Angular scale expansion theory and the misperception of egocentric distance in locomotor space

Abstract

Perception is crucial for the control of action, but perception need not be scaled accurately to produce accurate actions. This paper reviews evidence for an elegant new theory of locomotor space perception that is based on the dense coding of angular declination so that action control may be guided by richer feedback. The theory accounts for why so much direct-estimation data suggests that egocentric distance is underestimated despite the fact that action measures have been interpreted as indicating accurate perception. Actions are calibrated to the perceived scale of space and thus action measures are typically unable to distinguish systematic (e.g., linearly scaled) misperception from accurate perception. Whereas subjective reports of the scaling of linear extent are difficult to evaluate in absolute terms, study of the scaling of perceived angles (which exist in a known scale, delimited by vertical and horizontal) provides new evidence regarding the perceptual scaling of locomotor space.

Keywords: Space perception; distance estimation; psychophysics.

Figure 1

Panel A depicts the top view of a person who translates along the bold line past a target (dark circle) to his or her right. The dashed lines show the reported direction and distance to the target before and after translation. This apparent failure of triangulation when oblique blind walking is combined with verbally estimated target distance (Loomis & Philbeck, 2008) is shown in Panel A. But Panel B shows that subjective triangulation was actually successful so long as the perception of walked distance (dashed bold line) is also underestimated, as is to be expected if visual egocentric distance is underperceived.

Figure 2

The angular expansion theory of distance underestimation. Angular (or gaze) declination (γ), depicted here as the line from the head to the cone on the ground in side view, is a distance cue. If perceived angular declination (the dashed line) relative to straight ahead (the dotted line) is greater than the actual angular declination, then the perceived egocentric ground distance will be reduced accordingly.

Figure 3

When asked to match their egocentric distance from a pole to the height of a pole (left), people set themselves much too far away, consistent with the underestimation of egocentric distance. The matched position across multiple experiments (shown at right) can be predicted by a model (the solid line in the graph) that assumes perceived angular deviations from the horizontal are exaggerated with a gain of 1.5. The model has no free parameters, but it can be used to predict both perceived egocentric distance (as shown in Figure 2) and perceived height (i.e. by also expanding the angle above eye-level) by simple trigonometry (Li et al., 2011).

Figure 4

Panel A depicts that, in the dark, people act as if objects on the floor (black circles) are actually hovering in the air (gray circles). Their actions (walking and then reaching down to the perceived location) are consistent with the correct perception of the direction of their gaze from the starting position (Ooi, Wu & He, 2001, 2006). But the actions of such a person are also consistent with the concurrent misperception of both direction and distance illustrated in Panel B. The lifelong calibration of perceived walked distance to perceived visual distance is sufficient to make actual action effective (along the line of sight, as in panel A) even though the actor’s perception of the situation -- including their amount of self motion -- remains distorted (as in Panel B).