International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
Internat 
  
spectral bands is possible, giving misclassification rates about 
1%, as shown Table 2. 
  
— 7 - 
Number of spectral 
s bands selected by 
Pair of p n i 
UT the decision tree / Spectral bands 
Classes 
Misclassification 
rate 
  
], 2,3, 4/11, 37,38, 4] 
59, 103, 105, 106, 107, 
110, 139, 140, 142, 143 
144,150, 153,.157,.161 
173, 178, 185, 193, 194 
1,2/3,4, $617,910. 
11:13, 23, 40, 48, 77, 
78 92, 103, 105, 106, 
108, 109, 138, 142, 143, 
144, 164, 183, 186, 188, 
190 
12.35.68 973,93, 
96, 102, 106, 124, 144, 
153,162, 172 173,174, 
181, 190, 193 
Table 2. Bands selected to discriminate between pairs of classes 
when CART is applied and misclassification rate 
Corn and 
: 28 /1.0% 
Corn no till 
  
Corn and 
A : 31/1 195 
Corn min. 
  
Corn min and 
2 205 
Corn no till. 22/1.2*( 
  
  
  
In despite of the similar spectral response of the classes, CART 
can differentiate between them using fewer bands than those 
available in the full image. 
4. FINAL REMARKS 
The main conclusion of this work is that decision trees can be 
used to select features, even in high-dimensional space. When 
classes with very different spectral response are used, the data 
reduction is interesting because the spectral bands most useful 
for separating classes are identified. The results were even 
satisfactory for distinguishing between classes with similar 
spectral response, since it was possible to reduce the 
dimensionality considerably, whilst securing low rates of 
misclassification. 
The results show that decision trees employ a strategy in which 
a complex problem is divided into simpler sub-problems, with 
the advantage that it becomes possible to follow the 
classification process through each node of the decision tree. 
The software used (GenStat) can construct decision trees for 
separating three classes, in space of dimension p=195 and with 
numbers of pixels per class greater than 1500, in less than two 
minutes on a desk-top PC. This suggests that the use of the 
CART procedure to identify bands is a viable procedure. It 
must be emphasized that it is the GenStat algorithm itself that 
decides which spectral bands are to be retained, and which are 
to be discarded, when it constructs the decision tree. 
References 
Bittencourt, H. R., Clarke, R. T. 2003a. Logistic Discrimination 
Between Classes with Nearly Equal Spectral Response in High 
Dimensionality. Proc. 2003 IEEE International Geoscience and 
69 
Remote Sensing Symposium, Toulouse, France, July 21-25, pp. 
3748-3750. 
Bittencourt, H. R., Clarke, R. T. 2003b. Use of Classification 
and Regression Trees (CART) to Classify Remotely-Sensed 
Digital Images. Proc. 2003 IEEE International Geoscience and 
Remote Sensing Symposium, Toulouse, France, July 21-25, pp. 
3751-3753. 
Breiman, L., Friedman, J. H., Olshen, R. A., Stone, C. J. 1984. 
Classification and Regression Trees. Wadsworth, Belmont-CA. 
Cheriyadat and Bruce, 2003. Why Principal Component 
Analysis is not an Appropriate Feature Extraction Method for 
Hyperspectral Data. Proc. 2003 IEEE International Geoscience 
and Remote Sensing Symposium, Toulouse, France, July 21-25, 
pp. 3420-3422. 
Haertel, V., Landgrebe, D., 1999. On the classification of 
classes with nearly equal spectral response in remote sensing 
hyperspectral image data. /EEE Transactions on Geoscience 
and Remote Sensing, 37 (5), pp. 2374-2386. 
McLachlan, G. J., 1992. Discriminant Analysis and Statistical 
Pattern Recognition. Wiley Interscience, New York, pp. 323- 
332. 
Acknowledgments 
The authors would like to thank Victor Haertel and Denis 
Altieri from Centro Estadual de Pesquisas em Sensoriamento 
Remoto, RS, Brazil for contributions to the work. H.R.B. 
extends his warmest thanks to the PUCRS, especially Prof. 
Alaydes Biachi, for supporting this work. 
APPENDIX A 
This appendix shows the GenStat output to separate Corn from 
Soybean. 
***** Summary of classification tree: 
Corn and Soya 
Number of nodes: 117 
Number of terminal nodes: 59 
Misclassification rate: 0.064 
Variables in the tree: 
ais: , BÍ146], B[I88], B[11] ,oB[69]., Bis , 
BÍ4d9] , B[35]., P[172], Bf1031, B[144], B[152], 
BÍI34], BÍ33] , BI145], B[77] + BI393 , B[I143 ,; 
PÍS30] , B[4] , Bill + BIS! , BISSL, B[173], 
BIST , B[114], B(75] , BÍ1071, B[165], B[142], 
B[141], B[12] ,'"B[151], BÍ195], B[179]. 
i B[3]«4600 2 
B{[3]>4600 50 
2°Bl1461<1228 3 
B[146]>1228 21 
3 B[11]«4162 4 
B[11]>4162 7 
4 B[35]«3721 5 
B(35]>3721 soya 
5 B[152]«1224 6 
B[152]>1224 corn 
6 B[14]«4120 corn 
B[14]>4120 soya 
7 B[1721<1252 8 
B[172]>1252 14 
8 B[134]«1648 corn 
B[134]>1648 9