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

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Thursday, 14 January

Reading

Ch 2.3

http://www.bway.net/~jscruggs/film.html

(color film)

1

- What we covered:
- Image geometry
- Color vs. B/W, shape and composition
- Interpretation of some images

2

Color

Color is a sensation that can be predicted and controlled

Color has 3 dimensions and can be simulated by

radiances at three different l’s

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

3

The electromagnetic spectrum

Light is energy - Q =hnin ergsor joules (J)where

h = Planck’s constant, 6.63·10-34 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 radianceL and the units are W m-2 sr-1.

WattsW (power) are energy per unit time (J s-1)

Sr stands for steradian and is the solid angle subtended by the pixel

4

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 p*C. 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.

Let’s 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

5

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 = 10-3mm

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Additive Color

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Red

Red

Green

Green

Blue

Blue

The spectrum and color

Spectral yellow

Gray

brightness

Wavelength, l (mm)

Red

Green

Blue

Cartoon spectrum –

A useful tool

8

Red

Red

Red

Red

Green

Green

Green

Green

Blue

Blue

Blue

Blue

=

Additive Color

+

9

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

11

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

12

A simple perceptual

color space (HSI)

HUE

SATURATION

INTENSITY (LIGHTNESS)

13

2) RGB radiance space

r=R/(R+G+B)

g=G/(R+G+B)

b=B/(R+G+B)

B

b

G

g

0

r

R

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3) Transformed data space

r=R/(R+G+B)

g=G/(R+G+B)

b=B/(R+G+B)

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 coordinatesrgb.

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

15

g

Additive mixtures

r

b

16

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

17

Natural color

Intensity

Transformed

Viking Lander

RGB images

of Mars

SAT

HUE

INT

18

Color is created by selective Absorption

Bouguer

If L is the radiance from a source at strength Loafter passage

through an absorbing medium such as the atmosphere, then:

L = e-kz LoW 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)

19

Fraction of light transmitted

Thickness, mm

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

20

- 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)

21

A word about filters…

Filters

Transmittance

l, mm

Filter functions

22

“Subtractive” Color

23

Red

Red

Red

Green

Green

Green

Blue

Blue

Blue

“Subtractive” Color

Red-transmitting filter

Input spectrum

100%

1%

1%

*

Filtered spectrum

=

Filter

Scene

24

Remember: “subtractive” mixing is physically done by multiplication

white

light

green

light

dark

green

light

green

filter

yellow

filter

R: 1.0 * 0.0 = 0.0; * 0.8 = 0.0

G: 1.0 * 0.9 = 0.9; * 0.8 = 0.7

B : 1.0 * 0.0 = 0.0; * 0.0 = 0.0

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