The perception of size and distance under monocular observation

A relative-perceived-size hypothesis is proposed to account for the perception of size and distance under monocular observation in reduced-cue settings. This hypothesis is based on two assumptions. In primary processing, perceived size is determined by both proximal stimulation on the retina and distance information from primary cues such as oculomotor cues. In secondary processing, the relation of two primary perceived sizes determines another relation of secondary perceived distances, so that an object of smaller primary perceived size is judged to be further away. An experiment was designed to test this hypothesis, especially the assumption of secondary processing, by making ratio judgments of perceived size and perceived distance for two successively presented targets. The Standard square was presented at a constant distance and varied in visual angle; the variable square was presented with a constant visual angle in distance. The results showed that an inverse relation between size and distance estimates held regardless of whether the visual angles of the targets were the same or different.     

Size-distance invariance: Kinetic invariance is different from static invariance

The static form of the size-distance invariance hypothesis asserts that a given proximal stimulus size (visual angle) determines a unique and constant ratio of perceived-object size to perceived object distance. A proposed kinetic invariance hypothesis asserts that a changing proximal stimulus size (an expanding or contracting solid visual angle) produces a constant perceived size and a changing perceived distance such that the instantaneous ratio of perceived size to perceived distance is determined by the instantaneous value of visual angle. The kinetic invariance hypothesis requires a new concept, an operating constraint, to mediate between the proximal expansion or contraction pattern and the perception of rigid object motion in depth. As a consequence of the operating constraint, expansion and contraction patterns are automatically represented in consciousness as rigid objects. In certain static situations, the operation of this constraint produces the anomalous perceived-size-perceived-distance relations called the size-distance paradox.     

Size-distance invariance: kinetic invariance is different from static invariance.

The static form of the size-distance invariance hypothesis asserts that a given proximal stimulus size (visual angle) determines a unique and constant ratio of perceived object size to perceived object distance. A proposed kinetic invariance hypothesis asserts that a changing proximal stimulus size (an expanding or contracting solid visual angle) produces a constant perceived size and a changing perceived distance such that the instantaneous ratio of perceived size to perceived distance is determined by the instantaneous value of visual angle. The kinetic invariance hypothesis requires a new concept, an operating constraint, to mediate between the proximal expansion or contraction pattern and the perception of rigid object motion in depth. As a consequence of the operating constraint, expansion and contraction patterns are automatically represented in consciousness as rigid objects. In certain static situations, the operation of this constraint produces the anomalous perceived-size-perceived-distance relations called the size-distance paradox.     

Does retinal size have a unique correlate in perceived size?

Subjects estimated the size and distance of a single electroluminescent disc in the absence of distance cues and without the use of visual comparators. For different groups of Ss the disc subtended a visual angle of 1, 2, 4, or 8 deg. The size estimates varied directly with visual angle and the distance estimates varied inversely with visual angle. These results were considered in relation to the question of whether or not retinal size hasa direct correlate in perceived size.     

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.     

Are rats short-sighted? Effects of stimulus distance and size on visual detection

Behavioural evidence concerning short-sightedness in rats is apparently conflicting: in some experiments rats have performed poorly with visual stimuli further than about 60 cm distant, while in others they have made efficient use of more distant cues, for example to find their way through mazes. However, in the experiments suggesting short-sightedness, the physical size of the stimuli was not varied, so that stimulus distance and visual angle were confounded. In the present experiment, therefore, the size and distance of the stimuli to be detected were varied independently. Over the range tested (30-160 cm), distance was found to produce relatively slight effects on the smallest detectable visual angle, and these tended to diminish with practice. Thus, no good evidence was found for short-sightedness in rats up to 160 cm, a finding consistent with current views of the structure and image-forming capacities of the rat's eye. The smallest detectable targets were, however, surprisingly large in view of the rat's visual acuity (which is about 1c/deg): at the distances tested, animals required considerable training to run reliably to targets subtending less than 5-10° of visual angle. Difficulties in responding to stationary stimuli of this size are likely to restrict severely the use that rats make of vision both in the laboratory and in their natural surroundings.     

