Brightness - Remote Sensing and GIS Laboratory

WILD 5750/6750
LAB 6 – 10/08/2007
PRINCIPAL COMPONENT ANALYSIS
PCA
&
BRIGHTNESS– GREENNESS – WETNESS
BGW

Lecture review…
Transformation of a set of correlated
variables (i.e. bands) into a new set of
uncorrelated variables (PC).
Rotation of the original axes to new
orientations ti that t are orthogonal to
each other with little or no correlation
between variables
For remote sensing studies = predominantly exploratory in nature
Used to help in the extraction of features and to reduce dimensionality of data
After Lillesand and Keifer, 1994 – Lecture materials

Imagine… inputs + process
Interpreter Spectral Enhancement Principal Components
Save disk space: Stretch (0 – 255) but no further math post-
processing
Obtain Eigenvectors matrix + Eigenvalues table

Imagine… inputs + process
Interpreter t Spectral Enhancement Pi Principal i lComponents
Keep the
output t as
Float
Eigenvectors
matrix
Eigenvalues table
Number of
PC to keep:
1= Not
useful
6: Too
many

Imagine… results
Eigenvalues table:
% _ Variance
eigenvalueλ
px100
= 6
∑
p=1
eigenvalueλ λ p
How much variability was
captured in each new PC
Eigenvectors matrix:
How each new PC band is
obtained
Multiply each original TM
band by the eigenvectors
Sum the products to
Sum the products to
obtain the new Digital
numbers DN

Imagine… results
ViewerFile
FileOpen
OpenMulti layer arrangement
1 2 3
4 5 6
1: > Variance // 6: < Variance ~ Noise

Imagine… results
Factor loadings = what type of component (i.e. visible, infrared) is it
R
kp
=
a
kp
x
S
k
λ
p
Rkp: Factor loading
akp:Eigenvectorp for band k and component p
λp: Eigenvalue for the pth component
Sk: Standard deviation for band k

Assignment – Part A
•Brief description of PCA as a general statistical tool and its use for image processing –
use your book, lecture materials and Internet.
•Perform the PCA analysis for an image of your choice (if you do not have one of your own,
then use a small subset of the Rich county image)
•http://leupold.gis.usu.edu/~alex/WILD6750_lab_6/PCA_image_Calcs/
•Create snapshots of the input file, the output file, and individual bands.
•Report the table for the Eigenvalues and the matrix of Eigenvectors
•Determine the amount (%) of information contained in each band using the
Eigenvalues
•Interpret each output band and describe what the information contained in each
consists of (visual interpretation & factor loadings).
•http://leupold.gis.usu.edu/~alex/WILD6750_lab_6/PCA_image_Calcs/
•Of what use - if any - are the last set of components
Jensen, 2005 -

Lecture review…
Brightness defined in the direction of soil
reflectance variation. Obtained from a weighted
sum of all bands. i.e. urbanized and bare soil
areas are evident in this image.
Greenness defined in the direction of
vegetation reflectance variation. Obtained from
the contrast of the visible bands (high absorption)
with the infrared bands (high reflectance). i.e. the
greater the biomass, the brighter the pixel value
in this image.
Greenness
Water
Healthy – dense
vegetation
Clear Turbid
Brightness
Concrete
Bare soil
Wetness information concerning the moisture
status of the environment (soil & plant moisture).
Obtained from the contrast of the sum of visible
and near-infrared with the sum of longer-infrared
bands. i.e. water bodies are very bright – greater
the moisture content = brighter response.
Third
Water
Clear Turbid
Wet soil
Brightness
Concrete –
Bare soil
Dry soil
Jensen - 2005

Imagine… input + process
Float
1 st three channels are:
(1) Brightness, (2)
Greenness, and (3)
Wetness
Huang and others, 2002
At-sensor reflectance coefficients

Imagine… input + process
We need a model will the following components:
a) Input image: Landsat TM Bands 1, 2, 3, 4, 5, and 7
b) Transformation coefficients i for each band and for each
main axis B, G, W
c) A linear combination function
d) Output image (float)

Imagine… results
ViewerFileOpenThree layer arrangement
B
G
W

Assignment – Part B
• We have 3 images for 3 different periods for the Camp Williams – Utah Lake area
(CWUL_Aug99.img, CWUL_Oct99.img, and CWUL_May00). Obtain BGW indices
for each of these images using the previously defined model and coefficients.
• Provide snapshots of the 3 results similar to the depiction in the previous slide.
Please label appropriately for each temporal scenario.
• By visually comparing the indices, what major changes do you see i.e. brightness differences
among temporal scenarios. What do you think is the cause for such changes - If any –
-----------------------------------------------------------------------------------------------------------------------------------
• We also have as ancillary data an image (GAP-CWUL.img) which contains land cover
categories from the SWRGAP project. This image can be used - Hopefully !! – to see the
rationale of our 3 Greenness indices across time.
(a) Briefly, how would you derive simple inferences Hint! – Think about seasonal precipitation
and phenology patterns
(b) Choose two land cover categories (of your choice), and record 5 values for each land cover
category and for each temporal scenario (Greenness indices only). Prepare a table with these
values and a simple graph and include them in your report. Does this help you for answering (a)
(c) Briefly, mention 3 examples for which you would use BGW indices
Have fun!

a) In a viewer, load the Land cover image
b) Select two land cover categories – your choice -
c) For each category, determine the location (X, Y coordinates) for 5 points of your choice – try to
select these points so that they are spread over the image but within the land cover category that
you are assessing
d) Write down those coordinates
e) In a new viewer, load one of the BGW images you just derived
f) Extract the pixel information – not the LUT value! – for each one of the 5 points for the
GREENNESS channel
g) Repeat (e) and (f) for the other two BGW images
h) Record your values in a table / prepare a simple graph and annotate your observations

Suggested readings…
• Your book! Jensen – 2005 – Image enhancement – Vegetation transformation indices Chapter 8
• I will send digital copies of these by email
I will send digital copies of these by email
• Christ & Cicone – 1984 – A physically-based transformation of Thematic Mapper Data – The TM
Tasseled Cap
• Christ & Kauth – 1986 – The Tasseled Cap De-Mystified
• Huang and others – 2002 - Derivation of a Tasseled Cap transformation based on Landsat 7
at-satellite reflectance