International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
F:Qx Xx r — Q is the stochastic state 
transition function 
O:Q — Y is the stochastic output function 
Q(t + 1) = T(Q(0) is the reinforcement scheme. 
C = {c¢j, 0 <j < o} is the penalty probability 
distribution. 
r= {r;,0 <j<c00}is the reinforcement signal. 
5. USING CELLULAR LEARNING ATOMATA FOR 
POSTCLASSIFICATOIN 
In order to use cellular learning automata for improving 
classification accuracy, a cellular learning with 8 neighbour 
structures is considered, and the following steps which include 
choosing an action by automata, compute penalty probability by 
environment, updating neighbour functions and updating inner 
state are considered. 
5.1.1 Action: Action @; is choosing one of two classes 
which have more probability; at initial state it choose randomly 
by automata. 
5.1.2 Penalty probability: penalty probability c; is 
associated with action a; which is chosen by environment. The 
environment considers two criteria for evaluating action 
automata: pixel entropy for local optimization and omission 
error for global optimization of each class. Once the automata 
choose an action that lead to increase the entropy of pixel, 
environment gives it penalty. After each iteration if the 
omission error decreased the environment will give reward to 
the automata's action. Amount of reward and penalty is 
compute as follows: 
C= a*C,i+b*Cy (1 1) 
0<a,b<l , atb=l 
where C2i =omission error 
a pera, (x) 
C UT is AL 
The amount of C; maps to 0 and 1 as follows: 
If (Ci « 0.5 ) then B=1 else B=0 (13) 
5.1.3 Neighbour function between automata: in order to 
compute the inner state of automata it should compute 
neighbour function between automata. We use equation 5 in 
which way that the C; affects on neighbour function between 
automata. 
5.1.4 Computing inner state of automata: in this stage, at 
first the local probabilities of pixels based on two stage of 
percipience memory of neighbour pixel which refers to penalty 
probability are computed. Then, an updating probability role 
which depends on local probabilities, initial inner state and 
neighbor function was introduced. After that, inner state of 
automata is computed by probability role. 
The algorithm executes the steps mentioned already and 
continues until reach to a best situation; the best situation is a 
state where pixels have less entropy with the classes having less 
omission error. 
6. EVALUATION AND EXPERIMENT RESULTS 
In order to evaluate the algorithm of post processing, a subset 
image (Figure 3) which is a portion of the Airborne 
Visible/Infrared Imaging Spectrometer  (AVIRIS) of 
hyperspectral data is used. This image was taken over an 
agricultural area of California, USA in 1994. This data has 220 
spectral bands about 10 nm apart in the spectral region from 0.4 
to 2.45 um with a spatial resolution of 20 m. The subset image 
is 145 by 145 pixels and its corresponding ground truth map is 
shown in Figure 4 .the image area has 12 classes. 
  
  
aur ™ REA 
Figure 4. Grand truth of area with 12 classes 
  
At first some noisy bands were put away. In order to separate 
noise, and to extract original signal from image bands the 
minimum noise fraction transform was performed. Based on 
eigenvalue of components we chose components which had 
high variance; therefore the original image dimension Wäs 
reduced. We used 46 components which contain high percent of 
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