Perceptual scale expansion: an efficient angular coding strategy for locomotor space

Abstract

Whereas most sensory information is coded on a logarithmic scale, linear expansion of a limited range may provide a more efficient coding for the angular variables important to precise motor control. In four experiments, we show that the perceived declination of gaze, like the perceived orientation of surfaces, is coded on a distorted scale. The distortion seems to arise from a nearly linear expansion of the angular range close to horizontal/straight ahead and is evident in explicit verbal and nonverbal measures (Experiments 1 and 2), as well as in implicit measures of perceived gaze direction (Experiment 4). The theory is advanced that this scale expansion (by a factor of about 1.5) may serve a functional goal of coding efficiency for angular perceptual variables. The scale expansion of perceived gaze declination is accompanied by a corresponding expansion of perceived optical slants in the same range (Experiments 3 and 4). These dual distortions can account for the explicit misperception of distance typically obtained by direct report and exocentric matching, while allowing for accurate spatial action to be understood as the result of calibration.

Figure 1

Scale-expanded perceptual coding (γ_p and β_p) of both gaze declination (γ) and optical slant (β) amplifies departures of the ground plane from horizontal (β_p - γ_p), while leaving level ground appearing flat, but distance along it foreshortened. Expanded scaling of these angular variables may enhance coding of ground distance and surface slant for action control, while producing known biases in the perception of slant and distance.

Figure 2

All eight target locations in the uphill condition of Experiment 1. Only one target was visible at a time.

Figure 3

Gaze declination estimates in Experiment 1 as a function of true declination. Filled circles are judgments of observers facing up the hill; empty circles represent judgments made while facing down the hill. Smoothed fit lines for the two conditions are shown, as is an overall linear fit (dotted line) with an intercept of 6.9° and slope of 1.53.

Figure 4

Mean angular declination to target object when at apparent horizontal/vertical bisection point (perceived gaze declination of 45°), as a function of slanding platform height. Standard errors of the means are shown.

Figure 5

Example gravel boards (left) and mean estimates of slant (right). Standard errors of the means are shown.

Figure 6

A view from the side of simulated gravel surfaces at each of the five gaze declinations for the slant task of Experiment 3. Only one surface was visible at a time in the experiment. Note that the 3D gravel textures were presented on both sides of the surfaces. The avatar depicts the participant’s viewing location and was not represented in the experimental displays.

Figure 7

Results of Experiment 4. (A) Mean geographical slant estimates as a function of simulated geographical slant and direction of gaze. (B) Gaze declination estimation data from solitary white balls presented in the same virtual environment. Mean verbal estimates are plotted as a function of actual declination of gaze (negative values represent gaze elevation). Standard errors of the means are shown. (C) Inferred perceived optical slant (estimated geographical slant – perceived gaze declination) as a function of simulated optical slant (simulated geographical slant – gaze declination) on the (false) assumption that gaze declination was perceived veridically. (D) Inferred perceived optical slant (estimated geographical slant – perceived gaze declination) as a function of simulated optical slant (simulated geographical slant – gaze declination) based on direct estimates of geographical slant and of gaze declination. For simulated optical slants between 4° and 50°, the slope is 1.52. The plateau near 0° indicates that when optical slant was shallow, reports of geographical slant corresponded to later reports of perceived gaze declination.

Figure A1

Diagrammatic depiction of L-shape task for layout ABC, hypothesized to appear as being at a nearer location, such as A’B’C’. The underestimation of length

Figure A2

Extent anisotropy data for elevated observers (Loomis & Philbeck, 1999) expressed as perceived optical slant as a function of true optical slant. The linear fit to the data indicates a gain of about 1.57.