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How our brains develop disparity tuned V1 and V2 cells and then integrate binocular disparity into 3-D perception of the visual world is still largely a mystery. Moreover, computational models that take into account the role of the 6-layer architecture of the laminar cortex and temporal aspects of visual stimuli are elusive for stereo. In this paper, we present cortex-inspired computational models that simulate the development of stereo receptive fields, and use developed disparity sensitive neurons to estimate binocular disparity. Not only do the results show that the use of top-down signals in the form of supervision or temporal context greatly improves the performance of the networks, but also results in biologically compatible cortical maps-the representation of disparity selectivity is grouped, and changes gradually along the cortex. To our knowledge, this work is the first neuromorphic, end-to-end model of laminar cortex that integrates temporal context to develop internal representation, and generates accurate motor actions in the challenging problem of detecting disparity in binocular natural images. The networks reach a subpixel average error in regression, and 0.90 success rate in classification, given limited resources.