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The analysis of visual motion divides naturally into two stages: the first is the measurement of motion, for example, the assignment of direction and magnitude of velocity to elements in the image, on the basis of the changing intensity pattern; the second is the use of motion measurements, for example, to separate the scene into distinct objects, and infer their three-dimensional structure. In this paper, we present a computational study of the measurement of motion. Similar to other visual processes, the motion of elements is not determined uniquely by information in the changing image; additional constraint is required to compute a unique velocity field. Given this global ambiguity of motion, local measurements from the changing image, such as those provided by directionally-selective simple cells in primate visual cortex, cannot possibly specify a unique local velocity vector, and in fact, specify only one component of velocity. Computation of the full two-dimensional velocity field requires the integration of local motion measurements, either over an area, or along contours in the image. We will examine possible algorithms for computing motion, based on a range of additional constraints. Finally, we will present implications for the biological computation of motion.