\ Ieep o1 suq uorldr-rrsclr B r-lcrls cJurs 'slJofqo pe,trccrcd pur uorlllllt-unllr pe,rrecred ;o ,{e1d.re1ur oql qlr,\\ pcterrossc lclcr.rotl eqtJo uorldrrcsop leueluouäqd eq1 rog riuniuul 1r:r -tleloätll elq€llns c Jo )cel lno ul sJll uollun]ls :^lql ro.+ uosueJ Jarllouv scpoo ecusJeeddu :llur.rclo.rddt Jo uol]3nJlsuoJ eql rlror.+ pe JJôrp eq ol spuJl sopoc JoloJ luepuedepur uorleurlullllr Jo rrollJll.lls -uoc eql'Älluenbcsuo3'ecuerueddc luorSolnueurou -eqd.1o uorlureprsuoc Äue lrurpr cll rllpol uJl.Jo a.tll slsrcrs,{qdoqc,(sd leuorlelndr"rroc tr?rll J14 rrlt ol .np .{llred st srql 'se,trlceds.rad ;eut'rrlulndLuot ur uorl -erca:dde peducse e,teq ecue.leeddc ur se:lro:o.L1r1'r leueruouaqd ellqns uetJo eq3-',(lLZ'd '1 y1,1 'zlu; ) .,ll1l-] ol euord are 'uorlt?urunllr leJrlcluollJ rrr ,\\cl,\ ..1o splou ur peJalunooue eq uuJ 1t:t11 s:tor-rr:r:edtht roloJ o] lenba ere s1o:ldse; llu rrr lerll Llol]uurur -r1llr Ieturou ,(1e,rr1u1r1unb ul ,re r^ Jo plel.l c urrltr.\\ secue:ecdde loloc qsrlqelsJ o1 sldr-r-re11y,, rrolluu r ul -nllr leluJou rcpun pololunoJus 3q louul?J lltrll pLili e Jo rolceJ€qc ,n:rlnoed u eleq uollpulrunllt Jlluu-l -orqc repun serue;eedde loloJ leql po,\Jesqo oslu otl,tt 'zlc) Äq pessarts ,(peetlu su,\\ srrlf .ut'rrlcl.rr -:ed go cporu, s.rêresqo Jql pul? ISul 1c1ucru31-rnl' or{l uo spucdcp Surureu esoq,r .se tuu.rucclchr ,roloc Jo Ä1r1unbc, Jo uotlou u errnbcr lJqlu.r soucf,s xe1duro3 suorluurunllr ]uoleJJrp ô\l lJprnl .eunts rrlt Iool. ar o.\\l lltrll asr -.\J.\\otl ':^l : -oclruor ql8 -.ri'lJlr.llrr.lJ ä J.rotu trl ol Jq1 'Osuls s -trror tqirl : 'ltidur ,uo:^r Jq uul rrurll u .J o .loloJ. : rru .rorllul ]11( -tltull:^a UU l ll)ntilt slr ql It)n)^1.\ etll ( .lr lul)LuJs. I irr rluurrlsor: lt sr suouJL Jql lurll rul -r.re;nil-e.r 1u: -uo.ll.\rra sJI eql qinoql -J-illsuJI-U Ctl '1y1.'61 'ori8r ln.tltsrls lttr fo lnrB atll -rlln-u.1lJ.\r,r.\\ su il.nrau 'ii Jtll ulo{ 's uorldmled r Iuieuaö- ]sor u ruo.u sIJ .sJqt '(.pll( ,1urrä-o1oraeuo pepr.\o.r PUI) rqt.io ! roloJ I J( Jrll uo sr 'IuotUu0 lnoqc suorl[ uuJ lPql äJu -luLrr.I['lurLl 0 s.,r:ruo1uhtr's u ipnul:er s s_lolo,) uol tt7sa,tr1oads.ra6 puorlulnduro; puu lucr8olorg g'71 1 4 1 12. Color Perception: From Grassman Codcs to a Dual Codc fbr Objcct and l l lunrinatiorr Col6r-s derived from the goal of recovering spectral reflectances, the question again arises in which way adaptive properties of the internal coding of' color can be described more appropriately. Observations like the ones above may then providc strong heuristics about what the actual achievements of the visual system with respect to color perception arc and about how the attribute ofcolor is intcrlocked with spatial aspects that in tum are interrelated with the ' interpretat ion'of the scenes in terms of 'objects'and ' i l lumination' (one cannot overemphazise the point stressed by Koflka, 1936, p. 129, that "a general theory of color must at the same time be a general theory of space and form"). 