计算机图形学colour-anonymous

ColorModel

1

Outline

□Introduction

□Spectraldistributions

□SimpleModelfortheVisualSystem

□SimpleModelforanEmitterSystem

□GeneratingPerceivableColors

□C1E-RGBColorMatchingFunctions

2

Outline

□CIE-RGBChromaticitySpace

□CIE-XYZChromaticitySpace

□ConvertingBetweenXYZandRGB

□ColorGamutsandUndjsnlayableColorsy

□Summaryrendering:WhatToDoIn业」''

Practice

3

PrimitivesofColor

Thedifferentvisual

lightspectrum

distribution

lllumina+ion

stimulatetheeyes

andcausethecolor・Reflec+ance

perception

SpectralDistributions

□Radiometry(radiantpower,radianceetc)

■Measurementoflightenergy

□Photometry(luminanceetc)

■Measurementincludingresponseofvisualsystem

□Kn(X)/Xspectra1radiantpowerdistribution

□GenerallyC(X)definesspectralcolordistribution

Xe[%%J=Ac

□Incomputergraspuhsiuca^l)lyradiance.

5

SpectrumCharacterofColor

700nm400nm

1041061081(TMO121O141016101

>frequency(Hz)

-I~I_I~I~I_Il~I~F-wavelength(nm)

10151013101110910710510310110-1104

11

>।1\'HA\1

AMradio/microwave\ultraviolet\gammarays

FMradio,TVinfraredx-rays

6

ColorandWaveLength

Mostlightweseeisnotjustasinglewavelength,

butacombinationofmanywavelengthslikebelow.

Thisprofileisoftenreferredtoasaspectrum,or

spectralpowerdistribution.

7

ColorAsSpectralDistributions

8

SpectrumEfficiencyCurve

Q

A

o

u

e

p

E

e

s

n

o

u

E

n

l

e

z

D

eI

d

9

HumanColorPerception

■TheHumanRetina

-Theeyeisbasicallyjustacamera

-Eachneuroniseitherarodoxacone.

-Rodsarenotsensitivetocolor,butthecones

are!

10

LightIntensityandBrightness

■Intensitydescriesthephysicalamountofenergy,

brightnessdescribesourperceptionofthisenergy;

■Ourperceptionoflightisfunctionofoureyes,

whichperformsnumerousunconscious

correctionsandmodifications.Forexample,the

equaldensitiesofcoloredlightareperceivedas

beingofdifferentbrightnessdependingonthe

color.

11

MonochromaticLight(PureColor)

□6(1)=0,九wOO

□f5(X)dX=1/

□Jb⑴f(x-t)dt=f(x)

□C(X)=5(X-Xo)isspectraldistributionforpure

colorwithwavelengthXo

12

VisibleSpectrum

13

收工INVISIBLE

SUN

SchematicRepresentation

ofColorSpectra

EARTH

ColorSpace

□Spaceofallvisiblecolor^^quivalenttosetof

allfunctionsC:A—R

■C(X)>OallXI-J

■C(X)>0someX(atleast

□(Cardinalityofthisspaceis2C)

15

Perceptionand

TheSixthSense5Movie

□Wedonot'see9C(X)directlybutasfiltered

throughvisualsystem.

□Twodifferentpeople/animalswil「see'<(R)

differently.

□DifferentC(九)scanappearexactlythesametoone

individual(metamer).

□(Ignoringall'higherlevefprocessing,which

basicallyindicates66weseewhatweexpecttosee").

16

InfinitetoFinite

□Colorspaceisinfinitedimensional

□Visualsystemfilterstheenergydistribution

throughafinitesetofchannels

□Constructsafinitesignalspace(retinallevel)

□Throughopticnervetohigherorderprocessing

(visualcortex).

17

ASimpleModelforVisualSystem

OPTIC

NERVE

HumanEyeSchematic18

PhotosensitiveReceptors

□Rods-130,000,000nightvision+

peripheral(scotopic)

□Cones-5-7,000,000,daylightvision+

acuity(onepointonly)(Photopic)

□Cones

19

LMSResponseCurves

□I=fc(X)L(X)dX

□m=fc(X)M(X)dX

□s=fC(X)S(X)dX

口C—(trichromati£jheory)

□LMS(C)=(l,m5)

□LMS(Ca)=LMS(Cb)thenCa,Cbare

metamers.

