Keeping track of the distance from home by leaky integration along veering paths

Abstract

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.

The Effect of Extended Sensory Range via the EyeCane Sensory Substitution Device on the Characteristics of Visionless Virtual Navigation

“…Another interesting factor to explore in this future experiment is whether the absolute-distance conveyed by the EyeCane directly will cause users to avoid the 'compression' effect reported by previous studies (Frissen et al, 2011;Lappe et al, 2011;Li et al, 2011;Philbeck et al, 1995) in which virtual distances are misjudged.…”

Sources of path integration error in young and aging humans

“…Thus, it is implausible that subjects exhibit substantial biases in velocity gain that are not discovered by the analysis model. Second, the subjects in Lappe et al (2007Lappe et al ( , 2011 have access only to optic flow for motion estimation, while subjects in our study additionally have access to richer, body-based motion cues including vestibular signals. In rodent studies, when motion cues are less rich (passive transport on trolleys; head-fixed animals in virtual environments), displacements are underestimated, similar to the finding in Lappe et al, suggesting that a decreased availability of sensory motion cues in Lappe et al may account for the dominant contribution of a velocity estimation bias in their findings.…”

“…The full model was highly favored ("very strong" evidence in support, or Δ (Δ ) ≫ 10) relative to alternatives, including models with no reporting noise (Full-AN+CN-AB-RN, Full-RN) or non-accumulating (constant) noise (Full-AN+CN-AB-RN, Full-AN+CN), consistently across both age groups (Young: Full vs. 1957). Specifically, the full model outcompeted the Full-AN+CN-AB-RN variant, whichwith non-accumulating noise, no additive bias in integration, no reporting noise, but biased and leaky velocity integrationis the closest analogue to a leading existing model of human path integration performance (Lappe et al, 2007(Lappe et al, , 2011).…”

“…The computational model we use differs from previous models of path integration error (e.g., Lappe et al, 2007Lappe et al, , 2011 in several ways: First, we use time-resolved models in which moment-by-moment errors during a trajectory can interact with the moment-by-moment unfolding of the trajectory, and detailed, signed errors can be predicted over time. The richer model allows us to distinguish a large number of sources of noise and bias, and take into account reporting errors in which subjects are only able to report an imperfect representation of their internal location estimates.…”

“…The richer model allows us to distinguish a large number of sources of noise and bias, and take into account reporting errors in which subjects are only able to report an imperfect representation of their internal location estimates. Unlike previous models that fit path-integration biases using trialaveraged data by minimizing the mean square error (Lappe et al, 2007(Lappe et al, , 2011, we model both biases and variances using a well-defined log-likelihood. This approach has several advantages: We can fit a more heterogeneous dataset where each trajectory is only repeated a few times, location estimates are weighted inversely proportional to the model-predicted variance (mainly influenced by the traveled distance), making the fit less biased and more data-efficient, and the log-likelihood allows a systematic model-comparison using cross-validation and the Bayesian Information Criterion (BIC).…”