Light and Color

Jehee Lee Seoul National University

With a lot of slides stolen from Alexei Efros, Stephen Palmer, Fredo Durand and others

The Eye

• The human eye is a camera!

– –

Iris

-

Pupil

colored annulus with radial muscles the hole (aperture) whose size is controlled by the iris – What’s the “film”?

• photoreceptor cells (rods and cones) in the

retina

Cross-section of eye

The Retina

Cross section of retina Pigmented epithelium Ganglion axons Ganglion cell layer Bipolar cell layer Receptor layer

Retina up-close

Light

Two types of light-sensitive receptors

C on es

cone-shaped less sensitive operate in high light color vision

Rods

rod-shaped highly sensitive operate at night gray-scale vision © Stephen E. Palmer, 2002

Rod / Cone sensitivity

The famous sock matching problem…

Distribution of Rods and Cones

Fovea Blind Spot 150,000 100,000 Rods Rods 50,000 Cones Cones 0 80 60 40 20 0 20 40 60 80 Visual Angle (degrees from fovea) Night Sky: why are there more stars off-center? © Stephen E. Palmer, 2002

Electromagnetic Spectrum

Human Luminance Sensitivity Function http://www.yorku.ca/eye/photopik.htm

Visible Light

Why do we see light of these wavelengths?

…because that’s where the Sun radiates EM energy © Stephen E. Palmer, 2002

The Physics of Light

Any patch of light can be completely described physically by its spectrum: the number of photons (per time unit) at each wavelength 400 - 700 nm.

# Photons (per ms.) 400 500 600 700 Wavelength (nm.) © Stephen E. Palmer, 2002

The Physics of Light

Some examples of the spectra of light sources A. Ruby Laser B. Gallium Phosphide Crystal 400 500 600 700 Wavelength (nm.) C. Tungsten Lightbulb 400 500 600 700 Wavelength (nm.) D. Normal Daylight 400 500 600 700 400 500 600 700 © Stephen E. Palmer, 2002

Radiometry

Radiant exitance

Radiometry

Irradiance

Radiance

Radiometry

Radiant intensity

Photometry



i

, 

i

,  

e

, 

e

,  Radiometry for color Horn, 1986

BRDF

 Spectral radiance: power in a specified direction, per

f

unit area, per unit solid angle, per unit wavelength ( 

i

, 

i

, 

e

, 

e

,  )

L E

(  ( 

e i

, ,  

i e

, ,   ) ) Spectral irradiance: incident power per unit area, per unit wavelength

Simplified rendering models: reflectance Often are more interested in relative spectral composition than in overall intensity, so the spectral BRDF computation simplifies a wavelength-by-wavelength multiplication of relative energies.

.*

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

=

Simplified rendering models: transmittance

.*

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

=

The Physics of Light

Some examples of the reflectance spectra of surfaces Red Yellow Blue Purple 400 700 400 700 400 700 400 700 Wavelength (nm) © Stephen E. Palmer, 2002

The Psychophysical Correspondence

There is no simple functional description for the perceived color of all lights under all viewing conditions, but …...

A helpful constraint: Consider only physical spectra with normal distributions mean # Photons 400 area variance 500 600 Wavelength (nm.) 700 © Stephen E. Palmer, 2002

The Psychophysical Correspondence Mean Hue

blue green yellow Wavelength © Stephen E. Palmer, 2002

The Psychophysical Correspondence Variance Saturation

hi.

high med.

medium low low Wavelength © Stephen E. Palmer, 2002

The Psychophysical Correspondence Area Brightness

B. Area Lightness bright dark Wavelength © Stephen E. Palmer, 2002

Physiology of Color Vision

Three kinds of cones: 440 530 560 nm.

100 S M L 50 400 450 500 550 600 650 WAVELENGTH (nm.) © Stephen E. Palmer, 2002

More Spectra

metamers

Metameric Whites

Metameric lights

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

Color Matching

Q

 

r

(  )

R



g

(  )

G



b

(  )

B

Color matching experiment 1

Color matching experiment 1

p 1 p 2 p 3

Color matching experiment 1

p 1 p 2 p 3

Color matching experiment 1

The primary color amounts needed for a match p 1 p 2 p 3

Color matching experiment 2

Color matching experiment 2

p 1 p 2 p 3

Color matching experiment 2

p 1 p 2 p 3

Color matching experiment 2

We say a “negative” amount of p 2 was needed to make the match, because we added it to the test color’s side.

The primary color amounts needed for a match: p 1 p 2 p 3 p 1 p 2 p 3 p 1 p 2 p 3

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

Grassman’s Laws

• For color matches: – symmetry: – transitivity: U=V <=>V=U U=V and V=W => U=W – proportionality: U=V <=> tU=tV – additivity: if any two (or more) of the statements U=V, W=X, (U+W)=(V+X) are true, then so is the third • These statements are as true as any biological law. They mean that additive color matching is linear.

Forsyth & Ponce

Color Matching Functions

p 1 p 2 p 3 = 645.2 nm = 525.3 nm = 444.4 nm

Since we can define colors using almost any set of primary colors, let ’ s agree on a set of primaries and color matching functions for the world to use …

CIE XYZ color space

• Commission Internationale d ’ Eclairage, 1931 • “… as with any standards decision, there are some irratating aspects of the XYZ color-matching functions as well … no set of physically realizable primary lights that by direct measurement will yield the color matching functions.

