Color and Color Models

Einführung in Visual Computing 186.822

Werner Purgathofer

Color problem specification light and perception colilorime try device color systems color ordering systems color symbolism

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1 Color - Why Do We Care? Computer Graphics is all about the generation and the manipulation of color images proper understanding and handling of color is necessary at every step

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What is Light? “light” = narrow frequency band of electromagnetic spectrum red border: 380 THz ≈ 780 nm violet border: 780 THz ≈ 380 nm visible radio radio d TV rared raviolet rays icrowaves f t t M M - - M M ……n n F a in A m ul X

wavelength 1016 1014 1012 1010 108 106 104 102 100 10-2 (nm)

102 104 106 108 1010 1012 1014 1016 1018 1020 frequency (Hz) Werner Purgathofer 3

2 Light - An Electromagnetic Wave light is electromagnetic energy monochrome light can be described either by freqqyuency f or wavelen gth  c =  f (c = speed of light) E t shorter wavelength equals higher frequency 

red  700 nm violet  400 nm

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Light – Spectrum normally, a ray of light contains many different waves with individual frequencies the associated distribution of wavelength intensities per wavelength is referred to as the spectrum of a given ray or light source

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3 Dominant Wavelength | Frequency energy white light energy greenish light

wave- E wavelength W length

400 nm 700 nm dominant wavelength dominant wavelength | frequency (hue, color) brightness (area under the curve) E ...dominant energy density purity ED  EW D EW...white light energy density ED Werner Purgathofer 6

The Human Eye

cornea aqueous [Hornhaut] retina contains [Augenkammer] iris [Regen- rods: b/w bogen- cones: color lens haut]

vitreous humor [Glaskörper] optical axis visual axis rods optic disc [Papille] fovea cones retina [Netzhaut] nerve macula lutea [gelber Fleck]

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4 The Human Eye 3 types of cones

different fraction of wavelength absorbed light sensitivities: 16% 8% red 4% green 2% 1% blue λ 400 440 480 520 560 600 640 680

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Color Blindness red/green blindness red & green cones too similar

fraction of absorbed light 16% 8% 4% 2% 1% λ 400 440 480 520 560 600 640 680

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5 Color Blindness red/green blindness red & green cones too similar

fraction of blue blindness absorbed light 16% no blue cones 8% 4% other 2% 1% cones missing λ cones too similar 400 440 480 520 560 600 640 680

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Color Blindness Tests

5 = normal 2 = red/green weak nothing = red/green blind nothing = normal

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6 Color Blindness Tests

8 = normal 8 = red/green blind 3 = red/green weak 12 = blue/yellow blind nothing = r/g blind 182 = normal

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Color Spaces (CS) Color Metric Spaces (CIE XYZ, L*a*b*) used to measure absolute values and differences - roots in colorimetry Device Color Spaces (RGB, CMY, CMYK) used in conjunction with device Color Ordering Spaces (HSV, HLS) used to find colors according to some criterion

the distinction between them is somewhat obscured by the prevalence of multi-purpose RGB in computer graphics

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7 What is our Goal?

to be able to quantify color in a meaningful, expressive, consistent and reproducible way.

problem: color is a perceived quantity, not a direct, physical observable

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Color - A Visual Sensation

light nerve object eye brain stimulus signal

electromagnetic color rays sensation

realm of direct realm of psychology observables

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8 Colorimetry CM is the branch of color science concerned with numerically specifying the color of a physically defined visual stimulus in such manner that stimuli with the same specification look alike under the same viewing conditions stimuli that look alike have the same specifica tion the numbers used are continuous functions of the physical parameters

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Colorimetry Properties Colorimetry only considers the visual discriminability of physical beams of radiation fthfor the purposes of ClColor ime try a „col“ilor“ is an equivalence class of mutually indiscriminable beams colors in this sense cannot be said to be “red”, “green” or any other “color name” discriminability is decided before the brain - Colorimetry is not psychology

