by John Nordlie
UNDER CONSTRUCTION
1.0 INTRODUCTION
As part of my work with Dr. Richard Parker in Space Studies
491, I wrote several computer programs dealing with image
processing and seven dimensional distances.
1.1 THE DATA
For image processing data, I obtained a subset of a landsat
thematic mapper dataset of the drift plains of North Dakota. This
subset consisted of six files (thematic mapper bands 1, 2,
3, 4, 5, and 7), each 1024 pixels across by 825 pixels long.
Each pixel was represented by one byte, and represents an albedo
value in its respective band.
1.2 THE PROGRAMS
Turbo Pascal ver. 5.5 was chosen for the programming
language. The first program I wrote (program #1) did not access
the landsat data. Instead, it calculated the number of possible
ways to generate a given distance between two points in a seven
dimensional matrix. The program used the brute force method, and
hence was quite a long time in running, so the runs were
restricted to -5 to 5 on all seven axes. The data generated by
program #1 is represented in the graph in fig. 1. Frequency vs.
distance squared was calculated in all graphs, rather than
frequency vs. distance. The reason for this was to save
processing time. Program #2 calculates the spectral distance
between neighboring points in the six dimensional landsat data.
Dr. Parker's theory was that neighboring pixels would stand a
good chance of being composed of similar substances, and hence
would have little spectral variation. The graph in fig. 2 shows
this theory to be basically correct. Other characteristics of
the image are present in fig. 2, but later programs were written
to subtract these out. You may note that the last distance
squared value in the graph in fig. 2 is quite large. This is
because instances of pixel distance squared of over 4097 were
placed here, serving as an overflow catcher. Dr. Parker also
wanted to compare pixels that would most likely be of differing
substances, so program #3 was written to compare a pixel with
another pixel 32 spaces away. This worked very well, as you can
see in the graph in fig. 3. The smoothness of the graph
indicates that the pixels compared were of differing substances
most of the time. Program #4 is a mixing algorithm which takes
the data from fig. 3 and calculates the mixing fraction between
the pixels. The results of this program can be seen in fig. 4.
The last program (#5) I wrote takes the data from neighbor and
mixed and subtracts them. This has the effect of removing the
random mixing variations from fig. 2, and hence indicating the
deviation of spectral distances between pixels considered to be
composed of identical substances. Ideally, all identical pixels
would have zero distance between them, but as you can see in fig.
5, this is not the case.
1.3 CONCLUSION
Research of the actual ground track of the landsat thematic
mapper sensors indicates that the programs I wrote were too
unsophisticated to accurately accomplish their intents, but since
the output data looks essentially correct, I think that they came
close. This project is far from over, but the semester, and
hence SpSt 491, is over.
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