Mirror vision: perceived size and perceived distance of virtual images

We investigated spatial perception of virtual images that were produced by convex and plane mirrors. In Experiment 1, 36 subjects reproduced both the perceived size and the perceived distance of virtual images for five targets that had been placed at a real distance of 10 or 20 m. In Experiment 2, 30 subjects verbally judged both the perceived size and the perceived distance of virtual images for five targets that were placed at each of five real distances of 2.5-45 m. In both experiments, the subjects received objective-size and objective-distance instructions. The results were that (1) size constancy was attained for a distance of up to 45 m, (2) distance was readily discriminated within this distance range, although virtual images produced by the mirror of strong curvature were judged to be farther away than those produced by the mirrors of less curvature, and (3) the ratio of perceived size to perceived distance was described as a power function of visual angle, and the ratio for the convex mirror was larger than that for the plane mirror. We compared the taking-into-account model and the direct perception model on the basis of a correlation analysis for proximal, virtual, and real levels of the stimuli. The taking-into-account model, which assumes that visual angle is transformed into perceived size by taking perceived distance into account, was supported by an analysis for the proximal level of stimuli. The direct perception model, which assumes that there is no inferential process between perceived size and perceived distance, was partially supported by an analysis for the distal level of the stimuli.     

Failure of familiar size to determine a metric for visually perceived distance

The use of knowledge of the familiar sizes of objects in determining the apparent distances of those objects is known as the familiar size cue to distance. If effective, this cue might be one of the factors responsible for supplying the metric (scalar) characteristics of perceptions of spatial extent within a visual display in which other information concerning scalar extents has been reduced to a minimum. Two groups of observers were presented with realistic objects of the same angular, but different assumed, sizes presented in such a cue-restricted display. Perceptions of size and distance within the display did not differ significantly as a function of the type of object initially presented. This result was consistent with the notion that scalar perceptions under these conditions probably are determined by a factor known as the specific distance tendency, rather than by the experiential factor of familiar size.     

An indirect method of measuring perceived distance from familiar size

Two methods of measuring perceived distance as a function of familiar size were compared in five experiments. The method which uses the perception of motion concomitant with a motion of the head, unlike the method of verbal report, is considered to provide a measure of perceived distance that is unaffected by factors of cognitive distance. The results of the experiments indicate that although the perceived egocentric distance of an object can vary somewhat as a function of the cue of familiar size, the larger variation often found with verbal reports of distance is based upon cognitive, not perceptual, information. The cognitive information is interpreted as resulting from the perception of the object as off-sized and the observer’s assumption that the perceived size of an object will vary inversely with its physical distance.     

Effects of motion parallax and perspective cues on perceived size and distance

In three experiments we examined the relative effectiveness of motion parallax and two perspective cues for the perception of size and distance. The experimental stimuli consisted of two ellipses (a standard and a comparison) and a horizontal line that indicated the horizon. The subject's task was to report the apparent size and distance of the comparison stimulus relative to the standard stimulus. Two perspective cues were given by the relative heights of the two stimuli and the absolute height of the standard stimulus below the horizon. Motion parallax was defined by both the ratio and the difference in angular velocities between the two stimuli on the display. In experiment 1 we examined the effects of the two perspective cues and the motion parallax. In experiment 2 we eliminated the horizon line, and examined the role of the horizon in size and distance perception. In experiment 3 we separately evaluated the effects of motion parallax and the relative height cues. The results from the three experiments showed that the effect of motion parallax and the two perspective cues were different in three ways. First, the relative effectiveness of motion parallax and the two perspective cues differed for size and distance estimates. For size estimates, the motion parallax was more effective than the perspective cues (experiments 1 and 3). For distance estimates, the motion parallax was as effective as the two perspective cues (experiments 1 and 3). Second, the role of the horizon differed for size and distance estimates. The size estimates were strongly affected by the horizon, while the distance estimates were not affected much by the horizon (experiment 2). Third, the effective perspective cues differed for the size estimates and the distance estimates: size estimates were affected by the perspective cues as a combination of the horizon and relative height; distance estimates were affected by the perspective cues as an interaction between the absolute and relative heights without the horizon line.     

Psychophysical functions for perceived and remembered distance

Two separate groups of subjects made magnitude estimations of the distances to fifteen objects (from 20 ft to 14.28 miles away) situated in a landscape. On day 1 of the experiment both groups learned the names and locations of the objects while viewing them from the top of a small mountain. On day 2 the perception group (N = 19) judged the distances to the objects while viewing them from the top of the mountain, whereas the memory group (N = 18) judged the distances while visualizing the landscape from memory. The data for both groups were well fit by power functions; the exponent was reliably smaller for the memory group (0.596) than for the perception group (0.811). Both groups drew maps of the landscape (reproduction task) from memory and the exponents were 0.483 and 0.514 for the memory and perception groups, respectively. The results are discussed in light of possible transformations performed on the original stimulus inputs by the sensory/perceptual and the memorial systems.     

