The perception of relative target movement from a dynamic observer is an unexamined psychological three body problem. To test the applicability of explanations for two moving bodies participants repeatedly judged the relative movements of two runners chasing each other in video clips displayed on a stationary screen. The chased person always ran at 3?m/s with an observer camera following or leading at 4.5, 3, 1.5 or 0?m/s. We harmonized the chaser speed in an adaptive staircase to determine the point of subjective equal movement speed between runners and observed (i) an underestimation of chaser speed if the runners moved towards the viewer, and (ii) an overestimation of chaser speed if the runners moved away from the viewer, leading to a catch-up illusion in case of equidistant runners. The bias was independent of the richness of available self-movement cues. Results are inconsistent with computing individual speeds, relying on constant visual angles, expansion rates, occlusions, or relative distances but are consistent with inducing the impression of relative movement through perceptually compressing and enlarging inter-runner distance. This mechanism should be considered when predicting human behavior in complex situations with multiple objects moving in depth such as driving or team sports.
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