EE 7700

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EE 7700

• Color

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References

• On Color Wikipedia, Gonzalez, Poynton, many
  others
• On HDR Slides and papers by Debevec, Ward,
  Pattaniak, Nayar, Durand, et al
• http//people.csail.mit.edu/fredo/PUBLI/Siggraph20
  02/

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Color

• Color is a perceptual property.
• It comes from the spectrum of light (energy
  distribution of light versus wavelength)
  interacting with the spectral sensitivities of
  the light receptors (photoreceptors) in the eye.

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Human Visual System

• Human visual system is sensitive to a narrow
  range of the electromagnetic spectrum.
  (Approximately from 380nm to 740nm.)

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Human Visual System

• The diameter of the eyeball is around 22mm.
• Retina is a thin layer of neural cells that lines
  the back of the eyeball.
• Retina contains photoreceptors (rods and cons)
  that respond to light.
• Fovea is the most sensitive part of the retina
  it is responsible for our sharp central vision.
• Some birds (such as hawks) have more than one
  fovea. (two).
• The axons (coming from receptors) exit the eye
  at the optic disc (blind spot), forming the optic
  nerve.
• There are 1.2million axons in the optic nerve.
• There are 130million photoreceptors. ? A large
  amount of pre-processing is done within the
  retina. 10 of the axons are devoted to the fovea
  area.

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0.5mm
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Human Visual System

• There are two classes of receptors cones and
  rods.
• Cones
• Sensitive to color (there are three cone types in
  humans)
• Produces high-resolution vision
• 6-7 million cone receptors, located primarily in
  the central portion of the retina
• Rods
• Not involved in color vision
• 75-150 million rod receptors, distributed over
  retina
• Sensitive to low levels of illumination. Not
  effective in bright light.
• Produces lower-resolution vision

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Human Visual System

• There are three types of cones in humans

65 sensitive to Long-wavelength 33 sensitive to
Medium 2 sensitive to Small

• 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.

Human lens and cornea are increasingly
absorvative to smaller wavelengths, which sets
wavelength sensitivity limit to around 380nm.
Humans lacking lens reported to see ultraviolet.
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Human Visual System

• Light is reduced to three color components by
  the eye.
• These values are called tristimulus values.
• The set of all possible tristimulus values
  determines the human color space.
• It is estimated that humans can distinguish
  around 10million colors.

The mechanisms of color vision within the retina
are explained well in terms of tristimulus
values. The way the values sent out of eye is
little different A dominant theory says that
color is sent out of the eye in three opponent
channels a red-green channel, a blue-yellow
channel and a black-white "luminance" channel.
These channels are constructed from the
tristimulus values.
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Human Visual System

• Color constancy (Chromatic adaptation) The
  perceived color of objects remains relatively
  constant under varying illumination conditions.
  This helps us identify objects.
• A red apple appears red in sunlight, at sunset,
  in florescent illumination, etc. Of course, this
  works only if the illumination contains a range
  of wavelengths. The HVS determines the
  approximate composition of the illuminating
  light, and then discounted to obtain the objects
  true color or reflectance.

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Human Visual System
Which square is darker? A or B?
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Human Visual System
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Human Visual System
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A Color Blindness Test
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3
5
2
56
8
26
6
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Human Visual System

• Colors consisting of a single wavelength are
  called pure spectral or monochromatic colors.
• Most light sources are mixtures of various
  wavelengths of light. If they produce a similar
  stimulus in the eye, a non-monochromatic light
  source can be perceived as a monochromatic light.
• For a non-monochromatic light source, we may talk
  about the dominant wavelength (or color), which
  identifies the single wavelength of light that
  produces the most similar sensation.
• Of course, there are many color perceptions that
  cannot be identified by pure spectral colors,
  such as pink, tan, magenta, achromatic colors
  (black, gray, white).

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Human Visual System

• Two different light spectra that have the same
  effect on the three color receptors will be
  perceived as the same color.
• Most human color perceptions can be generated by
  a mixture of three colors, called primaries.
• This is used to reproduce color in photography,
  printing, TV, etc.

