Size-distance Invariance Research Articles

Size and distance are perceived independently in an optical tunnel: Evidence for direct perception

The historical but questionable size-distance invariance hypothesis (SDIH) features computation over geometric, oculomotor, and binocular cues and the coupling of percepts—perceived size, S′, is mediated by perceived distance, D′. A contemporary non-mediational hypothesis holds that S′ and D′ are specific to distinct optical variables. We report two experiments with an optical tunnel, an arrangement of alternating black and white concentric rings, that allows systematic manipulation of the optic array at a point of observation while controlling a variety of size and depth cues. Participants viewed targets of different sizes at different distances monocularly, reporting S′ and D′ via magnitude production. In Experiment 1, the target was either placed in a continuous tunnel (extending 164cm) or in a tunnel that truncated at the target’s location. Experiment 2 included a third tunnel, one that was truncated with a flat depiction of the posterior surface structure that would have been visible in the continuous tunnel. In both experiments, S′ decreased with D but D′ was unaffected by S. Partial correlation analyses showed that the relationship between S′ and D′ was not significant when the contributions of other variables were removed. Importantly, S′ and D′ were affected differently by manipulations of the optical tunnel’s continuity while computationally obvious visual cues were controlled. These outcomes suggest that D′ is not a mediator of S′. Rather S′ and D′ are independently determined with correlated but different optical bases, results that support the direct model.

The Perspective Structure of Visual Space.

Luneburg’s model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg’s model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg’s model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances.

The Influence of Ground Contact and Visible Horizon on Perception of Distance and Size under Severely Degraded Vision

For low vision navigation, misperceiving the locations of hazards can have serious consequences. Potential sources of such misperceptions are hazards that are not visually associated with the ground plane, thus, depriving the viewer of important perspective cues for egocentric distance. In Experiment 1, we assessed absolute distance and size judgments to targets on stands under degraded vision conditions. Normally sighted observers wore blur goggles that severely reduced acuity and contrast, and viewed targets placed on either detectable or undetectable stands. Participants in the detectable stand condition demonstrated accurate distance judgments, whereas participants in the undetectable stand condition overestimated target distances. Similarly, the perceived size of targets in the undetectable stand condition was judged to be significantly larger than in the detectable stand condition, suggesting a perceptual coupling of size and distance in conditions of degraded vision. In Experiment 2, we investigated size and implied distance perception of targets elevated above a visible horizon for individuals in an induced state of degraded vision. When participants' size judgments are inserted into the size-distance invariance hypothesis (SDIH) formula, distance to above-horizon objects increased compared to those below the horizon. Together, our results emphasize the importance of salient visible ground-contact information for accurate distance perception. The absence of this ground-contact information could be the source of perceptual errors leading to potential hazards for low vision individuals with severely degraded acuity and contrast sensitivity.

Oculomotor Effects in the Size-Distance Paradox and the Moon Illusion

Drawing on 2 concepts—the resting position of the eyes and a binocular geometry for perceived size, the moon illusion is explained as the consequence of different oculomotor adjustments caused by change in the direction of gaze contingent upon the viewing conditions of the moon. Hence, each particular moon will be viewed with a different vergence state which, in turn, yields a different amount of binocular disparity. The vergence state will determine the perceived size of an object whereas disparity will determine its perceived distance. It is further contended that the perceived size of the moon is based on a new binocular information source for size perception enabling the size of an object to be perceived even in the absence of egocentric distance information. Discussion focuses on the paradoxical aspect of the moon illusion and how the size-distance invariance hypothesis may have contributed to its effect.

The position of objects relative to the horizon affects size-distance invariance

The position of objects relative to the horizon affects size-distance invariance

Perceptual distance and the moon illusion

The elevated moon usually appears smaller than the horizon moon of equal angular size. This is the moon illusion. Distance cues may enable the perceptual system to place the horizon moon at an effectively greater distance than the elevated moon, thus making it appear as larger. This explanation is related to the size-distance invariance hypothesis. However, the larger horizon moon is usually judged as closer than the smaller zenith moon. A bias to expect an apparently large object to be closer than a smaller object may account for this conflict. We designed experiments to determine if unbiased sensitivity to illusory differences in the size and distance of the moon (as measured by d') is consistent with SDIH. A moon above a 'terrain' was compared in both distance and size to an infinitely distant moon in empty space (the reduction moon). At a short distance the terrain moon was adjudged as both closer and smaller than the reduction moon. But these differences could not be detected at somewhat greater distances. At still greater distances the terrain moon was perceived as both more distant and larger than the reduction moon. The distances at which these transitions occurred were essentially the same for both distance and size discrimination tasks, thus supporting SDIH.

