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 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.     

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.     

The influence of object familiarity on magnitude estimates of apparent size.

Three magnitude-estimation experiments were used to determine the exponents of the power function relating size judgments and physical size for two-dimensional familiar and unfamiliar stimuli. The exponent of the power function was used to index the effect of familiar size on perceived size under a variety of conditions, from full-cue to reduced-cue viewing conditions. Although the value of the exponents varied across the three experiments, within each experiment the exponent of the familiar stimulus was not significantly different from that of the unfamiliar stimulus, indicating that familiar size does not influence the rate of growth of perceived size. The results of a fourth experiment excluded a possible explanation of the findings of experiments 1-3 in terms of subjects responding to relative angular size as a consequence of the successive presentation of the different-sized representations of the familiar stimulus. Taken together, the present findings are consistent with the hypothesis that the influence of familiar size on estimates of size mainly reflects the intrusion of nonperceptual processes in spatial responses.     

Visual selective attention with virtual barriers

Previous studies have shown that interference effects in the flanker task are reduced when physical barriers (e.g., hands) are placed around rather than below a target flanked by distractors. One explanation of this finding is the referential coding hypothesis, whereby the barriers serve as reference objects for allocating attention. In five experiments, the generality of the referential coding hypothesis was tested by investigating whether interference effects are modulated by the placement of virtual barriers (e.g., parentheses). Modulation of flanker interference was found only when target and distractors differed in size and the virtual barriers were beveled wood-grain objects. Under these conditions and those of previous studies, the author conjectures that an impression of depth was produced when the barriers were around the target, such that the target was perceived to be on a different depth plane than the distractors. Perception of depth in the stimulus display might have led to referential coding of the stimuli in three-dimensional (3-D) space, influencing the allocation of attention beyond the horizontal and vertical dimensions. This 3-D referential coding hypothesis is consistent with research on selective attention in 3-D space that shows flanker interference is reduced when target and distractors are separated in depth.     

Speed constancy and the perception of distance

The distance-calibration hypothesis states that retinal velocity is scaled by using distance cues, and judged velocity remains unchanged when distance is changed. The relational hypothesis states that judged velocity depends on retinal velocities, and is proportional to judged distance. These hypotheses were compared in three experiments where the movements of the standard stimulus and the comparison stimulus were manipulated by the ratio of the angular velocity of the comparison stimulus to the angular velocity of the standard stimulus. The presentation conditions of the standard stimulus and the comparison stimulus, and the colour cues of the two stimuli were also manipulated in order to change the strength of the cues available to the observers. The results indicate that judged velocities and the relationship of judged distance and velocity depend on the strength of the cues. When cues are strong, the distance-calibration hypothesis adequately explains speed constancy. When cues are weak, judged velocity and the relationship between judged distance and velocity are consistent with the prediction of the relational hypothesis. The perceived speed of a stimulus depends not only on the physical speed of the stimulus but also on non-motion cues, some of which are distance cues involved in depth perception.     

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 perceived size depend on perceived distance? An argument from extended haptic perception

Two experiments were directed at the comparison between two perspectives on the perception of size achieved by probing the gap between two occluded distal surfaces by means of a hand-held rod. One perspective was the classical size—distance invariance hypothesis developed for the problem of visual size perception with a central role for perceived distance; the other was the hypothesis that the extended haptic perception of gap size is specific to a physical invariant λ of the dynamics of probing. Experiment 1 examined the relation between haptically perceived gap size and haptically perceived gap distance. No causal connection between the two was found, and all the variance in perceived size was accounted for by?. Experiment 2 manipulated the rotational inertia of the probe. Its effect was different for the two perceptions of size and distance, underscoring their independence. The indifference of perceived size to perceived distance was discussed in reference to identifying invariants for both the haptic and the visual perception of size at a distance.     

Perception of three-dimensional form from patterns of optical texture

The research described in the present article was designed to investigate how patterns of optical texture provide information about the three-dimensional structure of objects in space. Four experiments were performed in which observers were asked to judge the perceived depth of simulated ellipsoid surfaces under a variety of experimental conditions. The results revealed that judged depth increases linearly with simulated depth although the slope of this relation varies significantly among different types of texture patterns. Random variations in the sizes and shapes of individual surface elements have no detectable effect on observers' judgments. The perception of three-dimensional form is quite strong for surfaces displayed under parallel projection, but the amount of apparent depth is slightly less than for identical surfaces displayed under polar projection. Finally, the perceived depth of a surface is eliminated if the optical elements in a display are not sufficiently elongated or if they are not approximately aligned with one another. A theoretical explanation of these findings is proposed based on the neural network analysis of Grossberg and Mingolla.     

The effects of binocular and motion-generated information on the perception of depth and height

The perception of distance and size in the presence of optical gradient information was investigated under four viewing conditions—binocular view with and without head motion, and monocular view with and without head motion. Subjects (60 adults) matched distance intervals (from 15 to 127 cm) and heights of a target triangle (from 5 to 15 cm) by adjusting the length of a metal tape. Both linear and power functions were fitted to each individual’s distance judgments, and the competing perceptual models were compared. For both models, it was found that binocular information was sufficient to specify relative, but not absolute, distance, that monocular information was sufficient to specify an orderly relation between target distance and judgment but not absolute distance, that average error was less in the binocular conditions, and that perceived distance was not affected in either condition by the addition of head motion. The analysis of size judgments revealed that monocular and binocular judgments did not differ, that matches made with and without head motion did not differ, and that, in all conditions, matches exceeded target heights by an average 30% to 40%. Judged size was also analyzed as a function of target distance. In all conditions but monocular view with head motion, the effect of distance was to increase size judgments. The distance judgments support the hypothesis (Purdy, 1958) that the binocular stimulus carries information that the monocular stimulus does not; they fail to support the hypothesis (Gibson, 1966) that observer motion adds information to the static stimulus. The size judgments support neither hypothesis but suggest an independence of perceived size from perceived distance.     

