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• Light and the EM spectrum• The H.V.S. and Color Perception
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What is an ImageWhat is an Image? ? • An image is a projection of a 3D scene into a 2D
projection plane.• An image can be defined as a 2 variable function I(x,y) ,
where for each position (x,y) in the projection plane, I(x,y) defines the light intensity at this point.
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Camera trial #1
scene film
Put a piece of film in front of an object.
source: Yung-Yu Chuang
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Pinhole cameraPinhole camera
scene film
Add a barrier to block off most of the rays.• It reduces blurring• The pinhole is known as the aperture• The image is inverted
barrier
pinhole camera
source: Yung-Yu Chuang
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X
Y
(x,y,z)
(x,y)
center of projection(pinhole)
d
d – focal length
The Pinhole Camera Model (where)The Pinhole Camera Model (where)
Z
10/100
0010
0001
Z
Y
X
dw
y
x
d
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The Shading Model (what)The Shading Model (what)
Shading Model: Given the illumination incident at a point on a surface, what is reflected?
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Shading Model ParametersShading Model Parameters
• The factors determining the shading effects are:
– The light source properties:• Positions, Electromagnetic Spectrum, Shape.
– The surface properties:• Position, orientation, Reflectance properties.
– The eye (camera) properties:• Position, orientation, Sensor spectrum sensitivities.
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Newton’s Experiment, 1665 Cambridge.Discovering the fundamental spectral components of light.(from Foundations of Vision: Brian Wandell, 1995.
The Light PropertiesThe Light Properties
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A prism
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Electromagnetic Radiation - SpectrumElectromagnetic Radiation - Spectrum
Wavelength in nanometers (nm)
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Electromagnetic WaveElectromagnetic Wave
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MonochromatorsMonochromators
Monochromators measure the power or energy at different wavelengths
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The Spectral Power Distribution (SPD) of a light is a function e() which defines the relative energy at each wavelength.
Wavelength ()
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0.5
1R
ela
tive
Pow
er
Spectral Power Distribution (SPD)Spectral Power Distribution (SPD)
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Examples of Spectral Power Distributions
Blue Skylight Tungsten bulb
Red monitor phosphor Monochromatic light
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1
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1
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1
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• Interactions between light and matter depends on the physical characteristics of light as well as the matter.
• Three types of interactions:
– Reflection
– Absorption
– Transmittance
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The Surface PropertiesThe Surface PropertiesIncoming Light
Transmitted Light
Reflected Light
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The Bidirectional Reflectance The Bidirectional Reflectance Distribution Function (BRDF)Distribution Function (BRDF)
• A BRDF describes how much light is reflected when light makes contact with a certain material
),,(
),,(
ii
ee
E
LBRDF
Spectral radiance: quantity of light reflected in direction (e,e)
Spectral irradiance: quantity of light arriving from direction (i,i)
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Specular reflection mirror like reflection at the surface
Diffuse (lambertian) reflection Reflected randomly between color particlesreflection is equal in all directions.
Incident light Specular reflection
Diffuse reflection
normal
Simplified ModelSimplified Model
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Different Types of Surfaces
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Simplified rendering models: reflectanceSimplified 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.
.* =
B. Freeman, and Foundations of Vision, by Brian Wandell,
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400 500 600 700
0.2
0.4
0.6
0.8
1
400 500 600 700
0.2
0.4
0.6
0.8
1
400 500 600 700
0.2
0.4
0.6
0.8
1
400 500 600 700
0.2
0.4
0.6
0.8
1
Surface Body Reflectances (albedo)
Yellow Red
Blue Gray
Wavelength (nm)
Spectral Property of Lambertian SurfacesSpectral Property of Lambertian Surfaces
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Forsyth, 2002
Some reflectance spectraSome reflectance spectra
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Optic NerveFovea
Vitreous
Optic Disc
Lens
Pupil
Cornea
Ocular Muscle
Retina
Humor
Iris
The Eye PropertiesThe Eye Properties
Cornea - קרנית Pupil - אישון Iris - קשתית Retina - רשתית
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The Visual PathwayThe Visual Pathway
Retina
Optic Nerve
Optic Chiasm
LateralGeniculateNucleus (LGN)
Visual Cortex
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Eye v.s. CameraEye v.s. Camera
Yaho Wang’s slides
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light
rods cones
horizontal
amacrine
bipolar
ganglion
The Human RetinaThe Human Retina
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• Retina contains 2 types of photo-receptors– Cones:
• Day vision, can perceive color tone
– Rods: • Night vision, perceive brightness only
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Cones:• High illumination levels (Photopic vision)• Sensitive to color (there are three cone types: L,M,S)• Produces high-resolution vision• 6-7 million cone receptors, located primarily in the central
portion of the retina
Wavelength (nm)
Re
lativ
e s
en
sitiv
ity
Cone Spectral Sensitivity
400 500 600 7000
0.25
0.5
0.75
1ML
SM
A side note:• Humans and some monkeys have three types of cones (trichromatic vision); most other mammals have two types of cones (dichromatic vision).• Marine mammals have one type of cone.• Most birds and fish have four types. •Lacking one or more type of cones result in color blindness.
