Computer Vision CS 776 Spring 2014 Color Prof. Alex Berg (Slide credits to many folks on individual slides)
Dec 16, 2015
Computer VisionCS 776 Spring 2014
Color
Prof. Alex Berg
(Slide credits to many folks on individual slides)
What is color?
Color is the result of interaction between physical light in the environment and our visual system.
Color is a psychological property of our visual experiences when we look at objects and lights, not a physical property of those objects or lights.
-- S. Palmer, Vision Science: Photons to Phenomenology
The Physics of Light
Any source of light can be completely describedphysically by its spectrum: the amount of energy emitted (per time unit) at each wavelength 400 - 700 nm.
© Stephen E. Palmer, 2002
400 500 600 700
Wavelength (nm.)
# Photons(per ms.)
Relativespectral
power
Computer Vision - A Modern Approach
Set: Color Slides by D.A. Forsyth
Causes of colorThe sensation of color is caused by the brain. Some ways to get this sensation include:
• Pressure on the eyelids• Dreaming, hallucinations, etc.
Main way to get it is the response of the visual system to the presence/absence of light at various wavelengths.
Light could be produced in different amounts at different wavelengths (compare the sun and a fluorescent light bulb).
Light could be differentially reflected (e.g. some pigments).It could be differentially refracted - (e.g. Newton’s prism)Wavelength dependent specular reflection - e.g. shiny copper
penny (actually most metals).Flourescence - light at invisible wavelengths is absorbed and
reemitted at visible wavelengths.
Computer Vision - A Modern Approach
Set: Color Slides by D.A. Forsyth
Radiometry for colour
All definitions are now “per unit wavelength”
All units are now “per unit wavelength”
All terms are now “spectral”Radiance becomes spectral radiance
• watts per square meter per steradian per unit wavelength
Radiosity --- spectral radiosity
Computer Vision - A Modern ApproachSet: Color
Slides by D.A. Forsyth
Measurements of relative spectral power of sunlight, made by J. Parkkinen and P. Silfsten. Relative spectral power is plotted against wavelength in nm. The visible range is about 400nm to 700nm. The color names on the horizontal axis give the color names used for monochromatic light of the corresponding wavelength --- the “colors of the rainbow”. Mnemonic is “Richard of York got blisters in Venice”.
Violet Indigo Blue Green Yellow Orange Red
Computer Vision - A Modern Approach
Set: Color Slides by D.A. Forsyth
Relative spectral power of two standard illuminant models --- D65 models sunlight,and illuminant A models incandescent lamps. Relative spectral power is plotted against wavelength in nm. The visible range is about 400nm to 700nm. The color names on the horizontal axis give the color names used for monochromatic light of the corresponding wavelength --- the “colors of the rainbow”.
Violet Indigo Blue Green Yellow Orange Red
Computer Vision - A Modern Approach
Set: Color Slides by D.A. Forsyth
Measurements of relative spectral power of four different artificial illuminants, made by H.Sugiura. Relative spectral power is plotted against wavelength in nm. The visible range is about 400nm to 700nm.
Spectra of Light Sources
.
# P
hoto
ns
D. Normal Daylight
Wavelength (nm.)
B. Gallium Phosphide Crystal
400 500 600 700
# P
hoto
ns
Wavelength (nm.)
A. Ruby Laser
400 500 600 700
400 500 600 700
# P
hoto
ns
C. Tungsten Lightbulb
400 500 600 700
# P
hoto
ns
Some examples of the spectra of light sources
© Stephen E. Palmer, 2002
Rel
. pow
erR
el. p
ower
Rel
. pow
erR
el. p
ower
Reflectance Spectra of Surfaces
Some examples of the reflectance spectra of surfaces
Wavelength (nm)
% L
ight
Ref
lect
ed Red
400 700
Yellow
400 700
Blue
400 700
Purple
400 700
© Stephen E. Palmer, 2002
Computer Vision - A Modern Approach
Set: Color Slides by D.A. Forsyth
Spectral albedoes for several different leaves, with color names attached. Notice that different colours typically have different spectral albedo, but that different spectral albedoes may result in the same perceived color (compare the two whites). Spectral albedoes are typically quite smooth functions. Measurements by E.Koivisto.
