Psychophysical studies suggest that figure-ground organization is a largely autonomous process that guides--and thus precedes--allocation of attention and object recognition. The discovery of border-ownership representation in single neurons of early visual cortex has confirmed this view. Recent theoretical studies have demonstrated that border-ownership assignment can be modeled as a process of self-organization by lateral interactions within V2 cortex. However, the mechanism proposed relies on propagation of signals through horizontal fibers, which would result in increasing delays of the border-ownership signal with increasing size of the visual stimulus, in contradiction with experimental findings. It also remains unclear how the resulting border-ownership representation would interact with attention mechanisms to guide further processing. Here we present a model of border-ownership coding based on dedicated neural circuits for contour grouping that produce border-ownership assignment and also provide handles for mechanisms of selective attention. The results are consistent with neurophysiological and psychophysical findings. The model makes predictions about the hypothetical grouping circuits and the role of feedback between cortical areas.