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Rods:• Low illumination levels (Scotopic vision).• Highly sensitive (respond to a single photon).• Produces lower-resolution vision• 100 million rods in each eye.• No rods in fovea.
Wavelength (nm)
Re
lativ
e s
en
sitiv
ity
400 500 600 7000
0.25
0.5
0.75
1
Rod Spectral Sensitivity
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31rods
S - Cones
L/M - Cones
Foveal Periphery photoreceptors
Photoreceptor DistributionPhotoreceptor Distribution
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Cone Receptor Mosaic(Roorda and Williams, 1999)
L-cones M-cones S-cones
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Distribution of rod and cone photoreceptors
Degrees of Visual Angle
Rec
epto
rs p
er s
quar
e m
m
-60 -40 -20 0 20 40 60
2
6
10
14
18x 104
rodscones
Cone’s Distribution:• L-cones (Red) occur at about ~65% of the cones throughout the retina.
• M-cones (green) occur at about ~30% of the cones.
• S-cones (blue) occur at about ~2-5% of the cones (Why so few?).
fovea
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The Cone ResponsesThe Cone Responses
Assuming Lambertian Surfaces
IlluminantSensors Surface
e() – Fixed, point source illuminantk() –surface’s reflectancel(),m(),s() – Cone responsivities
Output
)()()( kelL
)()()( kemM
)()()( kesS
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Metamer - two lights that appear the same visually. They might have different SPDs (spectral power distributions).
400 500 600 7000
400
800
400 500 600 7000
100
200
Wavelength (nm)
Pow
er
The phosphors of the monitor were set to match the tungsten light.
Tungsten light Monitor emission
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The Trichromatic Color TheoryThe Trichromatic Color Theory
Thomas Young (1773-1829) - A few different retinal receptors operating with different wavelength sensitivities will allow humans to perceive the number of colors that they do. Suggested 3 receptors.
Helmholtz & Maxwell (1850) - Color matching with 3 primaries.
Trichromatic: “tri”=three “chroma”=color color vision is based on three primaries (i.e., it is 3D).
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Color Matching ExperimentColor Matching Experiment
+ -
+ -
+ -
test match
Primaries
• Given a set of 3 primaries, one can determine for every spectral distribution, the intensity of the guns required to match the color of that spectral distribution.
• The 3 numbers can serve as a color representation.
bBgGrRT
R()
G()
B()
T()
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Color matching experiment 1
from: Bill Freeman
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Color matching experiment 1
p1 p2 p3 from: Bill Freeman
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Color matching experiment 1
p1 p2 p3 from: Bill Freeman
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Color matching experiment 1
p1 p2 p3
The primary color amounts needed for a match
from: Bill Freeman
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Color matching experiment 2
from: Bill Freeman
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Color matching experiment 2
p1 p2 p3 from: Bill Freeman
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Color matching experiment 2
p1 p2 p3 from: Bill Freeman
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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
from: Bill Freeman
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Color matching experiment for Monochromatic lights
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
Primary Intensities
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r()
g()b()
400 500 600 700
0
1
2
3
Wavelength (nm)
Pri
ma
ry In
ten
sity
Stiles & Burch (1959) Color matching functions. Primaries are: 444.4 525.3 and 645.2
Problems: Some perceived colors cannot be generated. This is true for any choice of visible primaries.
