cs380: introduction to computer graphics color (2) chapter ... · 18/05/17 1 min h. kim (kaist)...
TRANSCRIPT
18/05/17
1
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
CS380:IntroductiontoComputerGraphicsColor(2)Chapter19
MinH.KimKAISTSchoolofComputing
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
SUMMARYColor(1)
2
18/05/17
2
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorBases• Wecaninsertany(nonsingular)3-by-3matrixManditsinversetoobtain:
3
!c(l(λ))= !c(l436)!c(l546)
!c(l700)⎡⎣
⎤⎦M
−1( ) Mk436(λ)l(λ)dλΩ∫k546(λ)l(λ)dλΩ∫k700(λ)l(λ)dλΩ∫
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
⎛
⎝
⎜⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟⎟
=!c1!c2!c3
⎡⎣
⎤⎦
k1(λ)l(λ)dλΩ∫k2(λ)l(λ)dλΩ∫k3(λ)l(λ)dλΩ∫
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorBases• Wherethedescribeanewcolorbasisdefinedas
• Thek(λ)functionsformthenewassociatedmatchingfunctions,definedby:
4
!c1!c2!c3
⎡⎣
⎤⎦=
!c(l436)!c(l546)
!c(l700)⎡⎣
⎤⎦M
−1 ci
k1(λ)k2(λ)k3(λ)
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
=Mk436(λ)k546(λ)k700(λ)
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
18/05/17
3
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Howdoescomputationwork?
• Illuminationonasurfacecolor(element-by-elementproduct)
• Reflectedcolor
• ThreeCMFsforXYZ
• Trichromaticresponseasscalar(sumofenergy)
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
COLOR(2)Chapter19
6
18/05/17
4
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
RememberThisColor
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Mapofcolorspace(lassocurve)
8
LassocurveinLMScoordinates
NormalizedlassocurveinLMScoordinates
18/05/17
5
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Mapofcolorspace(lassocurve)• Asweletλvary,suchvectorswilltraceoutalassocurveinspace.
• Thelassocurveliescompletelyinthepositiveoctantsinceallresponsesarepositive.
• Thecurvebothstartsandendsattheoriginsincetheseextremewavelengthsareattheboundariesofthevisibleregion,beyondwhichtheresponsesarezero.
• ThecurvespendsashorttimeontheSaxis(shownwithbluetintedpoints)
9
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Mixedinvisible• Aswelookatallpossiblemixedbeams,the
resultingcoordinatessweepoutsomesetofvectorsin3Dspace.
• Sincecanbeanypositivefunction,thesweptsetiscomprisedofallpositivelinearcombinationsofvectorsonthelassocurve.
• Thus,thesweptsetistheconvexconeoverthelassocurve,whichwecallthecolorcone.
• Vectorsinsidetheconerepresentactualachievablecolorsensations.
• Vectorsoutsidethecone,suchastheverticalaxisdonotarisethesensationfromanyactuallightbeam,whetherpure(monochromatic)orcomposite
10
l(λ)[L,M ,S]t
l(λ)
18/05/17
6
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
CIEXYZcolorspacein3D• Centralstandardizedspace.• Specifiedbythethreematchingfunctionscalled
• Thecoordinatesforsomecolor(aspectrum)withrespecttothisbasisisgivenbyacoordinatevectorthatwecall.
• Theseparticularmatchingfunctionswerechosensuchthattheyarealwayspositive,andsothattheY-coordinateofacolorpresentsitsoverallperceived“luminance”.ThusYisoftenusedasablackandwhiterepresentationofthecolor.
• Theassociatedbasisismadeupofthreeimaginarycolors;theaxesareoutsideofthecolorcone. 11
kx(λ),ky(λ)andkz(λ)
[X ,Y ,Z ]t
[cx ,cy ,cz ]
t
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
HowtocomputeCIEXYZ
• Emittingcolors(radiance)– SincewehavethespectralpowerdistributionsofradianceL(powerperwavelength)
X =Km L(λ)x(λ)Δλλ
∑ ,
Y =Km L(λ)y(λ)Δλ ,λ
∑
Z =Km L(λ)z(λ)Δλ ,λ
∑
whereKm = 683lm/W .– HeretheYvaluecorrespondstoluminance(cd/sqm)
Noticethedifference!