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.

Perceptual distance and the constancy of size and stereoscopic depth

The relationship between distance and size perception is unclear because of conflicting results of tests investigating the size-distance invariance hypothesis (SDIH), according to which perceived size is proportional to perceived distance. We propose that response bias with regard to measures of perceived distance is at the root of the conflict. Rather than employ the usual method of magnitude estimation, the bias-free two-alternative forced choice (2AFC) method was used to determine the precision (1/sigma) of discriminating depth at different distances. The results led us to define perceptual distance as a bias free power function of physical distance, with an exponent of approximately 0.5. Similar measures involving size differences among stimuli of equal angular size yield the same power function of distance. In addition, size discrimination is noisier than depth discrimination, suggesting that distance information is processed prior to angular size. Size constancy implies that the perceived size is proportional to perceptual distance. Moreover, given a constant relative disparity, depth constancy implies that perceived depth is proportional to the square of perceptual distance. However, the function relating the uncertainties of depth and of size discrimination to distance is the same. Hence, depth and size constancy may be accounted for by the same underlying law.

Evidence for the Formal Equivalence between Emmert’s Law and Size-Distance Invariance Hypothesis

Evidence for the Formal Equivalence between Emmert’s Law and Size-Distance Invariance Hypothesis

Why do objects appear enlarged under water?

Objects appear enlarged in water by less than the 4/3 angular magnification. They usually appear beyond their optical distance and slightly enlarged in linear size, but not in accordance with size-distance invariance (SDI). We investigated whether misperceptions of angular size could explain the discrepancies. Twenty observers viewed targets of various sizes and distances within transparent tanks 40 cm long containing air or water. They judged distance by hidden reaching, and linear or angular size by adjusting the size of a target in air at a further distance. Matched distance was close to physical distance in air and optical distance in water. All size matches were close to true linear size, and were larger in water than in air. Angular size matches were much too small to explain departures from SDI. Size perception under water is best explained by incomplete adaptation to optical distortion, and by the use of various size cues.

Cleomedes (c. 1st century AD) on the celestial illusion, atmospheric enlargement, and size-distance invariance.

Cleomedes (Kleomedes) is a little-known Greek author (c. 1st century AD) who produced what is probably the earliest extant statement of size-distance invariance. He supported the Stoic philosophy and was concerned to discredit the Epicurean position that we perceive objects as having their true size. He explained the celestial illusion (the apparent enlargement of the sun near the horizon) in two ways: partly as a refractive effect of the atmosphere similar to angular enlargement when looking into water; and partly as a linear enlargement due to increased apparent distance in a misty atmosphere. He is the earliest extant author to offer apparent distance as a clear explanation of the celestial illusion. He attributed these views to Posidonius (c. 135-50 BC). His explanations remained at the geometrical level, and he did not speculate on sensory mechanisms.

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.

Size-Distance Variance and Eye Accommodation: The Ways of an Investigator

Biased judgments of size and distance are encountered with all types of imaging displays, and the literature on visual perception is replete with violations of the size-distance invariance hypothesis, including the paradoxical moon illusion. To sort out the basic variables that relate these seemingly unrelated events calls for unfettered multifactor experimentation rather than the severe reduction of traditional psychophysical methodology. The high correlation among the focal distance of the eyes, apparent size, and changes in the locus of the retinal blind spot would never have been discovered if all cues to distance other than accommodation had been eliminated, as called for by experimental reductionists.

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 effects of size, clutter, and complexity on vanishing-point distances in visual imagery.

