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.     

Familiar size and linear perspective as distance cues in stereoscopic depth constancy

Both the image size of a familiar object and linear perspective operate as distance cues in stereoscopic depth constancy. This was shown by separating their effects from the effect of the oculomotor cues by creating cue conflicts between either the familiar size cue or linear perspective, on the one hand, and accommodation and convergence, on the other. In the case of familiarsize, this cue was used deceptively. In the case of linear perspective, spectacles caused nonveridical oculomotor adjustments.     

Adaptation in distance perception based on oculomotor cues

Accommodation and convergence primarily serve to adjust the eyes to the distance of the object viewed, but, once made, these oculomotor adjustments serve as cues for the object’s distance. Experiments are reported that show that the relation between oculomotor adjustments and the distances they signify can be changed by adaptation to glasses that cause alteration in the oculomotor adjustments with which objects are viewed. This changed relation manifested itself in marked alterations of size perception. Wearing, for 30 min, glasses that caused a change in accommodation and convergence corresponding to a smaller object distance and equivalent to 1.5 lens diopters caused subsequent mean size increases that ranged from 50% to 65%. Adaptation to glasses that changed oculomotor adjustments in the same amount but in the opposite direction resulted in decreases in perceived sizes that varied from 18% to 40%, dependent on the distance of the test object. These were the results of size estimates obtained before and after the adaptation period under conditions where only accommodation and convergence served as cues for distance. A newly developed test of size perception was also used, in which S adjusted the size of the projected image of an array of familiar objects on a screen until the size of the objects appeared normal. Again, such adjustments were made before and after the adaptation period, and size differences were obtained that were in the direction to be expected of adaptation and varied in amount between 12% and 33%, dependent on the distance of the screen. The reason for the different amounts of size change measured by the two kinds of tests was investigated.     

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.     

Visual and proprioceptive adaptation to altered oculomotor adjustments

Adaptation to spectacles that alter in equivalent amounts the accommodation and the convergence with which objects are viewed was produced under two conditions. In one, S alternately pushed away or pulled toward him a screen that exhibited only a single vertical contour while wearing glaaaes that caused decreases in accommodation and convergence equivalent to 1.5 lens diopters. Here kinesthesis for these arm movements provided the only veridical distance cues, A small, but highly significant, adaptation effect was obtained with a teat in which S, before and after the adaptation period, pointed to the location of a test line in the distance dimension. Corresponding tests consisting in size and in depth estimates did not show an adaptation effect. In the other condition of adaptation, S moved objects by hand toward and away from himself while wearing spectacles that increased accommodation and convergence by the equivalent of 1.5 lens diopters. In addition to the altered oculomotor cues, some veridical visual cues for distance such as are caused by perspective were present. This condition yielded changes in size and depth estimates indicative of an adaptation in visual distance perception and a larger effect of adaptation measured by the pointing test. We concluded that the excess of the adaptation effect measured by pointing over that measured by size estimation represents an adaptation in proprioception, as did the pointing effect produced by our first adaptation condition.     

On counteradaptation

Often adaptation to artificially altered stimulation takes place because veridical stimulation that produces the same perceptual property that is produced by the altered stimulation is also received. In these cases, an assimilation of the two perceptual processes produced by the two different stimulations (the altered and the veridical) is supposed to be responsible for the adaptation that is achieved. This hypothesis, which was formulated by Wallach and Karsh (1963), would be confirmed by demonstrating a modification of the perceptual process produced by veridical stimulation rather than the one produced by the altered stimulation. We demonstrated this by having S observe in the dark for 20 min a luminous figure that objectively expanded as it moved toward S and contracted as it moved away. But instead of testing for changes in size perception as such, we tested for a change in the relation between accommodation and convergence on the one hand and registered distance on the other. In one experiment, such a change was measured by obtaining estimates of perceived size and depth before and after the adaptation period. Highly significant changes of size and significantly greater changes of stereoscopic depth were obtained. Inasmuch as stereoscopic vision was totally absent from the adaptation conditions, the change in stereoscopic depth that was larger than the size change can only be ascribed to a change in registered distance. In another experiment, we tested for a change in distance by having S point from the side to a vertical line, before and again after the adaptation period, under conditions where only accommodation and convergence could serve as distance cues. Significant changes in the pointing distance were measured, indicating more directly a change in the relation between these oculomotor adjustments and perceived distance. We propose the term counteradaptation for such modification of a perceptual process away from veridicality.     

Target distance and adaptation in distance perception in the constancy of visual direction

Hay and Sawyer recently demonstrated that the constancy of visual direction (CVD) also operates for near targets. A luminous spot in the dark, 40 cm from the eyes, was perceived as stationary when S nodded his head. This implies that CVD takes target distance, as well as head rotation, into account as a stationary environment is perceived during head movements. Distance is a variable in CVD because, during a turning or nodding of the head, the eyes become displaced relative to the main target direction, the line between the target and the rotation axis of the head. This displacement of the eyes during head rotation causes an additional change in the target direction, i.e., a total angular change greater than the angle of the head rotation. The extent of this additional angular displacement is greater the nearer the target. We demonstrated that the natural combination of accommodation and convergence can supply the information needed by the nervous system to compensate for this additional target displacement. We also found that wearing glasses that alter the relation between these oculomotor adjustments and target distance produces an adaptation in CVD. An adaptation period of 1.5 h produced a large adaptation effect. This effect was not entirely accounted for by an adaptation in distance perception. Measurements of the alteration between oculomotor cues and registered distance with two kinds of tests for distance perception yielded effects significantly smaller than the effect measured with the CVD test. We concluded that the wearing of the glasses had also produced an adaptation within CVD.     

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.     

