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 - 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
The Retina
Cross-section of eye
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
Cones
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
# Receptors/mm2
.
Fovea
150,000
Rods
Blind
Spot
Rods
100,000
50,000
0
Cones
Cones
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
.
B. Gallium Phosphide Crystal
# Photons
# Photons
A. Ruby Laser
400 500
600
700
400 500
Wavelength (nm.)
700
Wavelength (nm.)
D. Normal Daylight
# Photons
C. Tungsten Lightbulb
# Photons
600
400 500
600
700
400 500
600
700
© Stephen E. Palmer, 2002
Radiometry
Radiometry
Radiant exitance
Irradiance
Radiometry
Radiance
Radiant intensity
Photometry
i ,i , 
e ,e , 
Radiometry
for color
Horn, 1986
Spectral radiance: power in a specified direction, per
unit area, per unit solid angle, per unit wavelength
L( e , e ,  )
BRDF  f ( i , i , e , e ,  ) 
E ( i , i ,  )
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
% Photons Reflected
Some examples of the reflectance spectra of surfaces
Red
400
Yellow
700 400
Blue
700 400
Wavelength (nm)
Purple
700 400
700
© 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
area
# Photons
400
500
variance
600
700
Wavelength (nm.)
© Stephen E. Palmer, 2002
The Psychophysical Correspondence
# Photons
Mean
blue
Hue
green yellow
Wavelength
© Stephen E. Palmer, 2002
The Psychophysical Correspondence
# Photons
Variance
Saturation
hi. high
med. medium
low
low
Wavelength
© Stephen E. Palmer, 2002
The Psychophysical Correspondence
Area
Brightness
# Photons
B. Area
Lightness
bright
dark
Wavelength
© Stephen E. Palmer, 2002
Physiology of Color Vision
Three kinds of cones:
440
RELATIVE ABSORBANCE (%)
.
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
p1 p2
p3
Color matching experiment 1
p1 p2
p3
Color matching experiment 1
The primary color
amounts needed
for a match
p1 p2
p3
Color matching experiment 2
Color matching experiment 2
p1 p2
p3
Color matching experiment 2
p1 p2
p3
Color matching experiment 2
We say a
“negative”
amount of p2
was needed to
make the match,
because we
added it to the
test color’s side.
p1 p2
p3
The primary color
amounts needed
for a match:
p1 p2
p3
p1 p2
p3
Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995
Grassman’s Laws
• For color matches:
–
–
–
–
symmetry:
U=V <=>V=U
transitivity:
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
p1 = 645.2 nm
p2 = 525.3 nm
p3 = 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
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).
Forsyth & Ponce
• CIE chromaticity
diagram encompasses
all the perceivable
colors in 2D space
(x,y) by ignoring the
luminance
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.
Forsyth & Ponce
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
• C2 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
600
700 nm
400
500
600
700 nm
400
500
600
700 nm
blue
magenta
500
green
400
yellow
red
cyan
Color names for cartoon spectra
400
500
600
700 nm
400
500
600
700 nm
400
500
600
700 nm
red
Additive color mixing
500
600
700 nm
400
500
600
700 nm
yellow
green
400
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
=
cyan
Subtractive color mixing
500
600
700 nm
yellow
400
500
600
700 nm
green
400
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…
Green!
400
500
600
700 nm
NTSC color components: Y, I, Q
0.114  R 
 Y   0.299 0.587
  
 
 I    0.596  0.274  0.322 G 
 Q   0.211  0.523 0.312  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
• X0, Y0, and Z0 are used to colorbalance: 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