Large perceptual distortions of locomotor action space occur in ground-based coordinates: Angular expansion and the large-scale horizontal-vertical illusion

Abstract

What is the natural reference frame for seeing large-scale spatial scenes in locomotor action space? Prior studies indicate an asymmetric angular expansion in perceived direction in large-scale environments: Angular elevation relative to the horizon is perceptually exaggerated by a factor of 1.5, whereas azimuthal direction is exaggerated by a factor of about 1.25. Here participants made angular and spatial judgments when upright or on their sides to dissociate egocentric from allocentric reference frames. In Experiment 1, it was found that body orientation did not affect the magnitude of the up-down exaggeration of direction, suggesting that the relevant orientation reference frame for this directional bias is allocentric rather than egocentric. In Experiment 2, the comparison of large-scale horizontal and vertical extents was somewhat affected by viewer orientation, but only to the extent necessitated by the classic (5%) horizontal-vertical illusion (HVI) that is known to be retinotopic. Large-scale vertical extents continued to appear much larger than horizontal ground extents when observers lay sideways. When the visual world was reoriented in Experiment 3, the bias remained tied to the ground-based allocentric reference frame. The allocentric HVI is quantitatively consistent with differential angular exaggerations previously measured for elevation and azimuth in locomotor space. (PsycINFO Database Record

Figure 1

Diagram showing how egocentric distance underestimation (D′) and misperception of the height/distance ratio (H/D) can be understood in terms of visual direction: The exaggeration of perceived elevation relative to straight ahead (with a gain of 1.5) foreshortens perceived ground distance relative to eye-height.

Figure 2

Diagram illustrating the differential angular expansions in elevation (1.5 gain) and azimuth (1.25 gain) that have been measured in large-scale spaces.

Figure 3

Cart (top left) and light pole (top middle) and water tower (top right) used in Experiment 1; images used when instructing participants for the height-distance matching task (bottom left) and explicit angular direction task (bottom right). The cart platform could be raised up for a sideways observer (as shown), lowered down (for a seated observer) or tilted at 45°, by lowering only the foot-supporting end of the platform.

Figure 4

Optical direction in elevation from horizontal perceived as 45° (estimated match point) in both tasks of Experiment 1. Dashed line represents predictions based on an angular gain of 1.5 (Angular Expansion Hypothesis). Bars show 95% CIs for each viewing condition and task.

Figure 5

Photograph of the experimental setup in Experiment 2. The participant (left) either lay sideways on the wooden cart (as shown) or stood in the same location. Their task was to direct the experimenter (holding a short pole) to move left or right until the perceived distance between the tall pole and the short pole matched the perceived height of the tall pole.

Figure 6

Results of Experiment 2. Left: Mean perceived gravitational height-to-width ratio as a function of body orientation and of pole height. 95% CIs are shown. Right: The implied allocentric and egocentric components contributing to the outdoor horizontal vertical illusions at each pole height. (Dashed lines represent expected allocentric – 20% – and egocentric – 5% – contributions based on prior studies). CIs were computed for the allocentric component by calculating the implied allocentric contribution for each observer assuming a 5% retinotopic HVI.

Figure 7

Screen-shots (cropped) of immersive stereoscopic displays from Experiment 3. At left, the basic scene consisted of a tall stationary pole and a shorter pole that could be moved along the ground to set the pole-to-pole horizontal distance. At right are shown a rotated world version of the same scene. Avatars were present (bottom row) near the poles for half the observers.

Figure 8

Results of Experiment 3. Left: The mean HVI ratio (i.e. the ratio between perceived pole height and perceived width with respect to the scene reference frame) for the upright and sideways scene orientation conditions. Right: the estimated magnitudes of the ground-relative (allocentric) and other (non ground-based) components of the outdoor HVI with respect to the scene reference frame. Confidence intervals (95%) are shown.