-We decided to work on the grey scale version of the thermal infrared.
-This one has lower resolution then the rest of the bands, with 120m
-spatial resolution while the others have 30m spatial resolution.
-
-The high pass filtering seem to enhance the borders between the
-pixels. Edge detection gave us the positions of glaciers and water.
-We tried a gradient filter using this 3x3 matrix: [ 1 2 -1 / 2 0 -2 /
-1 -2 -1 ]. It gave a similar result to the edge detection.
-
-
-We also tried unsharp filtering using this 3x3 matrix: [ -1 -1 -1 / -1
-8 -1 / -1 -1 -1 ]. This gave similar results to the edge detection
-too.
-
-We started to suspect that the reason the 3x3 filters gave almost the
-same result was that the fact that the spatial resolution of the
-thermal band is actually 4x4 pixels. Because of this, we tried with a
-5x5 matrix, making sure it sums up to 0.
-
- -1 -1 -1 -1 -1
- -1 -1 -1 -1 -1
- -1 -1 24 -1 -1
- -1 -1 -1 -1 -1
- -1 -1 -1 -1 -1
-
-Next, we tried some different weight:
-
- -1 -1 -1 -1 -1
- -1 -2 -2 -2 -1
- -1 -2 32 -2 -1
- -1 -2 -2 -2 -1
- -1 -1 -1 -1 -1
-
-This one gave more lines showing the borders between the thermal
-pixels.
-
-From: shanette Dallyn <shanette_dallyn@yahoo.ca>
-Subject: Re: My notes from todays exercise
-To: Petter Reinholdtsen <pere@hungry.com>
-Date: Sat, 30 Apr 2005 15:16:59 -0400 (EDT)
-
-Hey Petter!
- Allright, I looked up some stuff on statistics and the most valuable
-conclusion that I can come up with for the histograpm peak question is:
-"The peak values of the histograms represent the the spectral sensitivity
-values that occure the most often with in the image band being analysed"
-
-For the grey level question go to http://www.cs.uu.nl/wais/html/na-dir/sci/
-Satellite-Imagery-FAQ/part3.html I found this and thought that the first major
-paragraph pretty much answered the question for the grey levels.
-
-theory of convolution:
-
- Specialty Definition: Convolution
-
- (From Wikipedia, the free Encyclopedia)
-
-In mathematics and in particular, functional analysis, the convolution
-(German: Faltung) is a mathematical operator which takes two functions and and
-produces a third function that in a sense represents the amount of overlap
-between and a reversed and translated version of .
-
-The convolution of and is written . It is defined as the integral of the
-product of the two functions after one is reversed and shifted.
-
-The integration range depends on the domain on which the functions are
-defined. In case of a finite integration range, and are often considered as
-cyclically extended so that the term does not imply a range violation. Of
-course, extension with zeros is also possible.
-
-If and are two independent random variables with probability densities and ,
-respectively, then the probability density of the sum is given by the
-convolution .
-
-For discrete functions, one can use a discrete version of the convolution. It
-is then given by
-
-When multiplying two polynomials, the coefficients of the product are given by
-the convolution of the original coefficient sequences, in this sense (using
-extension with zeros as mentioned above).
-
-Generalizing the above cases, the convolution can be defined for any two
-square-integrable functions defined on a locally compact topological group. A
-different generalization is the convolution of distributions.
-
-I hope this will help!
-
-Shanette
+<img src="jotunheimen-band4.jpeg" width="40%">'
+<p clear="all">We decided to work on the grey scale version of the
+near infrared (band4). We changed the colour assignment to use this
+band for all three colours, giving us a gray scale image.</p>
+
+<img src="jotunheimen-band4-low3.jpeg" width="40%">'
+<p clear="all">We applied the 3x3 low pass filter on this image, and
+this gave us almost the same image as the original. If you look
+closely you can see that some white dots in the original disapper, and
+some of the water edges seem to blur very slightly.</p>
+
+<img src="jotunheimen-band4-high3.jpeg" width="40%">'
+<p clear="all">We also tried the 3x3 high pass filter on the band4
+grey scale image. This gave a very noisy image. Edges of vallies and
+ice are not well defined. The black waters are still obvious.</p>
+
+<img src="jotunheimen-band4-edge3.jpeg" width="40%">'
+<p clear="all">We also tried the 3x3 edge detection, and this gave us
+an image that makes it difficult to distinguish elevation features
+such as the valleys. Rather, edge detection allows us to study main
+features in an area like the lakes. (insert band4 edge 3 image)
+
+<img src="jotunheimen-band4-grad3.jpeg" width="40%">'
+<p clear="all">We tried a gradient filter using this 3x3 matrix. The
+matrix was chosen to make sure the sum of all the weights were zero,
+and to make sure the sum of horizontal, vertical and diagonal numbers
+were zero too.</p>
+
+<p><table align="center">
+ <tbody><tr><td>1</td><td>2</td><td>-1</td></tr>
+ <tr><td>2</td><td>0</td><td>-2</td></tr>
+ <tr><td>1</td><td>-2</td><td>-1</td></tr>
+</tbody></table></p>
+
+<p>The gradient filter used gave us enhancement on lines in the
+vertical, horizontal and diagonal directions. This is seen by the
+white lines that outline certain areas of main features like the
+rivers within the vallies and some of the lakes.</p>
+
+<img src="jotunheimen-band4-neg1.jpeg" width="40%">'
+<p>When we rework the matrix to equal negative one, we end up with a
+lot of noise in the image that also seems to blurr the image. Using a
+negative one matrix is not optimal if you are trying to obtain
+sharpness.</p>
+
+<p><table align="center">
+ <tbody><tr><td>-1</td><td>-1</td><td>-1</td></tr>
+ <tr><td>-1</td><td>7</td><td>-1</td></tr>
+ <tr><td>-1</td><td>-1</td><td>-1</td></tr>
+</tbody></table></p>
+
+<img src="jotunheimen-band4-plus1.jpeg" width="40%">'
+<p clear="all">We then tried with a 3x3 matrix were the sum of all
+values equals 1, to enhance the high frequency parts of the image.</p>
+
+<p><table align="center">
+ <tbody><tr><td>-1</td><td>-1</td><td>-1</td></tr>
+ <tr><td>-1</td><td>9</td><td>-1</td></tr>
+ <tr><td>-1</td><td>-1</td><td>-1</td></tr>
+</tbody></table></p>
+
+<p clear="all">This gave us a sharper looking image compared to the
+result of the negative 1 filter. This is not really obvious unless
+one is comparing the two images carefully. In order to see more
+differences the matrix sums would have to be more then plus/minus one.</p>
+
+<h2>References</h2>
+
+<ul>
+ <li><a href="http://www.cs.uu.nl/wais/html/na-dir/sci/Satellite-Imagery-FAQ/part3.html">Satellite-Imagery-FAQ</a>
+</li></ul>
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