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.     

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     

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.     

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.     

The organization of perceived space

Summary Perceptions tend often to be proportional to proximal stimuli with reduced conditions of observation and proportional to distal stimuli under multicue conditions. Two explanations of this phenomena are examined. One, termed the core context hypothesis, postulates that the response to the proximal stimulus (the core) is modified by distance information (the context). The second, termed invariance hypotheses, postulates an interaction between two or more perceptions, one of which is often perceived distance. In order for invariance hypotheses to be valid it is necessary that a perceived distance occur under reduced cues of distance. It is asserted that perceived distance under these conditions is supplied by observer tendencies termed the specific distance and equidistance tendency. Perceptual interactions occur in situations other than those relevent to invariance hypotheses and the evidence for perceptual interactions is discussed in relation to perceived motion, perceived depth from exocentric cues, the adjacency principle, and other phenomena. It is suggested that the analysis of many perceptions in terms of perceptual interactions is parsimonious in that the effect of the independent perception, e.g., perceived distance, upon the dependent perception, e.g., perceived size, motion, or depth, is the same regardless of the cues by which the particular value of the independent perception is achieved.Preparation of this chapter was supported by PHS research grant number MH 15651 from the National Institute of Mental Health and PHS research grant number NS 18883 from the National Institute of Neurological Diseases and Stroke.     

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.     

Influence of flicker on perceived size and depth

Previous research (e.g., Wong & Weisstein, 1984a, 1985) has shown that flickering stimuli appear to be more distant than nonflickering stimuli at the same physical distance. Given this relation between flicker and perceived depth, inappropriate constancy scaling theories predict that flickering stimuli should be perceived as larger than nonflickering ones. In contrast, links between flicker and motion perception suggest that flickering stimuli should be perceived as smaller than nonflickering ones. Two experiments tested these contrasting predictions. In Experiment 1, 22 subjects compared flickering and nonflickering vertical lines and reported that the flickering stimulus appeared significantly smaller than the nonflickering one. In Experiment 2, 21 subjects reported that the stimuli used in Experiment 1 produced depth effects similar to those reported in previous experiments: flickering stimuli were perceived as more distant than nonflickering ones. The observed effect of flicker on perceived size was contrary to predictions from inappropriate constancy scaling theory, but consistent with views that motion and flicker are processed by the same pathway.     

The nature of adaptation in distance perception based on oculomotor cues

In previous work by the senior authors, brief adaptation to glasses that changed the accommodation and convergence with which objects were seen resulted in large alterations in size perception. Here, two further effects of such adaptation are reported: alterations in stereoscopic depth perception and a change when distance is represented by a response of S’s arm. We believe that the three effects are manifestations of one primary effect, an alteration of the relation between accommodation and convergence on the one hand and the distance they represent in the nervous system (registered distance) on the other. This view was supported by the results of two experiments, each of which demonstrated that the alterations in stereoscopic depth perception could be obtained after adaptation periods which had provided no opportunity to use stereoscopic vision, and that the adaptation effect was larger for depth perception than for size perception when it was obtained under the same conditions; the latter finding was expected if both effects resulted from the same change in registered distance. In three of the five experiments here reported, the variety of cues that could represent veridical distance during the adaptation period was limited. In one condition of adaptation, only the pattern of growth of the retinal images of objects that S approached and the kinesthetic cues for S’s locomotion served as cues to veridical distance. In two other conditions S remained immobile. In one of these, only the perspective distortion in the projection of the scene that S viewed mediated veridical distance, and in the other one familiar objects of normal size were successively illuminated in an otherwise totally dark field, conditions from which opportunities to use stereoscopic vision were again absent. After exposure to each of these adaptation conditions, adaptive changes in perceived size and larger ones in perceived stereoscopic depth were obtained. Because we found that familiar size may serve as the sole indicator of veridical distance in an adaptation process, we concluded that it can function as a perceptual as distinguished from an inferential cue to distance.     

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.     

The absence of depth constancy in contour stereograms

Stereoscopic surfaces constructed from Kanizsa-type illusory contours or explicit luminance contours were tested for three-dimensional (3-D) shape constancy. The curvature of the contours and the apparent viewing distance between the surface and the observer were manipulated. Observers judged which of two surfaces appeared more curved. Experiment 1 allowed eye movements and revealed a bias in 3-D shape judgment with changes in apparent viewing distance, such that surfaces presented far from the observer appeared less curved than surfaces presented close to the observer. The lack of depth constancy was approximately the same for illusory-contour surfaces and for explicit-contour surfaces. Experiment 2 showed that depth constancy for explicit-contour surfaces improved slightly when fixation was required and eye movements were restricted. These experiments suggest that curvature in depth is misperceived, and that illusory-contour surfaces are particularly sensitive to this distortion.     