The portrayal of vanishing-point distances in visual imagery was examined in six experiments. In all experiments, subjects formed visual images of squares, and the squares were to be oriented orthogonally to subjects' line of sight. The squares differed in their level of surface complexity, and were either undivided, divided into 4 equally sized smaller squares, or divided into 16 equally sized smaller squares. Squares also differed in stated referent size, and ranged from 3 in. to 128 ft along each side. After subjects had formed an image of a specified square, they transformed their image so that the square was portrayed to move away from them. Eventually, the imaged square was portrayed to be so far away that if it were any further away, it could not be identified. Subjects estimated the distance to the square that was portrayed in their image at that time, the vanishing-point distance, and the relationship between stated referent size and imaged vanishing-point distance was best described by a power function with an exponent less than 1. In general, there were trends for exponents (slopes on log axes) to increase slightly and for multiplicative constants (y intercepts on log axes) to decrease as surface complexity increased. No differences in exponents or in multiplicative constants were found when the vanishing-point was approached from either subthreshold or suprathreshold directions. When clutter in the form of additional imaged objects located to either side of the primary imaged object was added to the image, the exponent of the vanishing-point function increased slightly and the multiplicative constant decreased. The success of a power function (and the failure of the size-distance invariance hypothesis) in describing the vanishing-point distance function calls into question the notions (a) that a constant grain size exists in the imaginal visual field at a given location and (b) that grain size specifies a lower limit in the storage of information in visual images.

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.

Apparent size and distance in an imaging display.

The size-distance invariance hypothesis suggests that the perceived size and the perceived distance of objects in a field viewed naturally are closely related. However, this relationship breaks down when scenes are viewed through high-power optical systems. When natural scenes are viewed through an imaging display of unity magnification, there is a reduction in their apparent size. This raises the question of whether the relationship breaks down when scenes are viewed through a low-power imaging display. A single-lens reflex camera was used as an imaging display that enabled subjects to vary the size of imaged real-world scenes. Judgments of size were found to vary with depth information in scenes and between monocular and binocular viewing, consistent with a previous finding, but judgments of distance did not vary significantly across either of these conditions. The results suggest that judgments of size and judgments of distance with imaging displays are not influenced uniformly by environmental and task variables.

Modeling shifts in perceived spatial frequency between the fovea and the periphery

A quantitative multiple-channels model can account for changes in perceived spatial frequency between foveally and peripherally viewed patterns; these frequency shifts are as large as 0.47 octave (38.5%). Factors that change as a function of eccentricity and that can alter the appearance of visual patterns include (1) scaling of receptive-field sizes, (2) overall sensitivity, and (3) steepness and nonlinearity of contrast-transfer functions (CTF's). Computations based on receptive-field size scaling, combined with fixed perceptual labels, predict higher perceived spatial frequency for peripheral patterns. Computations based on reduced sensitivity, however, predict the opposite result and thus partially offset the effect of receptive-field size scaling. The predicted perceived-frequency shifts based on changes in CTF's are quite small and can be ignored. Both individual differences and visual-field-location differences in magnitudes of perceived-frequency shifts are predicted by the model. An alternative perceptual explanation based on size-distance invariance and size constancy is also evaluated.

Imagery, memory, and size-distance invariance.

The size-distance invariance hypothesis (SDIH) was examined for remembered and imaged stimuli. In Experiment 1, subjects gave remembered and imaged distances of familiar objects and imaged distance of nondescript rods. The relationship between stated size and distance is more adequately described by power functions with exponents less than 1 than by the more restricted SDIH (exponent of 1). In Experiment 2, subjects gave distance estimates to recalled and imaged familiar objects and described the visual context in which each object was situated. A different group then sorted the contexts into categories based on general similarity. There were no significant differences between distance estimates based on memory and those based on imagery, and the visual contexts were not sorted according to whether they were generated in the memory or in the imagery conditions. In Experiment 3, subjects estimated the distances to objects in an outdoor setting. A linear relationship was found between estimated and physical distance, suggesting that the lower exponents obtained in Experiments 1 and 2 were not artifacts of the distance judgment procedure.

Overflow, first-sight, and vanishing point distances in visual imagery.

The relationship between the size of a familiar object and the distances at which it is imaged is examined in three experiments. The distance at which an imaged object overflows the visual field is linearly related to object size, a result consistent with the size-distance invariance hypothesis (Kosslyn, 1980). The distance at which an object is initially imaged, first-sight distance, is related to the object size by a power function with an exponent less than 1. In addition, time required to scan from the first-sight to the overflow distance increases as a function of the difference between the two distance estimates. The distance at which an imaged object becomes too small to be identified, vanishing point distance, is related to object size by a power function with an exponent less than 1. This result does not support predictions made from the size-distance invariance hypothesis or Kosslyn's model of visual imagery. Implications for a theory of visual imagery and memory are discussed.