Interaction of light and surfaces
Reflected color is the result of interaction of light source spectrum with surface reflectance
Slide by Svetlana Lazebnik
Interaction of light and surfaces
What is the observed color of any surface under monochromatic light?
Olafur Eliasson, Room for one color
The Eye
The human eye is a camera!• Lens - changes shape by using ciliary muscles (to focus on
objects at different distances)• Pupil - the hole (aperture) whose size is controlled by the
iris• Iris - colored annulus with radial muscles• Retina - photoreceptor cells
Slide by Steve Seitz
Rods and cones, fovea
Rods are responsible for intensity, cones for color perception
Rods and cones are non-uniformly distributed on the retina• Fovea - Small region (1 or 2°) at the center of the visual field containing
the highest density of cones – and no rods
Slide by Steve Seitz
cone
rod
pigmentmolecules
Demonstration of visual acuity
With one eye shut, at the right distance, all of these letters should appear equally legible (Glassner, 1.7).
Slide by Steve Seitz
Blind spot
With left eye shut, look at the cross on the left. At the right distance, the circle on the right should disappear
(Glassner, 1.8).
Slide by Steve Seitz
© Stephen E. Palmer, 2002
.
400 450 500 550 600 650
RE
LATI
VE
AB
SO
RB
AN
CE
(%)
WAVELENGTH (nm.)
100
50
440
S
530 560 nm.
M L
Three kinds of cones:
Physiology of Color Vision
• Ratio of L to M to S cones: approx. 10:5:1• Almost no S cones in the center of the fovea
Physiology of Color Vision: Fun facts
“M” and “L” pigments are encoded on the X-chromosome• That’s why men are more likely to be color blind http://
www.vischeck.com/vischeck/vischeckURL.php• “L” gene has high variation, so some women may be
tetrachromatic
Some animals have one (night animals), two (e.g., dogs), four (fish, birds), five (pigeons, some reptiles/amphibians), or even 12 (mantis shrimp) types of coneshttp://www.mezzmer.com/blog/how-animals-see-the-world/
http://en.wikipedia.org/wiki/Color_visionSlide by D. Hoiem
Color perception
Rods and cones act as filters on the spectrum• To get the output of a filter, multiply its response curve
by the spectrum, integrate over all wavelengths– Each cone yields one number
S
M L
Wavelength
Power
• How can we represent an entire spectrum with 3 numbers?• We can’t! Most of the information is lost
– As a result, two different spectra may appear indistinguishable» such spectra are known as metamers
Slide by Steve Seitz
Standardizing color experience
We would like to understand which spectra produce the same color sensation in people under similar viewing conditions
Color matching experiments
Wandell, Foundations of Vision, 1995
Color matching experiment 1
p1 p2 p3
The primary color amounts needed for a match
Source: W. Freeman
Color matching experiment 2
p1 p2 p3 p1 p2 p3
We say a “negative” amount of p2 was needed to make the match, because we added it to the test color’s side.
The primary color amounts needed for a match:
p1 p2 p3
Source: W. Freeman
Trichromacy
In color matching experiments, most people can match any given light with three primaries• Primaries must be independent
For the same light and same primaries, most people select the same weights• Exception: color blindness
Trichromatic color theory• Three numbers seem to be sufficient for encoding
color• Dates back to 18th century (Thomas Young)
Slide by Svetlana Lazebnik
Grassman’s Laws (~linearity)
Color matching appears to be linearIf two test lights can be matched with the
same set of weights, then they match each other: • Suppose A = u1 P1 + u2 P2 + u3 P3 and B = u1 P1 + u2 P2 +
u3 P3. Then A = B.
