Travel distance estimation from visual motion by leaky path integration

Visual motion can be a cue to travel distance when the motion signals are integrated. Distance estimates from visually simulated self-motion are imprecise, however. Previous work in our labs has given conflicting results on the imprecision: experiments by Frenz and Lappe had suggested a general underestimation of travel distance, while results from Redlick, Jenkin and Harris had shown an overestimation of travel distance. Here we describe a collaborative study that resolves the conflict by tracing it to differences in the tasks given to the subjects. With an identical set of subjects and identical visual motion simulation we show that underestimation of travel distance occurs when the task involves a judgment of distance from the starting position, and that overestimation of travel distance occurs when the task requires a judgment of the remaining distance to a particular target position. We present a leaky integrator model that explains both effects with a single mechanism. In this leaky integrator model we introduce the idea that, depending on the task, either the distance from start, or the distance to target is used as a state variable. The state variable is updated during the movement by integration over the space covered by the movement, rather than over time. In this model, travel distance mis-estimation occurs because the integration leaks and because the transformation of visual motion to travel distance involves a gain factor. Mis-estimates in both tasks can be explained with the same leak rate and gain in both conditions. Our results thus suggest that observers do not simply integrate traveled distance and then relate it to the task. Instead, the internally represented variable is either distance from the origin or distance to the goal, whichever is relevant.