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Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Color Science
CS 4620 Lecture 15
1 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
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What light is
- Light is electromagnetic radiation
- exists as oscillations of different frequency (or, wavelength)
[La
wr
ence Berk
ele
y Lab / Micr
oW
orlds]
Measuring light
wavelength
band
(width d !)
amount of light = 180 d!
(relative units)
wavelength (nm)
- Salient property is the spectral power distribution (SPD)
- the amount of light present at each wavelength
- units: Watts per nanometer (tells you how much power you’ll
find in a narrow range of wavelengths)
- for color, often use “relative units”
when overall intensity is not
important
Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
What color is
- Colors are the sensations that arise from light energy
of different wavelengths
- we are sensitive from about 380 to 760 nm—one “octave”
- Color is a phenomenon of human perception; it is not
a universal property of light
- Roughly speaking, things appear “colored” when they
depend on wavelength and “gray” when they do not.
5 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
The problem of color science
- Build a model for human color perception
- That is, map a Physical light description to a
Perceptual color sensation
Physical
Perceptual
[Stone 2003]
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The eye as a measurement device
- We can model the low-level
behavior of the eye by thinking
of it as a light-measuring machine
- its optics are much like a camera
- its detection mechanism is also
much like a camera
photoreceptors in the retina
- they respond to visible light
- different types respond to different
wavelengths [Gr
eger et al.
1995]
A simple light detector
- Produces a scalar value (a number) when photons land
on it
- this value depends strictly on the number of photons
detected
- each photon has a probability of being detected that depends
on the wavelength
- there is no way to tell the difference between signals caused
by light of different wavelengths: there is just a number
- This model works for many detectors:
- based on semiconductors (such as in a digital camera)
- based on visual photopigments (such as in human eyes)
Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Cone responses to a spectrum s
13 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Colorimetry: an answer to the problem
- Wanted to map a Physical light description to a
Perceptual color sensation
- Basic solution was known and standardized by 1930
- Though not quite in this form—more on that in a bit
Physical Perceptual
[Stone 2003]
s
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Basic fact of colorimetry
- Take a spectrum (which is a function)
- Eye produces three numbers
- This throws away a lot of information!
- Quite possible to have two different spectra that have the
same S, M, L tristimulus values
- Two such spectra are metamers
Pseudo-geometric interpretation
- A dot product is a projection
- We are projecting a high dimensional vector (a
spectrum) onto three vectors
- differences that are perpendicular to all 3 vectors are not
detectable
- For intuition, we can imagine a 3D analog
- 3D stands in for high-D vectors
- 2D stands in for 3D
- Then vision is just projection onto a plane
Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Pseudo-geometric interpretation
- The information available to the visual system about a
spectrum is three values
loss of information
analogous to
projection on a plane
produce the same
response are
metamers
17 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Basic colorimetric concepts
- Luminance
- the overall magnitude of the the visual response to a
spectrum (independent of its color)
- corresponds to the everyday concept “brightness”
- determined by product of SPD with the luminous efficiency
function V !
that describes the eye’s overall ability to detect
light at each wavelength
to improve their luminous
efficiency (tungsten vs.
fluorescent vs. sodium vapor)
[Stone 2003]
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Luminance, mathematically
- Y just has another response curve (like S , M , and L )
is really called “ V !
V
is a linear combination of S , M , and L
- Has to be, since it’s derived from cone outputs
More basic colorimetric concepts
- Chromaticity
- what’s left after luminance is factored out (the color without
regard for overall brightness)
- scaling a spectrum up or down leaves chromaticity alone
- Dominant wavelength
- many colors can be matched by white plus a spectral color
- correlates to everyday concept “hue”
- Purity
- ratio of pure color to white in matching mixture
- correlates to everyday concept “colorfulness” or “saturation”
Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Combining Monitor Phosphors with
Spatial Integration
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25 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Color reproduction
- Say we have a spectrum s we want to match on an
RGB monitor
- “match” means it looks the same
- any spectrum that projects to the same point in the visual
color space is a good reproduction
- So, we want to find a spectrum that the monitor can
produce that matches s
- that is, we want to display a metamer of s on the screen
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Color reproduction
the combination of
r, g, b that will project
to the same visual
response as s.
Color reproduction as linear algebra
- The projection onto the three response functions can
be written in matrix form:
Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Color reproduction as linear algebra
- The spectrum that is produced by the monitor for the
color signals R, G, and B is:
- Again the discrete form can be written as a matrix:
29 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Color reproduction as linear algebra
- What color do we see when we look at the display?
- Feed C to display
- Display produces s a
- Eye looks at s a
and produces V
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- Goal of reproduction: visual response to s and s a
is the
same:
- Substituting in the expression for s a
Color reproduction as linear algebra
color matching matrix for RGB
Subtractive Color
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Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
A universal color space: XYZ
- Standardized by CIE ( Commission Internationale de
l’Eclairage, the standards organization for color science)
- (^) Based on three “imaginary” primaries X , Y , and Z
(in math, s = X X + Y Y + Z Z )
- imaginary = only realizable by spectra that are negative at
some wavelengths
- key properties
- any stimulus can be matched with positive X , Y , and Z
- separates out luminance: X , Z have zero luminance, so Y
tells you the luminance by itself
37 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Separating luminance, chromaticity
- Luminance: Y
- Chromaticity: x , y , z , defined as
- since x + y + z = 1, we only need to record two of the three
- usually choose x and y , leading to ( x , y , Y ) coords
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Chromaticity Diagram
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spectral locus
purple line
Chromaticity Diagram
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Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Color Gamuts
Monitors/printers can’t
produce all visible colors
Reproduction is limited
to a particular domain
For additive color (e.g.
monitor) gamut is the
triangle defined by the
chromaticities of the
three primaries.
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41 Cornell CS4620 Fall 2008 •!Lecture 15 © 2008 Steve Marschner •
Perceptually organized color spaces
- Artists often refer to colors as tints , shades , and tones of
pure pigments
- tint: mixture with white
- shade: mixture with black
- tones: mixture with
black and white
(aka. neutral)
- This seems intuitive
- tints and shades are inherently related to the pure color
- “same” color but lighter, darker, paler, etc.
grays
tints
shades
white
black
pure
color
[after FvDFH]
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Perceptual dimensions of color
- Hue
- the “kind” of color, regardless of attributes
- colorimetric correlate: dominant wavelength
- artist’s correlate: the chosen pigment color
- Saturation
- the “colorfulness”
- colorimetric correlate: purity
- artist’s correlate: fraction of paint from the colored tube
- Lightness (or value)
- the overall amount of light
- colorimetric correlate: luminance
- artist’s correlate: tints are lighter, shades are darker
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Perceptual dimensions: chromaticity
luminance/chromaticity
space),Y corresponds to
lightness
then like polar
coordinates for
chromaticity (starting at
white, which way did you
go and how far?)
Perceptual organization for RGB: HSV
- Uses hue (an angle, 0 to 360), saturation (0 to 1), and
value (0 to 1) as the three coordinates for a color
RGB colors are those
with one of R,G,B
equal to 1 (top surface)
the surface of a sub-cube
of the RGB cube [FvDFH]
(demo of HSV color pickers)
Perceptually uniform spaces
- Two major spaces standardized by CIE
- designed so that equal differences in coordinates produce
equally visible differences in color
- LUV: earlier, simpler space; L *, u *, v *
- LAB: more complex but more uniform: L *, a *, b *
- both separate luminance from chromaticity
- including a gamma-like nonlinear component is important
