Binocular disparity, the slight differences between the images registered by our two eyes, provides an important cue when estimating the three-dimensional (3D) structure of the complex environment we inhabit. Sensitivity to binocular disparity is evident at multiple levels of the visual hierarchy in the primate brain, from early visual cortex to parietal and temporal areas. However, the relationship between activity in these areas and key perceptual functions that exploit disparity information for 3D shape perception remains an important open question. Here we investigate the link between human cortical activity and the perception of disparity-defined shape, measuring fMRI responses concurrently with psychophysical shape judgments. We parametrically degraded the coherence of shapes by shuffling the spatial position of dots whose disparity defined the 3D structure and investigated the effect of this stimulus manipulation on both cortical activity and shape discrimination. We report significant relationships between shape coherence and fMRI response in both dorsal (V3, hMT+/V5) and ventral (LOC) visual areas that correspond to the observers' discrimination performance. In contrast to previous suggestions of a dichotomy of disparity-related processes in the ventral and dorsal streams, these findings are consistent with proposed interactions between these pathways that may mediate a continuum of processes important in perceiving 3D shape from coarse contour segmentation to fine curvature estimation.