12.6 Center-Surround Configurations as Minimal Stimuli for Triggering a Dual Code for 'Object Colors 'and 'Illumination Colors' The ecological perspcctive on color perception heuristically starts out from a physical description of the sensory input in tcrms of complex achievcment-related conccpts such as 'surfäce', 'spccular highl ights' , 'shadows', etc. I t then attempts to construct complex abstract color codes backwards, as it were, from an appropriate physical description ofthe perccptual achieventents, say color constancy. F-or instance, one tries to find color codes (considercd as functions ofthe input) that are equal i f the rcflectanccs that are part of the physical input descript ion are cquivalent ( i .e., cqual up to mult ipl icat ion). Approaches l ikc these again amount to succumbing to thc physical ist ic trap, sincc they presuppose that the pcrceptual categories (e.g., of ' l ight 'or 'surfäce') are consti tuted by the corresponding physical categories (ofphysical l ights or surfaces). Such an assumption, however, cannot bc dcrived fiom the cvolutionary requirement of an adaptive coupling of perceptual categories to biological ly relevant physical oncs. In point of fact, the perceptual categorics 'surface colors'vs. ' i l lumination colors' are not consti tutcd by thc corresponding categorics ofphysics and t ied to them in the sense of the latter being neccssary and sufficient conditions for the former. Rather they arc constituted by a set of biologically relevant l-eatures that are specif ic to physical ly contingenr organism-environment relations. A proper physical descript ion of these rclat ions should therefore not be couched in the vocabularv o l s t i l l to -beidcn t i f ied percep lua l carcgor ies . N. r r much is known today about the intemal semantics. as it were, of the visual system, but therc are good reasons to assume that basic 'scmantic' units ol ' perceptlon are predetermined and tied to ccrtain spatio-temporal characteristics of tl.re inconting energy. Approaches to deal with thc problcrn of the internal perceptual semantics of organisnts werc developed by v. Uexkül l , v. Frisch, Lorenz. Tinbergen, ancl for si tuations where, l ike in visual perception, the unit of analysis is not the cntirc organism but certain (often abstractly ideal izcd) 'nrechanisms', by Lashley, Bühlcr, Brunstvik and Barlow, to mention only a few names. l]arlou (1961, p .219) summed up th is perspcc t ive under the watchword "passw,ortl hypothesi.s ": "specific classes of st imuli act as 'rcleasers' and evoke spccif ic responses; these classes of st inrul i arc thought of as 'passwords'which have to bc dist inguishcd from al l other st imuli , and i t is suggestec that their detection may be the ir.nportant function of sensory relays." An cxposit ion of these ethological perspcctives as applied to the problem of how elcnrentary perceptual categorics comc about is beyond the scol.rt' of this paper and wil l be given elsewhere. In the present context only some heurist ic intuit ions ivi l l bc addressed as to the general question whethcr therc are cri t ical minimal st imulus characterist ics that already trigger attempts of thc visual systenr to ' interpret ' them in tcrms of certain perccptual categories. Arc the perceptual categories of i l lumination color ' and 'objcct color ' internal ly constituted not by an extensive set of propcrties ot' corrcsponding physical enti t ies, but rathcr by a few 'representative' ones? If so, these physical characteristics could bc ir.rstantiated by an othcrwise highly reduced st ir .nulus, which thcn rvould suffice to trigger an internal perccptual structurc whose complexity far excccds thc contplcxity of thc tr iggeri sensory rnp innatcly spe scnrant ics ' . Accordinl relat ionship in a pcrcept ( correspond tion of the I rounding f ie optical flow: the i l l umin t rvhich this problem oft vicrv. r-nisre accounts. l f s e n t i n g ' t h e organizatior