What is color for?

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What is color for?
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Color

• Physics
• Light is E-M radiation of different frequencies.
• Superposition principle
• Perception
• 3 cones -gt 3D color space. (Metamers).
• Convex subset of 3D linear space.
• Color matching cant represent w/ 3 primaries.
• Color Spaces
• CIE a standard
• RGB a bit more intuitive, Monitors, OpenGL
• CMYK subtractive, what we learn in art class.
• HSV More intuitive
• More Perception
• Perceptual distance
• Context
• Refs HB Chapter 12 The Foundations of Color
  Measurement and Color Perception, by Brian
  Wandell
• ftp//white.stanford.edu/users/brian/ise/sid-colo
  rnotes.pdf

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Newtons drawing
(Wandell)
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(Varshney)
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Color is a function
(Angelopoulou)
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Superposition

• Light is linear.
• Light from source A light from source B Light
  from sources A B.
• Any color is a combination of pure colors.
• Doubling intensity of source doubles amount of
  light reaching us.

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Human Color Perception

• Cones allow color perception.
• 3 types of cones sensitive to different
  frequencies
• Perceptual color depends on how these are
  stimulated.

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Metamers
(Wandell)
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Perceptual color space

• 3D
• Convex subspace
• Cones dont have negative response
• In general, any three colors projected onto this
  space span it.
• But not with non-negative coefficients.

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Color Matching
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Some colors cant be matched

• There isnt a unique color for each cone.
• Green light also excites red cones.
• So to produce some greenish lights we need
  negative red light.
• But we can match that color a primary color,
  using the other two primaries.
• Adding red to our color is like matching it with
  negative red.
• All colors can be matched like this
• Shows perceptually color is 3D
• But we cant have negative light in a display.
• Display space is convex too, but cant match
  perceptual convex space.

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(Wandell)
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Grassmans Additivity Law

• Color matching follows superposition
• If we know how to produce all pure colors, we can
  produce any color.

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CIE Model

• CIE International Commission on Illumination
  (1931)
• Describes any visible color with only positive
  primaries
• Primaries are called X, Y, Z
• Color is described by
• chrominance x, y, and
• luminance Y

Apart from the very approximate relationship
between Y and brightness, there is almost nothing
intuitive about the XYZ color-matching functions.
While they have served us quite well as a
technical standard, they have served us quite
poorly in explaining the discipline to new
students and colleagues or as an intuition about
color appearance. - Wandell
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Additive Color Model RGB

• Mix Red, Green, Blue primaries to get colors
• Cartesian Coordinate System with origin as black.
  
• Used in display devices CRTs, LCDs.

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Subtractive Color Model CMYK

• Start with white and subtract different
  subtractive primaries
• Cyan ink Absorbs red
• Magenta ink Absorbs green
• Yellow ink Absorbs blue
• Used in color printing
• CMY Black, but
• added fourth black ink for
• good black color and also
• to preserve CMY ink for
• black text

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Color Specification

• Hue Distinguishes among colors
• red, yellow, blue
• Saturation Color Purity (difference from white)
• blue and sky blue
• Lightness Perceived intensity of reflected light
• blue and darker shades of blue
• Brightness Perceived intensity of self-luminous
  objects
• Artists
• Tint Add white (decrease saturation)
• Shade Add black (decrease lightness)

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Perceptual Color Model HSV
V
Yellow
Green
Red
Cyan
White
Blue
Magenta

• R 0o, G 120o, B 240o
• Complementary colors are 180o apart
• S 0 Gray levels

H
S
Black
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Logarithmic Perception

• Constant ratios of intensities are perceived as
  being equally different
• Example intensities of 0.01 and 0.02 will be
  perceived to be have the same difference between
  them as intensities of .5 and 1.0
• Other examples of logarithmic perception
• Decibel scale sound
• Richter scale earthquakes

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Logarithmic Display

• Uniformly partitioning the displayable intensity
  range into equidistant arithmetic intervals is
  wasteful
• Each intensity should differ from the previous by
  a constant ratio.
• I0 minimum non-zero displayable intensity
• In maximum displayable intensity 1.0
• I1 r I0, I2 r I1 r2 I0 ,
  I3 r I2 r2 I1 r3 I0
• In rn I0 Þ r (1/ I0)1/n

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Intensity depends on context (Adelson)
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http//neuro.physik.uni-marburg.de/wachtler/cc.ht
ml
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Color Constancy Our color vision is based on
signals of the the three photoreceptor types
which respond to light of three different
wavelength regions. But if we look at an object,
its color that we perceive is not only determined
by the spectral composition of the light coming
from the object. Object colors depend on the
context in which the object is seen.Look at the
image below. On the left are six color fields on
a grey field, representing six objects on a
background. On the right, esentially the same
arrrangement is shown, but all colors have a
slightly bluish tint. It is as if we see the same
scene under a bluish illumination. Incidentally,
the spectral composition of the light coming from
the three fields in the upper row on the right
side are exactly the same as those of the lower
row on the left side. Furthermore, the colors on
the right that match most closely those on the
left are the ones in the corresponding positions
of the scenes, not those with the same physical
spectrum
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But context is a subtle thing. (Knill and Kersten)
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Color constancy

• Interesting algorithms exist
• Mostly for somewhat controlled/idealized
  conditions
• Useful in applications, but not so much in
  natural images
• This makes it hard to use color in recognition.
• Segmentation can be ok as long as lighting is
  locally constant.

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Color Segmentation

• Color quantization
• Compression by using a small set of colors.
• Represent each color with one of these.
• Cost function of k-means is natural.
• Spatial position is irrelevant.

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Spatial information

• Meer maps pixels to space/color space.