The interaction of binocular disparity and motion parallax in determining perceived depth and perceived size.

Although binocular disparity and motion parallax are powerful cues for depth, neither, in isolation, can specify information about both object size and depth. It has been shown that information from both cues can be combined to specify the size, depth, and distance of an object in a scene (Richards, 1985 Journal of the Optical Society of America A 2 343-349). Experiments are reported in which natural viewing and physical stimuli have been used to investigate the nature of size and depth perception on the basis of disparity and parallax presented separately and together at a range of viewing distances. Observers adjusted the relative position of three bright LEDs, which were constrained to form a triangle in plan view with the apex pointing toward the observer, so its dimensions matched that of a standard held by the subject. With static monocular viewing, depth settings were inaccurate and erratic. When both cues were present together accuracy increased and the perceptual outcome was consistent with an averaging of the information provided by both cues. When an apparent bias evident in the observers' responses (the tendency to under-estimate the size of the standard) was taken into account, accuracy was high and size and depth constancy were close to 100%. In addition, given this assumption, the same estimate of viewing distance was used to scale size and depth estimates.     

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.     

A simple but powerful theory of the moon illusion

Modification of Restle's theory (1970) explains the moon illusion and related phenomena on the basis of three principles: (1) The apparent sizes of objects are their perceived visual angles. (2) The apparent size of the moon is determined by the ratio of the angular extent of the moon relative to the extents subtended by objects composing the surrounding context, such as the sky and things on the ground. (3) The visual extents subtended by common objects of a constant physical size decrease systematically with increasing distance from the observer. Further development of this theory requires specification of both the components of the surrounding context and their relative importance in determining the apparent size and distance of the moon.     

Transformation theory of size judgment.

Perception of size is assessed by having observers adjust a comparison target at a fixed distance to match the size of a standard located at different distances. Results depend on instructions, target orientation, and available stimulus cues. A mathematical theory assumes that the brain performs an inverse transformation on the proximal information impinging on the retina to recover the original distal size of the target. Results depend on the target visual angle, and the effective target distance and orientation applied in performing the inverse transformation. Effective values are linked to instructions, target location, and stimulus cues. Two models are developed and successfully fit to empirical data. One emphasizes the distance parameter; the second, the orientation parameter.     

Binocular cues in the perception of distance of a point source of light

The ability to make egocentric distance estimates of a single point source of light, seen in darkness and without the cues of changing size and luminance, was investigated in sixteen observers. The attenuation required to maintain constant luminance, when the target was viewed from different distances, was shown to follow the inverse square law providing the angle subtended by the light was less than 20 s arc. Distance changes were also simulated by means of a split mirror which produced vergence cues, or by test lenses to provide accommodation cues. Over the range 0.5 to 9.2 m distance estimates were surprisingly accurate, although there was some overestimation of near and underestimation of far distances. Most observers made good judgements when only convergence cues were varied, whereas no observers made consistently good judgements when only accommodation cues were varied. The difficulties are discussed in terms of the accommodation-convergence link. When distance was simulated by changing convergence and accommodation cues, estimates were not as good as when real distance was changed. Since good estimates were made with brief target exposures, these judgements were not based on subsequent convergence or accommodation changes. It is suggested that the metric or reference against which the apparently absolute judgements were made was the efferent demand signal associated with a 'resting' position of convergence in darkness.     

Relative distance cues contribute to scaling depth from motion parallax

The visual system scales motion parallax signals with information about absolute distance (M. E. Ono, Rivest, & H. Ono, 1986). The present study was designed to determine whether relative distance cues, which intrinsically provide information about relative distance, contribute to this scaling. In two experiments, two test stimuli, containing an equal extent of motion parallax, were presented simultaneously at a fixed viewing distance. The relative distance cues of dynamic occlusion and motion parallax in the areas surrounding the test stimuli (background motion parallax) and/or relative size were manipulated. The observers reported which of the two parallactic test stimuli appeared to have greater depth, and which appeared to be more distant. The results showed that the test stimulus specified, by the relative distance cues, as being more distant was perceived as having more depth and as being more distant. This indicates that relative distance cues contribute to scaling depth from motion parallax by modifying the information about the absolute distance of objects.     

