International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
1 Band 1 > 50 Class | (Terminal)
Band 1 <50 2 (3)
2 Band 5 <80 Class 2 (Terminal)
Band 5 > 80 . Class 3 (Terminal)
The form showed in (3) can be used when the classification tree
contains many nodes, which complicate graphical
representation. The next section gives results from applying
CART to a high-dimensional classification problem with real
data. The trees were constructed by software GenStat.
3. RESULTS USING HYPERSPECTRAL IMAGES
Two image segments of a rural area in the state of Indiana-USA
collected by the sensor AVIRIS were analysed and classified
using CART. Although the AVIRIS sensor has some 220 bands,
only 195 were used because 25 bands were excluded during the
pre-processing due to presence of the noise.
3.1 AVIRIS - Scene 1
In the first segment, three classes with relatively similar spectral
response were considerate: w;: woods, ws: soybean and w;:
corn. The spectral behaviour is presented in the Figure 3.
8000
7000 Woods Corn
5 6000 Corn Soybean
E 5000 ^ c Woods
e Soybean
£ 4000 A
2
e 3000
2000
1000 ; ipi ; "
0 2040.80.80. 100 120.140. 160.189 200 220
Bands
Figure 3. Mean spectral behaviour of the three classes denoted
by woods, soybean and corn
Reading only the data for Woods and Soybean, a very simple
tree classifies the 1747 pixels into two classes. The tree has
only three nodes, two of which are terminal nodes, and the
dichotomy is based solely on Band 9, as shown by Figure 4. If
the count in Band 9 is less than 4204, the pixel is classed as
Woods; otherwise it is Soybean. The misclassification rate is
Zero.
r—
Band 9 « 4204 ( £ )
y TN
7
w3
Figure 4. Decision tree to separate Woods (w;) from Corn (w3)
Similarly, the separation of Woods from Corn is equally simple,
and depends on the value in Band 10. If the count in Band 10 is
less than 3964, the pixel is classed as Woods; otherwise it is
Corn. Again, the misclassification rate is zero.
The separation of Soybean from Corn is more complex, as
shown by Table 1 and Appendix A. In this figure, the
separation requires 117 nodes, 59 of which are terminal nodes,
and the misclassification rate is 0.064 (6.4%).
Number of spectral
Pair of bands selected by
: the decision tree / Spectral bands
Classes aE 4
Misclassification
rate
Seeds 01 / 0.096 9
Soybean
Woods and 01 / 0.094 10
Corn
1:3,3,4, 5/8, 1, 12,14
33, 35, 39, 49, 69, 75,
Soybean and o 77.80 103 107 114,
Corn $376.46 134, 141, 142, 144, 145,
146, 151, 152, 163,172.
173, 179, 181,:188,.195
68
Table 1. Bands selected to discriminate between pairs of classes
when CART is applied and misclassification rate
CART really can operate as a data reduction technique, because
is possible to identify and retain those spectral bands which
result in small misclassification rates. From inspection of the
mean spectral behaviour of the classes, shown in Figure 3, it
can easily be seen that the separation of woods from the other
classes is easer than separating corn from soybean.
3.2 AVIRIS - Scene 2
The second image considered presents three classes of corn
with very similar spectral response: w,: corn, Wj. corn
minimum and w;: corn no till. The mean spectral behaviour is
presented in the Figure 5.
8000
7000 Corn
6000 Corn minimum
5000 Corn notill
4000
Digital numbers
3000
2000
1000
0 20 40 60 80 100 120 140 160 180 200 220
Bands
Figure 5. Mean spectral behaviour of the three classes denoted
by corn, corn minimum and corn no till
Construction of decision trees for the three corn classes, taken
in pairs, shows that a considerable reduction in the number of
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Pair of
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Corn and
Corn no till
Corn and
Corn min.
Corn min a
Corn no til
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