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Markus Lappe, Maren Stiels, Harald Frenz, Jack Loomis; Visual estimation of travel distance by leaky integration along veering paths. Journal of Vision 2011;11(11):930. https://doi.org/10.1167/11.11.930.
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When humans use vision to gauge the travel distance of an extended forward movement they often underestimate the movement's extent. This underestimation can be explained by leaky path integration, a process by which the movement is perceptually integrated to yield distance. Distance underestimation occurs because this integration is imperfect and contains a leak that increases with distance traveled. However, the leak might accumulate with walked distance or might accumulate according to represented distance from the starting point. For movements along a straight line these two possibilities cannot be distinguished, but for movements along a curvy path the distance traveled along the path and the distance accumulated from the origin become separated. We simulated movement along a path veering left and right off a straight line connecting the origin to the end of the movement. We asked observers to indicate the distance between origin and end point of the movement. By varying the amplitude of the veering we created differences between the distance of the movement and the length of the path that was traversed. We then measured the influence of the path length on the distance judgment. Leaky integration along the path makes the seemingly counterintuitive prediction that the estimated origin-to-end point distance should decrease with increasing veering, because the length of the path over which the integration occurs increases, leading to a larger leak effect. Thus, a single origin-to-end-point distance should yield progressively shorter distance estimates as the path length increases. The results matched the prediction: movements of identical origin-to-end point distance were judged as shorter when the path became longer. We conclude that leaky path integration for visual travel distance estimation takes place along the actually traversed path even when a straight beeline distance is calculated.
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