20

2-degreeconenormalised

responsecurves

D(

OU

cs—10

n10

o.20

)J',0

^0

Ao,8

usw.460

o20

'so

p0

匕

。o

d。.03

s456oo78

0000000000

wavelength(nm)

21

SimpleModelforanEmitter

System

□Generateschromaticlightbymixingstreams

ofenergyoflightofdifferentspectral

distributions

□Finitenumber(>=3)andindependent

22

Primaries（Basis）foranEmitter

□CE（九）=%E［仇）+a2E2（X）+（X3E3（九）

□Ejaretheprimaries（formabasis）

□以arecalled\h^^tensitiep

□CIE-RGBPrimariesare：

■ER仇）=5（X-，R）,九R=700nm

■EG（X）=3（九-九G），九G=546.Inm

■EB（X）=8（X-九B），九B=435.8nm

23

ComputingTheIntensities

□ForagivenC(X)problemistofindthe

intensities必suchthatCE(X)ismetamericto

CQ).

□FirstMethodtobeshownisn'tused,but

illustrativeoftheproblem.

24

ColorMatchingFunctions

□PreviousmethodreliedonknowingL,M,

andSresponsecurvesaccurately.

□Bettermethodbasedoncolormatching

functions.

□Definehowtogetthecolormatching

functions%Q)relativetoagivensystemof

primaries.

25

CIEColorMatchingExperiments

S

2

S

3

OdC

w

i

mi

OBSERVER

26

ColorMatchingExperiment

Mixingof3primaries

Targetcolor

overlap

Adjustintensitiestomatchthecolor

27

2-degreeRGBColorMatching

Functions

3o

.5

39o

2o

2.5o

A.0

1.5o

*so

u1.0

.5o

ol).0

u0.o

一0.

-0.50300350400450TOO550600650700750800

-1.00

wavelengthnm

28

ColorMetamer

Agivencolorthatweperceivedmatcheswith

unlimitedspectrumdistributions.Thisphenomenais

calledmetamer.Sothespectrumcannotbeusedas

coiorTneMcThestrategyistochoosethesimplist

spectrumtorepresentaspecificcolor.

29

___________RGBM2del

Acolorwecanperceivedcanbesynthesizedbyany

threepurecolorsthatmeetcertainrequirements.

Thesethreebasiccolorsarecalledprimitives.The

quiteoftenusedprimitivesareRed、Greenand

Blue。

30

⑴Colorspaceis3D,thethreestimulicanbe

dominantwavelength,saturation,and

intensity,orred,greenandblue；

(2)Anycolorcanberepresentedbytristimulus,

iftheyareredgreenandblue,then

C(C)=R(R)+G(G)+B(B)

31

H.GrassmannLaw

(3)Propertiesofcolormixingj

C3.1)iftwocolor

q(C)=R|(R)+O(G)+B[(B)

C2(C)=R2(R)+G2(G)+B2(B)aremixed,thentheresult

is：

C3(C)=(R1+R2)(R)+(G1+G2)(G)+(B1+B2)(B)

32

H.GrassmannLaw

C3.2)ifthetristimulusofcolorC(C)=

R(R)+G(G)+B(B)arescaledthesamektimes,then

thecolorwillalsobescaledktimes,thatis:

kC(C)=kR(R)+kG(G)+kB(B)

(3.3)ifC](Q=CCCJ,C2(C)=CfCJthen

C《)=C2(C)

(4Jthecolorspaceiscontinuous.33

C1E-RGBChromaticitySpace

□ConsiderCIE-RGBprimaries:

■ForeachC(X)thereisapoint(aR,aG,aB):

口

CQ)pOCRERQ)+aGEG(X)+aBEB(X)

■Consideringallsuchpossiblepoints

口(aR,aG,aB)

■Resultsin3DRGBcolorspace

■Hardtovisualisein3D

■soweMlfinda2Drepresentationinstead.

34

C1E-RGBChromaticitySpace

□Consider1stonlymonochromaticcolors：

■C(X)=3仇-九c)

□LettheCIE-RGBmatchingfunctionsbe

■rQ),gQ),b(九)厂

□Then,eg,(

■aR(X0)=f5(X-九0)r(X)dX=r(X0)'

□Generally

■(aR%),aG(Z0),aB(X0))=(r(X0),g&),b(X0))

35

C1E-RGBChromaticitySpace

□As九0variesoverallwavelengths

■(r(X0),g(X0),b(X0))sweepsouta3Dcurve.

□Thiscurvegivesthemetamerintensitiesfor

allmonochromaticcolors.

□Tovisualisethiscurve,conventionally

projectontotheplane

aR+aG+aB=1

36

C1E-RGBChromaticitySpace

□Itiseasytoshowthatprojectionof

(OIR,OCG,otB)onto+ocG+otB=1is：

■(0CR/D,01c/D,aB/D),

□D=aR+aG+aB

□Showthatinteriorandboundaryofthe

curvecorrespondtovisiblecolors.

