Size-distance paradox with accommodative micropsia

Two experiments tested the hypothesis that the paradoxical relative distance judgment associated with the size-distance paradox is due to the visual system’s assuming equal linear size and perceiving a smaller angular size for the closer stimulus equal in visual angle. In Experiment I, two different sized coins were presented successively, and 16 Ss were asked to give ordinal judgments of apparent distance and apparent size. When the two coins depicted the same figures, the closer stimulus was judged to be farther and smaller, more frequently, than when two coins depicted different figures. In Experiment II, 48 Ss were asked to give ratio judgments of apparent distance, apparent linear size, and apparent angular size for two stimuli which were presented successively. When the stimuli were of equal shape, the mean ratios of the far stimulus to the near stimulus were smaller for the apparent distance but larger for the apparent linear size and angular size than when the stimuli were of different shape. The obtained distance judgments were consistent with the hypothesis but the obtained judgments of linear size and angular size were not.     

The effect of verbal size information upon visual judgments of absolute distance

When an 0 views a blank triangle of light under completely reduced conditions, he is able to make use of verbally conveyed information about the size of this stimulus when he is attempting to judge the absolute distance of the stimulus. Although between-Os variance is rather large in this situation, group mean distance estimates are highly veridical. This is further evidence for the view that, when the 0 is given a retinal subtense, any kind of information about size enables him to make a judgment of absolute distance, just as information about distance enables him to make a judgment of absolute size.     

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.     

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.     

视觉表象扫描中的视角大小效应

采用视觉表象的几何距离扫描任务,通过两个实验首次揭示了视觉表象扫描中的视角大小效应。实验一采用3 (视角：2.7°,5.5°和8.2°) × 3 (扫描距离：0.0cm、0.4cm和0.8cm) 组内实验设计,探讨了视角大小这种表象前加工因素是否影响心理扫描的问题;实验二采用8 (视角：2.7°,4.1°,5.5°,6.9°,8.2°,9.6°,12.3°和17.1°) × 2 (扫描距离：0.4cm和0.8cm) 组内实验设计,探讨了视角大小如何影响心理扫描加工过程的问题。结果表明：（1）在视觉表象扫描中,扫描时间会受到表象对应刺激的视角大小影响,即使扫描的几何距离相等,不同视角大小条件下的扫描时间仍存在显著差异;（2）在4°到10°这个视角范围内心理扫描的时间显著短于这个范围之外的扫描时间,6.5°左右是视觉表象扫描的最佳视角。视角大小效应有别于心理扫描的大小效应和距离效应,为Kosslyn的表象计算理论增加了新的内容,具有重要的理论意义。同时它对仪表、图形设计以及棋牌游戏等工作和生活实践具有一定的应用价值     

非预想刺激的运动速率对无意视盲的影响

无意视盲是指由于对某些事物的专注而导致的眼前对象被忽视的现象。它受到诸如非预想刺激的位置、大小、颜色; 非预想刺激与注意刺激之间的关系; 被试的年龄、专业知识、加工能力等诸多因素的影响。本文通过改进的MR范式考察了“等时”和“等距”条件下非预想刺激的运动速率对无意视盲的影响。实验结果显示: (1)非预想刺激的运动速率和其呈现时间对无意视盲的比率有显著影响; (2)在一定的呈现时间范围内, 视盲率随运动速率的升高而降低, 但当维持相等的运动距离时, 视盲率没有显著变化; (3)当呈现时间超出一定范围时, 运动速率对无意视盲的影响急剧减小, 即呈现时间制约着运动速率对无意视盲的影响, 两者间呈倒U型曲线关系。文末就实验结果进行了详细分析和讨论。     

Generating nonsymbolic number stimuli

Studies investigating nonsymbolic numbers (e.g., dot arrays) are confronted with the problem that changes in numerosity are always accompanied by changes in the visual properties of the stimulus. It is therefore debated whether the visual properties of the stimulus rather than number can explain the results obtained in studies investigating nonsymbolic number processing. In this report, we present a program (available at ; note that the program is designed to work with the Psychophysics Toolbox in MATLAB) that exports information about the visual properties of stimuli that co-vary with number (area extended, item size, total surface, density, and circumference). Consequently, insight into the relation between the visual properties of the stimulus and numerical distance can be achieved, and post hoc analyses can be conducted to directly reveal whether numerical distance or (some combinations of) the visual properties of a stimulus could be the most likely candidate underlying the results. Here, we report data that demonstrate the program’s usefulness for research on nonsymbolic number stimuli.     

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.     

Size constancy in children: a new interpretation

Existing evidence indicates that there are differences between children and adults in size constancy when observation distances are large. Findings are reported which suggest that this phenomenon is based on a difference in the accessing of proximal stimulus information, which, in the case of size, refers to visual angle subtended. Age differences were found when a traditional size constancy task was used, but these differences disappeared when all the comparison objects subtended the same visual angle. Since this finding demonstrates that young children can make accurate size matches, it is suggested that the underconstancy previously reported is not necessarily the result of children's inability to use fully certain cues to distance. Rather, the findings suggest that children access proximal stimulus information more spontaneously than do adults.     

