mypapers/drafts/geg2210/assignment-8.html

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   9     <p><a href="http://www.geo.uio.no/geogr/geomatikk/oppgaver/bildeforbedring_eng.html">Assigment 8</a>
  10       in <a href="http://www.uio.no/studier/emner/matnat/geofag/GEG2210/index-eng.html">GEG2210</a>
  11       - Data Collection - Land Surveying, Remote Sensing and Digital
  12         Photogrammetry</p>
  13
  14     <h1>Image enhancement, filtering and sharpening</h1>
  15
  16     <p>By Petter Reinholdtsen and Shanette Dallyn, 2005-05-01.</p>
  17
  18 Logged into jern.uio.no using ssh to run ERDAS Imagine.  Started by
  19 using 'imagine' on the command line.  The images were loaded from
  20 /mn/geofag/gggruppe-data/geomatikk/
  21
  22 Tried to use svalbard/tm87.img, but it only have 5 bands.  Next tried
  23 jotunheimen/tm.img, which had 7 bands.
  24
  25 The pixel values in a given band is only a using a given range of
  26 values.  This is because sensor data in a single image rarely extend
  27 over the entire range of possible values.
  28
  29 <h2>Evaluation of the different bands</h2>
  30
  31 <h3>band 1, blue (0.45-0.52 um)</h3>
  32
  33   Visible light, and will display a broad range of values both over
  34   land and water.  Reflected from ice, as those are visible white and
  35   reflect all visible light waves.  Histogram show most values between
  36   30 and 136.  Mean values of 66.0668.  There are one wide peak with
  37   center around 50.  There are two peaks at 0 and 255.
  38
  39 <h3>band 2, green (0.52-0.60 um)</h3>
  40
  41   Visible light, and will display a broad range of values both over
  42   land and water.  Reflected from ice, as those are visible white and
  43   reflect all visible light waves.  Histogram show most values from 8
  44   to 120.  The mean value is 30.9774.  There are two main peaks at 20
  45   and 27.  There is also a pie at 0.
  46
  47 <h3>band 3, red (0.60-0.69 um)</h3>
  48
  49   Visible light, and will display a broad range of values both over
  50   land and water.  Reflected from ice, as those are visible white and
  51   reflect all visible light waves.  Histogram show most values from 33
  52   t 135, with one wide peak around 52.  There are also seem to be two
  53   peaks at 0 and 255.  The mean value is 34.3403.
  54
  55 <h3>band 4, near-infraread (0.76-0.90 um)</h3>
  56
  57   Water acts as an absorbing body so in the near infrared spectrum,
  58   water features will appear dark or black meaning that all near
  59   infrared bands are absorbed. On the other hand, land features
  60   including ice, act as reflector bodies in this band.  The histogram
  61   show most values between 7 and 110.  The mean is 40.1144.  There are
  62   two peaks at 7 and 40.
  63
  64 <h3>band 5, mid-infrared (1.55-1.75 um)</h3>
  65
  66   The ice, glaciers and water do not reflect any mid-infrared light.
  67   The histogram show most values between 1 and 178.  The mean is
  68   49.8098 and there are two peaks at 6 and 78, in addition to two
  69   peaks at 0 and 255.
  70
  71 <h3>band 6, thermal infrared (10.4-12.5 um)</h3>
  72
  73   Display the temperature on earth.  We can for example see that the
  74   ice is colder than the surrounding areas.  The histogram show most
  75   values between 36 to 122.  The mean is 102.734.  There are one wide
  76   peak around 53, in addition to two peaks at 0 and 255.
  77
  78 <h3>band 7, mid-infrared (2.08-2.35 um)</h3>
  79
  80   The ice, glaciers and water do not reflect any mid-infrared
  81   frequencies.  The histogram show most values between 77 and 150.
  82   The mean is 24.04, and there are one wide peak at 130 and a smaller
  83   peak at 83, in addition to one peak at 0.
  84
  85 Image enhancement
  86 -----------------
  87
  88 We can get a good contrast stretch by using the histogram
  89 equalisation.  This will give us the widest range of visible
  90 separation between features.
  91
  92 Displaying colour images
  93 ------------------------
  94
  95 Comparing a map we found on the web,
  96 <URL:http://home.online.no/~oe-aase/jotunheimen/jotun2000topper.jpg.>
  97 and the standard infrared image composition, we can identify some
  98 features from the colors used:
  99
 100  - water is black or green
 101
 102  - ice and glaciers are white, while snow is light green.
 103
 104  - vegetation is red.