18/05/17
7
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
RECAP:CIEXYZcomputation
• Illuminationonasurfacecolor(element-by-elementproduct)
• Reflectedcolor
• ThreeCMFsforXYZ
• Trichromaticresponseasscalar(sumofenergy)X Y
Z
CIECMFs
Reflection
ReflectanceIllumination
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Reflectionmodeling• Whenabeamoflightfromanilluminationsourcehitsasurfaceofareflectancefunction
• Thismultiplicationhappensonaper-wavelengthbasis.Metamerismhappensinourbrain.
• A3Dcolorrenderingcannothandlethis;instead,weneedtousemultispectralorhyperspectralrendering.
14
i(λ)r(λ)
l(λ) = i(λ)r(λ)
!c[i1(λ)ra(λ)]=
!c[i1(λ)rb(λ)]⇔ !c[i2(λ)ra(λ)]=!c[i2(λ)rb(λ)]
18/05/17
8
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
HowtocomputeCIEXYZ
• Relativereflectivecolors– SincewehavethespectralpowerdistributionsofilluminationIandsurfacereflectanceR
X =k I(λ)R(λ)x(λ)Δλλ
∑ ,
Y =k I(λ)R(λ)y(λ)Δλ ,λ
∑
Z =k I(λ)R(λ)z(λ)Δλ ,λ
∑
wherek = 100I(λ)y(λ)Δλ
λ
∑. NotethereisnoR(λ)inthedenominator!
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Chromaticityxyin2D• 2Dplotforchromaticinformation• What’sleftafterluminanceisfactoredout(thecolorwithoutregardforoverallluminance),thereforecommonlycoupledwithY
x = XX +Y + Z
,
y = YX +Y + Z
,
z = ZX +Y + Z
,
x + y + z = 1
18/05/17
9
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Chromaticityxyin2D• Scalesofvectorsintheconecorrespondtobrightnesschangesinourperceivedcolorsensation,soletsnormalizebyscale.
17
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Chromaticityxyin2D
• Spectrallocus– lassoin2D– Plotmonochromaticlightsinthevisiblespectrum(400-700nm)
• Isthisdiagramperfectforrepresentingcolors?
18/05/17
10
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
UniformChromaticityu’v’
• Chromaticityxyismathematicallyconvenient,notsuitableforevaluatingcolorinformationduetonon-uniformity
CIE1931xy CIE1976u’v’
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
UniformChromaticityu’v’
• CIT1976chromaticitycoordinatesu’v’• aregivenby
u ' = 4X / (X +15Y + 3Z )= 4x / (−2x +12y + 3)
v ' = 9Y / (X +15Y + 3Z )= 9y / (−2x +12y + 3)
18/05/17
11
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
CorrelatedColorTemperaturein1D
• Real-worldilluminantcanbeapproximatedasacolortemperatureofPlanckianblackbodyradiation(=thesun)
• Theclosestcolortemperatureontheblackbodylocusofthereal-worldilluminantiscalledcorrelatedcolortemperature(CCT)
• Unit:Kelvin
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
DeviceDependentColorSpaces• Exampe:RGBvalues• Pros:– Simpledescriptionofcolorforthedevice
– Natural,easywaytospecifycolortotheuser
• Cons:– Cannotcomparecolorsbetweendevices
– Notperceptuallyuniform
18/05/17
12
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Perceptualcolorspacein3D• WeonlydrawcolorsinthegamutoftheRGBmonitor
• Colorsalongtheboundaryoftheconearevividandareperceivedas“saturated”.
• Aswecirclearoundtheboundary,wemovethroughthedifferent“hues”ofcolor.