our perceptr cllv lr()nlllen approxlrnate couplcd to physical ob1 lather are pr Consequent can bctrigg logical st in' physical pro played a cru pfopc-ft les ( gcrecl they lcrnrs of a t 'object colo An intcre s t in ru l i a re t rad i t iona l l y color codinc pfoccssln-q) I lutcous conl un(le r natru rarclv clccurr can berelatc o f 'ach icv ing i .c . , thc co lo co lo r o f ne i sonrcthin-9 s ri.ltlon of snr larqc sttrrou eql ul prlnldeJ se ,{u,n cr.lrccds eq1 uo lqFr1 ,treu spcrls .uorlllul.rrn[[l J11üruolrlJ lepun lcofqo, ur: roJ rlrlrulls uSrs jo spurl sl? suorle.rn8r.luoo puno.t -lns-.relueJ sleprsuoc 1uq1 e.trlccdsled pcrrdsur_,{B -oloqle ue qll.{\ -teq1e8ol .ppo,r\ lensr^ -n1oJo rLr;o.+ Iernlcnrls eq1 3o ged JelueurepunJ B sr .roloJ uoll -eurutnlll. pue .lolo3 lcefqo, go puu .trrnrpeuj pul? lcefqo.,ro drqsuorleye.r rllccll?lp oLIl leq] eopr eqJ 'slucuoduror eJJrll erll lo LIJEo ur suorle[uo.]suer1 e,rr1ecr1drl1nru luepucdcp_lserl -uor 8urÄ1dde pue scpo.r Ä.rer"ur-rtj Jo sJJurJo.lltp 8ur1e1 se.,r1o,rul rlJll,r\,ro1e;eclo Jsu;luoJ e ,tq Xlieur -roJ pcqucscp sr plcrJur Jrll -lo oJur?lucddu .ro1oc eql loJ opoc luuolsuotulp_ce:q1 FurpuodselroJ oqt 'lcpout srql o1 Surp.roocv .[(S )$]'d uorlcLu.rojsue.rl e,tr1ecr1drl1nur luepuedep-punorlns r: o1 pelcefqns luouodruoc qree ro..1 puu pesseoord sl (S)O _ tVfO leql ^e,{\ e qtns ur pcreduroc oq ol sr V plcrJur cql qJrq,r qI.A\ <S'V> ,tq les l3^el erros Jo crnseoul u su pep;e8ar eq uer (S)0 ,tcpolt luetco eqt ul 6JOJOJ uorlBurrünJIL PUB .JoloJ lra[QO, JoJ epoJ luno B puu uorluluaur8ag luurtue'1 11g.ZI esoql ul pollesqo euourou:lqd or11 .spuno.r.rns ri;--n:1 ul bTlet.]ul pcleJJpurcp Ä1d.ruq:^ puu Iluttr:^.lo Uollu.l -n8rluctc leouleuoei eql lnoqu ;urrocss^ irrrrllrruos eq ol suees oleql .()^loofcp iur.roqqirilt .lo .rolo._) erl] rllr,r Ä;r,r 1ou plnoqs loeltlo rn).Jo -rolor .rlt ,.r.r 'sroleuBrscp,toloJ.to oJueue.\rrr :ru:los iur.rlr q.tu.; o luo8 ;euorlelndruoc luul.roclurr ot-lt ol lr.r,rl.., .q r.,,,. srurel ulcporu Lrr lcrll uolrolrroulqd r:1 slnl.ro .i;:r.rn.r lseJluoC )-nOeUUJllturrs suorJtpuoJ Iu.iltlurr .ripun lprp pcllosqo zlloqur I c g,(pue.r 1 y . 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ST ju -P -ti f.vz3po) Ience 3ur.ra33r.r1 loJ rJnujtlsleururl\ se suorle:n8rluo:) pullol-lnS_laluo..) 9.2 I 244 !: 91"t PercePtion: Frorn Grassmarr Clodes to a Dual Code fbr Objcct ancl l l lunrination ( 'olor.s rncrcmental ly l inear color code of thc Octant Model in i l ,hich in ccnter-surround configurat i o n s ' l a r g e d i s c i n f o r m a t i o n ' a n d ' s m a l l c l i s c infbmration' arc segrcgated by the visual systent. From this perspectivc, this segrcgation nt irrors processes that are related to the segregation of object and i l lumination infbrn.rat ion. l f the centcrsurround configurations contain physico-geometr ical propert ies that alreacly tr iggcr the visual system's ' intcrpretat ion' in terms of small , sharply demarcatcd ob.jccts under chromatic i l lumination, one should bc able to observe, under suitable cclndit ions, phenomena l ike those described in section I 2.5.2 also in center-surround configurations. lndeed, in our color-cancellat ion cxperiments we tbund phenomerra, where, again in Bühler\ worcls, "colors appear as if they were composed of the actual object color and a coating by the chromatic i l lurnination" and wherc in perceptual space one color is located behind the other. The fbl lowing example of an exporiment may