Color Representation

Home , Chromaticity, Color picker

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Lecture 3 Color Representation

CIEXYZ Color Space CIE Chromaticity Space HSL,HSV,LUV,CIELab

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CIEXYZ Color Coordinate System

1931 – The Commission International de l’Eclairage (CIE) Defined a standard system for color representation.

The CIE-XYZ Color Coordinate System.

In this system, the XYZ Tristimulus values can describe any visible color.

The XYZ system is based on the color matching experiments Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Trichromatic Color Theory

“tri”=three “chroma”=color

Every color can be represented by 3 values.

60 e1 40 e2 20 e3 0 400 500 600 700 Wavelength (nm)

Space of visible colors is 3 Dimensional. Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Calculating the CIEXYZ Color Coordinate System CIE-RGB

3 r(l)

b(l) g(l) 1 Primary Intensity 0

400 500 600 700 Wavelength (nm)

David Wright 1928-1929, 1929-1930 & John Guild 1931 17 observers responses to Monochromatic lights between 400- 700nm using viewing field of 2 deg angular subtense.

Primaries are monochromatic : 435.8 546.1 700 nm 2 deg field.

These were defined as CIE-RGB primaries and CMF.

XYZ are a linear transformation away from the observed data. Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIEXYZ Color Coordinate System

CIE Criteria for choosing Primaries X,Y,Z and Color Matching Functions x,y,z.

1) CMFs are non-negative over visible wavelengths. (i.e. any color is represented by 3 positive values).

2) Equal amounts of the Primaries produce white. (i.e. X=Y=Z for stimulus of equal luminance at each wavelength).

3) The y color matching function is defined to match the luminous-efficiency function of the human eye.

4) Primaries are as ‘tight’ as possible around the set of possible colors (Maxwell triangle Projects to equilateral in XYZ space). Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Luminous-Efficiency function of the human eye

0.6

0.2 Luminous Efficiency

400 500 600 700 Wavelength (nm) Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIEXYZ Color Coordinate System

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CIE-RGB to CIE-XYZ

CIE-RGB Chromaticity space (rg). * Cr, Cg, Cb must enclose the Gamut. * Line Cb-Cr is defined by Y being Luminance Function. (the Alychne = line of zero luminance). * Line Cr-Cg is tangent at 650+ (z is zero beyond 650). * Thus Cr is defined. * Equal Energy (x=y=z=1/3) puts constraint on Cb-Cg * Tight around Gamut -> line Cb-Cg is close to green. * Cb and Cg are defined. Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIE-RGB to CIE-XYZ

CIE RGB space to XYZ space. Map Cb Cg Cr to x=(0,0) y=(0,1) z=(1,0) Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIE Color Standard - 1931

1.8

1.4 z(l)

1 y(l) x(l) 0.6 Tristimulus values 0.2

400 500 600 700 Wavelength (nm)

• y is predefined. • Non negative over the visible wavelengths. (X,Z – Several Hundreds, Y – 0..100). • The 3 primaries associated with x y z color matching functions are unrealizable (negative power in some of the wavelengths). • Integral over the CMF gives equal values. • CMF are linear transformation away from CIE-RGB and from LMS. Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIE Color Standard - 1964

Stiles and Birch data (1959):

Color Matching Experiment with:

10 Deg view

Primaries: 444.4 525.3 645.2

CIE-XYZ10 Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Colorimeters Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Color matching functions vs LMS - cone photoreceptor responses

XYZ Tristimulus System Cone Spectral Sensitivity 1.8 1 x(l) L 1.4 y(l) M S z(l) 0.75 1 0.5 0.6

Tristimulus values 0.25 Relative sensitivity 0.2 0 400 500 600 700 400 500 600 700 Wavelength (nm) Wavelength (nm)

The cone responses form a 3D linear system. Cone responses are equivalent for metamers. thus The cone spectral sensitivities and the XYZ color matching functions are related by a 3 x 3 linear transformation.

X 1.9023 -1.4000 0.3544 L Y = 0.6371 0.3933 -0.0093 M Z 0.0007 0.0033 1.7462 S Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIE – RGB Primaries are monochromatic : 435.8 546.1 700 nm

X 1.9023 -1.4000 0.3544 R Y = 0.6371 0.3933 -0.0093 G Z 0.0007 0.0033 1.7462 B Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIEXYZ Color Coordinate System

x y z Color Matching Functions

1.8

1.4 z(l) y(l) 1 x(l) 0.6 Tristimulus values 0.2

400 500 600 700 Wavelength (nm) Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIEXYZ Color Coordinate System

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CIE Chromaticity Diagram

X X = x X+Y+Z Y Y = y 0.9 X+Y+Z 520 Z 530 Z = z X+Y+Z 510 540 550 x+y+z = 1 y 505 560

