A recent challenge to the completeness of some influential models of local-motion detection has come from experiments in which subjects had to detect a single dot moving along a trajectory amidst noise dots undergoing Brownian motion. We propose and test a new theory of the detection and measurement of visual motion, which can account for these signal-in-Brownian-noise experiments. The theory postulates that the signals from local-motion detectors are made coherent in space and time by a special purpose network, and that this coherence boosts signals of features moving along non-random trajectories over time. Two experiments were performed to estimate parameters and test the theory. These experiments showed that detection is impaired with increasing eccentricity, an effect that varies inversely with step size. They also showed that detection improves over durations extending to at least 600 cosec. An implementation of the theory accounts for these psychophysical detection measurements.