P, (Lk) - PU, (0B, DI (8) 
where B „„..(1) and I,,.(k) are the proportion which k-th 
category is 1 and rest are 0 and average multispectral vector 
of k-th category, respectively. The maximum error 
occurrence probability show the maximum probability which 
occurs in the case of composition of 2 categories. So if this 
value is larger, it can be assumed to be occurrence of larger 
estimation error. In Table 7, the maximum error occurrence 
probabilities calculated from previous 5 categories are 
shown. In the combination of grass land and bare soil and 
the combination of grass land and broad leaf tree, the 
probabilities are relatively large, so it can be predicted that 
relative large estimation error occur in the estimation of the 
proportion of grass land. This is because of the relatively 
large variance of this category. Fig. 1 shows the histogram 
of maximum RMSE. As it can expected, in the estimation 
of the proportion of grass land, the frequency of maximum 
RMSE is the largest. To make more accurate estimation, it 
has to reduce the maximum error occurrence probabilities 
among each category. 
6. CONCLUSIONS 
The previous results lead to the following conclusion. The 
observed multispectral vector is considered as probability 
variables along with the approximation that the supervised 
data of each category can be characterized by normal 
distribution. The results from simulated Mixel data show 
that this method can retrieve more accurate proportion of 
each category among Mixel's than the conventional 
generalized inversion method. And the maximum error 
occurrence probabilities can be a good index which can 
predict the estimation error in each category. 
7. REFERENCES 
*Amano, M., K. Furuya and T. Ishikawa. 1990. 
Classification of forest type based on satellite data. Proc. 
1990 Autumn Conf. of JSPRS, Nagasaki Japan, 73-78. 
Hallum, C. R. 1972. On a model for optimal proportions 
estimates for category mixture, Proc. 8th. Intl. Symp. on 
Remote Sens. of Env., ERIM, Vol. 2, pp. 951-958. 
*Inamura, M. 1987. Analysis of remotely sensed image data 
by means of category decomposition. J. of IECSE., J70- 
C(2), 241-250. 
*Ito, T, and S. Fujimura, 1987. Estimation of cover area of 
each category in a pixel by pixel decomposition into 
categories. Trans. of SICE., 23(8), 20-25. 
*Konno, H. and H. Yamashita, 1978. Non-linear 
programming. Nikka-Giren Pub. Co. pp. 354. 
Rodgers, C. D. 1976. Retrieval of atmospheric temperature 
and composition from remote measurement of thermal 
radiation. Rev. of Geophys. and Space Phys., 14(4), 609- 
623. 
"Takane, Y. 1980. Multidimensional scaling. Tokyo- 
Daigaku-Shuppan-Kai Pub. Co. pp.332. 
(*: Original text written in Japanese.) 
a 1 Av e of each cate 
Band Resid Bare Grass Broad Neddle 
1 122.60 143.98 109.33 98.52 100.40 
2 50.15 69.79 47.69 38.89 41.38 
3 50.27 80.74 43.68 32.44 33.86 
4 68.25 87.73 119.52 81.73 137.15 
5 75.19 107.64 113.34 60.23 95.32 
7 39.76 52.41 40.69 19.86 28.22 
able 2 Variance of each cat 
Band Resid Bare Grass Broad Neddle 
1 64.24 222.61 17.07 10.30 18.29 
2 14.73 96.21 60.45 1.19 2.22 
3 29.00 186.40 15.14 1.46 2.08 
4 75.49 136.85 193.23 121.76 228.44 
5 61.95 246.88 104.45 59.84 110.08 
7 40.94 49.05 29.53 53.45 9.04 
able orrelati € band 
Band 1 2 3 4 5 7 
1 1.00e+0 7.61e-1 8.43e-1 -5.29e-2 2.21e-1 5.20e-1 
2 7.61e-1 1.00e+0 9.22e-1 3.92e-1 6.64e-1 8.50e-1 
= 8.43e-1 9.22e-1 1.00e+0 1.34e-1 4.64e-1 7.56e-1 
4 -5.29e-2 3.92e-1 1.34e-1 1.00e+0 8.9le-1 6.12e-1 
5 2.21e-1 6.64e-1 4.64e-1 628.91e-1 1.00e«0 8.73e-1 
7 5.20e-1 8.50e-1 7.56e-1 6.12e-1 8.73e-1 1.00e+0 
  
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