Adaptation in distance perception with head-movement parallax serving as the veridical cue

When head-movement parallax functioned as the sole veridical distance cue during exposure to spectacles that altered the eyes’ oculomotor adjustments, sizable adaptation was obtained. This result showed that a discrimination of the distances of 60 and 30 cm can be based on head-movement parallax. Using adaptation in demonstrating that head-movement parallax can serve as a distance cue circumvents the problem that the presence of accommodation normally presents when such a demonstration is attempted. The usual contamination of head-movement parallax with accommodation is avoided, because accommodation is altered by the spectacles and does pot function as a veridical cue along with head-movement parallax.     

Effect of disparity and viewing distance on perceived depth

It is shown that veridical depth perception presupposes the processing of both the magnitude of retinal disparity and observation distance according to a square-law function specified by the underlying geometrical stimulus relations. In the present study, after testing its existence, this constancy of depth perception was investigated by measuring perceived depth as a function of retinal disparity and observation distance. In addition, the relative effectiveness of convergence and accommodation as possible indicators of distance was examined through a conflicting-cues paradigm. It was shown that in the perception of depth the visual system computes distance by taking into account the convergence parameter only, rather than that of accommodation or of both.     

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.     

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.     

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.     

The time it takes to imagine1

Stanley and Furedy (1966), using the paired-comparisons technique, reported that under conditions where size constancy held, Emmert’s law failed as distance increased beyond 90 in. Experiment 1, designed to check this report with a shorter-duration induction flash, did not yield 90 in. as the point of failure. However, although complete size constancy for direct images was again obtained, the results did not unambiguously suggest strict proportionality between afterimage size and distance. To allow a less ambiguous assessment of proportionality, Experiment 2 used magnitude-estimation procedures. Distance estimates were completely veridical, but afterimage size varied only linearly, and not proportionally, with apparent distance. It was concluded the Boring (1940) was mistaken in his attempt to reduce size constancy and Emmert’s law to the same principle.     

Distance adaptation depends upon plasticity in the oculomotor control system

Maintaining binocular fixation on a target at 20 cm in the absence of secondary cues to distance produced changes in apparent distance and lateral phoria. Positive lenses of 0, .5, 2.0, 3.5, and 5.0 spherical diopters (SD) were used to manipulate the level of accommodative convergence in force during the period of maintained fixation. An inverse relationship was found between the stimulus to accommodation and the magnitude of the induced esophoria, the phoria being linearly related to an increase in apparent distance. The distance aftereffect obtained in the condition with the lowest net accommodative stimulus li.e., 0 D) equaled that typically produced by base-out prism adaptation with full secondary cues to distance available. In a second experiment, subjects walked through a well-lit hallway while viewing through a pair of 5h base-out prisms. It was shown that increasing the stimulus to accommodation by adding negative lenses of 0, 1.5, 3.5, and 5.5 SD reduced the adaptive change in apparent distance, as well as the change in phoria produced by the conventional base-out prism adaptation paradigm. It was concluded that a change in the resting tonus of the disparity vergence system underlies such adaptation, rather than recalibration of the oculomotor cues to distance. Monocular exposure data indicated that a small change in the tonus control for the accommodative system may be present as well.     

Accommodation, occlusion, and disparity matching are used to guide reaching: a comparison of actual versus virtual environments.

The authors used a virtual environment to investigate visual control of reaching and monocular and binocular perception of egocentric distance, size, and shape. With binocular vision, the results suggested use of disparity matching. This was tested and confirmed in the virtual environment by eliminating other information about contact of hand and target. Elimination of occlusion of hand by target destabilized monocular but not binocular performance. Because the virtual environment entails accommodation of an image beyond reach, the authors predicted overestimation of egocentric distances in the virtual relative to actual environment. This was confirmed. The authors used -2 diopter glasses to reduce the focal distance in the virtual environment. Overestimates were reduced by half. The authors conclude that calibration of perception is required for accurate feedforward reaching and that disparity matching is optimal visual information for calibration.     

Children's size judgments when size and distance vary: Is there a developmental trend to overconstancy?

A review of the experimental literature on size constancy in children shows that studies permitting unrestricted viewing in natural settings provide only limited support for the hypothesis, proposed by Wohlwill, of a developmental trend from under- to overconstancy. A study is reported in which subjects aged 8 to 18 years made magnitude estimations of height for targets whose height and distance from them varied. For distances up to 15 m, and heights from 5 to 50 cm, size constancy prevailed at all ages: The same number was assigned to a given height at every distance. If a developmental trend exists, it requires either younger subjects or greater distances to be revealed.     

Porterfield and Wells on the motions of our eyes

William Porterfield (ca 1969-1771) and William Charles Wells (1757-1817) conducted experimental investigations on eye movements related to accommodation, binocular vision, and vertigo. Porterfield gave a correct interpretation of Scheiner's experiment and invented an optometer to measure the near and far points of distinct vision. He also demonstrated the involvement of the crystalline lens in accommodation by examining vision in an aphakic person. Wells devised an alternative means of measuring the limits of vision and noted his own deterioration of sight with age; he studied the effects of belladonna on pupil size and accommodation. Their analyses of binocular visual direction contrasted Porterfield's view that perceived location was innately determined with Well's argument that visual direction was innate whereas visual distance was learned. Both Porterfield and Wells investigated the involvement of eye movements in binocular vision and in postrotary visual motion. Porterfield maintained that the eyes did not move following body rotation, whereas Wells, using an afterimage as stabilised retinal image, described the characteristics of postrotary nystagmus and their dependence on head orientation. Despite the neglect of Well's work, he should be considered as laying the foundations for the study of vestibular-visual interaction, even though the function of the vestibular system was not known at that time.     

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.