 105
 106  - non-vegetation is brown or dull red when closer to snow and
 107    glaciers.
 108
 109 Next, we tried to shift the frequencies displayed to use blue for the
 110 red band, green for the near ir band and red for the mid ir (1.55-1.75
 111 um).  With this composition, we get some changes in the colours of
 112 different features:
 113
 114  - water is black
 115
 116  - ice and glaciers are light blue, while snow is dark blue.
 117
 118  - vegetation is light green and yellow.
 119
 120  - non-vegetation is red or brown.
 121
 122 <h2>Filtering and image sharpening</h2>
 123
 124 We decided to work on the grey scale version of the thermal infrared.
 125 This one has lower resolution then the rest of the bands, with 120m
 126 spatial resolution while the others have 30m spatial resolution.
 127
 128 The high pass filtering seem to enhance the borders between the
 129 pixels.  Edge detection gave us the positions of glaciers and water.
 130 We tried a gradient filter using this 3x3 matrix: [ 1 2 -1 / 2 0 -2 /
 131 1 -2 -1 ].  It gave a similar result to the edge detection.
 132
 133
 134 We also tried unsharp filtering using this 3x3 matrix: [ -1 -1 -1 / -1
 135 8 -1 / -1 -1 -1 ].  This gave similar results to the edge detection
 136 too.
 137
 138 We started to suspect that the reason the 3x3 filters gave almost the
 139 same result was that the fact that the spatial resolution of the
 140 thermal band is actually 4x4 pixels.  Because of this, we tried with a
 141 5x5 matrix, making sure it sums up to 0.
 142
 143    -1 -1 -1 -1 -1
 144    -1 -1 -1 -1 -1
 145    -1 -1 24 -1 -1
 146    -1 -1 -1 -1 -1
 147    -1 -1 -1 -1 -1
 148
 149 Next, we tried some different weight:
 150
 151    -1 -1 -1 -1 -1
 152    -1 -2 -2 -2 -1
 153    -1 -2 32 -2 -1
 154    -1 -2 -2 -2 -1
 155    -1 -1 -1 -1 -1
 156
 157 This one gave more lines showing the borders between the thermal
 158 pixels.
 159
 160 From: shanette Dallyn <shanette_dallyn@yahoo.ca>
 161 Subject: Re: My notes from todays exercise
 162 To: Petter Reinholdtsen <pere@hungry.com>
 163 Date: Sat, 30 Apr 2005 15:16:59 -0400 (EDT)
 164
 165 Hey Petter!
 166  Allright, I looked up some stuff on statistics and the most valuable
 167 conclusion that I can come up with for the histograpm peak question is:
 168 "The peak values of the histograms represent the the spectral sensitivity
 169 values that occure the most often with in the image band being analysed"
 170
 171 For the grey level question go to http://www.cs.uu.nl/wais/html/na-dir/sci/
 172 Satellite-Imagery-FAQ/part3.html I found this and thought that the first major
 173 paragraph pretty much answered the question for the grey levels.
 174
 175 theory of convolution:
 176
 177                       Specialty Definition: Convolution
 178
 179                    (From Wikipedia, the free Encyclopedia)
 180
 181 In mathematics and in particular, functional analysis, the convolution
 182 (German: Faltung) is a mathematical operator which takes two functions and and
 183 produces a third function that in a sense represents the amount of overlap
 184 between and a reversed and translated version of .
 185
 186 The convolution of and is written . It is defined as the integral of the
 187 product of the two functions after one is reversed and shifted.
 188
 189 The integration range depends on the domain on which the functions are
 190 defined. In case of a finite integration range, and are often considered as
 191 cyclically extended so that the term does not imply a range violation. Of
 192 course, extension with zeros is also possible.
 193
 194 If and are two independent random variables with probability densities and ,
 195 respectively, then the probability density of the sum is given by the
 196 convolution .
 197
 198 For discrete functions, one can use a discrete version of the convolution. It
 199 is then given by
 200
 201 When multiplying two polynomials, the coefficients of the product are given by
 202 the convolution of the original coefficient sequences, in this sense (using
 203 extension with zeros as mentioned above).
 204
 205 Generalizing the above cases, the convolution can be defined for any two
 206 square-integrable functions defined on a locally compact topological group. A
 207 different generalization is the convolution of distributions.
 208
 209 I hope this will help!
 210
 211 Shanette
 212
 213     <hr>
 214     <address><a href="mailto:pere@hungry.com">Petter Reinholdtsen</a></address>
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