• StartingfromtheLaxis,wemovealongtherainbowcolorsfromredtogreentoviolet.– Achievablebymonochromaticbeams.
23
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Perceptualcolorspacesin3D• Colorcone’sboundaryhasaplanarwedge(alinesegmentinthe2Dfigure).– Thecolorsonthiswedgearethepinksandpurples.– Theydonotappearintherainbowandcanonlybeachievedbyappropriatelycombiningbeamsofredandviolet.
• Aswemoveinfromtheboundarytowardsthecentralregionofthecone,thecolors,whilemaintainingtheirhue,de-saturate,becomingpastelandeventuallygrayishorwhitish.
24
18/05/17
13
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
DeviceIndependentColorSpaces
• Pros:– Basedonhumanvisualperception– Colorspecificationindependentofdevice– Interchangeablecoloramongdevices– Comparison,computationofsmallcolordifferences
• Cons:– CIEXYZ:notuniform– CIELAB,CIELUV,CIEXYZ,Munsell:alldependentontheilluminant
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Perceptualcolorspacesin3D• Uniformperceptualdistanceofdifferentcolors
• Opponentprimaries• Threedimensions:lightness,colorfulness,andhue(L,C,H)
• Relatedtoprocessesofhumanvisualperception
• Meaningfulwayofdescribingcolor
18/05/17
14
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
HSVColorSpace• notperceptuallydriven!• Value:
• Saturation:• Hue:
V = M = max(R,G,B).
m = min(R,G,B),C = M −m,S = C /V ,
H =360 + 60(G − B) /C if M = R120 + 60(B − R) /C240 + 60(R −G) /C
if M = Gif M = B
⎧
⎨⎪
⎩⎪
JacobRu
s
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
MunsellSystem(1915)• Fiveprimaryhues:• Valuerange:• Chromarange:
YellowRed Green Blue Purple
…0 5 … ∞
10RP4/10=aspecificreddishpurplehueof10RP,avalueof4,andachromaof10
… 105…0
18/05/17
15
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
CIEUniformColorSpaces(1976)• OriginatedfromHunterLab1948• Perceptuallyuniformcolordefinition
• DrivenfromCIEXYZ
L*=43.31a*=47.63b*=14.12
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
CIELABMath• Simplifiedconeresponse(XYZandacubicrootfunc.)• Coloropponenttheoryforcomputingchromaandhue• Lightness:• Coloropponents:
• Chroma:• Hue:
L* =116 f (Y /Yn)−16,a* = 500[ f (X / Xn )− f (Y /Yn )],
b* = 200[ f (Y /Yn )− f (Z / Zn )],
Cab* = (a*)2 + (b*)2 ,
hab = tan−1(b* / a*).
f (x) = x1/3, x > 0.0088567.787x +16 /116, x ≤ 0.008856
⎧⎨⎪
⎩⎪
18/05/17
16
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
RememberThisColor
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorDifferences
• ConventionalEuclideanmetricinaperceptuallyuniformcolorspace(CIELAB)
ΔEab* = ΔL*( )2 + Δa*( )2 + Δb*( )2
CIE ΔEab*
L*
b*
a*
18/05/17
17
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
sRGBcolorspace• ThereareavarietyofRGBstandards.• CurrentoneiscalledRec.709RGBspace(so-calledsRGB).
• Basisismadeupofthreeactualcolorsintendedtomatchthecolorsofthethreephosphorsofanidealmonitor/TVCRT(cathoderaytube)display.
• Colorswithnon-negativeRGBcoordinatescanbeproducedonamonitorandaresaidtolieinsidethegamutofthecolorspace.Thesecolorsareinthefirstoctantofthefigure.
33
[cr ,cg ,cb ]
t
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
sRGBvs.Pointer’sgamut• SomeactualcolorslieoutsidethesRGBgamut.
• Additionally,onamonitor,eachphosphormaxesoutat“1”,whichalsolimitstheachievableoutputs.
