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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV. Part B2. Istanbul 2004 
statistics,and try to simulate the heat object annealing so that we 
can find the global optimum solution. 
Suppose S-([S,S,....S, } is the set of all the possible 
combinations(or states).C:S — R is the non-minus objective 
function ,and so C(S) Z0 means the cost of the solution is S;. It 
is clear that the optimizing combination can be described 
formly with finding Ses , so that 
CS )sminC(S3S es 
Simulated Annealing processes mostly as follows: 
Procedure SA. 1) /* 1, is initial state, T, is the 
initial value of control parameter, C = C(S.) x) 
nS S, X z( 
(2) Repeat 
(3) Repeat 
( S, :— Generate( S); 
(5) EC. sc Then S S. 
/ 
/*S 1s current state*/ 
(6) Else If Accept( j, S) Then S. = S, ; 
(7) Until 'inner-loop stop criterion' /* “Inner-loop stop 
criterion" means the number of iterations of the SA in the 
temperature T */ 
(0 T,,, - Update(T, ); k < k +1; /* Tthe velocity 
of temperature's decline at a time with function update(T,) */ 
(9) Until “final stop criterion’ /* the finish of SA */ 
In Above algorithm, Generate(S) in the step(4) means generate 
the next state S; at random from N. If C X C .then accept j 
as the new current state,otherwise only accept j as the new 
current state with some probability .All that is the function of 
Accept(j.S). 
Usually function Accept processes as follows. 
Procedure Accept( j,S) f*in the 
step(6),only 
when C. c ‚call Accept */ 
(I) If exp [^ a AT, | » random(0,1) 
(2) Then Accept:=True 
Else Accept:=False 
The aim of using Simulated Annealing algorithm is to get 
globally optimize. In the errors arc reducing process, 
disturbance at random in some degree can get over the 
restriction of the local minima, and ensure the system keep 
away form disturbing when it converges to global optimum 
solution.This is just the problem which Simulated Annealing 
algorithm has settled. 
For aim of globally optimize, the following function specifies 
the random disturbing: 
Random(—1,+1) | (Q1 
W,=W, x| 1+ 
loop _ time 
Where Loop. time is the number of iterations, Random(-1,+1) 
initialized as randomized real numbers within the range —1 to 
+1 .From the above state we can see the Simulated Annealing 
algorithm as the gradient descent with noises , and when the 
temperature which identify the noise intensity is O(the number 
of iterations is infinity ),it is just the gradient descent. 
4. APPLICATION TO SAR IMAGE 
Image classification belongs to the division of patterns in eigen 
space. If it is supposed that existing samples xl, x2, x3, x4, ... , 
xn, in an image belong to certain categories Cl, C2, C3, 
C4, ....,Cm , (mcn), it is possible to select n samples to extract 
feature of each ground targets. The goal then of establishing 
supervised samples is to make use of multispectral features and 
couple them with those of texture and structural features and 
use them for training the BP nets. In preparation for the 
classification of the entire 224 by 224 scene, six input fields 
were used which comprised the training pixels — the three 
original channels (polarization combinations L-HH, L-HV and 
C-HV) and the three energy components ( 1, 2 and  3)as 
derived from the wavelet decomposition. These are referred to 
as the target samples. Thus, the BP nets have six nodes in the 
input layer and three nodes comprised the output layer based 
upon the desired classification (poplar, bushes and background). 
Broadly speaking, the number of nodes in the hidden layer is 
arbitrary although general guidelines exist e.g. (Lippmann, 
1987). In general, the more nodes in the hidden layer, the better 
the result of image classification but it takes a longer time for 
the network to learn the necessary knowledge for the 
classification and often results in a reduction of the network’s 
ability to generalize. The problem is therefore achieving a 
balance between accuracy and the time required for training. 
Through experimentation, four nodes were defined for the 
hidden layer since this was found to generate an optimal 
classification. In order to train the BP nets with the target 
samples, the input data was rescaled to comply within the limits 
of the Sigmoid activation function and set to 0.9 and 0.1 
respectively. Table | shows the possible responses of the output 
layer processing element. Data for training the network was 
accomplished by defining a 10 10 pixel window (100 samples 
of input data of each type) from the first three channels 
(polarization combinations L-HH, L-HV and C-HV). For the 
second three channels, the decomposed elements (1, 2 and 3) 
the window must contain sufficient resolution to preserve the 
essential information: considering the characteristic of texture 
and structure in high-resolution SAR images and the 
requirement of three level DWT, a window size of 32 32 pixels 
was adopted. 
  
  
Class Target Output 
O, O, O; 
Poplar Trees 0.9 0.1 0.1 
Bushes 0.1 0.9 0.1 
Background 0.1 0.1 0.9 
Table I. Response of the output layer processing element 
In the training process, an iteration is divided into two stages 
after the data are input into the input layer. First, the vector of 
the hidden-layer neuron 1s computed by the Sigmoid activation 
function: then the vector of the output-layer neuron is computed 
by the Sigmoid activation function. Second, the error between 
the observed output and the desired output is calculated at the