Apparent afterimage size, Emmert's law, and oculomotor adjustment

The apparent size of an afterimage viewed from distances between 5 cm and 580 cm was matched to that of a size-adjustable stimulus at a fixed distance (20, 30, 90, and 200 cm). The experiment was conducted under normal indoor illumination with a procedure that facilitated matching for angular size. The matched size was found to increase with focal distance within 1 m and very little beyond 1 m. Similar results were obtained with an equivalent series of real stimuli subtending a constant visual angle. These findings suggest a scaling in perceived angular size in proportion to the oculomotor adjustments for accommodation and convergence. The observations of perceived angular size of the afterimage complement what Emmert's law is meant to describe (perceived object size of the afterimage), even though as the focal distance decreases it may be increasingly difficult to tease out perceived object size and perceived angular size with the matching procedure.     

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.     

Oculomotor adjustments and size-distance perception

The relationship between perceived size and distance and oculomotor adjustments were assessed in two experiments. In both experiments, Ss were required to make scalar linear size, angular size, and distance judgments of stimuli subtending a constant retinal image size at different levels of convergence. The results of the first experiment indicate that the perceived linear size, angular size, and distance of the stimulus decreased with increased convergence, the decrease in perceived linear size being greater than that of perceived angular size. While again showing a decrease in perceived linear and angular size, the results of the second experiment also show that there was a smaller decrease in perceived distance with increased convergence when Ss continued to view the stimulus as convergence was changed than when they did not view the stimulus as convergence was changed. The implications these results have for size and distance perception are discussed.     

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.     

CONVERGENCE AS A CUE T O PERCEIVED SIZE AND DISTANCE

A wire mesh was used as stimulus object in the old 'wall-paper experiment'. Fixating a small object on the near side of the wire mesh, the mesh appears of course double. By adjusting the fixation object back and forth a position can be reached at which fusion of the double image is obtained. At this moment the wire mesh appears to shift location. A nearly perfect one-to-one correspondence obtained between the perceived distance of the 'fused.' wire mesh and the actual convergence distance. It is concluded that the convergence mechanism may provide perfectly specific information to the visual system concerning the spatial location of objects.     

Depth motion sensitivity functions

Functions reliably describing perception of motion in depth have been established experimentally by using psychophysical methods of size and distance estimations and threshold measurements. The stimuli were generated with a new hybrid technique yielding an image refresh rate of 1667 Hz. In this way it was possible to generate rapid expansions and contractions of the moving checkerboard pattern constituting the stimulus for depth motion perception. The results showed that perceived size constancy as well as depth impression varied with oscillation frequency. Under the conditions of slow motions (oscillation frequencies around 2 Hz), perfect size constancy was obtained. Above that limit, size constancy systematically decreased, and with oscillation frequencies of about 5 Hz the perceived size constancy was close to zero when small-sized patterns were used. Under the conditions of wide field stimulation (when the pattern subtended 66 degrees of visual angle), the cut-off limit increased to 16 Hz. Since the perception of depth motion amplitudes as well as perceived velocities of the visual object are related to perceived size constancy, the findings have certain implications for theoretical explanations of depth motion perception. Received: 15 December 1997 / Accepted: 21 December 1998     

A comparison of accommodative and fusional convergence as cues to distance

The effectiveness of fusional as compared with accommodative convergence (with accommodation present in both cases) in determining perceived distance was investigated in this study. Luminous frames of two different visual angles at a nearly constant distance were viewed binocularly to provide fusional convergence and monocularly to provide accommodative convergence. Although some differences in reported size and distance of the frames occurred on the first presentations for binocular as compared to monocular observation, the most systematic differences between these two types of observation were present for the second (successive) presentations of the two frame sizes to the same Os. This is attributed to the relative size cue to distance occurring as a function of the different retinal sizes on the successive presentations. It was found that this relative size cue was more effective in modifying the perceived size and distance of the second presentations for monocular than for binocular observation. It is suggested that this reflects the greater effectiveness as a cue to distance of fusional as compared with accommodative convergence. This conclusion is of importance for studies concerned with the evaluation of convergence as a determiner of perceived distance.     

