Several theories of early visual perception hypothesize neural circuits that are responsible for assigning ownership of an object's occluding contour to a region which represents the "figure". Previously, we presented a Bayesian network model which integrates multiple cues and uses belief propagation to infer direction of figure (DOF) along an object's occluding contour. In this paper, we use a linear integrate-and-fire model to demonstrate how such inference mechanisms could be carried out in a biologically realistic neural circuit. The circuit, modeled after the network proposed by Rao, maps the membrane potentials of individual neurons to log probabilities and uses recurrent connections to represent transition probabilities. The network's "perception " of DOF is demonstrated for several examples, including perceptually ambiguous figures, with results qualitatively consistent with human perception.