As we move through our environment, the flow of the deforming images on our retinae provides rich information about ego motion and about the three-dimensional structure of the external world. Flow-fields comprise five independent components, including radial and circular motion. Here we provide psychophysical evidence for the existence of neural mechanisms in human vision that integrate motion signals along these complex trajectories. Signal-to-noise sensitivity for discriminating the direction of radial, circular and translational motion increased predictably with the number of exposed sectors, implying the existence of specialized detectors that integrate motion signals of different directions from different locations. However, contrast sensitivity for complex motion did not increase greatly with sector number, implying that the specialized detectors are preceded by a first stage of local-motion mechanisms that impose a contrast threshold. These findings fit well with recent electrophysiological evidence in monkey showing that whereas motion-sensitive neurons in primary visual cortex respond best to local translation, many neurons in the medial superior temporal cortex have large receptive fields tuned to radial, circular or spiral motion.