• Imageswithcolorsoutsidethegamutneedsomekindofmapping/clippingtokeepinthegamut,so-calledgamutmapping.
34
Rec.709/sRGBvs.Pointer’sgamut(69.4%ofPointer’sgamut)
http://www.tftcentral.co.uk/articles/pointers_gamut.htm
18/05/17
18
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
XYZvs.sRGB
35
CIEXYZ sRGB
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Gammacorrection
• InheritedfromthetonereproductioncurveoftheCRTphosphors
• Tocompensatenon-linearresponse(^2.2)ofthedisplay,apply(^1/2.2)tothedisplaysignals(sRGB)
• Computationalredundancy(replacedwithLUT)
• RemovedfromHDTVsignals
18/05/17
19
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Gammacorrection• Eachpixelonadisplayisdrivenbythreevoltages,say.
• Lettingtheoutgoinglightfromthispixelhaveacolorwithcoordinates
• Wewanttoobtainsomespecificoutputfromapixel,thenweneedtodriveitwithvoltages:
• valuesarecalledthegammacorrectedRGBcoordiantes.
37
( ′R , ′G , ′B )
[R,G,B]t
R=( ʹR )2.2 ,G =( ʹG )2.2 ,B =( ʹB )2.2
[R,G,B]t
ʹR =(R)0.45 , ʹG =(G)0.45 , ʹB =(B)0.45
[ ′R , ′G , ′B ]t
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Gammacorrection• Linearvs.gamma-corrected
38
Linear
Gamma-corrected
18/05/17
20
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
NonlinearSRGBtolinearXYZ?
• (Step1)NormalizeRGBvalues• (Step2)Inversegammacorrection(γ=2.2)
• (Step3)TransformationfromsRGBtoCIEXYZ• sRGBàXYZ
• (cf)Inv.Trans:XYZàsRGB
XYZ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥=
0.4124 0.3576 0.18050.2126 0.7152 0.07220.0193 0.1192 0.9505
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
RGB
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
RGB
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥=
3.2406 −1.5372 −0.4986−0.9689 1.8758 0.04150.0557 −0.2040 1.0570
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
XYZ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
R=( ʹR )2.2 ,G =( ʹG )2.2 ,B =( ʹB )2.2
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Quantization• sRGBcoordinatesareintherealrange[0…1]• Afixedpointrepresentationisusedwithvalues[0…255](8-bitcolor)àunsignedcharinC
40
(realàbyte)byteR=round(realR*255);(byteàreal)realR=byteR/255.0;
(realàbyte)byteR=round(realR>=1.0?255:(realR*256)–0.5);(byteàreal)realR=(byteR+0.5)/256.0;e.g.:(realàbyte)0=round(0.7–0.5);1=round(1.0–0.5)
18/05/17
21
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorsinGLSL• Imagesaretypicallystoredingammacorrectedcoordinates,andthemonitorscreenisexpectingcolorsingammacorrectedcoordinates.
• Computergraphicssimulatesprocessesthatarelinearlyrelatedtolightbeams.Assuch,mostcomputergraphicscomputationsshouldbedoneinalinearcolorrepresentation.
• Inprofessionalcomputergraphics,weuselinearHDRradianceintheformatofOpenEXR
41
[R,G,B]t
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorsinGLSL• ByusingthecallglEnable(GL_FRAMEBUFF_SRGB),• Wecanpasslinearvaluesoutfromthefragmentshader,andtheywillbegammacorrectedintothesRGBformatbeforebeingsenttothescreen.
• glTexImage2D(GL_TEXTURE_2D,0,GL_SRGB,twidth,theight,0,GL_RGB,GL_UNSIGNED_BYTE,pixdata)
• Then,wheneverthistextureisaccessedinafragmentshader,thedataisfirstconvertedtolinearcoordinatesbeforegiventotheshader.
