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Markus Lappe, Michael Jenkin, Laurence Harris; Visual odometry by leaky integration. Journal of Vision 2007;7(9):147. doi: 10.1167/7.9.147.
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Visual motion can be a cue to travel distance when the motion signals are integrated. Previous work has given conflicting results on the precision of travel distance estimation from visual motion: Frenz and Lappe reported underestimation, Redlick, Jenkin and Harris overestimation of travel distance. In a collaborative study we resolved the conflict by tracing it to differences in the tasks given to the subjects. Self-motion was visually simulated in a immersive virtual environment. Subjects completed two tasks in separate blocks. They either had to report the distance traveled from the start of the movement as in earlier studies of Frenz and Lappe, or they had to report when they reached a predetermined target position as in earlier studies by Redlick et al. Consistent with both earlier studies, underestimation of travel distance occurred when the task required judgment of distance from the starting position, and overestimation of travel distance occurred when the task required judgment of the remaining distance to the previewed target position. Based on these results we developed a leaky integrator model that explains both effects with a single mechanism. In this model, a state variable, either the distance from start or the distance to target, is updated during the movement by integration over the space covered by the movement. 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.
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