Friday 11 February 2011
Lecture 12: Image Processing
Reading
Ch 7.1 - 7.6
Last lecture: Earth-orbiting satellites
Image Processing
Because of the way most remote-sensing
texts are organized, what strikes most students
is the vast array of algorithms with odd names
and obscure functions
What is elusive is the underlying simplicity.
Many algorithms are substantially the same –
they have similar purposes
and similar results
Image Processing
There are basically five families of
algorithms that do things to images:
1) Radiometric algorithms
change the DNs
Calibration
Contrast enhancement
2) Geometric algorithms
change the spatial arrangement of pixels or adjust
DN’s based on their neighbors’ values
Registration
“Visualization”
Spatial-spectral transformation
Spatial filtering
Contrast stretching & calibration
Enhancement: Imagine a DN histogram centered at 75 DN and running from 50 to 100. In lab, you would
move sliders to 50 and 100 DN to display it well.
Mathematically, you are saying that (100-50)=50 DN’s are going to be packed into 256 gray levels, DN’.
Furthermore, the center of the distribution will be 128 DN’.
DN’=gain *DN+offset
So the amplification factor or gain will be 256/(100-50)=5.12: DN’=5.12*DN+offset
Now if we take 75 DN, the central value that we want to be 128, and multiply it by 5.12, we get
384 DN’, so we need to subtract 256 to get the right answer: DN’=5.12*DN-256.
Check: DN’=5.12*50-256 = 0; DN’=5.12*75-256=128; DN’=5.12*100-256=156
Calibration: We measure radiance in DNs, but we want to know reflectance. So we can take a known target
(say, black and white cardboard with reflectances measured in the lab of 5 and 25%) and image them to find
out what radiance DN’s they give (say, 13 and 47, respectively). Then we can do a controlled contrast stretch
to give the image in reflectance units:
Now, the gain will be DDN /Drefl = (25-5)/(47-13)=0.59 (That is, refl=0.59*DN+offs, and we find offset by
Knowing 0.59*13=5, or offset = 5-0.59*13=5-7.67=-2.67, so refl=0.59*DN-2.67.
Check: 25=0.59*47-2.67=25.06 (roundoff)
Calibration is just a special kind of contrast stretch
Geometric registration
Acquired image,
distorted
Map with locations of
control points
Pixel locations in original and
corrected images
DN values in corrected image
are found by interpolation from
the nearest neighbors in the
acquired image
Image Processing
3) Spectral analysis algorithms
are based on the relationship of DNs within a given pixel
Color enhancement
Spectral transformations (e.g., PCA)
Spectral Mixture Analysis
4) Statistical algorithms
characterize or compare groups of radiance data
Estimate geophysical parameters
Spectral similarity (classification, spectral matching)
Input to GIS
Image Processing
5) Modeling
calculate non-radiance parameters from the radiance
and other data
Estimate geophysical parameters
Make thematic maps
Input to GIS
Image Processing
There is a dazzling array of things for the future
professional to become familiar with
We’re trying to over-simplify it to begin with
Most algorithms are handled pretty well in most
remote-sensing texts.
Spectral Mixture Analysis is an exception, so…
- we’ll look at Spectral Mixture Analysis next lecture
Image Processing Sequence
(single image)
Raw image
data
1.
Image display/inspection
2.
Instrument calibration
3.
Image rectification,
cartographic projection,
registration, geocoding
4.
Atmospheric compensation
5.
Pixel illumination-viewing geometry
(topographic compensation)
Working image
data
Pre-processing
Image Processing Sequence
(single image)
Working image
data
6.
Further image processing
7.
Spectral analysis
8.
Selection of training
data/endmembers
9.
10.
Initial classification or other type
of analysis
Interpretation/verification
or further analysis
Product
Processing
Ratios in 2-space
TM3
60
Ratio – 11
sunlit
50
Reflectance, %
TM4
TM4
Ratio – 1.5
40
30
20
10
Ratio - 1.1
shadowed
0
0
1
2
3
shadow
Wavelength, micrometers
TM3
Ratios
The Vegetation Index (VI) = DN4/DN3 is a ratio. Ratios
suppress topographic shading because the cos(i) term
appears in both numerator and denominator.
DN4 
I 4r4
cos(i )
DN3 
I 3r3
cos(i )