□C1E-RGBchromaticityspace.

37

C1E-RGBChromaticityDiagram

38

C1E-RGBChromaticity

□Define:

■VQ)=bj(.+b2M(X)+b3S(X)

□Specificconstantsbjresultsin

■Spectralluminousefficiencycurve

□OverallresponseofvisualsystemtoC(X)

■L(C)=KfC(X)V(X)dX

□ForK=680lumens/watt,andCasradiance,

calledthemin(candelaspersquaremetre)

39

SpectralLuminousEfficiency

Function

40

8-8壬+D-y+fdH(D)q■

6□

YP(Y>(Y)司8:

ypsAsfujy+

YP(Y)>(sfuFdn§□

UOIIJL□

母

gd8H+SD山£+(Y)/"au■

□

。

—

2P二pluojlo8D&JU

LuminanceandChrominance

口L(C)=aRlR+aGlG+aBlB

■andlRlG1Bareconstants

□Considersetofall(aR,aG,aB)satisfyingthis

equation...

■aplaneofconstantluminanceinRGBspace

□OnlyonepointonplanecorrespondstocolorC

■sowhatisvarying?

□Chrominance

■Thepartofacolor(hue)abstractingawaythe

luminance

□color=chrominance+luminance(independent)

42

LuminanceandChrominance

□Considerplaneofconstantluminance

■OR+aG+apk=L

□Leta*=（a，，a%,a,））beapointonthisplane.

■（ta，，toe，，ta'%）,t>0isalinefrom0througha"

□Luminanceisincreasing（tL）butprojectionon

aR+aG+otB=1isthesame.

□ProjectiononaR+aG+aB=1isawayof

providing2Dcoordsystemforchrominance.

43

ChangeofBasis

□EandFaretwodifferentprimaries

■C(X)«oc1E](入)+a2E2(X)+a3E3(X)

■^(1)+32F2(x)+P3F3(X)

□LetAbethematrixthatexpressesFintermsofE

■FQ)=AEQ)

□Then

■oc=pA

■YEj(X)=XiyFi(X)(CMFs)

44

CalculateTheTristimulus

Thinkoverthequestionofhowtocalculatethe

tristimulusofanexperimentallight.Wecansee

fromthematchingexperimentthat,whenRGBis

usedtomatchagivenwavelengthpurelight,the

tristimulusaredetermined.Foranyexperiment

lightwitharbitraryspectrumdistribution,wecan

giveafactortoeverywavelengh,andthensum

thethreestimuli.

45

Calculatethetristimulus

R=f：P(2)r-(2)J2=Z770P(2)r―(2)

G=C：7V)g-----⑷曲大尸770(㈤-g----(㈤

-770―

B=J8：P(2)Z?(2)J2=ZP(2)/;(2)

46

ExampleofColorCalculation

43.10

-

n

t

e

n

s

t一

y

1

0.8263

0.6027

380460540620700

435.8546.1700

wavelength47

ExampleofColorCalculation

R=尸(435.8)/(435.8)+尸(546.1)・r(546.1)+P(700)-r(700)

G=P(435.8)•g(435.8)+P(546.1)•g(546.1)+P(700)-g(700)

B=P(435.8)•b(435.8)+P(546.1)・仇546.1)+P(700)・3(700)

即

7?=43.10x0.0232=1

G=0.8263xL2102=l

5=0.6027x1.6592=1

CalculateIntensity

y=P(435.8)-V(435.8)

+尸(546.1)・V(546.1)

A

O

M

+P(700)-7(700)O

I

O

E

O

s

=0.6027x0.01779n

o

c

E-

+0.8263x0.9834z

、4

/

4M

-o

+43.10x0.0041aQ

=12

00i।--------1--------11r-...........I

1300400500600700800

Wavelengtti(nm)

HSVModel

Whenweusethewavelength,theproportion

ofwhitelightinthegivenlight,theintensityto

describeacolor,acolorsystemofHSVCHug,

50

CIEColorSpace

Inordertoachievearepresentationwhichusesonlypositivemixingcoefficients,

theCIE("CommissionInternationaled'Eclairage")definedthreenewhypothetical

lightsources,x,y,andz,whichyieldpositivematchingcurves：

•Definedin1931todescribethefullspaceofperceptiblecolors

•Revisionsnowusedbycolorprofessionals

•Cannotproducetheprimaries-neednegativelight!

