John Trinder 
  
Considering the configuration of W that contains the B-spline (or modified B-spline) and the feature of interest as the 
state 5, the SA based feature extraction technique attempts to provide its estimate of the feature of interest by minimizing 
the energy of the configuration. The energy, £s, corresponding to the state S at any instant is computed as 
p 
esm Ne (3) 
i1 
where, e; and p represent the energy at pixel z; and total number of pixels in the B-spline respectively. 
2.3.2. Simulated Annealing In SA, the temperature T' is first raised to Tax and then gradually cooled, according to 
some temperature schedule, to 7, ;,,. Let the initial state and its associated energy be represented by S and £s respectively. 
As mentioned earlier, the task of SA is to generate a new state S', reject or accept it based on the energy values of S and 
S', and attempt to minimize £s in the process. The basic steps of SA, are shown in Figure. 22. 
l Ti T uas 
2. Initialise state (S) with energy Es. 
3 whilec? 975.) 
4. begin 
5. for i-l to NT do /* N7 is the number of iterations at temperature T*/ 
6. begin 
7. Evolve state S' with energy £s; by randomly removing one pixel from S and subsequently adding one to it (i.e., to 
S) which is not in S. 
S (Es 43€ 0). cS 
9. Else S - S' with probability exp(— 55755) 
10. endfor 
la T «Ta 
12. endwhile 
Figure 1: Basic steps in SA 
Generation of 5' from S : From the B-spline or the modified B-spline (corresponding to S), a pixel x; is chosen 
randomly for mutation. This pixel (;) is replaced by another pixel x; in W which is not already in S to generate S'. The 
energy of S' is computed by 
Es = Es —e; +e;. 
Temperature scheduling : In this article we have used a geometric temperature schedule of the form Tri = aT, 
where a is a positive real number close to zero. The value of a in the range [0.6,0.9] and 7T,,,, = 50 were found to 
be well suited for our purpose. It was found that the rate of convergence of the process increased with the increase in o 
values within the specified range. As T, — 0, no more perturbations of the state were possible and hence the termination 
condition was assumed to be reached. In practice, the system state is found to be ‘frozen’ well before this step was 
reached. 
3 IMPLEMENTATION AND RESULTS 
The different steps used in the simulated annealing based feature extraction procedure are as follows. 
1. Preprocessing by image stretching 
2. Edge detection by 
e Canny operator for single edges, such as dividing lines between features or edges of roads on aerial photogra- 
phy. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 907