Relaxation labeling refers to a class of algorithms for assigning a label to each object in a graph

by iterating a transformation until a fixed point is reached. A probabilistic relaxation method is analytically derived in this paper

and a stochastic relaxation algorithm is also carried out step by step. We employ the MRF-Gibbs equivalence to calculate the local characteristics of the MRF

and take the maximum entropy (ME) estimate as the conditional neighborhood probabilities. At the last section of the paper

the two distinct approaches are compared and contrasted.