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07.03.2013
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EE 584MACHINE VISION
Color
Fundamentals
Color Mixing
Color Matching
Trichromacy
Color Spaces
Surface Color from Image Color
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
A
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Light is a radiant energy by which its action on the organs of vision, enables them to perform their function of sight
Light typically consists waves of different wavelengths (λ)
The following definitions apply in general for lightwaves:
� Radiant flux:power propagated as light radiation (W)
� Irradiance : amount of light falling on a unit surface (W/m2)
� Radiance: amount of light radiating from a unit surface towards a “solid” angle (W/m2 steradian)
� Radiant exitance (radiosity) : amount of light radiating from a unit surface (W/m2)
� Radiant intensity: amount of light radiating towards a “solid” angle (W/steradian)
Radiometry : Definitions
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Causes of color
• The 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
• 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.
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Black body radiators• Construct a hot body with near-zero reflectance (black
body)– Easiest way to do this is to build a hollow metal object with
a tiny hole in it, and look at the hole.
• The spectral power distribution of light leaving this object is a simple function of temperature
• Incandescent lamps = blackbody radiator at 1500-3000K
• This leads to the notion of color temperature– temperature of a black body that would look the same
E λ( )∝1λ5
1exp hc kλT( )−1
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
Spectral power distribution• The power per unit area at each wavelength of a radiant object
5 Figure © Stephen E. Palmer, 2002
400 500 600 700
Wavelength (nm.)
# Photons(per ms.)
• Some examples of the 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
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
Spectral power distribution Measurement
6 Foundations of Vision, B. Wandell
Spectroradiometer: separate input light into its different wavelengths, and measure the energy at each.
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
Radiometry vs. Photometry• Radiometric measurements: Quantitative
description of physical intensity
• Photometric measurements: Quantitative description of perceptual brightness
• Luminous flux (lumen, lm) :
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• Relative luminous efficiency, V(λ), describes the average visual sensitivity of the human eye to light of different wavelengths.
λλλ dVCKF m∫∞
=0
)()(
V(λ) : Low illum. vs High illum.
• Km = 685 lm/W• Spectral power distribution, C(λ)
Relative Luminous Efficiency(Human Luminance Sensitivity Function)
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Simplified rendering models: Reflectance
slide from T. Darrel
BRDF(λ) = radiance(λ) / irradiance(λ)Bidirectional Reflectance Distribution Func.
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Simplified rendering models: Transmittance
slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Violet Indigo Blue Green Yellow Orange Red
J. Parkkinen and P. Silfsten
Color of the sky
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Violet Indigo Blue Green Yellow Orange Red
Color of lightsources
(Day Light)
(100W Tungesten bulb)
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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spectral albedo ⇒ colorcolor ⇒ spectral albedo
Measurements by E.Koivisto.
Spectral albedoes for several different leaves
Spectral albedos are typically quite smooth functions.
Color of Surfaces
Spectral albedo== Spectral reflectance
A simplified model for surface color:
{ {{
irradiancespectral
albedospectral
radiosityspectral
SE )()()( λλρλ =
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Why specify color numerically?
• Accurate color reproduction is commercially valuable – Many products are identified
by color
• Few color names are widely recognized by English speakers -– About 10; other languages
have fewer/more, but not many more.
– It’s common to disagree on appropriate color names.
• Color reproduction problems increased by prevalence of digital imaging - eg. digital libraries of art. – How do we ensure that
everyone sees the same color?
• Colorimetry is the science of quantitatively measuring color
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
14 slide from T. Darrel
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
15 slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
16 slide from T. Darrel
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
17 slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
18 slide from T. Darrel
Note that the same experiment should initially be performed for a reference white color to determine its weights
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
19 slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
20 slide from T. Darrel
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
21 slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
22 slide from T. Darrel
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
23 slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
24 slide from T. Darrel
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
25 slide from T. Darrel
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
26
The principle of trichromacy
• Experimental facts Color Matching :
– Three primaries will work for most people, if we allow subtractive matching
• Exceptional people can match with two or only one primary.
– This could be caused by a variety of deficiencies.
– Most people make the same matches.• There are some anomalous trichromats, who use
three primaries but make different combinations to match.
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Grassman’s Laws• Color matching is (approximately) linear
– 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 statementsU=V,
W=X,
(U+W)=(V+X) are true, then so is the third
– A color match at one radiance level holds over a wide
range of levels
• If we mix 2 test lights, Ta & Tb
where
it has been experimentally shown that�
� Linearity
332211332211 & PPPTPPPT bbbbaaaa ωωωωωω ++=++=
333222111 )()()( PPPTT babababa ωωωωωω +++++=+
Here “=“ means “matches”.
