A central theme of computational vision research has been the re(cid:173) alization that reliable estimation of local scene properties requires propagating measurements across the image. Many authors have therefore suggested solving vision problems using architectures of locally connected units updating their activity in parallel. Unfor(cid:173) tunately, the convergence of traditional relaxation methods on such architectures has proven to be excruciatingly slow and in general they do not guarantee that the stable point will be a global mini(cid:173) mum. In this paper we show that an architecture in which Bayesian Be(cid:173) liefs about image properties are propagated between neighboring units yields convergence times which are several orders of magni(cid:173) tude faster than traditional methods and avoids local minima. In particular our architecture is non-iterative in the sense of Marr : at every time step, the local estimates at a given location are op(cid:173) timal given the information which has already been propagated to that location. We illustrate the algorithm's performance on real images and compare it to several existing methods.