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Color and sensors

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Colors and sensors
Slides from Bill Freeman, Fredo Durand, Rob Fergus, and David
Forsyth, Alyosha Efros
Agenda
•
•
•
•
Project 1 delayed till Thursday October 9th
Color
Sensors
Matlab intro
Project 1: Demosaicing
• Warning; it might take some time
– Getting familiar with Matlab
– Writeup solutions in html and submit to EEE
– I put up a project template (with sample code &
writeup)
Image Formation
Digital Camera
Film
The Eye
Digital camera
• A digital camera replaces film with a sensor
array
– Each cell in the array is light-sensitive diode that converts photons to electrons
– Two common types
• Charge Coupled Device (CCD)
• CMOS
– http://electronics.howstuffworks.com/digital-camera.htm
Slide by Steve Seitz
Sensor Array
CMOS sensor
Sampling and quantizing brightness
The real world of colored light:
why is color useful?
• Find things to eat
• Spot dangerous
things
What’s the physics behind color?
The Physics of Light
Any patch of light can be completely described
physically by its spectrum: the number of photons
(per time unit) at each wavelength 400 - 700 nm.
# Photons
(per ms.)
400 500
600
700
Wavelength (nm.)
В© Stephen E. Palmer, 2002
The Physics of Light
Some examples of the spectra of light sources
.
B. Gallium Phosphide Crystal
# P h o to n s
# P h o to n s
A. Ruby Laser
400 500
600
700
400 500
Wavelength (nm.)
700
Wavelength (nm.)
D. Normal Daylight
# P h o to n s
C. Tungsten Lightbulb
# P h o to n s
600
400 500
600
700
400 500
600
700
В© Stephen E. Palmer, 2002
The Physics of Light
% Photons Reflected
Some examples of the reflectance spectra of surfaces
Red
400
Yellow
700 400
Blue
700 400
Wavelength (nm)
Purple
700 400
700
В© Stephen E. Palmer, 2002
Electromagnetic Spectrum
Human Luminance Sensitivity Function
http://www.yorku.ca/eye/photopik.htm
Black body radiators
• Construct a hot body with near-zero albedo (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
пѓ¶пЂ 1
пѓ¦пЂ 1 пѓ¶пЂ пѓ¦пЂ E пЂЁпЃ¬ пЂ© п‚µ
пѓ·пЂ пѓЁпЂ пЃ¬ 5 пѓёпЂ пѓ§пЂ exp
hc
k
пЃ¬
T
пЂ­
1
пѓЁпЂ пЂЁ
пЂ© пѓёпЂ вЂў This leads to the notion of “color temperature” --- the
temperature of a black body that would look the same
Computer Vision - A Modern
Approach
Set: Color
Slides by D.A. Forsyth
Visible Light
Plank’s law for Blackbody radiation
Surface of the sun: ~5800K
Why do we see light of these wavelengths?
…because that’s where the
Sun radiates EM energy
В© Stephen E. Palmer, 2002
The Psychophysical Correspondence
There is no simple functional description for the perceived
color of all lights under all viewing conditions, but …...
A helpful constraint:
Consider only physical spectra with normal distributions
mean
area
# Photons
400
500
variance
600
700
Wavelength (nm.)
В© Stephen E. Palmer, 2002
The Psychophysical Correspondence
# Photons
Mean
blue
Hue
green
yellow
Wavelength
В© Stephen E. Palmer, 2002
The Psychophysical Correspondence
# Photons
Variance
Saturation
hi. high
med.
medium
low
low
Wavelength
В© Stephen E. Palmer, 2002
The Psychophysical Correspondence
Area
Brightness
# Photons
B. Area
Lightness
bright
dark
Wavelength
В© Stephen E. Palmer, 2002
Spectral Image Formation
I(О»)
Si(О»)
R(О»)
I(О») R(О»)
From Foundation of Vision by Brian Wandell, Sinauer Associates, 1995
Spectral Image Formation
Pi (О») = I(О»)R(О»)Si (О»)
I(λ) – Illumination Spectrum
Si(О») - Spectral sensitivity of photoreceptor i
R(О») - Surface reflectance/transmission
Pixel value / Perceived color depends on all 3 terms!
пѓ Problem of color constancy
Color appearance depends on nearby
colors
Top pink should
look stronger
Color names for cartoon spectra
600
700 nm
400
500
600
700 nm
400
500
600
700 nm
blue
magenta
500
green
400
yellow
red
cyan
Slide credit
W. Freeman
400
500
600
700 nm
400
500
600
700 nm
400
500
600
700 nm
red
Additive color mixing
500
600
700 nm
400
500
600
700 nm
yellow
green
400
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.