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CIE

• In 1931, the Commission Internationale de
  lEclairage (CIE) established standards for color
  representation. Subjects were shown color patches
  and asked to match the color by adjusting three
  monochromatic colors. Based on the experiments,
  they defined the color-matching-functions

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Tristimulus

• Let X, Y, and Z be the tristimulus values.
• A color can be specified by its trichromatic
  coefficients, defined as

X ratio
Y ratio
Z ratio
Two trichromatic coefficients are enough to
specify a color. (x y z 1)
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CIE Chromaticity Diagram
Input light spectrum
y
x
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CIE Chromaticity Diagram
Input light spectrum
y
x
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CIE Chromaticity Diagram
Input light spectrum
y
700nm
Boundary
380nm
x
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CIE Chromaticity Diagram
Input light spectrum
Boundary
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CIE Chromaticity Diagram
Light composition
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CIE Chromaticity Diagram
Light composition
Light composition
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CIE Chromaticity Diagram

• The CIE chromaticity diagram shows the human
  color space as a function of x and y.
• Boundary indicates the pure spectrum colors.
  (Full saturation.)
• Inside the boundary shows mixture of spectrum
  colors.

Boundary
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CIE Chromaticity Diagram

• The CIE chromaticity diagram is helpful to
  determine the range of colors that can be
  obtained from any given colors in the diagram.

Gamut The range of colors that can be produced
by the given primaries.
Source http//hyperphysics.phy-astr.gsu.edu/hbase
/vision/visioncon.htmlc1
http//www.brucelindbloom.com/index.html?Eqn_Chrom
Adapt.html
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CIE Chromaticity Diagram

RGB Gamma corrected values Green
Corresponding RGB with gamma 1.8 Orange with
gamma 2.2
Green ColorMatch primaries, D50 Orange sRGB
primaries, D65
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Mixtures of Light

• The primary colors (primaries) can be added to
  produce the secondary colors of light.

Example Color TV displays use this additive
nature of colors. An electron gun hits red,
green, blue phosphors (with different energies)
in a small region to produce different shades of
color.
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Mixtures of Light

• In printing, subtractive primaries are used
• Cyan absorbs only Red.
• Magenta absorbs only Green.
• Yellow absorbs only Blue.

M
Y
C
In printing, dark colors may be obtained by
addition of black ink. Such color systems are
known as CMYK systems.
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Color Space

• A color space relates numbers to actual colors
  it contains all realizable color combinations.
• A color space could be device-dependent or
  device-independent.

B
An RGB color space has three components Red,
Green, and Blue. But, it does not specify the
exact color unless Red, Green, and Blue are
defined.
R
G
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.
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Color Space
The Adobe RGB is developed by Adobe in 1998. It
was designed for printers it has a wider gamut
than sRGB.
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Color Space

• HSV color space defines color in terms of Hue,
  Saturation, and Value.
• Hue is the color type (such as, red, blue,
  yellow). (0-360 degrees)
• Saturation is the purity of the color. (0-100)
• Value is the brightness of the color. (0-100)
• HSV is not device-independent. It is defined in
  terms of RGB intensities.
• It is commonly used in computer graphics
  applications.

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Color Space

• YUV color space defines color in terms of one
  luminance (brightness) and two chrominance
  (color) components.
• YUV is created from RGB components.

YCbCr
YUV
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Color Space
Profile Connection Space
Output device
Input device
Color space conversion

• International Color Consortium (ICC) was
  established in 1993 to create an open color
  management system.
• The system involves three things color profiles,
  color spaces, and color space conversion.
• The color profile keeps track of what colors are
  produces for a particular devices RGB or CMYK
  numbers, and maps these colors as a subset of the
  profile connection space.

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Color Space
Profile Connection Space
Output device
Input device
Color space conversion
When there is gamut mismatch, There should be
color rendering.
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CIELAB (CIE Lab)

• It was found that CIExyz is not a perceptually
  uniform color space The minimum distance between
  two discernable colors differs in different parts
  of the CIExyz diagram.
• Perceptually linear means that a change of the
  same amount in a color value should produce a
  change of about the same visual importance. When
  storing colors in limited precision values, this
  can improve the reproduction of tones.