servc to i l lustrate such phenomena: We used under Maxwell ian-viewing cclndit ions using the apparatus shown in Figure l2. l a red surround ()" 649 nm, 1 50 td, 8 I 0') , where the 2"inf ielcl was composed of a mixture of monochromatic light (ARn.., @ AG5{,). The subjects had to perlbrm (by a two-alternative forced choice double-randor.n staircase) reddish/grecnish-judgrncnts and to make a setting where the infield appears neither reddish nor grcenish. While for most valucs of ' )h i . . t t , t l t ' r ' l , t c r . o r e d d s h + € o g r e e n i s h 5 6 0 5 6 5 5 7 0 5 7 5 5 8 0 5 8 5 5 9 0 5 9 5 6 0 0 n m Fig. 12,4: I tangc of rcddish/greenish appcarencc inf ielcl on red backgror-rnd of 1_50 td. st imulus paramcters sub.jects u, 'cre ablc to slt istv this. judgn.rcntal cr i ter ion (and r-r-rade sctt inss thal are consonant with prcdict ions clcr ired l ior l thc Octant Model), they reported tbr certain st intulus parameters ( large surrounds. contrasts nol t()o high, predominantly in the clecrentental ckrrnuin) sceing a reddish ar-rd a greenish con-rporrc-nt sintultaneously. Figurc 12.,1 shows lor a typical cxperinrcnt thc range of dominant wavelcngths o1'the inf iclcl 11irr dif ferent intensit ies) within rvhich a ret lcl ish antl greenish color appearance (with a. in Katz's words, "curious labi l i ty of colors") is scc'n sinrultaneously (thc lef l curve iudicates thc lou,cr bor-rnd of redcl ish appearances of thc inf icld. the r ight curve the upper bor,rnd of greenish appcarances. in between are infields that appcar r-cddish ancl greenish simultaneously ) SLrbjects were not able to completelv canccl thc amount of redness at thc posit ion of the inl ' iel t l by tncreasing the grecr.r componcnt o1' t l ic inf icl t l . Therc seem to be two layers betr,r,een r',hich thet.c is no complete trade-of ' | I consiclcr t l -r is obsct.r,ution as a further ir-rdication that ccnter--sr-rrrouncl 'lIluminotion colctr' lutt,r l:a'::., Ret inul intcu. : i t t , l t r t l i l , ' : Fig. 12.5: Laminar sity prof i l . sl tuat of th co lo r ' poner two c 12.6. ! 2.O So ta l'ation area t IenllS heurir that s ration gerini natior lamin AS SO establ conje path ' . t lon scl1l l t l or ls I t i be ing the p, Segnlr servlt hcre. transl are st than IIeOUS sidert a figr uc lch Vcrän u,erde Figur. of scgnrentatiou o1' thc rct irr i t l intcn- -lns-ielrroJ uee.{\leq Ä1txe1druoc1o suotllsuell snon -urluo J c1u8t1se.tur,{11el1e luelsÄs LI€o e,ll s Lto tlulll -3r3uoc snlnlullsJo spur{ eseq} Sursq per-ue1qo st uorle-rnir3uoc.1o edÄ1-uer:puot\l E sloleu-rerp e8rc1 ,{,re,t q1,n selorJ -rol '1tos.lo sse:33.o puno:81oeq u lsureie Jc.\\oU e Jo 'sêeol-1o punorSlceq t lsuru8e lrn{ -lo er:rrcl e ',(es 'elqutesu leql stt.tolltld ol spl?ol oleruerp aql Sutsee:cuy 'suotlu:nBtiuoc edÄ1 -ll]jncs sc rllllulls osclll ol loJel I 'slql-lo esneceg ( 1 rclduqc Jo 0Z't '3rg ees) Surlured 1o e1,{1s Irlsruorsseldull-oeN eq] Jo ltteostuttuol sl uollel -n8rguoc snlnurrls cqt pe.{oldute ere suollelnpolu JrJur.rrorqJ pue JJUEIjlLLtnl qloq -]l puu punollns rql J() sJIrrJ .1ql Jo sJttJtrtulp llt?l.us ,{.rcn .tog 'r-unuqtlrnbc ure.rfr -per e ol tqino:q oq ol sutl qcrq,u uee.ri puu päl Jo :rnlxlru c-lo slslsuo..r pue suotlelnil.luo.l PunoJllls -JclueJ snocueSoruoq qlr.'\\ llletutledxc snot,lord Jrll ur se szls erues eql scLl plelJut JtlI '(uolletl€A lurleds .;o qtpt.,\\puuq Sutut5ep) relsullllp uteJ,Iec u 3o (suorlcesrolut Surpnlcco t{tr.