186.

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Page 265

Figure 6.20 The probability for class replacement. As T is decreasing, only small increases of energy can be accepted.

figuration w is visited infinitely often, the distribution of generated configurations is guaranteed to converge to the Gibbs distribution. The second theorem concerns the temperature T of SA. It states that if the decreasing sequence of temperatures satisfies the following condition:

(6.50)

where

(6.51)

and m is the number of lattices (i.e. pixels), then convergence can be guaranteed. However, to decrease temperature T in terms of Equation (6.50) is too slow for practical applications. One may apply another temperature cooling function f defined as (Dubes and Jain, 1989):

(6.52)

The initial value of temperature T₀ is usually set to a value of 2 or 3.

The parameter N_inner in Figure 6.19 requires further discussion. Generally, the value of N_inner can be set as small as 10m or as high as 200m, depending on how many configurations are intended to be tried at each temperature.

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