Through the looking glass: how the relationship between an object and its reflection affects the perception of distance and size

This is the first study to test the extent to which reflections help locate objects in space and perceive their size. For planar mirrors, the relative size of a target and its reflection is informative about the absolute distance of the target in units of the distance between target and mirror surface. When the target is near the mirror, target and reflection are similar in size; as the target moves away from the mirror, the difference in size increases. Observers saw a pair of objects in front of a mirror and judged relative size and distance (separately). Other visual cues to size and distance were eliminated, except lateral offset, which was tested in experiment 3. Experiment 2 controlled for the presence of directional feedback. Results showed orderly psychophysical functions for both size and distance with steeper slopes for distance judgments. In experiments 4 and 5 stereograms were used. Even when binocular information was present, the additional cue provided by reflections increased the accuracy of size and distance judgments. The same pattern of results was observed in the absence of feedback.     

Depth,size and distance in stereoscopic vision

Evidence is presented to show that in stereoscopic vision a constant ratio of perceived size to perceived distance corresponds to a constant visual angle (the size-distance invariance hypothesis). The functions relating the size/ distance ratio to visual angle and the depth/distance ratio to disparity are determined for three as using the methods of magnitude estimation and magnitude production. The results for each a may be represented by power functions, the depth/ distance function having the higher exponent. These scales are used to predict the outcome of an experiment in which depth is matched to size. The agreement of predictions with results is good for the combined data of the group, but significant deviations occur from curves predicted for individual as. An experiment in which an oblique line is matched to a frontal extent yields data consistent with Luneburg’s hypothesis that the intrinsic geometry of visual space is non-Euclidean. The indicated curvature is negative for two as and varying from positive to negative for the third.     

The interaction of oculomotor cues and stimulus size in stereoscopic death constancy.

In the natural world, observers perceive an object to have a relatively fixed size and depth over a wide range of distances. Retinal image size and binocular disparity are to some extent scaled with distance to give observers a measure of size constancy. The angle of convergence of the two eyes and their accommodative states are one source of scaling information, but even at close range this must be supplemented by other cues. We have investigated how angular size and oculomotor state interact in the perception of size and depth at different distances. Computer-generated images of planar and stereoscopically simulated 3-D surfaces covered with an irregular blobby texture were viewed on a computer monitor. The monitor rested on a movable sled running on rails within a darkened tunnel. An observer looking into the tunnel could see nothing but the simulated surface so that oculomotor signals provided the major potential cues to the distance of the image. Observers estimated the height of the surface, their distance from it, or the stereoscopically simulated depth within it over viewing distances which ranged from 45 cm to 130 cm. The angular width of the images lay between 2 deg and 10 deg. Estimates of the magnitude of a constant simulated depth dropped with increasing viewing distance when surfaces were of constant angular size. But with surfaces of constant physical size, estimates were more nearly independent of viewing distance. At any one distance, depths appeared to be greater, the smaller the angular size of the image. With most observers, the influence of angular size on perceived depth grew with increasing viewing distance. These findings suggest that there are two components to scaling. One is independent of angular size and related to viewing distance. The second component is related to angular size, and the weighting accorded to it grows with viewing distance. Control experiments indicate that in the tunnel, oculomotor state provides the principal cue to viewing distance. Thus, the contribution of oculomotor signals to depth scaling is gradually supplanted by other cues as viewing distance grows. Binocular estimates of the heights and distances of planar surfaces of different sizes revealed that angular size and viewing distance interact in a similar way to determine perceived size and perceived distance.     