&\) selc.rn Surddel -.relo Jo ernlJnlls Luopuel e Äq ue,tr8 sl punollns lllJo suorltlre,t letludsgo lnoXe1 leoulcuoe8 eq1 srxe uecrS-per oql Suole uollulnpoluJo seerSep eql iurr{:e,t ,(q pe,terqce sctlteueSoutoqut lerleds srxe e3u€urlunl cql 8uo1e uouelnporl.Jo seerScp eql 3urÄre,r. Äq pa,terqce setlteueSoutoqur lerleds s0lJlJuedoLtl -oqur lerlcads Jo uorlurrc^ letleds ;o qlpl.A\pueq : sreleir-r€ru0 n ul.{\ollo-+ eq1 3ur,(.rr,r. ,{q pelcnrlsuoc sr '(pletiut cqt tuo{ eouelsrp Sursuarcut-1o suotSer lelnuu? Jell€rrls l?re -Aos urq}l,{\ put 'Ä11eqo13) sclllulploor uuEruss€rD o8ere,te-ecnds elues oql eleq qJlq,tt 'spunoJJns snoueSoruoqur Ä11er1uds 1o ,{1ttue1 c (seluutp.tooc ruuerusselD Sutpuodse;roc eql,(q pezuelcereqo) punor.rns snoeucSoutoq qo€e loC 'pur1 3ur,uo11o3 eqtlo (treeros lU,) e uo peluescrd) suotle-rn8t3uoc 3o ccuenbes u Äq uorle:n8tJuoc uetlpuot\J o] suotl -ernBrluoc punorJns-reluec snoeueSouoq tuol.+ de8 eql c8puq o1 peldurelle a,{\ soipuv seuueqof qlr,^\ uorlt?roqello.r ur \lutr.utledxe io_satles e u; '.lrn;irJ se pl3l.J le -lleuls pesolcuc eql e,trcc:ed o1 Äouepuel ]ullulluop -ard e sr eioql pletl snoeucSouoq .rc3:u1 qcnul e Äq pepunor:ns st ezts llEtus Jo p1rr.1 snoeurFout -or-[ e arol-1,{\ suollunlls ut .(,, 1a8atpluatttnpung,,) ..,{\lll le]uetuepunJ,, e pollEr (6/ d 'lZO t ) ulqnu .. llul.rôrerl pun.rD slll sJrlrlJ.\\'ttlJp tttt sltl'.rnit'1 slu s€p 'Jplac |.uep ut puls Ltlusl.ll.\\ .lJl.ltlls 'tlip.lJ.\\ 'l.rcrsuedruo>1 aSurq .rcp aqJuil .tJp ttt i;-ttn.t:ptltl.r.-r1 cpueqn.rJq Suntqrntqcg ua8rq.tu.l IJLIlr.]lltl .lp rqrlJ,\\ qJrnp 'uJ.rollel tlJlll.tltlez trc;;-rul!:r11-r Utlp .. , leq,AA ol Surp.tocru'ut'r tlclueruits ptttlo.ln--a.lni1., tl 3urre33u1 .ro.I uorlenlls 1urrd,(1o1o.rcl otlt sll po.l.Pls -uoo oq ttec uotlern8t.lttoJ puno.t.tlls-.laltlJf, sn()Jtl -eSouoq eq1 ,,'punori sc po,rtcr.tad st ll .ll tlutll a;nir3 se pe,lrec-rcd st uc-rc ullll.tet tl.1t .tciuo.tls :l.tt: ,{cuelsuoc roloc.Jo uol]JJllp etll tll suotlltttl.tolsull.l'l teql pêresqo (9S'd'1761) urqnl,tpr:r.r1y'r.tcq ccuel:odrur Jo sr lEtll ,^ruclsttor :t)Ior. ittt.r.trs -qns surs lueqf, eut J tseq s.tei;t.tl lcql tlot ltllttrtttirs punorS-c:nfrr3 ulcueJ e -+o Jlltlll.l.J ltlnldrr.trcl rtll reqleJ lnq' uo tlcrnStluor ptll1o.l.llls-.laltla J tl n-u I JCI jo ,(1,rcdo:d lcctrleuoe8-ols.{qcl :rt1t lou sr }l 'seue0s llltlolstlJLtllp-Ja.ltll .lo stloll -en1rs ed,{1-utr.rpuol,\ oltl'srLlo lurt;-o1om-ttttcs qlr,\\ seuo xelduroc a.tortt {litttscl.l:tul lll.\ tloll -unlrs leutrurut srLll slJäuLloJ llltll 'a.lJ'\\ lt st: ",q1tld snonurluoc, e [[sllqe]sJ ol surl aLlo 'l.tu1l:rlttol snll Jo role.+ ur eseo Sutcut,ruol J.lottl t:l qsllqtrlsa ol repro ul 'eurl srql iuolt: trolluJlpttt aLtlos su pclerdrelut oq uef, ,{pea:1c tlollltltlotttil-irs it}ulttltll .]o uoueuloueqd e.,roqe qi rlitroql'.s.tolor Llollutl -ltunl1, puu .srolor lrefqt'r, .ro..1 ePor 1t,lnp tr iur.r:rl- -3rr1 :o; Ilnlluls letrtturLLt se peplt:;-:l.t itl tltl:t stlolltl.l -n8rguoc punor,nls-Jcluet snoluriottlotl tlrns ltql sr o;eq pcsodo.rd qctolddc cql i;-tttÄ1.r:lptrtl f,llsl.lllitr lerlue3 cql suorlnqrrlsrp .{8.tctta 1tl.rlrrcls.1tt sttt-t:11 ur snooueSouroq ''a'r 'Lulollttn {llttrlcds st lutll lla.lll ue cl1 spuodselloJ purlo-rlns etll tlJltl'\\ tll sllolll].I -n311uoc pullollns-roluJJ ol po.r.rJ.+i.l ,{1tto 1 .tt4 o5 suollBrn3!JuoJ adÄ1-lurnag lstuluIN u! 6Jolo) uollBultunlll. PUE .roloJ tralqo, Jo uorls8er8rs Z'9'Zl 'sttrotutdtttol o.ru aseq].ro.