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Abstract

How do we decide whether an object approaching us will hit us? The optic array provides information sufficient for us to determine the approaching trajectory of a projectile. However, when using binocular information, two previous studies [1,2] have reported that observers overestimate the angular approach of a presented motion-in-depth trajectory. Specifically, observers report that an object on a collision course with their head will miss it. From an evolutionary perspective this appears to make little sense. However, here we consider whether this perceptual phenomenon might actually reflect “optimal” behaviour by the visual system. Our experiment consisted of two stages. First, we recorded thresholds for detecting an increment in a distance moved in depth (d) or a distance moved laterally (l). Second, we recorded observers’ reports of the perceived trajectory of a point moving towards them in depth. Trajectories were chosen to span a range of angles with respect to the mid-sagital plane and all trajectories consisted of lateral- and depth- components of motion. We then constructed a Maximum Likelihood model (cf. [3]) for weighting the lateral- and depth- components of the presented motion trajectory. Specifically, we broke down the presented trajectories into a component in depth and a lateral motion component. Then, using the d and l thresholds we weighted the two motion components in accordance with the observers’ sensitivity to each. Finally, using these weighted motion components we calculated a trajectory angle based on a simple trigonometric ratio. This simple model captured characteristic aspects of the observers’ behaviour, and in some cases a very good fit to the data. We suggest that at least part of the explanation for the apparent paradox in perceiving motion towards the head results from the discrepancy between sensitivity to lateral motion and motion-in-depth.