A critical step in the interpretation of the visual world is the integration of the various local motion signals generated by moving objects. This process is complicated by the fact that local velocity measurements can differ depending on contour orientation and spatial position. Specifically, any local motion detector can measure only the component of motion perpendicular to a contour that extends beyond its field of view. This "aperture problem" is particularly relevant to direction-selective neurons early in the visual pathways, where small receptive fields permit only a limited view of a moving object. Here we show that neurons in the middle temporal visual area (known as MT or V5) of the macaque brain reveal a dynamic solution to the aperture problem. MT neurons initially respond primarily to the component of motion perpendicular to a contour's orientation, but over a period of approximately 60 ms the responses gradually shift to encode the true stimulus direction, regardless of orientation. We also report a behavioural correlate of these neural responses: the initial velocity of pursuit eye movements deviates in a direction perpendicular to local contour orientation, suggesting that the earliest neural responses influence the oculomotor response.