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(5) 
X : vector associated to a pixel in the 
* multispectral space. 
P; : Caussian probability density function 
for class 'i', implementing the fuzzy 
mean and the fuzzy covariance matrix 
Note that: 
0 € f,00 g 1 X i,X 
n 
* F,(X) = 1 
; $ 
i=l 
'n' being the number of information classes. 
It should be recalled that, in the con- 
ventional approach, the largest £z(X) (i= 
l,...,n) would be set equal to one and the 
remaining (n-1) to zero. In the fuzzy 
approach the 'n' membership functions 
associated to a pixel are saved and 
interpreted as a contribution of each 
information class to the pixel spectral 
response. Thus, the pixel components X; 
are estimated by the membership functions. 
4. EXPERIMENTS AND RESULTS 
The Linear Mixture model | and the Fuzzy 
Mixture model have been applied to Landsat 
"TM data. The study. area is the Emas 
National Park in Brazil. The park is 
located in  central-western Brazil at 
approximately 189 south latitude(figure 1). 
62° 54° 46° 
  
  
  
  
  
Fig.l - Study Area Emas National Park 
The climate is tropical. Winter is mild and 
corresponds to the dry season (June through 
September). Rains occur during the summer 
season (October through May). 
The vegatation covering this region 
corresponds to the "cerrado". Vegetation 
cover density varies across the Emas N.P.. 
Areas with a higher degree of soil moisture 
present a higher vegetation density cover. 
Areas presenting lower soil moisture contents 
show more sparsely distributed vegetation. 
During the dry season vegetation covering 
the drier area becomes more susceptible to 
fires. The fire that occurred in the park 
in 1988 was confined to this area. 
Mixture pixels are clearly present. The 
"pure" information classes in this case are 
vegetation and soil. "Pure" vegetation 
909 
pixels can be found in areas with higher 
soil moisture contents (along the drainage 
lines). Most of the park is then covered 
by mixture pixels. The different proportions 
of vegetation and soil can then be used 
to estimate conditions across the park 
with respect to general environmental 
conditions. 
The classification process was performed 
considering five classes: two "pure" 
classes (vegetation and soil) and three 
mixture classes (0.75 vegetation and 0.25 
soil, 0.5 vegetation and 0.5 soil, 0.25 
vegetation and 0.75 soil).Computer programs 
were developed in order to implement the 
Linear Mixture model and the Fuzzy model 
for the Brazilian image processing system 
SITIM-150. 
The Linear Mixture model was applied, to 
estimate the mean vector and covariance 
matrix of the mixture classes. The  Caus- 
sian maximum likelihood classifier was 
then applied to the scene. Results are 
presented in figure 2. 
The Fuzzy model was also applied to the 
same scene. Equation 5 was used to esti- 
mate the membership grade of each pixel 
with respect to two information classes: 
vegetation and soil. A level slice criterion 
was then applied in orderto define borders 
between the three mixture classes. The 
results are presented in figure 3. 
The results of both methods are rather 
similar and in agreement with field data. 
The Linear Mixture model,however,presented 
a more accurate classification result. This 
method applies a maximum likelihood 
classifier which is capable of better 
estimating borders between the mixture 
classes. The level slice method used to 
define borders in the Fuzzy model clearly 
presents a poorer performance. 
5. CONCLUSION 
The implementation of the mixture concept 
to natural scenes can be a valuable tool 
in natural resources. Variations in ve- 
getation cover can be detected and 
quantified. Useful information can be 
obtained from this process. In the test 
area presented in this study, only the 
area with sparser vegetation, i.e., the 
area corresponding to dry vegetation was 
affected by a subsequent fire. This data 
can then be understood as a variation in 
soil and/or climate conditions. 
REFERENCES 
Haertel, V., Centeno, J. 1991, Utilizaçao 
do conceito de pixel mistura no processo 
de classificacao da cobertura vegetal em 
bacias hidrograficas. Revista Brasileira 
de Engenharia - Caderno de Recursos Hidri 
cos. 9(2):87-100, 
Heimes, J.F. 1977. Effects of scene pro- 
portions on spectral reflectance in 
lodgepole pine. M.Sc.thesis, Colorado 
State University, Fort Collins, Colorado. 
assisted 
Ranson, J.K. 1975, Computer