The influence of visual short-term memory on size perception

We show that perceived size of visual stimuli can be altered by matches between the contents of visual short-term memory and stimuli in the scene. Observers were presented with a colour cue (to hold in working memory or to merely identify) and subsequently had to indicate which of the two different-coloured objects presented simultaneously on the screen appeared bigger (or smaller). One of the two objects for size judgements had the same colour as the cue (matching stimulus) and the other did not (mismatching stimulus). Perceived object size was decreased by the reappearance of the recently seen cue, as there were more size judgement errors on trials where the matching stimulus was physically bigger (relative to the mismatching stimulus) than on trials where the matching stimulus was physically smaller. The effect occurred regardless of whether the visual cue was actively maintained in working memory or was merely identified. The effect was unlikely generated by the allocation of attention, because shifting attention to a visual stimulus actually increased its perceived size. The findings suggest that visual short-term memory, whether explicit or implicit, can decrease the perceived size of subsequent visual stimuli.     

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.     

An analysis of perceptions from changes in optical size

The allocation of perceived size and perceived motion or displacement in depth resulting from retinal size changes (changes in the visual angle of the stimulus) was investigated in situations in which all other cues of perceived changes in distance were absent. The allocation process was represented by the size—distance invariance hypothesis (SDIH), in which, for a given change in visual angle, the perceived depth was determined only by the amount of size constancy available. The changes in perceived size and perceived distance (perceived depth) were measured by kinesthetic observer (open-loop) adjustments in five situations. These situations consisted of optical expansions or contractions presented successively or simultaneously or as a mixture of successive and simultaneous presentations. The amounts of perceived motion or perceived displacement in depth obtained by kinesthetic measures were compared with those obtained from size constancy measures as applied to the SDIH. This latter measure accounted for more of the perceived depth obtained from simultaneous and mixed situations than it did for the perceived depth from the successive situations and more for the perceived depth obtained from the expansion than from the contraction situations, whether these were simultaneous or mixed. Perceived rigidity of the stimulus (perfect size constancy) clearly was not obtained in any of the situations. Significant partial size constancy and some predictive ability of the perceived sagittal motion was found using the SDIH in all the situations except in the successively presented contraction situation, with the predictive ability from the SDIH increasing with increases in the amount of size constancy. The difference between the observer’s measures of the perceived motion or displacement in depth and the amount of perceived motion or displacement predicted from the perceptions of linear size using the SDIH is asserted to be due to a cognitive process associated with the perception of the different stimulus sizes as off-sized objects.     

Overflow, first-sight, and vanishing point distances in visual imagery

The relationship between the size of a familiar object and the distances at which it is imaged is examined in three experiments. The distance at which an imaged object overflows the visual field is linearly related to object size, a result consistent with the size-distance invariance hypothesis (Kosslyn, 1980). The distance at which an object is initially imaged, first-sight distance, is related to the object size by a power function with an exponent less than 1. In addition, time required to scan from the first-sight to the overflow distance increases as a function of the difference between the two distance estimates. The distance at which an imaged object becomes too small to be identified, vanishing point distance, is related to object size by a power function with an exponent less than 1. This result does not support predictions made from the size-distance invariance hypothesis or Kosslyn's model of visual imagery. Implications for a theory of visual imagery and memory are discussed.     

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.     

Induced self-motion in central vision

Previous research on visually induced self-motion found that stimulation of the central visual field (up to 30 degrees in diameter) results in perceived object motion while self-motion requires peripheral stimulation. In the present study, perceived self-motion was induced with a radially expanding pattern simulating observer motion through a space filled with dots, with visual angles of 7.5 degrees, 10.6 degrees, 15 degrees, and 21.2 degrees. Speed and texture density were also varied. The duration of reported self-motion (a) decreased with increased speed, (b) failed to increase with increased visual angle, and (c) decreased with visual angle at the highest speed level. In a second experiment, subjects rated the perceived depth of the displays. The speed and speed/area interaction effects on judged depth matched those found for induced self-motion. These results suggest an extension of the focal/ambient theory: In addition to a more primitive ambient processing mode that requires peripheral vision, there is a higher level system concerned with ambient processing that functions in the central visual field and uses more complex stimulus information, such as internal depth represented in a radially expanding pattern.     

Oculomotor adjustments in darkness and the specific distance tendency

Two experiments were performed to investigate the relationship between the oculomotor adjustments assumed in total darkness and perceived distance under reduced visual conditions. Experiment I compared the dark focus of accommodation with the perceived distance of a monocular light point presented in a dark environment. Experiment II compared the convergence angle assumed in darkness (dark convergence) with the perceived distance of the light point. Both accommodation and convergence were found to assume intermediate values in darkness. Perceived distance of the monocular light point was significantly correlated with dark convergence and unrelated to the dark focus of accommodation. It was suggested that ocular vergence is a major determinant of perceived distance under reduced visual conditions, and thus provides a possible mechanism for the specific distance tendency.     

