Two of the most successful approaches in image restoration are mathematical morphology and Bayesian image restoration. They arise from different philosophies and are formulated very differently. Mathematical morphology involves a basic set of elementary operators that are usually combined to perform non-linear filtering of noisy images. The Bayesian approach involves finding the best interpretation of the images assuming a probabilistic model. Our aim is to investigate the possible relationships between these two approaches. The interest of such a study is twofold. On one hand, most morphological operators can be implemented in such a way that they require little computation while the Bayesian approach may require simulated annealing and may be computationnaly more demanding. On the other hand, providing mathematical morphology with some statistical analysis could lead to better insight into how to implement it in practice. We will first review some basic definitions of mathematical morphology and one of the most used iterative algorithms in Bayesian image restoration, Besag's Iterated Conditional Modes (ICM) algorithm. We will concentrate on the binary image case and show that for some values of the parameters, ICM can actually be viewed as a succession of local morphological operators. This formulation reveals some interesting features of ICM. Under certain conditions the algorithm does not depend on the specific values of the parameters. We will discuss the possibility of deriving a restoration algorithm which does not require full knowledge of the parameters.