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9 Color Matching Experiments observers had to match monochromatic test lights by combining 3 fixed primaries

test green test R+G+B

010101 goal: find the unique RGB coordinates for each stimulus

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Color Matching Experiments observers had to match monochromatic test lights by combining 3 fixed primaries

R = 700.0 nm viewer G = 546.1 nm controls independently B = 435.8 nm variable ppyrimary sources

masking viewing test screen screen source

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10 Tristimulus Values

the values RQ, GQ and BQ test green test

of a stimulus Q that fulfill R+G+B

Q  RQ  R  GQ  G  BQ  B

are called the tristimulus values of Q

ihin the case o f a monochihromatic stilimulus Q, the values R, G and B are called the spectral tristimulus values

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Color Matching Procedure

(1) test field = 700 nm-red with radiance Pref observer adjusts luminance of R (G=0, B=0) (2) test light wavelength is decreased in

constant steps (radiance Pref stays the same) observer adjusts R, G, B (3) repeat for entire visible range

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11 Color Matching Result !?

100 no match possible !?!?

0 350 400 450 500 550 600 650 700 nm observers want to „subtract“ red light from the match side...!?

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Color Matching Experiment Problem for some colors observers want to reduce red light to negative values…!? but there is no negggative light…!

test green G+B est t t + + R ? 010101

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12 “Negative” Light in a Color Matching Exp. if a match using only positive RGB values proved impossible, observers could simulate a subtraction of red from the match side by adding it to the test side

test green +B t + R s G G te

01 010101

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CIE RGB Color Matching Functions

b(λ) r(λ) 100 g(λ)

? 0 350 400 450 500 550 600 650 700 nm 435.8 nm 546.1 nm 700.0 nm

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13 CIE XYZ problem solution: XYZ color system tristimulus system derived from RGB bd3based on 3 iiimaginary priiimaries all 3 primaries are imaginary colors Y only positive XYZ values can occur! 1931 by CIE (Commission Internationale de l’Eclairage) X Z Werner Purgathofer 26

RGB vs. XYZ negative component disappears y() is the achromatic luminance sensitivity

RGB system XYZ system

b(λ) r(λ) z(λ) g(λ) y(λ) x(λ) 1

0 350 400 450 500 550 600 650 700 nm 350 400 450 500 550 600 650 700 nm amounts of RGB primaries amounts of CIE primaries needed needed to display spectral colors to display spectral colors

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14 CIE Color Model Formulas XYZ color model C() = XX + YY + ZZ (X, Y, Z are primaries) normalized chromaticity values xyx, y X Y x  y  X Y Z X Y Z Y ( z = 1 –x –y ) 1

complete description of color: x, y, Y 1 X 1 Z Werner Purgathofer 28

CIE Chromaticity Diagram identifying spectral colors complementary colors determining dominant wavelength, purity comparing color gamuts

spectral color positions purple line are along the boundary curve

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15 Properties of CIE Diagram (2)

reppgresenting complementary colors on the chromaticity diagram C1 C

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Properties of CIE Diagram (3)

determining dominant wavelength Cs and purity with the chromaticity diagram Csp

C1 → Cs C1

C C2 → Cp? → complement Csp C2

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16 Color Spaces (CS) Color Metric Spaces (CIE XYZ, L*a*b) used to measure absolute values and differences - roots in colorimetry Device Color Spaces (RGB, CMY, CMYK) used in conjunction with device Color Ordering Spaces (HSV, HLS) used to find colors according to some criterion

the distinction between them is somewhat obscured by the prevalence of multi-purpose RGB in computer graphics

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RGB Color Model

green (0,1,0) yellow primary colors (1,1,0) red, green, blue cyan white (0,1,1) (1,1,1) additive color model red black (1,0,0) (for monitors) (0,0,0) blue (0,0,1)

magenta (1,0,1)