C1E-XYZChromaticitySpace

□CIE-RGBrepresentationnotideal

■colorsoutside1stquadrantnotachievable

■NegativeCMFfunctionranges

□CIEderivedadifferentXYZbasiswithbetter

mathamaticalbehaviour

■X(九)，Y(九)，Z(X)basisfunctions(imaginaryprimaries)

■X,Zhavezeroluminance

■CMFforYisspectralluminousefficiencyfunctionV

□KnownmatrixAfortransformationtoCIE-RGB

52

C1E-RGBChromaticityDiagram

53

CIE-XYZSystem

■CIE-RGBhasnegtivecoordinates;

■ChooseaXYZtriangletosurroundallthe

spectrumcurves;

■Makethesidesclosewithspectrumcurves;

■ChooseprimitiveYtorepresentintentsity;

54

CIEChromaticityDiagram

■Normalized

AmountsofXand

YforColorsin

VisibleSpectrum

55

C1E-XYZSpace

■Irregular3Dvolumeshapeis

difficulttounderstand

■Chromaticitydiagram(the

samecolorofthevarying

intensity,Y,shouldallendup

atthesamepoint)

x—____x____

X+Y+Z

Y

y~

X+Y+Z

56

CIEXYZChromaticityCoordinates

x

X+Y+Z

y

x+y+z

z

x+Y+z

57

UseCIEChromaticityDiagram

ToDetermineaColor

Tonguelikecontourlinerepresentsallthevisible

lights'wavelengthtrails,thefigurebesidethe

contouristhewavelengthofthevisiblelight.The

linesegmentthatconnectsthetwoendsofthetrailis

calledpurpleline,representsthemixedcolorthat

synthesizedbythepurelightsatthetwoends.The

areainsidethetonguerepresentsallthecolorsthat

canbeproducedbythereallight.Thenormalized

whitelightlocateat(0.333,0.333J.

58

CalculateUsingCIE

Chromaticitypiagram

UseCIEchromaticityDiagramcalculatethe

dominantwavelength;

■Calculatesaturation;

Determinethecolor-givetheintensityY;

59

ExampleofCalculation

Let。］（玉，y，乂），02（%2,为，毛）themixedcolor

C12（%12,必2,乂2）isG2=（X1+X2）+（Y+H）+（Z]+Z2）

thenbasedonthex,y,zequeation.wederive

thecoordinatesofC12：

玉7]+xj?yZ+2

X\2,>12

T^T2

60

CIEChromaticityDiagram

Define三院司用忠阁辱率=&stenni隹

©OIOF◎。国BlernentarvDomff喀郡的触普揖厢出

GamutsandPs拄犀

61

CalculateXYZtristimulus

7-----770-----

xIf80°P(2)x(2)t/2=EP(2)x(2)

■：0PU)yU)-----〃=#Q7)70y(9------

z=篮尸⑷-z---(2)"=Z770P(2)z----(-2)

62

CalculateMatchingFunction

■Howtocalculatecolormatching

functionx(X),y(X),z(九)?

63

寸

I9

U2o

O«l!—

W;+-p>

s

U二

o

S

RU』

Oq

YJ

Uo

3-j

So

J

1U

oU

S

PJO(((

dI

一NNN

gQ①)))

4.z

II>2Z

e

PU+++

x」q

(((

2J7(

NNN

①e①))))

m

。p(

S(((

u

P」①S+++

(

s(二;(

3NN——(

NON

))))

二U

，XKH

>SHK

oOI

PeH'PH"

j(J』((

D、

NON7

)))

uJoO2/

i£s。(

CalculateMatchingFunction

FromEquation:y(2)=V(2),weobtain:

7(2)=受4)V(A)

y(4)

7(^)=v(2)

Z(A)=Z(A)V(2)

y(2)

65

2-degXYZColorMatching

Functions

2

1.5

1

0.5

o

300

-0.5

wavelengthnm

66

C1E-XYZChromaticitySpace

□CQ)2X.X(X)+Y.Y(九)+乙Z(九)

■X=fC(X)x(X)dX

■Y=fC(X)y(X)dX[luminance]

■Z=fC(X)z(X)dX

■x,y,zaretheCMFs

67

YSystem:EBU(PAL/SECAM)

Primaryilluminants(X,Y)

0.9Red:0,6400,0,3300

Green:0,2900,0,6000

Blue:0.1500,0.0600

0.8一point(X,Y):0327,0.3221

51fl

0.7

CIE-XYZ505

Chromaticity0.6

Diagram

0.5

0.3

0.2

0.1

ConvertingBetweenXYZandRGB

□SystemhasprimariesRQ),G(X),BQ)

□Howtoconvertbetweenacolorexpressedin

RGBandviceversa?