The The ColorColor Matching Functions (CMF) Matching Functions (CMF)
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48Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 from: Bill Freeman
The superposition principle
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• Observation - Color matching is linear:– if (SP) then (S+NP+N) – if (SP) then ( S P)
• Let T()=c(-0)+d(-1) a double chromatic color: How should we adjust the 3 primaries?
101010 ;; bdbcbgdgcgrdrcr
0 1
cd
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• Outcome 1: Any T() can be matched:
• Outcome 2: CMF can be calculated for any chosen primaries U(), V(), W():
dbTbdgTgdrTr ;;
b
g
r
ccc
bbb
aaa
w
v
u
321
321
321
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• The CIE (Commission Internationale d’Eclairage) defined in 1931 three hypothetical lights X, Y, and Z whose matching functions are positive everywhere:
The CIE Color StandardThe CIE Color Standard
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TristimulusTristimulus
• Let X, Y, and Z be the tri-stimulus values.• A color can be specified by its trichromatic
coefficients, defined as
X
xX Y Z
Y
yX Y Z
Zz
X Y Z
X ratio
Y ratio
Z ratio
Two trichromatic coefficients are enough to specify a color (x + y + z = 1).
From: Bahadir Gunturk
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Input light spectrum
x
y
From: Bahadir Gunturk
CIE Chromaticity DiagramCIE Chromaticity Diagram
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Input light spectrum
x
y
From: Bahadir Gunturk
CIE Chromaticity DiagramCIE Chromaticity Diagram
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Input light spectrum
x
y
From: Bahadir Gunturk
CIE Chromaticity DiagramCIE Chromaticity Diagram
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Input light spectrum
Boundary
x
y
380nm
700nm
From: Bahadir Gunturk
CIE Chromaticity DiagramCIE Chromaticity Diagram
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Input light spectrum
Boundary
From: Bahadir Gunturk
CIE Chromaticity DiagramCIE Chromaticity Diagram
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Light composition
From: Bahadir Gunturk
CIE Chromaticity DiagramCIE Chromaticity Diagram
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CIE Chromaticity DiagramCIE Chromaticity Diagram
Light composition
Light composition
From: Bahadir Gunturk
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• The sRGB is a device-independent color space. It was created
in 1996 by HP and Microsoft for use on monitors and printers.
• It is the most commonly used color space.
• It is defined by a transformation from the xyz color space.
The sRGB Color StandardThe sRGB Color Standard
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Color matching predicts matches, Color matching predicts matches, not appearance not appearance
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Color AppearanceColor Appearance
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Color AppearanceColor Appearance
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Color AppearanceColor Appearance
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Color SpacesColor Spaces
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RGB Color Space (additive)RGB Color Space (additive)
• Define colors with (r, g, b) ; amounts of red, green, and blue
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CMY Color Space (subtractive)CMY Color Space (subtractive)
• Cyan, magenta, and yellow are the complements of red, green, and blue– We can use them as filters to subtract from white– The space is the same as RGB except the origin is white
instead of black
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Color names for cartoon spectraColor names for cartoon spectra
400 500 600 700 nm
400 500 600 700 nm
400 500 600 700 nm
red
gree
nbl
ue
400 500 600 700 nm
cyan
mag
enta
yello
w
400 500 600 700 nm
400 500 600 700 nm
From: B. Freeman
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Additive color mixingAdditive color mixing
400 500 600 700 nm
400 500 600 700 nm
red
gree
n
Red and green make…
400 500 600 700 nm
yello
w
Yellow!
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.
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Subtractive color mixingSubtractive color mixing
When colors combine by multiplying the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons.
400 500 600 700 nm
cyan
yello
w
400 500 600 700 nm
Cyan and yellow (in crayons,called “blue” and yellow)
make…
400 500 600 700 nmGreen!gr
een
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Red
Green Blue
Magenta
Cyan
Yellow
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HSV color spaceHSV color space
• Hue - the chroma we see (red, green, purple).• Saturation - how pure is the color (how far the color from
gray ).• Value (brightness) - how bright is the color.
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HSV color spaceHSV color space
Value
Saturation
Hue
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T H E E N D