Deterministic pseudo-annealing (DPA) is a new deterministic optimizati
on method for finding the maximum aposteriori (MAP) labeling in a Mark
ov random held, in which the probability of a tentative labeling is ex
tended to a merit function on continuous labelings. This function is m
ade convvex by changing its definition domain. This unambiguous maximi
zation problem is solved, and the solution is followed down to the ori
ginal domain, yielding a good, if suboptimal, solution to the original
labeling assignment problem. The performance of DPA is analyzed on ra
ndomly weighted graphs.