Lecture 4: The spectrum, color theory and absorption and photogrammetry

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Lecture 4 The spectrum, color theory and
absorptionand photogrammetry
Friday, 14 January
Reading Ch 2.3 photography basics
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What was covered in the previous lecture

• Tuesdays lecture?
• Color, shape and texture
• Lighting and shadows
• Image examples
• Photogrammetry
• Orbits
• Image geometry
• Parallax and stereo

• LECTURES
• Jan 05 1. Intro
• Jan 07 2. Images
• Jan 12 3. Photointerpretation previous
• Jan 14 4. Color theory today
• Jan 19 5. Radiative transfer
• Jan 21 6. Atmospheric scattering
• Jan 26 7. Lamberts Law
• Jan 28 8. Volume interactions
• Feb 02 9. Spectroscopy
• Feb 04 10. Satellites Review
• Feb 09 11. Midterm
• Feb 11 12. Image processing
• Feb 16 13. Spectral mixture analysis
• Feb 18 14. Classification
• Feb 23 15. Radar Lidar
• Feb 25 16. Thermal infrared
• Mar 02 17. Mars spectroscopy (Matt Smith)
• Mar 04 18. Forest remote sensing (Van Kane)

• Today
• Color and the spectrum
• Color perception
• Additive subtractive color mixing
• Ternary diagrams and color transformations
• Selective absorption of light

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Color
Color is a sensation that can be predicted and
controlled Color has 3 dimensions and can be
simulated by radiances at three different
ls In natural color those are red, green and
blue but In remote sensing any 3 may be combined
as a false-color image Therefore we need to
understand color Color is created by selective
absorption, so we need to understand that first
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The electromagnetic spectrum
Light is energy - Q hn in ergs or joules (J)
where h Plancks constant, 6.6310-34 J s n
frequency (s-1) c/l (c speed of light,
3.00x108 ms-1, l wavelength (µm,nm,mm,cm,m)
For SI units frequently used in Remote Sensing,
see back cover of text
In remote sensing we commonly measure the flux of
photons from a unit surface for a certain amount
of time and by a camera or scanner a certain
distance away with a lens of a particular
diameter This flux is called the radiance L and
the units are W m-2 sr-1. Watts W (power) are
energy per unit time (J s-1) Sr stands for
steradian and is the solid angle subtended by the
pixel
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Review On Solid Angles, class website (Ancillary
folder Steradian.ppt)
On solid angles
On a plane, we can measure the angle q between 2
vectors sharing endpoint P, the center of a
circle of radius r. A radian is defined as the
angle that subtends an arc on a circle equal to
the radius. It is about 57 degrees (360/2p). A
circle is divided into 360 degrees, or 2p
radians.
In a volume, we can measure solid angles as shown
to the right, where P is the center of a sphere
of radius r and q is the solid angle of a cone
that intersects the sphere in a small circle of
circumference pC. A sphere (area 4pr2)
contains 4p steradians, where a steradian (sr) is
the unit of solid angle. The cone defined to the
right subtends a solid angle of 1 sr.
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Lets start with how humans sense
color Cone-shaped cells within the eye absorb
light in 3 wavelength ranges RGB They send
signals to the brain proportional to how much
light is absorbed The brain turns these signals
into the sensation of color Color has three
attributes hue, saturation, and intensity or
lightness color (perception) is related to
radiance (physical flux)
Section of the eye
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DAY Bright light
NIGHT Dim light
Rods are more sensitive than cones In bright
light, the three sets of cones send strong
signals to the brain that drown out the signal
from the rods. The signals are interpreted as the
sensation of color In dim light, the signal
from the single set of rods is dominant. It is
interpreted as the sensation of black/white (gray)
1 nanometer (nm) 10-9 m 10-3 mm
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Additive Color
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The spectrum and color
Spectral yellow
Gray
brightness
Wavelength, l (mm)
Red
Green
Blue
Cartoon spectrum A useful tool
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Additive Color

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Additive mixtures another framework
0, 100, 0
g
50, 50, 0
33, 33, 33
r
b
0, 0, 100
100, 0, 0
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A D D I T I V E M I X I N G
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To work with color, we use three different data
spaces Perceptual data space how we sense
color intuitively (Hue, saturation,
intensity) Radiance data space how the
color stimulus is described by the measured
image data Transformed DN
space a mathematical description of color
that is related to radiance
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A simple perceptual color space (HSI)
HUE
SATURATION
INTENSITY (LIGHTNESS)
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2) RGB radiance space
rR/(RGB) gG/(RGB) bB/(RGB)
B
b
G
g
0
r
R
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3) Transformed data space
rR/(RGB) gG/(RGB) bB/(RGB)
The CIE system characterizes colors by a
brightness parameter Y plus two color coordinates
x and y. The response of the eye is best
described in terms of three tristimulus
coordinates rgb. Colors that can be matched by
combining a set of three primary colors (ie, Red,
Green, Blue) are represented on the chromaticity
diagram by a triangle joining the coordinates for
the three colors. Any H,S pair can be expressed
in terms of the CIE color coordinates x and y,
but intensity is not represented.
g
y
r
b
x
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g
Additive mixtures
r
b
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Transformation from a Cartesian XYZ radiance
space to a spherical color space Longitude
hue (H) Co-latitude saturation (S) Radius
intensity (I)
XYZ may be any three tristimulus fluxes but are
treated as RGB
Z
Y
0
X
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Transformed Viking Lander RGB images of Mars
HUE
SAT
INT
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Color is created by selective Absorption
Bouguer
If L is the radiance from a source at strength
Lo after passage through an absorbing medium
such as the atmosphere, then L e-kz Lo W m-2
sr-1 (Beer-Lambert-Bouguer
Law) Light must either be reflected, absorbed,
or transmitted This is the rat law of
conservation L Lr La Lt e-kz describes
the of light transmitted through the medium
(assuming Lr 0) k is a value characteristic of
the absorptivity of the medium z is the length
of passage through the medium (which we take to
be homogeneous)
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Absorption by a homogeneous medium is a
constant-rate process for every mm of material
the light passes through, a certain fraction is
absorbed.
If it goes through z mm of medium, the total
light remaining is e-kz , where 1/k is the
scale depth that is, for every 1/k passage
through the medium, 1/e 1/2.718 36.8 of
the light remains.
Graph of absorption as a function of medium
thickness
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Absorption and color

• k is commonly different from wavelength to
  wavelength (kl)
• eg, more light might be absorbed in green than in
  red or blue
• When we see light having passed through such a
  filter, it appears magenta to us (ie, no green).
  
• We need to consider remote-sensing fluxes to be
  functions of wavelength
• Thus, radiance L (W m-1 sr-1) becomes spectral
  radiance Ll (W m-1 sr-1 µm-1)

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A word about filters
Filters
Transmittance
l, mm
Filter functions
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Subtractive Color
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Subtractive Color
Red-transmitting filter
Input spectrum
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100
1

Filtered spectrum

Filter
Scene
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• What was covered in todays lecture?
• Color, shape and texture
• Lighting and shadows
• Image examples
• Photogrammetry
• Orbits
• Image geometry
• Parallax and stereo

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What will be covered in next Tuedays lecture?

• Radiative transfer theory
• - where light comes from and how it gets
  there
• - we will trace radiation from its source to
  camera
• - the atmosphere and its effect on light
• - the basic radiative transfer equation DN
  aIgr b

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