Creation of discontinuities must be favored either by the presence of a ``large'' difference in the z values of the nearby DPs, or by the presence of a partial discontinuity structure that can be improved.
To measure the two effects in a quantitative way, it is useful to introduce
two functions: cost and benefit. The benefit
function for a vertical LP is 
, and analogously for a horizontal
one. The idea is that the activation of one LP is beneficial when this
quantity is large.
Cost is a function of neighborhood configuration. A given LP updates its value in a manner depending on the values of nearby LPs. These LPs constitute the neighborhood, and we will to refer to its members as the LPs connected to the original one. The neighborhood is shown in Figure 6.24.
Figure 6.24: ``Connections'' Between Neighboring Line Processes, at the Same
Scale and Between Different Scales
The updating rule for the LPs derived from the above requirements is:
Because Cost is a function of a limited number of binary variables, we used a look-up table approach to increase simulation speed and to provide a convenient way for simulating different heuristical proposals.
A specific parametrization for the values in the table is suggested in [Battiti:90a].