Because 
is discrete, minimizing (2.19) is a
combinatorial problem. The minimal solution 
is the optimally
restored image in the configuration space 
. The simplest
algorithm is steepest local energy descent or the ``greedy'' method. It
proceeds as follows: Start with an initial configuration
; for site i, choose the new label 
among all 
, 
, that
minimizes 
locally; the iteration continues
until no further energy descent is possible. An example of such greedy
algorithms is the iterative conditional modes (ICM) [Besag 1986]; see
Section 8.2.1 for details.
This simple algorithm finds a local energy minimum whose quality depends
much on the initial estimate 
. Global minimization algorithms
such as simulated annealing [Geman and Geman 1984] need be used if global
solutions are required. This is the subject in
Chapter 9.