Figure 9.2: Cliques for a second-order neighborhood, where a, d1,.09 are the cliques coefficients for second-order neighborhood system.

Figure 9.3: Numbering and order coding of the neighborhood structure.

where F is the potential function for single-pixel cliques and H is the potential function for all cliques of size 2. The parameter w depends on the size of the neighborhood around each site. For example, w is 2, 4, 6, 10, and 12 for neighborhoods of orders 1, 2, 3, 4, 5, respectively.

Using the Derin-Elliott model [15] to compute F and H, we have

F(xt) = ax and H(xt, xt:+r) = 0rI(x, x(t: +r)), where I (a, b) is called indicator function where

0 0

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