+ opoc roloJ lllltp ll ol cst.t :r,rti ptttl S al ernirg Xq polcJtput,(11t'tct.toqcltllrtr,r sl lttrttocl -LUOJ,l()l().1 UOI lI]tllttln I I l. ttu Pttt: lttltttrdtIl(]l ..1()l().1 lcefqo, ue olur ep.lord (ysuclul lltullJ.l Jtll lo uorlulueur8es Jeurutel u .reiir-r1,tpuo.r1n suolltlnlls >/crpoJ l€nq u 3urra33rr1 rol IIn[lt]S llltulutt\ se suotlurttFt3tlL).) Pl'lllol.lllS-.l.1ltlr.) 9 al 246 12. Colol Pcrception: Frotn Cirassman Codcs to a Dual Codc fbl Object and I l lumination ( olors Fig. 12.6: Seurat confignrations of intenncdiate bandwiclth of spatial variat ion of the sun'ouncl and of thc sarrrc sptrt ial ly-averaged chromatici t ies. rvi th spal ial urninance modulal ion incrcasing on the vcrttcul axis. anrl chr.ornrt ici ty ntoclulat ion incrcasing on the horizontai axis. t hc \ gs ' r i r 1 o o S r b c p t I ( }n ihr ' 1 ao.'l-,n lt tkr l l t t l l l to\\ i] orr1e \ \ c r t i r c s t i r c : thc I bo th Fo i . c . . r ari l ' s l.torr th r tn su f f ( su f f ( pr()p i l l l l t i l-r) t l l l g fL'e Lrp . i to\\ a l \ e f l F ig. l l l t t i r ror:nd type st imuli with a hortogencolls surround ancl Mondrian-type configuratior.rs and thcrcby study those physical propert ics of such configurations that lriggcr an intcrpretation in tcrn.rs ol the clcrnentary perceptual catcgories of 'ob.jcct color ' anc l ' i l l L r rn ina t ion co lo r ' . Fol an intcrmecliatc banclwidth of spatial variat ion of the surrouncl, FigLrre 12.6 sl iows typical conf isurations r.vith spatial I u rni nance rnodr_r I ation increasing on thc vert ical axis, and chromatici ty modr-r lat ion increasing on the horizontal axis. For al l r" cl isplays in this i igure thc space-averagc (lrassmann cocles ofthe surrounds arc identical to the ones of the hornogcncolrs surrouucl in the display in thc r-rpper lcft . According to tracl i t ional adaptational ntodels al l these st irnul i iue functional ly eclLrir ,alent. i .c.. ur.c cxpectccl to exhibit thc samc clTect on thc uniquc yel low sett ings at thc locatior.r of thc infrcld. A typical cxanrplc of a sin.rplc aclaptat iort nrodcl of a spacc-averaged von Krics-ty1'rc scnsit ir i1r ' control assulnes that rD(A,S) can bc unclcrstoocl irr t e m r s o f s o m e l i n e a r ' p o o l i n g n t c c l r a n i s n t ' Q,(S) I , w,, <p'(S(y1)), rvhelc S(y,) r lenotcs rhc spectral cnergy cl istr ibutions of the sur.r-ouncl a1 lhc location y;, and \\ '1; e [0. 1] are location-t lcpcndcnt weigl.rts (possibly clecreasing rvith distancc to thc inf iclcl), summing up to l . Whilc our r lata clcarlv reveal that in our Scurat-typc st intul i , surrorincls with eqr-ral spacc-averagcd ( irassr-nann coor-d i natcs grossly violale any fr-rnct ional cqr-r ivalcnce rr i th respccl to the r-Lniclue y l low sett ings o1'thc inf icld. 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Aleq ecuereJJrp eq1) 'p1eryut eqlJo sepoc roloc oIü roJ ecuerJelul ouecs eleurlxordde Sur,terqce 3o leo8 IeuorlcunJ eql 01 paleler eq u€c spunoJJns ]ueullu -nlosr roJ Sutputs oIIJ'(966I) IIêoqS T' sseuuef ,(q peurelqo ueeq seq slop ueer8 pue e1rq,r,r. esreds qll^\ plelJ punorS>1ceq per e roJ llnser r€llrils ,(1e,tr1e1r1enb V'punoJJns clleuroJqc€ pe8eJô€ -eceds e Jo punoJJns {JBp e Jo souo eq} spre/y\ol pepuel ,(18uorts Surlles .ro.o11e.{ nbrun eq1 'e't 'dn pe,lAoqs 1ce;ge gsoddo eq1 ,(1uo uorlelnporu ueerS -per lerleds 8uor1s qy.al (w31t 1'r, '8tg) punor -Jns lueurulnlosl ueJo os€c eql Joc 'Ouecs po]eulu -nlll ue se uorlernSr3:uoc eq] ]erdrelur o1 Älrsuedo:d qurels.