C() = RR + GG + BB

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17 RGB Color Model Images

3 views of the RGB color cube

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Gamuts of RGB Monitors monitor gamuts can be very different no monitor can display all colors

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18 CMY Color Model

magenta primary colors (0,1,0) blue (1,1,0) cyan, magenta, red black yellow (011)(0,1,1) (1,1,1) subtractive color cyan model (for white (1,0,0) hardcopy devices) yellow (0,0,0) (0,0,1) C=G+B, using C “subtracts” R green (1,0,1)  C  1 R M   1  G        Y  1 B Werner Purgathofer 36

CMY Color Model Images

3 views of the CMY color cube

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19 Gamuts of CMY(K) Printers printer gamuts can be very different no printer can display all colors

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Color Spaces (CS) Color Metric Spaces (CIE XYZ, L*a*b) used to measure absolute values and differences - roots in colorimetry Device Color Spaces (RGB, CMY, CMYK) used in conjunction with device Color Ordering Spaces (HSV, HLS) used to find colors according to some criterion

the distinction between them is somewhat obscured by the prevalence of multi-purpose RGB in computer graphics

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20 Colour Ordering Systems (COS) primary aim: enable the user to intuitively choose colour values according to certain criteria choice can yield single or multiple colour values examples: HSV, HLS, Munsell, NCS, RAL Design, Coloroid used in bottom-up parts of a design process sometimes physical samples are provided

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HSV Color Model more intuitive color specification derived from the RGB color model: when the RGB color cube is viewed along the diagonal from white to black, the color cube outline is a hexagon

RGB Color Cube Color Hexagon Werner Purgathofer 41

21 HSV Color Model Hexcone

color components: hue (()H)  [0°, 360°] saturation (S)  [0, 1] value (V)  [0, 1]

HSV hexcone

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HSV Color Model Hexcone

color components: hue ()(H)  [0°, 360°] saturation (S)  [0, 1] value (V)  [0, 1]

HSV hexcone

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22 HSV Color Definition color definition select hue, S=1, V=1 add black ppgigments , i.e., decrease V add white pigments, i.e., decrease S

cross section o f the HSV hexcone showing regions for shades, tints, and tones Shades

S Werner Purgathofer 44

HLS Color Model

color components: hue (()H)  [0°, 360°] lightness (L)  [0, 1] saturation (S)  [0, 1]

HLS double cone

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23 Color Model Summary Colorimetry: CIE XYZ: contains all visible colours

Device Color Systems: RGB: additive device color space (monitors) CMY(K): subtractive device color space (printers) YIQ: television (NTSC) (Y=luminance, I=R-YQ=BY, Q=B-Y)

Color Ordering Systems: HSV, HLS: for user interfaces

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Color Symbolism: Some Aspects 6 to 11 basic colors categories, hierarchies ddtdependent on contttext / applica tion large variation in use what is red? what is blue? what is white?!? !

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24 Color in Religion Islam: green Buddhism: yellow, orange, red & purple Hinduism: orange, blue & blue-violet Christs: liturgical colors without theological connex

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Political Symbol Colors parties revolutions / movements flags

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25 Color Labeling at home water pipes electrical wires waste separation traffic traffic signs traffic lights parking concepts public transport ...

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Color Labeling technology resistors thermochrome colors nature courtship [Balz] warning colors protective mimicry [Tarnfarben] …

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26 Color Effect: BLUE distance faithfulness, loyality didesire phantasy male devine peace cold …

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Color Effect: RED blood energy love female rich, noble labor movement warm corrections …

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27 Color Effect: GREEN profit young love hope prematurity, unripe poison nature neutral environment protection …

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Color Effect: YELLOW sun optimism enlig htenmen t jealousy [Neid] stinginess [Geiz] warning color warm …

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28 Color Effect: BLACK end, death sadness negative emotions bad luck elegance emptiness cold …

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Einführung in Visual Computing 186.822

Color and Color Models

The End