Perceived speed of motion in depth modulates misjudgements of approaching trajectories consistently with a slow prior.

Previous studies have shown that the angle of approach is consistently overestimated for approaching (but passing-by) objects. An explanation based on a slow-motion prior has been proposed in the past to account for this bias. The mechanism relies on the (less reliable) in-depth component of the motion being more attracted towards the slow motion prior than the (more reliable) lateral component. This hypothesis predicts that faster speeds in depth will translate into a greater bias if the perception of velocity in depth follows Weber's law. Our approach is different than the one used in previous studies where perceived speed and direction were measured in different experiments. To test our hypothesis, we conducted an experiment in which participants estimated approaching angles via a pointing device, while at the same time comparing the speed of the approaching object with a lateral velocity reference. This way, we couple perceived speed with perceived trajectory for each approaching angle in the same trial. Our results show that the directional bias is larger for faster objects, which is consistent with motion in depth following Weber's law. The differential biases can be accounted for by a Bayesian model that includes a slow motion prior.