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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
po (Wi | + QU (Wi | 
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ow, js (6) 
where P;“ (cm, )= the probability of pixel i belongs to class «y 
of the t-th iteration 
qi" («)-7 neighborhood function of pixel i belongs to 
class c of the t-th iteration; 
Therefore relaxation is an iterative technique which 
probabilities of neighbouring pixels are used iteratively to 
update the probabilities for a given pixel based on a relation 
between the pixel labels specified by compatibility coefficient. 
This approach is computationally intensive and robust to image 
noise (zur Erlangung, 1999). 
3. LEARNING ATOMATA AND ENVIRONMENT 
The goal of many intelligent problem-solving systems is to be 
able to make decisions without a complete knowledge of the 
consequences of the various choices available. In order for a 
system to perform well under conditions of uncertainty, it has to 
be able to acquire some knowledge about the consequences of 
different choices. This acquisition of the relevant knowledge 
can be expressed as a learning problem. 
Learning Automata is a model of computer learning which has 
been used to model biological learning systems and to find the 
optimal action which is offered by a random environment. 
Learning automata has found applications in system that 
process incomplete knowledge about the environment in which 
they operate. These applications includes parameter 
optimization, statistical decision making, telephone routing, 
pattern recognition, game playing, natural language processing, 
modeling ^ biological learning systems, and object 
partitioning(Oommen|, 2003). The learning loop involves two 
entities: the environment and learning automata; the actual 
process of learning is represented as a set of interactions 
between the environment and the learning automata the 
learning automata is limited to choosing only one of actions at 
any given time from a set of actions!a;, .., à,} which are 
offered by the environment. Once the learning automata decide 
on an action a; this action will serve as input to the 
environment. The environment will then respond to the input by 
either giving a reward, or a penalty, based on the penalty 
probability c; associated with a; . This response serves as the 
input to the automata. Based upon the response from the 
environment and the current information accumulated so far, 
the learning automata decide on its next action and the process 
repeats. The intention is that the learning automata gradually 
converge toward an ultimate goal. 
lO n. 1 
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Random Environment 
  
  
  
  
  
  
Learning Automata — |« 
  
  
  
Figure2: Interaction between environment and automata 
3.1 Fixed Structure Learning Automata 
Fixed structure automata exhibit transition and output matrices 
which are time invariant. A-ía,B,F,G.q! is a fixed structure 
automata which a= {a,, …, @,} is the set of r actions offered by 
the environment that the learning automata must choose from, 
B= (0, 1j is the set of inputs from the environment, q is set of 
inner state of automata, F is set of updating inner state automata 
based on exist state automata and penalty and reward of 
environment, G is choosing action function based on new state 
of automata 
3.2 Variable Learning Automata 
Variable structure automata exhibit transition and output 
matrices which are change with time, a variable learning 
automata can be formally defined as a quadruple (Oommenl, 
2003): 
Ao, P, b, T! (7) 
where, à = {dy, …, 0,} is the set of r actions offered by the 
environment that the LA must choose from. 
P = [pi(n), ..., p,(n)] is the action probability vector 
where pi represents the probability of choosing action 
a; at the nth time instant. 
B = (0, 1} is the set of inputs from the environment 
where ‘0’ represents a reward and ‘1° a penalty. 
T: P x B — P is the updating scheme. and defines the 
method of updating the action probabilities on 
receiving an input from the environment. 
If(B=1&& à; is chosen ) then P,(n+1)=P;(n)+o[1- P;(n)] 
If(B— L&& a; is chosen ) then Pj(n*1)- 1-a)P;(n) 2 jv (8) 
H(B=0&& «; is chosen ) then Pi(n+1)=(1-b)P;(n) 
If(B-0&& a; is chosen) then Pi(n* 1)-b/(r-1 )+(1-b)P;(n) = jvi 
According to equation 8 if a and b be equal the learning 
algorithm will be known as linear reward penalty. If b««a the 
learning algorithm will known as linear reward epsilon penalty 
and if b-0 the learning algorithm will be a linear reward 
inaction. 
4. LEARNING CELLULAR ATOMATA 
Learning cellular automata A and its environment E are defined 
as follows (Fei Qian 2001). 
A 7 (U,.X, Y, QN, & FO, T) (9) 
E - (Y.C, r! (10) 
where, U = {u, j = Le 2, , A} is the cellular space. 
X7 (xj, Ox j € o] is the set of inputs 
Y 7 (yj, 0 xj € oo] is the set of outputs 
N = {nl, - - - , n[N]} is the list of neighborhood 
relations. 
Q 7 (qj, 0xj € oo] is the set of internal states. 
&£:U- QQ CU is the neighborhood state 
configuration function