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.     

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.     

Disparity increase with convergence for constant perceptual criteria

If a depth interval is matched to an egocentric distance, the disparity required increases with convergence by 50 to 130% (depth micropsia). If a depth interval is matched to a frontal extent of constant visual angle, disparity again increases with convergence, but the proportion increase is slightly smaller. This difference is attributed to the previously established effect of convergence on perceived size (size micropsia).     

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.     

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.     

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.     

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.     

Induced self-motion in central vision

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

Stereoillusory motion concomitant with lateral head movements

Stationary objects in a stereogram can appear to move when viewed with lateral head movements. This illusory motion can be explained by the motion-distance invariance hypothesis, which states that illusory motion covaries with perceived depth in accordance with the geometric relationship between the position of the stereo stimuli and the head. We examined two predictions based on the hypothesis. In Experiment 1, illusory motion was studied while varying the magnitude of binocular disparity and the magnitude of lateral head movement, holding viewing distance constant. In Experiment 2, illusory motion was studied while varying binocular disparity and viewing distance, holding magnitude of head movement constant. Ancillary measures of perceived depth, perceived viewing distance, and perceived magnitude of lateral head movement were also obtained. The results from the two experiments show that the extent of illusory motion varies as a function of perceived depth, supporting the motion-distance invariance hypothesis. The results also show that the extent of illusory motion is close to that predicted from the geometry in crossed disparity conditions, whereas it is greater than the predicted motion in uncrossed disparity conditions. Furthermore, predictions based on perceptual variables were no more accurate than predictions based on geometry.     

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.     

Size and distance judgments under reduced conditions of viewing

Magnitude estimations of the size and distance of a variable relative to a standard were obtained in the absence of distance cues. Estimates were provided by different groups under three conditions: (a) physical size and distance variant, visual angle of the variable constant and equal to the standard, (b) physical size constant, physical distance and visual angle of variable changing, and (c) physical distance constant, physical size and visual angle of the variable changing. The results in both experiments were very similar. In each case both size and distance estimates conformed to relative visual angle. The results are applied to an analysis of size-matches that are obtained when distance cues are eliminated.     

The common occurrence of errors of perceived distance

The effect on the perceived distance of a test object of fixating to a distance different from that of the test object was investigated using monocular observation and two methods for measuring perceived distance. One method, the size adjustment procedure, applying the size-distance invariance hypothesis, measured perceived distance by measuring perceived size. The results from this method were compared with those from a head-motion procedure which used the apparent concomitant motion resulting from head motion to measure perceived distance. The results from both procedures indicated that the apparent distance of the test object physically located at a constant distance varied directly as a function of the fixation distance. This occurred despite the presence of texture on the walls and floor of the visual alley. These and other perceptual effects are interpreted as demonstrating that errors in perceived distance (contrary to the theory of direct perception) are a common occurrence in ordinary visual fields.     

An empirical test of formal equivalence between Emmert's law and the size-distance invariance hypothesis

Emmert's law and the size-distance invariance hypothesis have been said to be formally equivalent, provided that Emmert's law means that the perceived size of an afterimage is proportional to the perceived distance of the projected surface of the afterimage. However, there have been very few studies that have attempted to verify this formal equivalence empirically. We measured both the perceived size and distance of afterimages and real objects with the same proximal size. Nineteen participants projected afterimages of 1 deg in visual angle on the wall located at distances of 1 to 23 meters from the participants. They also observed real objects, disc-shaped and made from a sheet of Styrofoam board, with the same proximal size as that of the afterimages, which were located at the same physical distances as those of the wall on which the afterimages were projected. Each participant reproduced the apparent sizes of the afterimages and real objects using the reproduction method and estimated the apparent distances using the magnitude estimation method. When the mean apparent sizes of the afterimages and real objects, represented as a function of apparent distance, were fitted to a linear function, the slopes for the afterimages and real objects did not differ significantly. These results are interpreted as evidence for the formal equivalence of Emmert's law and the size-distance invariance hypothesis.     

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.     

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     

Perceived depth of 3-D objects in 3-D scenes

Effects of information specifying the position of an object in a 3-D scene were investigated in two experiments with twelve observers. To separate the effects of the change in scene position from the changes in the projection that occur with increased distance from the observer, the same projections were produced by simulating (a) a constant object at different scene positions and (b) different objects at the same scene position. The simulated scene consisted of a ground plane, a ceiling plane, and a cylinder on a pole attached to both planes. Motion-parallax scenes were studied in one experiment; texture-gradient scenes were studied in the other. Observers adjusted a line to match the perceived internal depth of the cylinder. Judged depth for objects matched in simulated size decreased as simulated distance from the observer increased. Judged depth decreased at a faster rate for the same projections shown at a constant scene position. Adding object-centered depth information (object rotation) increased judged depth for the motion-parallax displays. These results demonstrate that the judged internal depth of an object is reduced by the change in projection that occurs with increased distance, but this effect is diminished if information for change in scene position accompanies the change in projection.     

Determinants of the rod and frame effect: The role of retinal size

In Experiment 1, base-out prisms were used to alter perceived size and distance to a luminous rod and frame while the retinal size remained unchanged. The rod-and-frame effect (RFE) was the same, whether the display was viewed directly or through the prisms. In Experiment 2, one large and one small rod-and-frame display were placed at distances such that they produced identical retinal angles. This was replicated at three different sets of distances. Perceived size and distance of the large and small frame of identical retinal angle interacted with the observation distance, such that at near distances the large frame was perceived as larger and farther than the small frame while, at far distances, both types of estimates converged to a constant value. In contrast, the RFE was identical for the large and small frames matched in retinal angle, but diminished with distance. In both experiments, the RFE varied precisely with variation in retinal angle. Implications of the role of retinal angle in the RFE and for the interpretation of individual differences were discussed.     

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.     

Perceived relative distance on the ground affected by the selection of depth information

Our visual space does not appear to change when we scan or shift attention between locations. This appearance of stability implies that the depth information selection process is not crucial for constructing visual space. But we present evidence to the contrary. We focused on space perception in the intermediate distance, which depends on the integration of depth information on the ground. We propose a selection hypothesis that states that the integration process is influenced by where the depth information is selected. Specifically, the integration process inaccurately represents the ground when one samples depth information only from the far ground surface, instead of sequentially from the near to the far ground. To test this, observers matched the depth/length of a sagittal bar (test) to the width of a laterally oriented bar (reference) in three conditions in a full-cue environment that compelled the visual system to sample from different parts of the ground. These conditions had the lateral reference bar placed (1) adjacent to the test bar, (2) at the far ground, and (3) at the near ground. We found that the sagittal bar was perceived as shorter in conditions (1) and (2) than in Condition 3. This finding supports the selection hypothesis, since only Condition 3 led to more accurate ground surface integration/representation and less error in relative distance/depth perception. Also, we found that performances in all three conditions were similar in the dark, which has no depth information on the ground, indicating that the results cannot be attributed to asymmetric visual scanning but, rather, to differential information selection.