570 500 0.5 580

495 590 600 610 490 650

485

480

470 0.0 450 0.50.0 1.0 x

A common representative of color signal: [x,y,Y] Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIE Chromaticity Diagram

(ax,ay,az)

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Color Naming

0.9 520 530 510 540 550 505 green 560 yellow- 570 500 green 0.5 580 y yellow 590 495 orange 600 white 610 490 cyan pink red 650

485 magenta blue 480 purple 470 450 0.0 0.5 1.0 x Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

CIE-RGB Primaries Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Blackbody Radiators and CIE standard Illuminants

CIE Standard Illuminants: A - tungsten light B - Sunset C - blue sky D65 - Average daylight E - Equal energy white (x=y=z=1/3)

0.8

0.6

4000 5000 3000 y 6000 2000 0.4 7000 8000 A 10000 B 20000 C E 0.2 D65

0 0 0.2 0.4 0.6 0.8 x Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Blackbody Radiators

3000K

3500K Relative energy

9000K

Wavelength (nm)

http://www.olympusmicro.com/primer/java/colortemperature/index.html Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Television Primaries and Gamut

R 1 G 1 B 1 - Primaries used for PAL R 2 G 2 B 2 - Primaries used for NTSC D65 - reference white for PAL C - reference white for NTSC

0.8 G NTSC 2 PAL 0.6 G1 y 0.4 D65 R1 E R2 C 0.2

B1 B 0 2 0 0.2 0.4 0.6 0.8 x

CIE Chromaticity + Gamut applet : http://www.cs.rit.edu/~ncs/color/a_chroma.html Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Signal Lights Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

XYZ Color Space

Hue vs Saturation Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Chromaticity in Polar Coordinates

Given a reference white.

Dominant Wavelength – wavelength of the spectral color which added to the reference white, produces the given color.

0.8 550

0.6

0.4 490 630 Reference white 0.2

0 0 0.2 0.4 0.6 0.8 Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Chromaticity in Polar Coordinates

Given a reference white.

Complementary Wavelength – wavelength of the spectral color which added to the given color, produces the reference white.

0.8

0.6 570

0.4 485 Reference white 0.2

Chromaticity in Polar Coordinates

Given a reference white.

Purity – the ratio of the lengths between the given color and reference white and between the dominant wavelength and reference white. Ranges between 0 .. 1.

0.8

0.6

0.2 0.4

Reference white 0.2 0.4

EXAMPLE: Reference white is CIE standard illuminant - C.

Dominant Wavelength of color S1 is D1 of color S2 is D2.

Complementary Wavelength of color S1 is‘ D1. S2 does not have a complimentary wavelength.

Excitation Purity of S1 is the ratio CS1/CD1 of S2 is the ratio CS2/CD2 of S3 is the ratio CS3/CD3

0.8 D2

0.6 S2 S

0.4 D1 S1 C D1‘ 0.2 S3 D3

Chromaticity in Polar Coordinates

0.8

Dominant/complimentary 0.6 Wavelength Y 0.4 purity

reference white 0.2

Color Description Hue (red, green, yelow, blue ...)

Saturation (pink,bright red, ....)

Lightness (black, grey, white ....) (Value) White

G Hue R Saturation B

Brightness

Munsell Color System (1915) Equal perceptual steps in Hue Saturation Value.

Hue: R, YR, Y, GY, G, BG, B, PB, P, RP (each subdivided into 10) Chroma: 0 ... 20 (neutral ... saturated) Value: i0 ... 10 (dark ... pure white)

10/

5/ Value 10R 5R 5YR 10YR /10 10RP 1/ /6 /8 /2 /4 5RP 5Y 10P 10Y

5P 5GY /2 10PB 10GY /4 5PB /6 5G Example: 10B /8 5YR 8/4 /10 10G 5B 10GB 5GB Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Munsell Book of Colors

Atlas of thr Munsell Color System (1915) Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Color Polytopes

Applets: http://www.cs.rit.edu/~ncs/color/a_spaces.html http://www.nacs.uci.edu/~wiedeman/cspace/me/rgbhsv.html Generated by Foxit PDF Creator © Foxit Software http://www.foxitsoftware.com For evaluation only.

Color Space Summary

Spectral Power Distribution (SPD) – High Dimensional

3 Dimensional Spaces:

LMS - Human Cone responses. Given by the cone sensitivity curves.

CIE–RGB - Based on color Matching Experiments by Wright+Guild. Defined by Primaries R G B (monochromatic 435.8 546.1 700 nm) and cmf r g b.

CIE-XYZ - Standard Color space. Linear transformation of above that confirms to set of constraints. Defined by Primaries X Y Z (unrealizable) and cmf x y z.

Munsell Color Space – Perceptually equally spaced samples in 3 dimensions: Hue, Chroma, Value.