Object-based anisotropies in the flash-lag effect

The relative visual position of a briefly flashed stimulus is systematically modified in the presence of motion signals. We investigated the two-dimensional distortion of the positional representation of a flash relative to a moving stimulus. Analysis of the spatial pattern of mislocalization revealed that the perceived position of a flash was not uniformly displaced, but instead shifted toward a single point of convergence that followed the moving object from behind at a fixed distance. Although the absolute magnitude of mislocalization increased with motion speed, the convergence point remained unaffected. The motion modified the perceived position of a flash, but had little influence on the perceived shape of a spatially extended flash stimulus. These results demonstrate that motion anisotropically distorts positional representation after the shapes of objects are represented. Furthermore, the results imply that the flash-lag effect may be considered a special case of two-dimensional anisotropic distortion.     

Visual angle and apparent size of objects in peripheral vision

Measurements of apparent size were obtained by distance adjustment of a peripherally viewed stimulus to produce a match to a foveally viewed standard. As eccentricity increased, the peripheral stimulus was adjusted at distances of progressively greater visual angle, indicating that a continuous diminution in apparent size occurs with increased eccentricity. This effect was found to be stable for several conditions of illumination and for changes in the light adaptive state of S. Apparent size diminution and apparent distance increase were also found for familiar objects viewed in an open field.     

Effects of laterality and visual angle on time judgments: a phenomenological investigation of time durations

20 students from an undergraduate class participated in an experiment designed to study the effects of laterality and visual angle on time judgments. Using a standard two-field tachistoscope , subjects were exposed to two experimental conditions, (1) stimulus cards with a single red or blue dot in the center and several dots clustered on both sides near the center and equidistant from it (visual angle of .6 degrees) and (2) stimulus cards with a single red or blue dot in the center and several dots clustered on both sides away from the center on the edge of the card (visual angle of 2.6 degrees). Five cards containing a single red or blue dot were used to control for response bias. The subjects were asked to indicate whether they saw dots in the left, right, or both fields, and whether they perceived a time duration between fields. No difference in time duration existed, however, as all cards were exposed to both fields for equal durations. The predictions that the judged duration of dot patterns would be more accurate favoring the left visual-field and more accurate where the distance between the point of fixation and stimulus was larger were supported.     

Determinants of the perception of sagittal motion.

This study examines the change in the perceived distance of an object in three-dimensional space when the object and/or the observer's head is moved along the line of sight (sagittal motion) as a function of the perceived absolute (egocentric) distance of the object and the perceived motion of the head. To analyze the processes involved, two situations, labeled A and B, were used in four experiments. In Situation A, the observer was stationary and the perceived motion of the object was measured as the object was moved toward and away from the observer. In Situation B, the same visual information regarding the changing perceived egocentric distance between the observer and object was provided as in Situation A, but part or all of the change in visual egocentric distance was produced by the sagittal motion of the observer's head. A comparison of the perceived motion of the object in the two situations was used to measure the compensation in the perception of the motion of the object as a result of the head motion. Compensation was often clearly incomplete, and errors were often made in the perception of the motion of the stimulus object. A theory is proposed, which identifies the relation between the changes in the perceived egocentric distance of the object and the tandem motion of the object resulting from the perceived motion of the head to be the significant factor in the perception of the sagittal motion of the stimulus object in Situation B.     

Determinants ofthe perception of sagittal motion

This study examines the change in the perceived distance of an object in three-dimensional space when the object andlor the observer’s head is moved along the line of sight (sagittal motion) as a function of the perceived absolute (egocentric) distance of the object and the perceived motion of the head. To analyze the processes involved, two situations, labeled A and B, were used in four experiments. In Situation A, the observer was stationary and the perceived motion of the object was measured as the object was moved toward and away from the observer. In Situation B, the same visual information regarding the changing perceived egocentric distance between the observer and object was provided as in Situation A, but part or all of the change in visual egocentric distance was produced by the sagittal motion of the observer’s head. A comparison of the perceived motion of the object in the two situations was used to measure the compensation in the perception of the motion of the object as a result of the headmotion. Compensation was often clearly incomplete, and errors were often made in the perception of the motion of the stimulus object. A theory is proposed, which identifies the relation between the changes in the perceived egocentric distance of the object and the tandem motion of the object resulting from the perceived motion of the head to be the significant factor in the perception of the sagittal motion of the stimulus object in Situation B.