CEE 615: Digital Image Processing
Due: Monday, 15 April
Problem set
7
: Principal Components Analysis
1.
PCA with multiband data:
TM scene for Boulder, Colorodo
Use the can_tmr image in the ENVI data directory. This is a 6

band sub

image of a Thema
tic Mapper
image (the thermal channel is excluded). Compute and display the statistics for the full scene
:
Basic
Tools => Statistics => Compute
New
Statistics
.
Be sure to request the covariance image and
eigenvalue plots. Save the statistics as a text f
ile.
a)
[3
]
Based on the
combined statistics (covariance matrix,
correlation matrix
,
and the first three PC
eigenvectors computed using the covariance matrix, which of the
original
bands
appears to
carr
y
the most information. Put another way, if variance is
taken to be equivalent to information,
elimination of which and how many of the original images would result in the least loss of
information in the first 3 PC images computed using the covariance matrix?
b)
[
2
]
Recompute the eigenvector statistics using
the correlation matrix as a base.
Transform => Principal Components => Forward PC Rotation =>
Compute new stats
Make sure to specify that the PC computation be based on the correlation matrix.
To see the
statistics, select
Basic Tools => Statistics => V
iew Statistics File
Then select the statistics file created during the PC computation.
Based on the correlation matrix
and the first three PC eigenvectors computed using the correlation matrix, which of the original
bands
appear to be
the most important.
c)
[
4
]
Visually inspect
the
PC images
created using the covariance and correlation matrices.
i.
How many of the images in each set appear to have any useful information?
Please describe
what you see and evaluate the utility of the images. Contrast what you se
e with the valuation
based on the eigenvalues.
There is no "right" answer here. This is a qualitative evaluation.
I find it helpful to view the
animation tool to view image sequences
[Select
Tools > animation
in the image window]
.
This will be particular
ly useful
later
for viewing hyperspectral image data sets.)
Another helpful
(but more time

consuming)
approach to comparing a relat
ively small set of
images is to
display all
the
im
age
s using the Scroll/Zoom mode:
1.
right click in the image,
2.
select
Display
Window Style > Scroll
/
Zoom
),
3.
turn off the auto placement feature (right click
> Zoom position
>
Auto Placement Off
)
,
4.
arrange the zoom images for easy comparison,
5.
link the images
6.
Navigate using the scroll window, view comparable regions in the zoom wi
ndow.
2.
PCA with multiband data:
MISI data of Rochester, NY
.
Use the
63

band
MISI
image
(ginna_2000_sub.img)
on the course assignments web page
.
Compute
and display the statistics for the scene (
Basic Tools => Statistics => Compute Statistics
)
.
Be sure
to request the covariance statistics and eigenvalue plot. Save the statistics as a text file. The
correlation and covariance matrices will be much easier to interpret (qualitatively) using the images
of the matrices. (The center wavelength of each band
will be displayed in the Available Bands
List.)
a)
[
1
]
Based on the image statistics using the covariance matrix, how many PC images are required
to account for 99.
0
% of
the variance? What about 99.
9
%?
I
n
each
case, how much more
variance would be explain
ed by adding one additional component
b)
[3
]
Based on the
correlation
matrix and the first three PC eigenvectors computed using the
covariance matrix
(shown graphically below)
, which of the original bands carry the most
information.
c)
Visually examine
the covariance PC images using the animation tool in ENVI.
i.
[1]
Does
noise
appear to
increase and information decrease steadily
with higher order PC
images? (Use the animation tool.)
ii.
[4]
Based on visual inspection, how many PC images would you keep?
There is no
"right" answer for this. I'm looking for your rationale for deciding whether there is useful
information in an image.
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