Jehee Lee
Seoul National University
With a lot of slides stolen from
Alexei Efros, Stephen Palmer, Fredo Durand and others

• The human eye is a camera!
– Iris colored annulus with radial muscles
– Pupil 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
Cross section of retina
Pigmented epithelium
Ganglion axons
Ganglion cell layer
Bipolar cell layer
Receptor layer

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

The famous sockmatching 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

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

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

Radiant exitance
Irradiance

Radiance
Radiant intensity


,

, 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

metamers

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

Q

 r (

) R
 g (

) G
 b (

) B

p
1 p
2 p
3

p
1 p
2 p
3

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

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

• 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

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 …

• 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 blackbody 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

• The color gamut for n primaries in CIE chromaticity diagram is the convexhull of the color positions

• Illuminant C (Average sunlight)

• 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

• 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!

• 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 cube
– Easy for devices
– But not perceptual
– Where do the grays live?
– Where is hue and saturation?

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

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

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
=

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!

Y 0 .
299


I
Q


 

0 .
596
0 .
211
0 .
587

0 .
274

0 .
523

0
0
.
114
0 .
322
.
312





R
G
B




 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

• 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]

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

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

• Blackbody radiators