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.     

A consistent failure of the power law for lifted weight

The apparent size of squares was determined as a function of physical area and of surface complexity using the method of magnitude estimation. Apparent area increases as a power function of physical area with a slope of about 0.90. The judged areas also increased as a function of complexity of patterns upon the surface, the most complex surfaces being judged approximately 30% larger than the most simple surfaces.     

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 moon illusion: I. How high is the sky?

The most common explanations of the moon illusion assume that the moon is seen at a specific distance in the sky, which is perceived as a definite surface. A decrease in the apparent distance to the sky with increasing elevation presumably leads to a corresponding decrease in apparent size. In Experiment 1 observers (N = 24) gave magnitude estimates of the distance to the night sky at different elevations. The results did not support the flattened-dome hypothesis. In Experiment 2 observers (N = 20) gave magnitude estimates of the distance to the sky at points around a 360 degrees circle just above the horizon. The results were consistent with those of Experiment 1, and in addition, estimates were highly correlated with the physical distances of buildings at the horizon. In a third, control experiment, observers (N = 20) gave magnitude estimates of the distances of buildings at the horizon. A power function fit the relation between estimated and physical distance (exponent = 1.17) as well as the relation between estimates of the sky points above the buildings (Experiment 2) and estimates of building distances (exponent = .46). Taken together, the results disconfirm all theories that attribute the moon illusion to a "sky illusion" of the sort exemplified by the flattened-dome hypothesis.     

Judgments of voluntary and physical causes in causal chains: probabilistic and social functionalist criteria for attributions

Four experiments investigated judgments about voluntary human actions and physical causes that were embedded in causal chains ending in negative outcomes (e.g., a forest fire). Causes were judged for their explanatory quality, their effect on the probability of the outcome, and the extent to which they could be socially controlled. Results supported legal theorists' claim that voluntary actions are judged better explanations than physical causes. Indices derived from theories of probability change generally failed to predict the preference for voluntary actions. In contrast, this preference was mediated by the perceived extent to which voluntary versus physical causes may be brought under social control. These results suggest that causal explanation, at least within causal chains, is not driven solely by changes in the probability of an outcome when a cause is added, and that observers recognize the potential social function of explanations in drawing attention to socially controllable causes. Copyright © 2006 John Wiley & Sons, Ltd.     

The effect of perceived distance on induced movement

The magnitude of induced movement was measured as a function of the perceived depth between the test object and the plane of the induction object, with this perceived depth produced by stereoscopic cues. Three experiments were conducted. In each experiment, the induction object (a frame of constant physical size) was positioned at one of three distances with the test object (a point of light) placed successively at each of the three distances. Predictions of the magnitude of induction as a function of the depth separation of the test and induction object were made from the subject-relative and object-relative hypotheses of induced motion. It was expected, however, that neither of these hypotheses would predict the results independently of a factor described in the adjacency principle. This principle states that the effectiveness of whatever cues or processes determine the induced movement will decrease with increased depth between the test and induction object. The data indicate that the adjacency principle must be considered in explaining the results. The subject-relative rather than object-relative hypothesis as modified by the adjacency principle was most successful in predicting the results. Control conditions in which the frame was stationary and the point of light was physically moving were also used. Despite the fact that the relative displacement of the objects on the eye in the experimental and control conditions were the same, the results indicate that O could distinguish between these two kinds of conditions. Although the apparent movement was greater in the control conditions than in the experimental conditions, the reverse is true if the total perceived movement of the test and induction object are considered together.     

Effects of voluntary eye movement and convergence on the binocular appreciation of depth

Scaling techniques were employed to establish the relation between perceived distance ratio and physical distance ratio. Measurements were made both with and without free eye movement and under two states of convergence. The results were confirmed using a matching technique. With free eye movement, the perceived ratio is a monotonic increasing function of the physical ratio. Without eye movement, the perceived ratio generally increases, then decreases, as the physical ratio increases. For a given physical ratio, perceived distance ratio is less in the absence of voluntary eye movements. Convergence produces depth micropsia when eye movements are permitted, but not in their absence.     

Visual distance estimation in static compared to moving virtual scenes

Visual motion is used to control direction and speed of self-motion and time-to-contact with an obstacle. In earlier work, we found that human subjects can discriminate between the distances of different visually simulated self-motions in a virtual scene. Distance indication in terms of an exocentric interval adjustment task, however, revealed linear correlation between perceived and indicated distances but with a profound distance underestimation. One possible explanation for this underestimation is the perception of visual space in virtual environments. Humans perceive visual space in natural scenes as curved, and distances are increasingly underestimated with increasing distance from the observer. Such spatial compression may also exist in our virtual environment. We therefore surveyed perceived visual space in a static virtual scene. We asked observers to compare two horizontal depth intervals, similar to experiments performed in natural space. Subjects had to indicate the size of one depth interval relative to a second interval. Our observers perceived visual space in the virtual environment as compressed, similar to the perception found in natural scenes. However, the nonlinear depth function we found can not explain the observed distance underestimation of visual simulated self-motions in the same environment.     

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.