Red and green make…
Yellow!
400
500
600
700 nm
Slide credit:
W. Freeman
Additive color mixing of
illuminants
cyan
Subtractive color mixing
500
600
700 nm
yellow
400
500
600
700 nm
green
400
When colors combine by
multiplying the color spectra.
Examples that follow this
mixing rule: most photographic
films, paint, cascaded optical
filters, crayons.
Cyan and yellow (in crayons,
called “blue” and yellow)
make…
Green!
400
500
600
700 nm
Slide credit
Subtractive color mixing of
materials
• Light reflecting off colored object
• E.g. printing inks
Wikipedia
Color matching experiment
Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995
Color matching experiment 1
Color matching experiment 1
p1 p2
p3
Color matching experiment 1
p1 p2
p3
Color matching experiment 1
The primary color
amounts needed
for a match
p1 p2
p3
Color matching experiment 2
Color matching experiment 2
p1 p2
p3
Color matching experiment 2
p1 p2
p3
Color matching experiment 2
We say a
“negative”
amount of p2
was needed to
make the match,
because we
added it to the
test color’s side.
p1 p2
p3
The primary color
amounts needed
for a match:
p1 p2
p3
p1 p2
p3
Measure color by color-matching paradigm
• Pick a set of 3 primary color lights.
• Find the amounts of each primary, e1, e2, e3, needed
to match some spectral signal, t.
• Those amounts, e1, e2, e3, describe the color of t. If
you have some other spectral signal, s, and s matches
t perceptually, then e1, e2, e3 will also match s, by
Grassman’s laws.
• Why this is useful—it lets us:
– Predict the color of a new spectral signal
– Translate to representations using other primary lights.
Goal: compute the color match for any
color signal for any set of primary colors
• Examples of why you’d want to do that:
– Want to paint a carton of Kodak film with the Kodak
yellow color.
– Want to match skin color of a person in a photograph
printed on an ink jet printer to their true skin color.
– Want the colors in the world, on a monitor, and in a
print format to all look the same.
Color matching functions for a particular
set of monochromatic primaries
p1 = 645.2 nm
p2 = 525.3 nm
p3 = 444.4 nm
Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995
Questions?
Some other color spaces…
NTSC color components: Y, I, Q
пѓ¦ Y пѓ¶ пѓ¦ 0 . 299
пѓ§ пѓ· пѓ§
пѓ§ I пѓ· пЂЅ пѓ§ 0 . 596
пѓ§ Q пѓ· пѓ§ 0 . 211
пѓЁ пѓё пѓЁ
0 . 587
пЂ­ 0 . 274
пЂ­ 0 . 523
0 . 114 пѓ¶ пѓ¦ R пѓ¶
пѓ·пѓ§ пѓ·
пЂ­ 0 . 322 пѓ· пѓ§ G пѓ·
0 . 312 пѓ·пѓё пѓ§пѓЁ B пѓ·пѓё
NTSC - RGB
HSV hexcone
Forsyth & Ponce
Hue Saturation Value
•
•
•
•
Value: from black to white
Hue: dominant color (red, orange, etc)
Saturation: from gray to vivid color
HSV double cone
value
saturation
hue
saturation
CCD color sampling
The eye’s approach to color
imaging
Cross-section of eye
Cross section of retina
Pigmented
epithelium
Ganglion axons
Ganglion cell layer
Bipolar cell layer
Receptor layer
Two types of light-sensitive receptors
Cones
cone-shaped
less sensitive
operate in high light
color vision
Rods
rod-shaped
highly sensitive
operate at night
gray-scale vision
В© Stephen E. Palmer, 2002
Human eye photoreceptor
spectral sensitivities
What colors would these look like?
Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995
Color Sensing in Camera (RGB)
• 3-chip vs. 1-chip: quality vs. cost
• Why more green?
Why 3 colors?
http://www.cooldictionary.com/words/Bayer-filter.wikipedia
Slide by Steve Seitz
CCD color filter pattern
detector
The cause of color moire
detector
Fine black and white detail in image
mis-interpreted as color information.
Typical color moire patterns
Blow-up of
electronic camera
image. Notice spurious
colors in the regions
of fine detail in the
plants.
Color sampling artifacts
Human receptors vs CCD sensors
Distribution of incoming luminance into CCD sensors
Gamma correction
• Iout = Iin^(gamma), where gamma < 1
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