Averaged relative reflectance is shown in Fig.3. In the 
following, the covariance matrices of the classes are as- 
sumed to be identical. 
  
0.6 : à; x 
0.5 | 
0.4 r 
03} 
0.2 | es Spates 
Relative Reflectance 
oil 
  
  
  
  
0 L L L 1 A 
500 550 600 650 700 750 
Wavelength [nm] 
Fig.3 Spectral reflectance of objects 
( A~E : Leaves of plant ) 
After reducing and normalizing the data to 7 orthogonal 
components, features were extracted from one to another. 
At first we selected class A as the most important class 
to be classified. The first feature was set between class 
A and the nearest class from A (B in Fig.3). The next 
feature was set between A and the next nearest class D. 
There remains no other classes whose distance from A is 
less than that between A-B. The two features characterize 
the weighting factors are shown in terms of wavelength in 
Fig. 4. 
In this case the distance of each class from class A is shown 
in Table 1: (a) in the original 7 dimensional space, (b) 
1 dimension (the first feature), and (c) two dimensional 
space made by the first two features. From (c), it is seen 
that the minimum distance is that between A and B which 
was already obtained in (a). Thus, the two features are 
sufficient for this case. 
To confirm the validity of this method when compared 
with canonical analysis, the classification accuracy was es- 
timated by test data of 196 samples for each class. Each 
sample was classified by a maximum likelihood method. 
Figure 5 shows the classification accuracy for the class A 
Table 1 Distance from class A (Relative distance) 
( A~E: Leaves, F: Soil, G: Stone, H: Concrete ) 
(a) Distance in 7 dimension 
B. C D E F G H 
A 44 97 183 155 161 160 171 
  
  
  
  
  
  
(b) Distance in 1 dimension 
B uu D E F G H 
A144. 74 16 3.4 2.0: 19: ..2.5 
  
  
  
  
  
  
(c) Distance in 2 dimension 
B C D E F G H 
A. ].2:4..9.5,..18.3.,12.5.. 15.0. .15.2...16.3 
  
  
  
  
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
in terms of the number of features. 
The accuracy depends on the number of features used, 
and is higher than that by canonical analysis about 19% 
(one feature) and 896 (2 features). The confusion matrix 
is shown in Table 2. 
  
PN es 
ples ee name 
L L L 
500 550 600 650 700 750 
© N 5 ©& 
Weight Value [a.u.] 
  
  
  
Wavelength [nm] 
(a) Feature 1 
  
Weight Value [a.u.] 
  
  
  
-6 A à 1 
500 550 600 650 700 750 
Wavelength [nm] 
(b) Feature 2 
  
Fig.4 Weighting factors for the significant class A 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
— 100 
ae 
- 90 doy 
Su td oqieionub-p t su e 
S 80 as 2 
3 70 
5 60} z 
2 50 J Proposed method —— 
9 Canonical analysis --—— 
8 40 
Q 30 
1 2 3 
Number of Features 
Fig.5 Classification accuracy of calss A versus 
number of features 
   
  
  
  
  
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