tion of 
ogram 
ram is 
Nithin- 
WN in 
(5) 
ct the 
ng an 
(6) 
e use 
ptimal 
in one 
rplane 
2s are 
; have 
ecting 
ch the 
of the 
n tree. 
| data, 
wn the 
roduct 
node, 
ne the 
son. 
. 
raining 
ber as 
nents. 
divide 
8)If all data in a subgroup have the same identifier, stop the 
further division of the subgroup, else repeat procedures 5) 
- 7) until only one identifier is observed in the subgroup. 
9)Classify whole image by flowing pixel data down the tree. 
Figure 2 indicates the procedures. 
SIMULATION 
We evaluate the performance of MLDF in terms of accuracy 
and efficiency by comparison with that of MLH and that of 
| Selection of training data] 
  
  
  
| Compression of training data | 
  
  
  
[Production of 8 histograms using PCA | 
| 
  
  
[Selection of the optimal boundary | 
1 
  
Making new node and store 
projection vector & threshold 
  
  
  
  
  
   
      
   
All members of 
all subgroups have the 
same identifier ? 
No 
  
   
  
Classification of whole image 
  
End 
Fig. 2 Processing flow of MLDF. 
BDT. These three methods were applied to an artificial 
image (256 columns x 256 lines x 3 bands) having 16 uniform 
areas with multidimensional normal noise component whose 
variance covariance matrix is 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
50 50 20 
20 40 E] [s0 
30 40 
60 80 
E^ SE 
Band 1 Band Z Band 3 
Fig. 3 Spectral densities of the artificial image. 
10965 0.996 —0.833 
ZZ = |0.99%6 15.718 -—1.830 
-0.833 .—1.830 4239 
(7) 
Figure 3 shows spectral densities of the image. The image 
has 12 categories. We selected upper-left 10 x 10 pixels 
Square as training area for every category. We applied 
MLH, BDT and MLDF to the image with changing the 
329 
  
(a) (b) 
  
(c) (d) 
Fig. 4 An example of data set (a = 1) : (a) original image, (b) 
result processed by MLH, (c) one by BDT and (d) by MLDF. 
Accuracy Efficiency 
——Ho— EE BLDE 
-——e---0-- MH 
100 —-4-—"#—-A-- BDT 40 
av) 
o 3055 
2 20 + 
3 =. 
3 8 
10 = 
  
  
  
1 2 3 4 5 
Noise magnitude u 
Fig. 5 Accuracy and efficiency of MLH, BDT and MLDF. 
magnitude of noise components by aX (a 2 1-5). In these 
processes, we consider that generality of training data is 
perfectly satisfied. Figure 4 shows the original image (a), 
result processed by MLH (b), one by BDT (c) and by MLDF 
(d), where ao = 1. The result of numerical evaluation is 
indicated in Fig. 4, where we plot mean correct classification 
rate and processing time for several magnitudes of noise 
component. From these result, we see that accuracies for 
all methods decrease with increase of noise, but accuracy 
of MLDF is always as same as that of MLH. On the other 
hand, MLDF is highly efficient as well as BDT. 
ACTUAL IMAGE PROCESSING AND DISCUSSION 
We evaluate the performance of MLDF by using two types 
of actual remote sensing images. 
COASTAL REGION IMAGE 
Some coastal region images include urban and sea areas in 
their scenes. Data in the former area have very large 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996