{s l€nsr^ eql eseeJcul ol sruees punolJns eql uI sepoc roloc Jo ecuelI€^ pecnper v 'punorrns snoeueSouroq Surpuodseuoc oql roJ seuo eql ueql qlSuelerrervr re8uo1 sprertrol UIqs JeSuoIS e pe,l.roqs s3ur11es umrrqrlnbe ueerS-pe.r eqt .,(po uoIleIJÊ ecueurrunl lerleds pue uolleuê ueerS-pe; ou ''e't '\leI L'ZI '3rg) punorrns cll€tuortlcosl ue rod 'paxgl'e?ercrc lerleds eql Surdeel ellq.^d. 'sexe qloq 3uo1e .,(lsnoeuellntuls pue .,(1uo stxe ecueulrunl eql 3uo1e ',(po srxe ueerS-per eql 3uo1e punorJns oql pele1nporu.,(11epeds pue(.upc 6 :1) punorrns eql sB eJueurunl etues oql te pleuur eql ldel ,tlou eA\ 'pe,rreserd eq 01 lunrJqrlrnbe uearS-per e roJ JepJo ur 'uru ggg o1 ''3'e 'sq]3ue1err.e,t re8uol spre.r,rol pourqs äq ol speeu plorJur eqt -ro1 ql8uela,te,tr tueut -Luop eql '(-o gOS tes Jo q]8uele,\ê\ ]ueulwop e q1r,r,r.) punorms qslpper snoeueSouroq e ,{q pepuno: -ms sr'uru glggo qfuele,{e,^ lu?ulruop e q1r,Lr ''3 e '1ods 1sa1 ,Lto11e,{ enbrun e JI 'lxetuoc luese:d eql ur lsJrelur Jo äJB luql sllnsel ôllelllenb auos uotl -ueru .(geuq .,(po 11eqs 1 ',(leleredes peqsryqnd eq 11rrrr slueurrredxe Jno Jo goder peltlep e oculs '.ro[oJ uorleulunllt. pue ,.ro1or ltafqo. ot poleler seuo8elec lenldecred .fte1ueue1e go Suue8 -3rr1 e;o sIuJel uI uotlelerdrelut ue 1se33ns ,{eq1 LbZ epoJ IenC e 3urra33u1 .lo3: rlnrups I?urulr\l se suotlem8r;uoJ punolJns-lolueJ 9'ZI ,18 12 . Co lorPercept ion : Fror r rGrass tnanCodcs toaDua l Coc le lb rOb. jcc tapd l l lL r l r i r l r l i 6pC '6 l6 r .s Fcchner, G. T. ( 18,10). Übcr dic sutrjcct ivc Nlchbi l i lcr und Nebcnbilclcr. Pougendorff ' .s Aunir lcn clcr Physik und Chcmie.t/) , l t ) i 221:121 170. Forsy th . D. A . ( 1990) . ( 'o lour ( 'ons tancv . In : A. tslake and T. Tlosci lnko (Ecls.). AI lnci thc Evc (pn . 20 I 227t . ( l r ie l t cs rc r ' : \ \ i l c r . Fostcr ' , D. H. and Nascirrrcl t lo. S. N{. ( ' . ( l9g-+) Relat ional Clolour C't ' rnstatrcv f l-otn Irrvariant ( 'oncExcitat ion Ratios. Ploce-cdinss ol ' thc I lovl l S o c i e t y L o n d o n B : 5 7 , I l 5 l l l . Frurnkina, R. M. ( 1984). Colour.. N{clnins. i lncl Similari ty. Aspccts o1' Psycltol ineuist ic Atralvsis (User, cN,'rbrcJ'r, cxo/i tcrnoa). ( in l tuss.) I \4oscou: Nar-rka. Fuchs, W. (1923). Irxperintcntel lc LJrr lcrsuchungcn über das si l lul tanc Hintcrcinanclcr.se hcn aul 'dcrsclben Schrichtr.rng. Zeitschl i f i l i i r psvcholoeic 91. t45 235. Cielb. A. ( 1929). Dic 'Falbcnkonsranz' clcr Schdinsc In: A. Bcthe, Ci. r : Bcrgntann. ( i . l - .rnbclen. lncl A. E,l l inger (Eds.). Hanclbuch t lcr nonnalcn urrt l pa tho log ischcr . r Phvsro log ic . i ld . l l . l . l l i i l t r c . Rcceptronsorgane II (pp. Sq+ (r7l l) . I lcr. l in: Spriugcr.. Grassmann, H. (18-53). Zur l 'hcor. ic dcr Fitrhmischung. Poggendorff 's Annalcn t1cr. physi i i und Chenrie 89, 69 8zl. He lurho l tz , H . r ' . ( l9 l l ) . Handbuch dcr . phvs io lou i schcn Opt ik ( l .Ed . , 3 \b1 . . Eds . \ \ l Naec l . A . ( iu l l strancl J. i'. Krics). IJanrburg: \(rlil. I ler ing. E. ( 1888). Ucbel dic Thcoric t lcs sirnLrl t i rnc-r: Contrastes I 'on Helntholtz. l \ i Mitthci lung. I) ic sutrJectivc 'Trennung dcs Lichtcs in zuci cornpleurcn1äre Port ioncn. ' Pf1üger"s Archir ' f ' i i r . t l ic gcsanrntlc Physiologic des Mcnschcn uutl dcr Thicr.c J-1. I I L Hcr ing , E (1920) . G lun t lz i i sc dcr [ . chr .c ro r l Lichtsinn. Berl in: Springcr. Heyer , D . ( 1996) . The Rc la t ion o l ' ( 'onrnrs r ( 'o t l ing in the Octant Model and C)ltponent