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Color Matching Functions• Pick a set of 3 primary color lights, P1, P2 & P3
• For a single wavelength (λ) unit source, U(λ),find experimentally the weight of each primary to match this source
• For an arbitrary source, S, in order to find the corresponding weights for each primary :
332211 )()()()( PfPfPfU λλλλ ++=
( ) ( ) ( ) 332211
332211
)()()()()()( PdfSPdfSPdfS
PPPS
∫∫∫ ++=
++=
λλλλλλλλλ
ωωω
Here “=“ means “matches”.
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
29 slide from T. Darrel
)(),(),( 321 λλλ fff
332211 )()()()( PfPfPfU λλλλ ++=
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
30 slide from T. Darrel
( ) ( )( ) ( )( ) ( )
=
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07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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How to translate between different primaries?
332111
332211
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Here “=“ means “matches”.
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
32
How to translate between different primaries?
[ ] [ ]
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,, primaries theof in terms Write
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ωωω
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Here “=“ means “matches”.
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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How does it work in the eye?
cone
rod
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
34 slide from T. Darrel
How does it work in the eye?
∫= λλλσ dEp kk )()(
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Color Spaces : RGB
Z( ) ( ) ( ) 332211
332211
)()()()()()( PdfSPdfSPdfS
PPPS
∫∫∫ ++=
++=
λλλλλλλλλ
ωωω
• Three primaries are Red, Green and Blue which have single wavelengths
Since some of the color matching functions are negative, some colors could only be obtained by subtractive color matching
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
36 slide from T. Darrel
Color Spaces : CIE XYZ
Z
X
Y
1
1
1
Y is the “luminance”, perceived relative brightness
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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• Note that brightness is assumed to constant (normalized) in CIE (x,y) space.
•A qualitative rendering of the CIE (x,y) space.
• The blobby region represents visible colors.
• There are sets of (x,y) coordinates that do not represent real colors,
• the primaries are not real lights• the color matching functions could be positive everywhere
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
38
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Spectral locusLine of purplesBlack-body locusIncandescent lighting
CIE x,y color space
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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Non-linear color spaces: HSV• HSV: Hue, Saturation, Value are non-linear functions
of XYZ.
– hue relations are naturally expressed in a circle
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
Non-linear color spaces: HSV
• The Psychophysical Correspondence– Consider physical spectra as normal distributions
41
yellowgreenblue
# P
hoto
ns
Wavelength
Mean Hue Variance Saturation
Wavelength
high
medium
low
hi.
med.
low# P
hoto
ns
© Stephen E. Palmer, 2002
Area Value/Brightness
# P
hoto
ns
Wavelength
B. Area Lightness
bright
dark
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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• Uniform: equal (small!) steps give the same perceived color changes.
• McAdam ellipses 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 changes in color.
Non-linear color spaces: Uniform
size of the ellipse represents the scatter of lights that the human observers tested would match to the test color;
Ellipses on the left have been magnified 10x for clarity.
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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• CIE (u’v’ ) is a projective transform of x, y. • We transform x,yso that ellipses are most like one another. • Figure shows the transformed ellipses.
++++=′′
ZYX
Y
ZYX
Xvu
315
9,
315
4),(
Non-linear color spaces: CIE u’v’
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
44
Color constancy
• The spectral radiance (received light power) at the camera depends on two terms– surface albedo– illuminant spectral radiancethe effect is much more pronounced than most people
think (see following slides)
• We would like an illuminant invariant description of the surface– e.g. some measurements of surface albedo– need a model of the interactions
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
45
• The color of light at the camera varieswith the illuminant color
• A uniform reflectance illuminated by five different lights, and the result plotted on CIE x,y
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
46
• The color of light at the camera varieswith the illuminant color
• A uniform reflectance illuminated by five different lights, and the result plotted on CIE x,y
07.03.2013
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
47
Lightness Constancy
• Lightness is defined as the estimate of a surface reflectance obtained from visual data
• Lightness constancy– how “light” is the surface, independent of the
brightness of the illuminant– issues
• spatial variation in illumination• absolute standard
– Human lightness constancy is very good
• Assume– frontal 1D “surface”– slowly varying illumination– quickly varying surface reflectance
These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
48
The received light power, C, on a camera from an illuminated surface that has a piecewise constant reflectance (albedo), ρ. ( kc
is the camera gain)
)(log)(loglog)(log)()()( xxIkxCxxIkxC cc ρρ ++=⇒=
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These slides are modified from COMP 256 (UNC) Lecture Notes by Prof. Marc Pollefeys EE 584 Lecture Notes by A. Aydin Alatan 2013
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• How do we choose the constant of integration?– average lightness is
grey
– lightest object is white
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