Measures of perceived linear size, sagittal motion, and visual angle from optical expansions and contractions

Using monocular observation, open-loop measurements were obtained of the perceptions of linear size, angular size, and sagittal motion associated with the terminal (largest or smallest) stimuli of repetitive optical expansions and contractions using 1-D or 2-D displays produced on a video monitor at a constant distance from the observer. The perceptions from these dynamic conditions were compared with those from static conditions in which the stimuli were of the same physical size and at the same physical distance as the terminal dynamic stimuli, but that were not part of the optical expansions or contractions. One result, as expected, was that the measures of perceived linear and angular size differed, but also, unexpectedly, some substantial errors were associated with the measures of perceived angular size. Another result was that the amount of size constancy was considerably less than was expected from the obtained amount of perceived motion in depth. Consistent with the latter result, it was found that the size-distance invariance hypothesis (SDIH), using the physical visual angles of the terminal stimuli, predicted only about half of the perceived motion in depth obtained with the dynamic changes. Using the obtained measures of perceived visual angles in the SDIH increased rather than decreased the error in predicting the amount of motion in depth as perceived. An additional experiment suggests that at least some of the error in the measurement of the perceived visual angle is a consequence of error in the perceived origin of the visual angles. The absence of the expected relation between size constancy and perceived motion in depth in the dynamic conditions is hypothesized to be due to cognitive processes associated with off-sized perceptions of the stimuli.     

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.     

Intensity and reverberation as factors in the auditory perception of egocentric distance

Both auditory intensity and reverberation have previously been shown to be sufficient to produce systematically varying judgments of perceived distance when several values of the variable are presented repeatedly to the same observer. Such studies do not, however, indicate clearly whether these cues are functioning in an absolute or in a relative manner. An absolute cue to auditory distance would require that two groups presented with different values of the variable in question should report different values of perceived distance. Two experiments are reported in which intensity variation and reverberation are examined. The results showed that auditory intensity differences over a range of 20 dB did not serve as an absolute cue to auditory distance, but could serve as a strong cue to changes in such distance. A comparison of data obtained in a normally reverberatory setting (Experiment 1) and an anechoic chamber (Experiment 2) indicated that the state of reverberation could serve as an absolute cue, with greater reverberation being associated with greater perceived distances. Some of the results were discussed in terms of the possibility that the specific distance tendency (a concept developed to handle some phenomena in visual space perception) might have applicability to the study of auditory perceived distance as well.

     

Is size perception based on monocular distance cues computed automatically?

The study reported here examined whether size perception based on monocular distance cues is computed automatically. Participants were presented with a picture containing distance cues, which was superimposed with a pair of digits differing in numerical value. One digit was presented so as to be perceived as closer than the other. The digits were of similar physical size but differed in their perceptual size. The participants’ task was to decide which digit was numerically larger. It was found that the decision took longer and resulted in more errors when the perceptual size of the numerically larger digit was smaller than the perceptual size of the numerically smaller digit. These results show that perceived size affects performance in a task that does not require size or distance computation. Hence, for the first time, there is empirical support for the working assumption of the visual perception approach that size perception based on monocular distance cues is computed automatically.     

Distance perception within near visual space

We investigated the perception of distance of visual targets with constant size and luminance presented between 20 and 120 cm from subjects' eyes. When retinal disparity cues were present, the subjects could reproduce very accurately the distance of a seen reference in this area. When only extraretinal information was available, distance perception was still correct for distances of 40 cm or less. However, distances beyond 60 cm were underestimated. When forced to evaluate the distance between a reference and themselves, e.g. when evaluating the absolute distance or half the distance or twice the distance of a reference, subjects used an egocentric plane of reference located on average 10.4 cm in front of their eyes. Measurements of binocular eye movements indicated a clear relationship between vergence angle and target distance. The egocentric plane of reference at 10.4 cm also corresponds to the maximum achievable vergence. These results suggest that ocular convergence can be used as a reliable cue for distance within the arm's reaching space.