” • “ Although they have served quite well as a technical standard, and are understood by the mandarins of vision science, they have served quite poorly as tools for explaining the discipline to new students and colleagues outside the field.

” Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

CIE XYZ: Color matching functions are positive everywhere, but primaries are “imaginary” (require adding light to the test color’s side in a color matching experiment). Usually compute x, y, where x=X/(X+Y+Z) y=Y/(X+Y+Z) Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

Forsyth & Ponce A qualitative rendering of the CIE (x,y) space. The blobby region represents visible colors. There are sets of (x, y) coordinates that don’t represent real colors, because the primaries are not real lights (so that the color matching functions could be positive everywhere).

• CIE chromaticity diagram encompasses all the perceivable colors in 2D space (x,y) by ignoring the luminance

Forsyth & Ponce A plot of the CIE (x,y) space. We show the spectral locus (the colors of monochromatic lights) and the black body locus (the colors of heated black-bodies). I have also plotted the range of typical incandescent lighting.

Pure wavelength in chromaticity diagram • Blue: big value of Z, therefore x and y small

Pure wavelength in chromaticity diagram • Then y increases

Pure wavelength in chromaticity diagram • Green: y is big

Pure wavelength in chromaticity diagram • Yellow: x & y are equal

Pure wavelength in chromaticity diagram • Red: big x, but y is not null

Color Gamut

• The color gamut for

n

primaries in CIE chromaticity diagram is the convexhull of the color positions

Color Gamut

Complementary Colors

• Illuminant C (Average sunlight)

Dominant Wavelength

• The spectral color which can be mixed with white light in order to reproduce the desired color • C 2 have spectral distributions with subtractive dominant wave lengths

CIE color space

• Can think of X, Y , Z as coordinates • Linear transform from typical RGB or LMS • Always positive (because physical spectrum is positive and matching curves are positives) • Note that many points in XYZ do not correspond to visible colors!

Color Gamut of RGB

XYZ vs. RGB

• Linear transform • XYZ is rarely used for storage • There are tons of flavors of RGB – sRGB, Adobe RGB – Different matrices!

• XYZ is more standardized • XYZ can reproduce all colors with positive values • XYZ is not realizable physically !!

– What happens if you go “ off ” the diagram – In fact, the orthogonal (synthesis) basis of XYZ requires negative values.

RGB color space

• RGB cube – Easy for devices – But not perceptual – Where do the grays live?

– Where is hue and saturation?

HSV

• Hue, Saturation, Value (Intensity) – RGB cube on its vertex • Decouples the three components (a bit) • Use rgb2hsv() and hsv2rgb() in Matlab

Color names for cartoon spectra

400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm 400 500 600 700 nm

Additive color mixing

400 500 600 700 nm 400 500 600 700 nm When colors combine by

adding

the color spectra. Example color displays that follow this mixing rule: CRT phosphors, multiple projectors aimed at a screen, Polachrome slide film.

Red and green make… Yellow!

400 500 600 700 nm

Simplified rendering models: reflectance Often are more interested in relative spectral composition than in overall intensity, so the spectral BRDF computation simplifies a wavelength-by-wavelength multiplication of relative energies.

.*

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995

=

Subtractive color mixing

400 500 600 700 nm 400 500 600 700 nm When colors combine by

multiplying

the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons.

Cyan and yellow (in crayons, called “blue” and yellow) make… 400 500 600 700 nm Green!

NTSC color components: Y, I, Q

Y

0 .

299  

I Q

     0 .

596 0 .

211 0 .

587  0 .

274  0 .

523  0 0 .

.

114 0 .

322 312     

R G B

 

NTSC - RGB

  

CMY color model

subtractive model (colors of pigments are subtracted) used in color output devices  CMYK color model - K for black ink for reducing the amount of ink

Uniform color spaces

• McAdam ellipses (next slide) demonstrate that differences in x,y are a poor guide to differences in color • Construct color spaces so that differences in coordinates are a good guide to differences in color.

Forsyth & Ponce

Variations in color matches on a CIE x, y space. At the center of the ellipse is the color of a test light; the size of the ellipse represents the scatter of lights that the human observers tested would match to the test color; the boundary shows where the just noticeable difference is. The ellipses on the left have been magnified 10x for clarity; on the right they are plotted to scale. The ellipses are known as MacAdam ellipses after their inventor. The ellipses at the top are larger than those at the bottom of the figure, and that they rotate as they move up. This means that the magnitude of the difference in x, y coordinates is a poor guide to the difference in color.

Forsyth & Ponce

Perceptually Uniform Space: MacAdam • In perceptually uniform color space, Euclidean distances reflect perceived differences between colors • MacAdam ellipses (areas of unperceivable differences) become circles • Non-linear mapping, many solutions have been proposed Source: [Wyszecki and Stiles ’82]

CIELAB (a.k.a. CIE L*a*b*)

• The reference perceptually uniform color space • L: lightness • a and b: color opponents • X 0 , Y 0 , and Z 0 are used to color balance: they ’ re the color of the reference white Source: [Wyszecki and Stiles ’82]

White Balance

• Chromatic adaptation – If the light source is gradually changed in color, humans will adapt and still perceive the color of the surface the same

Color Temperature

• Blackbody radiators