A Bayesian approach to object matching is presented. An object and a scene are each represented by features, such as critical points, line segments and surface patches, constrained by unary properties and contextual relations. The matching is presented as a labeling problem, where each feature in the scene is assigned (associated with) a feature of the known model objects. The prior distribution of a scene's labeling is modeled as a Markov random field, which encodes the between-object constraints. The conditional distribution of the observed features labeled is assumed to be Gaussian, which encodes the within-object constraints. An optimal solution is defined as a maximum a posteriori estimate. Relationships with previous work are discussed. Experimental results are shown.