Proccssins: A thcoretical and Expcrinrental Ir trcst igatir tn. Tcchnicl l report, Inst i tute f i i r Psi icholosic. LJniver.sitr i t Kicl. H ippe l , A . r i ( 1880) . E in Fa l l von e insc i r igc r . . cor )scnitalcr Roth-Gri inbl indhcit bci nol.nlt lcnr I-arbcnsinn des ändcrcn Auges. Cini lcs Archir f i i r Ophtalnrologic 26, 176 186. I locheggcr, R. ( 1884). Dic seschichtl ichc l : lnr l icklung dcs Farbensinrres. lnnsbr-uck: \ /cr lag dcr Wagncr'schcn Universit l i tsbuchltandlung. Irwin, E,. (1974). C'oloul ' Tenls i tr ( ir .ccl i poctr.v. To |or r lo : Hakke | t . l ves . H. E . (1912) . The Rc la t ion [ ]c r *cer r rhc C 'o lo r o f the I l lun t inant and the C 'o lo r . o l ' the l l l u r r r in l t cd Objcc t . T ransac t ions o1 ' I l l un t ina t ing l ;ns inccr ing Society 7. 62 72. the fbrntat of innate semantic pcrceptual categorics of 'object color ' and ' i l lumination color,, rvhich in turn are intirnately interwoven with reprcsentations for elementaly perccptual categories for the representation of'surfaces, fbnr-r and space. According to this view, perceptual achievcments such as the segregati t ' rn o1'object and i l lurninant color are brought forth by the very organization ol the intcrnal rcpresentation of color rather than bcing cornpr"rtationally derived frorn properties of sensory inputs. This ref'lects the differcnce betwcen two diffcrent metaphors in perceptual theory: tr iggcring vs. computation. Acknowledgements I should l ike to thank Johannes Andres, Don Maclcod and Larry Maloney for their valuablc comments on an earlier draft of this paper. References Ahn, S .J . and Mac lcoc l , D . I .A . (1993) . L inkSpecific Adaptation in the Lurninance anc, Chron-ratic Channels. Vision Rcsearch -lJ, 2211 2286. Alpern, M., Kitahara, K., ancl Krantz, D. H. (1983) Perception of Coloul in Unilateral Tri tanopia. Journal o1-Physiology li , t , 683 697. Barlori , . I I . (1961 ). Possiblc Principles Underlying the Cotl ing of Sensory Messagcs. In: W Rosenbli th (Ed.), Serrsory communicarion (pp. 217 234). Cambridge, Mass.: MIT Press. Barlor 'v. H. (1982). What Causcs Trichromacy'/ A Tlicoretical Analysis Using Comb-Fil tered Spectra. Vision Rcsearch 22,635 643. Brt ickner, A. (1921). Zur Frage dcr Eichung von Farbsysterlen. Zeitschr. i f t 1ür Sinnes physiologie 5 8 . 3 2 2 3 6 2 . Br-rchsbaum. G. and Gottschalk. A. ( 1993). Trichromacy. Opponent Colours Coding and C)ptirnur-r-r Colour Information Transmission in the Rctirra. Proceedings of the Royal Society London 8 2 2 0 , 8 9 1 1 3 . Bühler, K. (1922). Die Erschcinungsrveiscn ler Farbcn. hr: K. Bühler (Ed.), Handbuch clcr psychologie. I . Tei l . 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J. and Valclon. .1. M. ( l t) l l ' l ) . Visutl Adaptation and Responsc Saturation. ln A. .1. Vln Doorn. W A. Van dc Cirind ancl J. .1. Kocndcrink (Eds.). Limits in pcrccptiorr. Utrecht: VNU Scicncc Press. West , G. and E l r i l l . M. l l . (1982) . Ncccssary and Sufl lcicnt Condit ions f or von Krics ( 'hronratic Adaptation to Give Colour Constancl ' . . lournal of Mathematical Biology 1-5, 249 25|i . Waetzold W. (1909). Das theoretischc unrl pmktischc Prob lem c le r Fr rbbcncnr r r r r rg . Zc i l sch l i l t l i i l A : r l rc t ik und al lgcmeine Kurrstrvissenschall . / . 149 199. Wyszeck i , C . , and St i les . W S. (1982) . Co lor Sc ience. Conccpts and Methods. Quanti tat ivc Datu and Formulae. (2nd Ed.). Nerv York: Wilcv.