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Table 3 Confusion matrix for MLH, BDT and MLDF. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
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1.67 98.33 
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1.23 98.77 
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98.77| 1.23 
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nl | pagan} Yc b SEA 1| AUN 
100.0C 
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100.00 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 4 Mean correct classification rate for 
MLH, BDT and MLDF. 
  
  
  
5 band 3 band 
Method| Accuracy |Time | Accuracy | Time 
MLH 96.79 [%] |303 [s]| 95.48 [96]| 133 [s] 
BDT 89.03 18 90.88 11 
MLDF | 94.06 20 92.73 19 
  
  
  
  
  
  
  
and 5, and evaluate the change of accuracy and efficiency 
using the identical training and test areas. Table 4 tells us 
that MCCRs slightly decrease or almost the same accordingly 
to reduction of number of spectral bands five to three, and 
that processing time in both MLH and BDT depends on the 
number of spectral bands. In MLDF, processing time fully 
depends on size of binary division tree, therefore, much 
information brought by larger number of spectral bands may 
331 
gives more suitable division boundary which efficiently 
reduces size of the tree. This is the reason why processing 
time of MLDF in classification of 5 spectral band image is 
almost as same as that of 3 band image. There is possibility 
that MLDF is more efficient than BDT. 
CONCLUSIONS 
We proposed a highly accurate and efficient method MLDF 
for supervised classification of remotely sensed multispectral 
images. The method MLDF is expanded from BDT which is 
very efficient. Image data are projected onto eight 1D 
subfeature spaces to produce histograms with compression 
of data. The division boundary is selected among all valleys 
in histograms using a clustering criterion that the optimal 
boundary minimizes the ratio of sum of within-group-sum- 
of-squares to intragroup-sum-of-squares. MLDF produces 
binary division tree by applying the division process 
recursively. Each node of the tree has coefficient vector for 
data projection and threshold for data division. 
As division boundary in histogram corresponds to hyperplane 
in full feature space, MLDF is regarded as a kind of linear 
discriminant function method. On the other hand, as no 
statistics for training data is used in selection of division 
boundary, MLDF is also regarded as a nonparametric 
supervised classification method. From evaluation of 
performance using artificial image and actual remotely 
sensed multispectral images, it is confirmed that MLDF has 
as high accuracy as MLH does and as high efficiency as 
BDT does. Improvement of MLDF in term of efficiency and 
analysis of classification with less generality training data 
are subjects for a future study. 
REFERENCES 
Fujimura, S. et al.,, 1978. Comparison of automatic 
classification methods for multispectral images. Trans. Soc. 
Instr. Contr. Eng., 14(3). pp.269-276. (Japanese) 
Inamura, M. et al., 1979. High speed processing of the 
multispectral Images by means of binary decision tree. Trans. 
Soc. Instr. Contr. Eng., 15(4). pp.486-491. (Japanese) 
Hanaizumi, H. et al., 1995a. A binary division algorithm for 
clustering remotely sensed multispectral images. IEEE 
Trans., IM-44 (3), pp.759-763. 
Hanaizumi, H. et al., 1995b. A binary division algorithm using 
a linear discriminant function for the cluster analysis of 
remotely sensed multispectral images. Proc. SPIE-2579. 
pp.182-187. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996