Visually perceived motion in depth resulting from proximal changes. I

According to a model for form and motion perception proposed by Johansson (1964), every two-dimensional change in the proximal stimulation is projected out as a motion in depth. The amount of perceived depth motion can then be predicted from the projective relationship between the proximal change and the projected motion. This prediction was tested in a series of experiments by using squares that continuously changed their sizes as stimuli, and measuring perceived distance of motion in depth. The obtained relationship between perceived and predicted distance of motion was curvilinear for all Ss. Furthermore, the majority of the Ss underestimated the motion systematically, the remainder overestimated it. Thus, the prediction given in the model could not be verified. However, an alternative projective relation based on the assumption that a fixed proportion of the change is not projected out as a motion but perceived as a change of size agreed quite well with the data, both with distance judgments and with judgments of perceived change of size.     

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.     

The role of suggested size in distance responses

A number of studies have concluded that suggested size can modify perceived size, as indicated by the effect on perceived distance. At least this effect seems to occur when verbal reports are used as the measure of the judged distance of the target. The present study supports a different explanation of this phenomenon. It is hypothesized that suggested size can result in the judgment that the target is larger or smaller than normal (an off-sized judgment) where normal is specified by the suggested size. Because the observer expects that a target judged as a small or large off-sized object must be at a greater or lesser distance, respectively. than its perceived distance, the off-sized judgment can provide a cognitive modification of reported distance. This explanation was tested by measuring the perceived distance of targets using a procedure (called the head motion procedure) that, in contrast with verbal reports of distance, is very unlikely to be influenced by off-sized judgments. Measures obtained with the head motion procedure, unlike those obtained from verbal reports, did not change with changes in the suggested size. It is concluded that the size suggestions had a cognitive, not a perceptual, effect on responses to the distance (and size) of the targets.     

Motion parallax as an independent cue for depth perception.

The perspective transformations of the retinal image, produced by either the movement of an observer or the movement of objects in the visual world, were found to produce a reliable, consistent, and unambiguous impression of relative depth in the absence of all other cues to depth and distance. The stimulus displays consisted of computer-generated random-dot patterns that could be transformed by each movement of the observer or the display oscilloscope to simulate the relative movement information produced by a three-dimensional surface. Using a stereoscopic matching task, the second experiment showed that the perceived depth from parallax transformations is in close agreement with the degree of relative image displacement, as well as producing a compelling impression of three-dimensionality not unlike that found with random-dot stereograms.     

Dynamic occlusion and motion parallax in depth perception

Random-dot techniques were used to examine the interactions between the depth cues of dynamic occlusion and motion parallax in the perception of three-dimensional (3-D) structures, in two different situations: (a) when an observer moved laterally with respect to a rigid 3-D structure, and (b) when surfaces at different distances moved with respect to a stationary observer. In condition (a), the extent of accretion/deletion (dynamic occlusion) and the amount of relative motion (motion parallax) were both linked to the motion of the observer. When the two cues specified opposite, and therefore contradictory, depth orders, the perceived order in depth of the simulated surfaces was dependent on the magnitude of the depth separation. For small depth separations, motion parallax determined the perceived order, whereas for large separations it was determined by dynamic occlusion. In condition (b), where the motion parallax cues for depth order were inherently ambiguous, depth order was determined principally by the unambiguous occlusion information.     

Perception of depth: Processing of simple positional disparity as a function of viewing distance

Dependency of perceived depth (relative to the fixation point) on disparity, viewing distance, and the type of the stereoscopic stimulus was investigated. Nearly complete constancy of depth, as required for a veridically matched perception, was observed only at small disparity values and with the larger square-formed stimulus; under these conditions, perceived depth corresponded well with real depth intervals for close viewing distances. Additionally, a model for perceptual processing of both variables, disparity and viewing distance, was applied to the data.     

Further consideration of size illusions in random dot stereograms.

It has been suggested that many geometric illusions are caused by the application of depth or size constancy rules to an image which does not have sufficient cues to establish that the elements lie in a flat plane. Thus, converging lines are taken as depth cues, and the attributed depth provides the basis for adjusting the perceived size of stimulus elements. It this is the case, one should not see a distortion of relative size if the disparity cues provide for strong statification, i.e., localization in depth of the linear perspective cues. This expectation is challenged by demonstrations that show distortions of relative size using random-dot stereograms. In 1971 Julesz provided such examples but did not comment on the implications for theories of depth. Here we redemonstrate these distortion of length and size in autostereograms which contain the Ponzo and Corridor configurations. The illusory distortions can be seen in the cyclopean view even though the linear perspective elements are well stratified. We suggest that the processing of binocular disparity cues, as required for judgments of absolute distance, may involve the dorsal stream of vision, i.e., activity passing into and including the parietal lobe. Pictorial cues, on the other hand, are likely passed through the ventral stream into the temporal lobe. The analysis of depth by this system provides for size constancy and, possibly, the calibration of relative motion.     

Apparent movement in phenomenal space

The spatial and temporal variables in Korte’s third law of apparent movement were studied in pictorial arrays in which size constancy could be expected to prevail. The thresholds for apparent movement were determined under conditions in which two squares appeared on a plane either with or without perspective information for depth. The results suggest that apparent movement varies with the perceived depth separation only if the size of the stimulus pair is congruent with contextual depth representations. The obtained psychophysical function relating thresholds for third-dimensional movement to pictorial depth scale supports the view that apparent movement preserves gradient-of-texture information.     

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.