• Lab color space was defined in 1976.
  Conversion from XYZ to Lab is

Xn, Yn and Zn are the CIE XYZ values of the
reference white point.
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White Point

• A white point is the reference point to define
  the color white.
• Primaries plus the white point (indicating power
  ratio of primaries) should be given.
• Depending on the application, different
  definitions of white are needed to get acceptable
  results. For example, photographs taken indoors
  may be lit by incandescent light, which are
  relatively orange compared to daylight. Defining
  white as daylight will give unacceptable
  results when attempting to color-correct a
  photograph.

A list of common white points
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High Dynamic Range (HDR) Imaging

• The range of radiances is more than 1012
  candela/m2

100
Range of human eye at an instant is around 1041
(4log units) Human eye can adapt to see much
wider range.
Candela is the unit of luminous intensity (power
emitted by a light source in a particular
direction, with wavelengths weighted by the
sensitivity of the human eye.
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HDR

• The range of radiances is more than 1012
  candela/m2

100
Range of Typical Displays from 1 to 100 cd/m2
0 255
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Sensitivity of Eye
Cone dominated
Gain
rod
cone
log Gain
1000 cd/m2
6
-2
-6
0
2
4
-4
log La
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Sensitivity of Eye
Rod dominated
0.04 cd/m2
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Sensitivity of Eye
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HDR

• The range of image capture devices is also low

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HDR

• The range of image capture devices is also low

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HDR

• HDR image rendered to be displayed on a LDR
  display.

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HDR Problems

• How to capture an HDR image with LDR cameras?
• How to display an HDR image on LDR displays?

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• Capture multiple images with varying exposure.
• Combine them to produce an HDR image.

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Creating HDR from Multiple Pictures
Measured intensity, z
t1
t2
Irradiance, E
t2
t1
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Creating HDR from Multiple Pictures
Measured intensity, z
t1
z1
t2
t2
t1
z2
E
Irradiance, E
z1 t1 E z2 t2 E
Estimates
Take a weighted sum of E1 and E2
E1z1/t1 E2z2/t2
w2
w1
E( w1E1 w2E2 ) / (w1w2)
E
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Creating HDR from Multiple Pictures
Measured intensity, z
t1
z1
t2
t2
t1
z2
E
Irradiance, E
z1 t1 E z2 t2 E
Estimates
Take a weighted sum of E1 and E2
E1z1/t1 E2z2/t2
w
E( w(z1)E1 w(z2)E2 ) / (w(z1)w(z2))
z
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Creating HDR from Multiple Pictures
In general, the camera response is not linear.
f
z1 f ( t1 E ) z2 f ( t2 E )
t2
t1
g
E1 g (z1) / t1 E2 g (z2) / t2
z
w
w is sometimes chosen as the derivative of f.
(Mann)
E( w(z1)E1 w(z2)E2 ) / (w(z1)w(z2))
z
Questions How to estimate g and t?
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Radiometric Self Calibration
Polynomial model
Exposure ratios
Cost function
Solve using
If exposure ratios are not known, solve
iteratively
(Nayar)
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Tone Mapping
Given an HDR image, how are we going to display
it in an LDR display?
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Tone Mapping
Given an HDR image, how are we going to display
it in an LDR display?
Linear
Nonlinear
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Durand Dorsey
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Durand Dorsey
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Durand Dorsey
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Durand Dorsey
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Durand Dorsey
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Durand Dorsey
Durand Dorsey
? Bilateral filter
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Durand Dorsey
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Durand Dorsey
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Durand Dorsey
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Spatially Varying Exposures

• Instead of capturing multiple pictures, allow
  different amounts of light pass for different
  pixel positions.
• Estimate the missing pixels.
• Combine to obtain an HDR image.

Nayar
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Image Reconstruction Interpolation
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Image Reconstruction Aggregation
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HDR image examples
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HDR image examples
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HDR image examples
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Retinex Image Processing
Received intensity is a product of illuminance
and reflectance I LR Illumination components
changes slowly. Reflectance component changes
fast. Take the logarithm of I log(I) log(L)
log(R) Apply a high-pass filter to obtain the
reflectance.
Homomorphic filter
Multi-scale retinex
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Retinex Image Processing
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Retinex Image Processing
http//dragon.larc.nasa.gov/
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Retinex Image Processing
http//dragon.larc.nasa.gov/
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Retinex Image Processing
Vivek Agarwal
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Retinex Image Processing