□Derivation...

69

ColorGamutsand

Undisplayablecolors

□DisplayhasRGBprimaries,withcorresponding

XYZcolorsCR,CG,CB

□ChromaticitiescR,cG,cBwillformtriangleon

CIE-XYZdiagram

□Allpointsinthetrianglearedisplayablecolors

■formingthecolorgamut

70

SomeColorGamuts

00.40.8

ClEx

UndisplayableColors

□SupposeXYZcolorcomputed,butnot

displayable?

□Terminology

■Dominantwavelength

■Saturation

72

ColorMightNotBeDisplayable

□Fallsoutsideofthetriangle(itschromaticity

notdisplayableonthisdevice)

■Mightdesaturateit,moveitalonglineQWuntil

insidegamut(sodominantwavelengthinvariant)

□colorwithluminanceoutsideofdisplayable

range.

■ClipvectorthroughtheorigintotheRGBcube

(chrominanceinvariant)

73

XYZW什hWh什ePoint

ForcoloratP

•Qdominantwave

•WP/WQsaturation

RGBcolorCube

white

sreen

75

RGBCubeMappedtoXYZSpace

RGBfXYZConversion

■Nowdeterminethelineartransformationwhich

mapsRGBtristimulusvaluestoXYZvalues.

■Thismatrixisdifferentforeachmonitor(i.e.

differentmonitorphosphors).

■Monitorshaveafiniteluminancerange(typically100

cd/m2),whereasXYZspaceisunbounded

■Needtobeconcernedwiththedisplayofbright

sources(e.g.thesun)

■tonemapping:reproducingtheimpressionofbrightness

onadeviceoflimitedluminancebandwidth.

77

RGBfXYZConversion

RecalllinearrelationshipbetweenXYZandRGB

spaces:

x“11ai3R

Ya22G

zB

■Linearsystemcanbesolvedifpositionsof3colors

areknowninbothspaces.

■Sometimesmanufacturersprovidetristimulus

valuesformonitorphosphors=(Xr,Yr,Zr)(X,Y,

Zg)痴Yb，Zb)78

RGBfXYZConversion

■Solutionofthelinearsystem:

Note:「尺[「i[「X[

G=0nY=匕

B0ZZr

■...andsimilarlyforG=1andB=1.79

XYZfRGBConversion

■Theoppositetransformationisgivenbythe

inverseoftheoriginalRGBtoXYZmatrix:

°XYZ=MRGBTXYZCRGB

CRGB~MRGBfXYZ^XYZ

■WecanthusdetermineanRGBvalue

associatedwiththeXYZvaluedetermined

earlierfromF(l)

80

XYZfRGBConversion

■UsuallyXYZtristimulusvaluesforeachphosphor

notprovided.

■Manufacturersprovidethechromaticityco­

ordinatesofthephosphorsandthewhitepoint

(colorwhenR=G=B=1):

（%，%）（乙，几）（/，%）（/，凡）

■...finallyweneedtoknowtheluminanceofthe

whitepointgivenasYw

V

Let纥=+匕+nxr=--

Er

^Xr=xrErYr=yrErZr=(l-xr-yr)Er

XYZfRGBConversion

■Similarconditionsholdfor(Xg,Yg,Zg)and

阳，丫〃ZJ

■ThereforetheonlyunknownsareE,Eand

一rog

E

X\rXgEgxhEhR

y=yrErybEhG

Z」［_(l-xr-yr)Er(1—与―儿)纥(1—%一券闽

X.1

■...butwealsorequirethat:匕M1

z”,1

82

XYZfRGBConversion

■Firstweneedtodetermine(Xw,Yw,Zw)

given鼠，yw,Yw)：

匕Y

=Xw+%+Zw=-

x卬+%+z卬几

X

4=>Xw="(Xw+%+zJ

Xw+匕+Zw

YY

and

・..alsoZw=(l-xw-yw)^

ywyw

83

XYZfRGBConversion

■TodeterminevaluesforEr,EgandEbweobservethat

Xg

X「xX",

ifR+G+B=Wthen+y.+

yr4匕

0ZgZgZ”,

•••Xw=Xr+Xg+Xb=xrEr+XgEg+xbEb

...andsimilarlyforYwandZwleadingtoanewlinear

systeminnounknownsthereforewecansolveforEr,

「Xx

EgandEb:xw%b

Eg

匕%yb

xxEb

Zw0-r0~g~yg）（1一4一%）

84

SharingColorsBetweenMon什ors

■Ifwewishtoguaranteethatacoloronmonitor1

looksthesameasonmonitor