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.     

Absolute localization of vibrotactile stimuli on the torso

Vibrotactile mobility systems present spatial information such as the direction of a waypoint through a localized vibration on the torso. Using these systems requires the ability to determine the absolute location of the stimulus. Because data are available only on the ability to determine the relative location of stimuli on the torso, we developed a novel method for measuring absolute localization on the basis of triangulation. For 15 observers, we calculated the subjective location of visual and tactile stimuli on the frontal half of the torso. The size of the 95% confidence intervals around the subjective tactile locations is about the size of the stimuli (1.66 cm) and is slightly larger than that around the subjective visual locations (mean difference, 0.17 cm). The error in tactile judgments over and above that in the visual judgments is present only for locations near the body midline. When the subjective visual and tactile locations are not co-located, the difference can best be described by a shift along the radius from the body midaxis. The same holds for the differences between the veridical and the subjective locations. Therefore, the difference between the veridical and the subjective directions of a stimulus is small. The results make us believe that stimulus locations on the torso are coded in polar coordinates of which the angle is perceptual invariant and the distance is less important, probably because it varies with changes in, among other things, posture and breathing.     

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.     

Visual size perception and haptic calibration during development

It is still unclear how the visual system perceives accurately the size of objects at different distances. One suggestion, dating back to Berkeley’s famous essay, is that vision is calibrated by touch. If so, we may expect different mechanisms involved for near, reachable distances and far, unreachable distances. To study how the haptic system calibrates vision we measured size constancy in children (from 6 to 16 years of age) and adults, at various distances. At all ages, accuracy of the visual size perception changes with distance, and is almost veridical inside the haptic workspace, in agreement with the idea that the haptic system acts to calibrate visual size perception. Outside this space, systematic errors occurred, which varied with age. Adults tended to overestimate visual size of distant objects (over‐compensation for distance), while children younger than 14 underestimated their size (under‐compensation). At 16 years of age there seemed to be a transition point, with veridical perception of distant objects. When young subjects were allowed to touch the object inside the haptic workspace, the visual biases disappeared, while older subjects showed multisensory integration. All results are consistent with the idea that the haptic system can be used to calibrate visual size perception during development, more effectively within than outside the haptic workspace, and that the calibration mechanisms are different in children than in adults.     

How the visual system detects changes in the direction of moving targets

To determine how the visual system represents information about change in target direction, we studied the detection of such change under conditions of varying stimulus certainty. Target direction was either held constant over trials or was allowed to vary randomly. When target direction was constant the observer could be certain about that stimulus characteristic; randomizing the target direction rendered the observer uncertain. We measured response times (RTs) to changes in target direction following initial trajectories of varying time and distance. In different conditions, the observer was uncertain about either the direction of the initial trajectory, or the direction of change or both. With brief initial trajectories in random directions, uncertainty about initial direction elevated RTs by 50 ms or more. When the initial trajectories were at least 500 ms, this directional uncertainty ceased to affect RTs; then, only uncertainty about the direction of change affected RTs. We discuss the implications of these results for (i) schemes by which the visual system might code directional change; (ii) the visual integration time for directional information; and (iii) adaptational processes in motion perception.     

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.     

The influence of synchronous audiovisual distractors on audiovisual temporal order judgments

Participants made unspeeded temporal order judgments (TOJs) regarding which occurred first, anauditory or a visual target stimulus, when they were presented at a variety of different stimulus onset asynchronies. The target stimuli were presented either in isolation or positioned randomly among a stream of three synchronous audiovisual distractors. The largest just noticeable differences were reported when the targets were presented in the middle of the distractor stream. When the targets were presented at the beginning of the stream, performance was no worse than when the audiovisual targets were presented in isolation. Subsequent experiments revealed that performance improved somewhat when the position of the target was fixed or when the target was made physically distinctive from the distractors. These results show that audiovisual TOJs are impaired by the presence of audiovisual distractors and that this cost can be ameliorated by directing attention to the appropriate temporal position within the stimulus stream.     

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 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.     

Illusory temporal order for stimuli at different depth positions

We used four experiments to examine how the perceived temporal order of two visual stimuli depends on the depth position of the stimuli specified by a binocular disparity cue. When two stimuli were presented simultaneously at different depth positions in front of or around a fixation point, the observer perceived the more distant stimulus before the nearer stimulus (Experiments 1 and 2). This illusory temporal order was found only for sudden stimulus presentation (Experiment 3). These results suggest that a common processing, which is triggered by sudden luminance change, underlies this illusion. The strength of the illusion increased with the disparity gradient and the disparity size (Experiment 4). We propose that this illusion has a basis in the processing of motion in depth, which would alert the observer to a potential collision with an object that suddenly emerges in front of the observer.