Judgments of visually perceived eye level (VPEL) in outdoor scenes: effects of slope and height

A day at the beach: Does visually perceived distance depend on the energetic cost of walking?

It takes less effort to walk from here to the Tiki Hut on the brick walkway than on the sandy beach. Does that influence how far away the Tiki Hut looks? The energetic cost of walking on dry sand is twice that of walking on firm ground (Lejeune et al., 1998). If perceived distance depends on the energetic cost or anticipated effort of walking (Proffitt, 2006), then the distance of a target viewed over sand should appear much greater than one viewed over brick. If perceived distance is specified by optical information (e.g., declination angle from the horizon; Ooi et al., 2001), then the distances should appear similar. Participants (N = 13) viewed a target at a distance of 5, 7, 9, or 11 m over sand or brick and then blind-walked an equivalent distance on the same or different terrain. First, we observed no main effect of walked terrain; walked distances on sand and brick were the same (p = 0.46), indicating that locomotion was calibrated to each substrate. Second, responses were actually greater after viewing over brick than over sand (p < 0.001), opposite to the prediction of the energetic hypothesis. This unexpected overshooting can be explained by the slight incline of the brick walkway, which partially raises the visually perceived eye level (VPEL) and increases the target distance specified by the declination angle. The result is thus consistent with the information hypothesis. We conclude that visually perceived egocentric distance depends on optical information and not on the anticipated energetic cost of walking.

Foreshortening affects both uphill and downhill slope perception at far distances

Perceived slope varies with the viewing distance, and is consistent with the effects of foreshortening. Distant viewing makes uphill slopes appear steeper and downhill slopes flatter than does near viewing. These effects are obvious to skiers and climbers in mountainous country. They have also been measured in outdoor experiments with controlled viewing distances. There are many other sources of slope illusions.

Short-lived effects of a visual inducer during egocentric space perception and manual behavior

A pitched visual inducer has a strong effect on the visually perceived elevation of a target in extrapersonal space, and also on the elevation of the arm when a subject points with an unseen arm to the target's elevation. The manual effect is a systematic function of hand-to-body distance (Li and Matin Vision Research 45:533-550, 2005): When the arm is fully extended, manual responses to perceptually mislocalized luminous targets are veridical; when the arm is close to the body, gross matching errors occur. In the present experiments, we measured this hand-to-body distance effect during the presence of a pitched visual inducer and after inducer offset, using three values of hand-to-body distance (0, 40, and 70 cm) and two open-loop tasks (pointing to the perceived elevation of a target at true eye level and setting the height of the arm to match the elevation). We also measured manual behavior when subjects were instructed to point horizontally under induction and after inducer offset (no visual target at any time). In all cases, the hand-to-body distance effect disappeared shortly after inducer offset. We suggest that the rapid disappearance of the distance effect is a manifestation of processes in the dorsal visual stream that are involved in updating short-lived representations of the arm in egocentric visual perception and manual behavior.

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

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.

The underestimation of egocentric distance: evidence from frontal matching tasks

There is controversy over the existence, nature, and cause of error in egocentric distance judgments. One proposal is that the systematic biases often found in explicit judgments of egocentric distance along the ground may be related to recently observed biases in the perceived declination of gaze (Durgin & Li, Attention, Perception, & Psychophysics, in press), To measure perceived egocentric distance nonverbally, observers in a field were asked to position themselves so that their distance from one of two experimenters was equal to the frontal distance between the experimenters. Observers placed themselves too far away, consistent with egocentric distance underestimation. A similar experiment was conducted with vertical frontal extents. Both experiments were replicated in panoramic virtual reality. Perceived egocentric distance was quantitatively consistent with angular bias in perceived gaze declination (1.5 gain). Finally, an exocentric distance-matching task was contrasted with a variant of the egocentric matching task. The egocentric matching data approximate a constant compression of perceived egocentric distance with a power function exponent of nearly 1; exocentric matches had an exponent of about 0.67. The divergent pattern between egocentric and exocentric matches suggests that they depend on different visual cues.

Perceived slant of binocularly viewed large-scale surfaces: a common model from explicit and implicit measures

It is known that the perceived slants of large distal surfaces, such as hills, are exaggerated and that the exaggeration increases with distance. In a series of two experiments, we parametrically investigated the effect of viewing distance and slant on perceived slant using a high-fidelity virtual environment. An explicit numerical estimation method and an implicit aspect-ratio approach were separately used to assess the perceived optical slant of simulated large-scale surfaces with different slants and viewing distances while gaze direction was fixed. The results showed that perceived optical slant increased logarithmically with viewing distance and the increase was proportionally greater for shallow slants. At each viewing distance, perceived optical slant could be approximately fit by linear functions of actual slant that were parallel across distances. These linear functions demonstrated a fairly constant gain of about 1.5 and an intercept that increased logarithmically with distance. A comprehensive three-parameter model based on the present data provides a good fit to a number of previous empirical observations measured in real environments.

Palm boards are not action measures: an alternative to the two-systems theory of geographical slant perception

Whereas most reports of the perception of outdoor hills demonstrate dramatic overestimation, estimates made by adjusting a palm board are much closer to the true hill orientation. We test the dominant hypothesis that palm board accuracy is related to the need for motor action to be accurately guided and conclude instead that the perceptual experience of palm-board orientation is biased and variable due to poorly calibrated proprioception of wrist flexion. Experiments 1 and 3 show that wrist-flexion palm boards grossly underestimate the orientations of near, reachable surfaces whereas gesturing with a free hand is fairly accurate. Experiment 2 shows that palm board estimates are much lower than free hand estimates for an outdoor hill as well. Experiments 4 shows that wrist flexion is biased and noisy compared to elbow flexion, while Experiment 5 shows that small changes in palm board height produce large changes in palm board estimates. Together, these studies suggest that palm boards are biased and insensitive measures. The existing literature arguing that there are two systems in the perception of geographical slant is re-evaluated, and a new theoretical framework is proposed in which a single exaggerated representation of ground-surface orientation guides both action and perception.