In immersive virtual environments (IVEs), users can control their virtual viewpoint by moving their tracked head and walking through the real world. Usually, movements in the real world are mapped one-to-one to virtual camera motions. With redirection techniques, the virtual camera is manipulated by applying gains to user motion so that the virtual world moves differently than the real world. Thus, users can walk through large-scale IVEs while physically remaining in a reasonably small workspace. In psychophysical experiments with a two-alternative forced-choice task, we have quantified how much humans can unknowingly be redirected on physical paths that are different from the visually perceived paths. We tested 12 subjects in three different experiments: (E1) discrimination between virtual and physical rotations, (E2) discrimination between virtual and physical straightforward movements, and (E3) discrimination of path curvature. In experiment E1, subjects performed rotations with different gains, and then had to choose whether the visually perceived rotation was smaller or greater than the physical rotation. In experiment E2, subjects chose whether the physical walk was shorter or longer than the visually perceived scaled travel distance. In experiment E3, subjects estimate the path curvature when walking a curved path in the real world while the visual display shows a straight path in the virtual world. Our results show that users can be turned physically about 49 percent more or 20 percent less than the perceived virtual rotation, distances can be downscaled by 14 percent and upscaled by 26 percent, and users can be redirected on a circular arc with a radius greater than 22 m while they believe that they are walking straight.

Optic flow fields provide rich information about the observer's self-motion. Besides estimation of the direction of self-motion human observers are also able to discriminate the travel distances of two self-motion simulations. Recent studies have shown that observers estimate the simulated ego velocity of the self-motion simulation and integrate it over time. Thus, observers use a 3-D percept of the ego motion through the environment. In the present work we ask if human observers are able to use this 3-D percept of the motion simulation to build up an internal representation of travel distance and indicate it in a static scene. We visually simulated self-motion in different virtual environments and asked subjects to indicate the perceived distances in terms of static virtual intervals on the ground. The results show that human observers possess a static distance gauge, but that they undershoot the travel distances for short motion simulations. In further experiments we changed the modality of the distance indication but the undershoot in distance estimation remained. This suggests that the undershoot is linked to the perception of the optic flow field.

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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, an integration of the movement to obtain distance. Distance underestimation occurs because this integration is imperfect and contains a leak that increases with distance traveled. We asked human observers to estimate the distance from a starting location for visually simulated movements in a virtual environment. The movements occurred along curved paths that veered left and right around a central forward direction. In this case, the distance that has to be integrated (i.e., the beeline distance between origin and endpoint) and the distance that is traversed (the path length along the curve) are distinct. We then tested whether the leak accumulated with distance from the origin or with traversed distance along the curved path. Leaky integration along the path makes the seemingly counterintuitive prediction that the estimated origin-to-endpoint distance should decrease with increasing veering, because the length of the path over which the integration occurs increases, leading to a larger leak effect. The results matched the prediction: movements of identical origin-to-endpoint distance were judged as shorter when the path became longer. We conclude that leaky path integration from visual motion is performed along the traversed path even when a straight beeline distance is calculated.