Perceived size and perceived distance in stereoscopic vision and an analysis of their causal relations

Effects of visual angle and convergence upon the perceived sizes and perceived distances of a familiar object (playing card) and a nonrepresentational object (blank white card) were investigated by means of a projector stereoscope with polarizing filters. The results obtained with six Ss indicated that size estimates increased nearly proportionally as the visual angle increased and decreased nearly linearly as the convergence increased. Distance estimates decreased nearly linearly as either the visual angle or the convergence increased. The ratio of the size estimate to the distance estimate for a given visual angle was almost constant irrespective of convergence. In this sense, the size-distance invariance hypothesis held. No clear effect of familiarity was found. Partial correlations were used to discriminate direct and indirect causal relationships between the stimulus variables and perceptual estimates. Both perceived size and perceived distance were found to be determined directly by the two stimulus variables, but to be mutually related only indirectly.     

The effect of perceived distance on perceived movement

Equations were developed to predict the apparent motion of a physically stationary object resulting from head movement as a function of errors in the perceived distances of the object or of its parts. These equations, which specify the apparent motion in terms of relative and common components, were applied to the results of two experiments. In the experiments, the perceived slant of an object was varied with respect to its physical slant by means of perspective cues. In Experiment I, O reported the apparent motion and apparent distance of each end of the object independently. The results are consistent with the equations in terms of apparent relative motion, but not in terms of apparent common motion. The latter results are attributed to the tendency for apparent relative motion to dominate apparent common motion when both are present simultaneously. In Experiment II, a direct report of apparent relative motion (in this case, apparent rotation) was obtained for illusory slants of a physically frontoparallel object. It was found that apparent rotations in the predicted direction occurred as a result of head motion, even though under these conditions no rotary motion was present on the retina.     

A distance judgment function based on space perception mechanisms: revisiting Gilinsky's (1951) equation

In her seminal article in Psychological Review, A. S. Gilinsky (1951) successfully described the relationship between physical distance (D) and perceived distance (d) with the equation d = DA/(A + D), where A = constant. To understand its theoretical underpinning, the authors of the current article capitalized on space perception mechanisms based on the ground surface to derive the distance equation d = Hcosalpha/sin(alpha + eta), where H is the observer's eye height, alpha is the angular declination below the horizon, and eta is the slant error in representing the ground surface. Their equation predicts that (a) perceived distance is affected by the slant error in representing the ground surface; (b) when the slant error is small, the ground-based equation takes the same form as Gilinsky's equation; and (c) the parameter A in Gilinsky's equation represents the ratio of the observer's eye height to the sine of the slant error. These predictions were empirically confirmed, thus bestowing a theoretical foundation on Gilinsky's equation.     

Quantitative functions for size and distance judgments

A psychophysical approach was used to obtain judgments of visual extent under three conditions. In tuvo conditions a comparison stimulus at each of two distances was matched in size to a standard which varied in distance. Stimuli were presented on a well-lighted table and were judged by two observers under Objective instructions. Both the standard and comparison were located in either a frontal or longitudinal plane. In a third condition relative distance estimates were given of two stimuli which varied in their relative positions along the table. The mean results for all conditions were described as a power function of physical stimulus measures. The exponent was greater than 1.0 for frontal size and usually less than 1.0 for flat size and distance. The position of the comparison affected the magnitude of the exponents to a lesser degree. These findings have relevance for interpretations of size and distance judgments.     

Linear perspective and perceived size

A recent investigation (McDermott, 1965) revealed individual cues to distance had little effect on the perception of size. The present investigation paired each distance cue with linear perspective to determine the effect on size of combined distance cues. Separate groups of Ss were run in each of six combined cue conditions at three distances. For the most part, size matches were made in terms of retinal image size. It was hypothesized that relative or familiar size may be more relevant to size perception than distance cues.     

Environmental context influences visually perceived distance

What properties determine visually perceived space? We discovered that the perceived relative distances of familiar objects in natural settings depended in unexpected ways onthe surrounding visual field. Observers bisected egocentric distances in a lobby, in a hallway, and on an open lawn. Three key findings were the following: (1) Perceived midpoints were too far from the observer, which is the opposite of the common foreshortening effect. (2) This antiforeshortening constant error depended on the environmental setting--greatest in the lobby and hall but nonsignificant on the lawn. (3) Context also affected distance discrimination; variability was greater in the hall than in the lobby or on the lawn. A second experiment replicated these findings, using a method of constant stimuli. Evidently, both the accuracy and the precision of perceived distance depend on subtle properties of the surrounding environment.     

Tool use influences perceived shape and perceived parallelism, which serve as indirect measures of perceived distance

Targets presented just beyond arm's reach look closer when observers intend to touch them with a reach-extending tool rather than without the tool. This finding is one of several that suggest that a person's ability to act influences perceived distance to objects. However, some critics have argued that apparent action effects were actually due to effects on the judgments rather than on the perception. In other words, the target does not actually look closer, but participants report that it is. To help counter this argument, the current experiments used an indirect measure of perceived distance: Participants reported perceived shape or perceived parallelism. The results revealed that triangles looked shorter and lines looked more horizontal to participants who reached with a tool, and therefore could reach the targets, than they did to participants who reached without the tool. These results demonstrate convergence across multiple types of judgments, a finding that undermines alternative, judgment-based accounts and suggests that the ability to reach an object changes the perceived distance to the object.