RATIO4,3 
I 4r4 cos(i )  I 4 r4

I 3r3 cos(i )  I 3 r3
NDVI
Normalized Difference Vegetation Index
DN4-DN3 is a measure of
how much chlorophyll
absorption is present, but it
is sensitive to cos(i) unless
the difference is divided by
the sum DN4+DN3.
DN 4
I 4r4

cos(i); DN3 
I 3r3

cos(i)
NDVI 
I 4r4 cos(i)  I 3r3 cos(i ) 
I 4r4 cos(i)  I 3r3 cos(i) 
NDVI 
I 4r4  I 3r3
I 4r4  I 3r3
Dimension rotation
y
 x '   cos sin   x 
 y '     sin cos   y 
  
 
  45
 x '   0.7070.707   x 
 y '     0.7070.707  y 
  
 
x '  0.707 x  0.707 y
y’
x’
0.7x,0.7y
-0.7x, 0.7y
+
x
y '  0.707 x  0.707 y
y
  60
 x '   0.5 0.866   x 
 y '     0.8660.5   y 
  
 
x '  0.5 x  0.866 y
0.5x,0.87y
y '  0.866 x  0.5 y
  90
-087x,0.5y
+
y
 x '   0.5 0.866   x 
 y '     0.8660.5   y 
  
 
x'  0 x  1 y
x’
x
0x,1y
y '  1 x  0 y
+
y’
x
-1x,0y
Principal Component Analysis (PCA)
Designed to reduce redundancy in multispectral
bands
Topography - shading
Spectral correlation from band to band
Either enhancement prior to visual interpretation
or pre-processing for classification or other
analysis
Compress all info originally in many bands into
fewer bands
http://en.wikipedia.org/wiki/Principal_component_analysis
Principal Component Analysis (PCA) The math behind the button
In the simple case of 45º axis rotation,
cos  sin 
-sin  cos 
[ ] [ ] [
PC1
DN1’
=
=
PC2’
DN2’
][ ]
DN1
DN2
Finding 
cov 
 = 45º
[
n11 n12
n21 n22
]
 DNi ,k  DN i 
n
var iance n i ,i 
2
k 1
n 1
;
 DNi  DN i DN j  DN j 
n
cov ariance n i , j 
k 1
n 1
Cov’=RTcovR; cov’ is the matrix having
eigenvalues as diagonal elements and
RT is the transpose of R. Eigenvalues
can be found by diagonalizing cov. R
has eigenvectors as column vectors
http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf
http://en.wikipedia.org/wiki/Principal_component_analysis
Principal Component Analysis
In the simple case of 45º axis rotation,
PC1 DN3 cos(45)  DN4 sin( 45)
PC2   DN3 sin( 45)  DN4 cos(45)
The rotation in PCA depends on the
data. In the top case, all the image
data have similar DN2/DN1 ratios but
different intensities, and PC1 passes
through the elongated cluster.
PC1
PC2
In the bottom example, vegetation
causes there to be 2 mixing lines
(different DN4/DN3 ratios (and the
“tasseled cap” distribution such that
PC1 still passes through the centroid
of the data, but is a different rotation
that in the top case.
Tasseled Cap Transformation
Transforms (rotates) the data so that the majority of the
information is contained in 3 bands that are directly
related to physical scene characteristics
Brightness (weighted sum of all bands – principal variation in
soil reflectance)
Greenness (contrast between NIR and VIS bands
Wetness (canopy and soil moisture)
Tasseled Cap Transformation (TCT)
TCT is a fixed rotation that is designed so that the mixing line
connecting shadow and sunlit green vegetation parallels one
axis and shadow-soil another. It is similar to the PCT.
Next lecture – Spectral Mixture Analysis