If we mix two test lights, then mixing the matches will match the result:• Suppose A = u1 P1 + u2 P2 + u3 P3 and B = v1 P1 + v2 P2 +
v3 P3. Then A + B = (u1+v1) P1 + (u2+v2) P2 + (u3+v3) P3.
If we scale the test light, then the matches get scaled by the same amount:• Suppose A = u1 P1 + u2 P2 + u3 P3.
Then kA = (ku1) P1 + (ku2) P2 + (ku3) P3. Slide by Svetlana Lazebnik
Linear color spaces
Defined by a choice of three primaries The coordinates of a color are given by
the weights of the primaries used to match it
mixing two lights producescolors that lie along a straight
line in color space
mixing three lights produces colors that lie within the triangle
they define in color space
Slide by Svetlana Lazebnik
Linear color spaces
How to compute the weights of the primaries to match any spectral signal?
p1 p2 p3
?
Given: a choice of three primaries and a target color signal
Find: weights of the primaries needed to match the color signal
p1 p2 p3
Slide by Svetlana Lazebnik
Linear color spaces
In addition to primaries, need to specify matching functions: the amount of each primary needed to match a monochromatic light source at each wavelength
RGB matching functionsRGB primaries
Slide by Svetlana Lazebnik
Linear color spaces
How to compute the weights of the primaries to match any spectral signal?
Let c(λ) be one of the matching functions, and let t(λ) be the spectrum of the signal. Then the weight of the corresponding primary needed to match t is
λ
Matching functions, c(λ)Signal to be matched, t(λ)
dtcw )()(
Slide by Svetlana Lazebnik
RGB space
Primaries are monochromatic lights (for monitors, they correspond to the three types of phosphors)
Subtractive matching required for some wavelengths
RGB matching functionsRGB primaries
Slide by Svetlana Lazebnik
Comparison of RGB matching functions with best 3x3 transformation of cone responses
Wandell, Foundations of Vision, 1995
Slide by Svetlana Lazebnik
Linear color spaces: CIE XYZPrimaries are imaginary, but matching
functions are everywhere positiveThe Y parameter corresponds to brightness
or luminance of a color2D visualization: draw (x,y), where
x = X/(X+Y+Z), y = Y/(X+Y+Z) Matching functions
http://en.wikipedia.org/wiki/CIE_1931_color_spaceSlide by Svetlana Lazebnik
Uniform color spacesUnfortunately, differences in x,y coordinates do
not reflect perceptual color differencesCIE u’v’ is a projective transform of x,y to make
the ellipses more uniform
McAdam ellipses: Just noticeable differences in color
Slide by Svetlana Lazebnik
Nonlinear color spaces: HSV
Perceptually meaningful dimensions: Hue, Saturation, Value (Intensity)
RGB cube on its vertex
Slide by Svetlana Lazebnik
Color perception
Color/lightness constancy• The ability of the human visual system to perceive
the intrinsic reflectance properties of the surfaces despite changes in illumination conditions
Instantaneous effects• Simultaneous contrast• Mach bands
Gradual effects• Light/dark adaptation• Chromatic adaptation• Afterimages
J. S. Sargent, The Daughters of Edward D. Boit, 1882 Slide by Svetlana Lazebnik
Checker shadow illusion
http://web.mit.edu/persci/people/adelson/checkershadow_illusion.html
Checker shadow illusion
Possible explanations• Simultaneous contrast• Reflectance edges vs. illumination edges
http://web.mit.edu/persci/people/adelson/checkershadow_illusion.html
Color Constancy by “Gamut” Approach…
Limited range of material reflectance properties
Limited range of possible illuminantsGiven observed colors we can work out
possible range of illuminants, combine those with some prior over known illuminants and obtain
More reading & thought problems
David Forsyth’s “Gamut” based reasoning for color constancy (IJCV 1990) http://luthuli.cs.uiuc.edu/~daf/papers/colorconst.pdf
I am very interested in pursing the line of reasoning I mentioned in class, where the above ideas for color constancy are extended to texture recognition.