42
[R,G,B]t
[R,G,B]t
18/05/17
22
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Colorconstancy• Althoughthespectralpowerdistributionofsceneilluminationchanges,wecanperceivecolors(reflective)consistently,so-calledcolorconstancy
• Thisvisualphenomenonisimplementedaswhitebalancingindigitalcameras.
• ThisisoftenimplementedasavonKriestransformintheLMSorXYZspacefromagivenilluminationtoatargetillumination.
43
i1(λ)i2 (λ)
M =
L2 /L1 0 00 M2 /M1 00 0 S2 /S1
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
whereL1 ,M1 ,S1 aretheconeresponsesundergiveni1(λ),L2 ,M2 ,S2 aretheconeresponsesundertargeti2(λ).
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Colorimetriccalculation
• AllcolorimetricvaluesarecomputedfromCIEXYZ
Radiance Reflectance CIEXYZ CIELuv
CIELAB
xy
sRGB
Drgb
Energyperunitareapersolidangle
Energyatagivenangle,relativetoenergyreflectedbyperfectdiffuser
Relativeamountsofthreeimaginaryprimariesrequiredtomatchthecolorappearance
18/05/17
23
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproduction• Imaginewehaveaspectrums;wanttomatchonRGBdisplay
• Practically,wecannotachieveaphysicallyidenticalspectrumbecausetheyaredifferentmedia
• Butcouldfindaspectrumsathatthedisplaycanproduce,whichisametamerofs
ssa
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproductionasLinearAlgebra
• WewanttocomputesathecombinationofR,G,B
• whichwillprojecttothesamevisualresponseass
• sawillbeametamerofs
RGB
XYZ
Spanofeye’sspectralresponsefunctions
Spanofdisplay’sprimaries
Adap
tedfrom
SteveM
arschn
er
Visualresponsetosandsa
Spectrums
Spectrumsa C
V
18/05/17
24
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproductionasLinearAlgebra
• Theprojectionontothethreeresponsefunctionscanbewritteninamatrixform:
• or,
XYZ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥= rX rY
rZ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
s
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥.
SpectralresponsivityofXYZ
V = MXYZs.
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproductionasLinearAlgebra
• ThespectrumthatisproducedbythedisplayforthecolorsignalsR,G,Bis:
• Againthediscreteformcanbewrittenasamatrix:
• or,
Sa (λ) = Rsr (λ)+Gsg (λ)+ Bsb (λ).
sa
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥=
sR sG sB
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
RGB
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥.
sa = MRGBC.SpectraofRGBphosphors
18/05/17
25
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproductionasLinearAlgebra
• Whatcolordoweseewhenwelookatthedisplay?
• FeedC(R,G,B)todisplay• Displayproducessa• EyeslookatsaandproduceV
V = MXYZMRGBC.
XYZ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥=
rX ⋅ sR rX ⋅ sG rX ⋅ sBrY ⋅ sR rY ⋅ sG rY ⋅ sBrZ ⋅ sR rZ ⋅ sG rZ ⋅ sB
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
RGB
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥.
RGB
XYZ
saC
V
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproductionasLinearAlgebra
• Goalofreproduction:visualresponsetosandsaisthesame:
• Substitutingintheexpressionforsa,
MXYZ s = MXYZ sa .
MXYZ s = MXYZMRGBC.
C = (MXYZMRGB )−1MXYZ s.
Colorreproductionmodelfordisplay
RGB
XYZ sa≈s
s
saC
V
18/05/17
26
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
ColorReproductionasLinearAlgebra
RGB
XYZ
Spanofeye’sspectralresponsefunctions
Spanofdisplay’sprimaries
Visualresponsetosandsa
Spectrums
Spectrumsa C
V
MinH.Kim(KAIST) Foundationsof3DComputerGraphics,S.Gortler,MITPress,2012
Wherearethecolortransforms?
• Nowadays,ineverydigitalimagingdevices:– TV,digitalcameras,camcorders,inkjetprinters,laserprinters,LCDdisplays,etc…
• Otherwise…
≠