Size-distance Invariance Research Articles

A two-process theory of the response to size and distance.

Evidence for a two-process theory of the observer’s visual judgment of size and distance is summarized and evaluated. The primary process, as expressed by the size-distance invariance hypothesis (SDIH), concerns the interrelation of perceived size (S’) and perceived distance (D’), independent of information derived from memory or suggestion. The secondary process involves information regarding size (from memory or suggestion) not contained in the immediate visual stimulus. If the primary and secondary sources of size information differ, the object is seen as off-sized. This off-sized perception can be used to modify the direct report of the distance of the object. In the case of the casual suggestion of size, the off-sized judgment produces a nonperceptual (cognitive) report of distance (Gogel, 1981b). In the case of the memory of the size of a familiar object, some of the effect on the direct report of perceived distance is perceptual, but most is cognitive (Gogel, 1976). In the case of optical expansion, the effect of off-sized judgments on distance responses produces a clear modification of perceived distance (Swanston & Gogel, 1986). The experimental distinction between primary and secondary processes is facilitated by comparing measures of perceived distance obtained from direct procedures (e.g., verbal reports of distance) with those obtained from indirect procedures (e.g., the head motion procedure). The former (direct) methods reflect both primary and secondary sources of information. The latter (indirect) methods are sensitive only to primary sources. The significance of the two-process theory for the specification of the SDIH and the explanation of other visual phenomena is discussed.

Perceived size and motion in depth from optical expansion.

The research investigated the perceived motion in depth resulting from the optical expansion or contraction of objects. A theoretical analysis of this cue was made in terms of the size-distance invariance hypothesis. For presenting stimuli, a computer simulation was developed which simulated the physical motion in depth of a constant-sized object at a constant velocity. A series of experiments showed that the extent of perceived motion in depth did not relate to the change in perceived stimulus size as predicted by the size-distance invariance hypothesis. Instead, substantial perceptions of depth motion occurred even though the ratio of the terminal perceived sizes was similar to the ratio of the terminal visual angles. Extending past research, a theoretical account based on the existence of two distinct processes involved in responding to size and distance was applied successfully. One process expressed by the size-distance invariance hypothesis determines the response to immediate, sensorily specified information. The second process involves the effect of size remembered from a previous perception (off-sized judgments) upon the response to distance. As determined by measurement obtained from using the head motion procedure, this remembered (representational) size, as it occurs in successive instants of the optical expansion pattern, can be translated by the visual system into a robust perception of distance.

Bigness is in the eye of the beholder.

This report reviews an investigation of judgments of size and distance as required of pilots in flight. The experiments covered a broad spectrum of basic psychophysiological issues involving the measurement of visual accommodation and its correlation with various other dependent variables. Psychophysiological issues investigated included the size-distance invariance hypothesis, the projection of afterimages, the moon illusion, night and empty-field myopia, the dark focus and its so-called Mandelbaum effect, the nature and locus of the accommodative stimulus, the relation between accommodation, retinal size, and perceived size, and possible relationships among accommodative responses, autonomic balance, and personality variables.

Colour constancy with change of viewing distance under water.

Colour constancy is commonly considered to be the product both of high-order (cognitive) and of lower-order (retinal) mechanisms. A study is reported of colour appearance in situations where the spectral radiance of an object changes significantly with viewing distance. Subjects were instructed to match the colour appearance of a number of coloured tiles in air and at various viewing distances in different types of water. Colour-constancy ratios were calculated by comparing the visual data with simultaneously obtained spectroradiometric and photometric data. The obtained constancy ratios were attributed to the role of distance estimation in the determination of colour appearance, an effect that is presumably masked under normal viewing conditions, where long viewpaths are necessary to produce significant radiance changes. A similarity to the size-distance invariance hypothesis is noted.

Agreement between indirect measures of perceived distance.

A test configuration consisting of either one or two points of light was made to appear at different distances on different trials. The perceived distance of the configuration on each trial was measured indirectly using two procedures. In the size adjustment procedure, the observer adjusted the vertical separation of two equidistant points to produce a criterion-perceived separation of 1 in. On the basis of this adjustment, the perceived distance of the two-point configuration was derived by means of the size-distance invariance hypothesis (Gilinsky, 1951; Kilpatrick & Ittelson, 1953). In the head-motion procedure, the observer indicated the motion of a physically stationary test point as it appeared to move concomitantly with the head. On the basis of the direction and magnitude of this apparent motion, the perceived distance of the test point was derived by means of the apparent-distance/pivot-distance hypothesis (Gogel, 1982).The measures obtained from these two procedures correlated highly. Since the size adjustment procedure provides a measure of perceived distance that generally is accepted as valid, the results indicate that the head-motion procedure has a similar validity. Past research with the head-motion procedure often concerned the apparent motion or apparent distance of a single object presented in a dark surround. An analysis of the present results supports the conclusion that the apparent-distance/ pivot-distance hypothesis applies equally to situations in which objects in addition to the test object are present.

Effect of Distance Instructions on Size Judgments

The proposition that in a reduced-cue setting subjects could use cognitive information about an object's distance to make accurate judgments of its size was tested. An improved paradigm was used to determine the effects of distance instructions per se. This paradigm also allowed independent tests of the effectiveness of cue reduction. The data indicated that cue reduction was successful and that the specific distance tendency governed size judgments when there were no distance instructions. When distance instructions were given, they produced size judgments in precisely the ratio predicted by the size-distance invariance hypothesis. However, there was a large constant error, which reflects a tendency of college students to overestimate the amount of distance signified by a verbal instruction. Hence, cognitive information in the form of verbal distance instructions has precise effects on size judgments, but the latter are not veridical, even in the absence of anchor effects from the specific distance tendency and residual perceptual cues.

Instruction effects on size and distance judgments.

The hypotheses that size judgments of unfamiliar objects are affected by distance informa­ tion, and distance judgments by size information, were tested. Subjects made size or distance estimates in a cue-reduced situation, with or without distance or size information, and also made calibrated estimates in full-cue conditions. Size judgments in the no-information condition were correlated with the retinal image, whereas distance information produced size estimates closer to the actual size of the objects. Subjects given no information about size produced dis­ tance estimates that were randomly distributed, whereas size information yielded a weak effect in the appropriate direction. Implications for the size-distance invariance hypothesis and the specific distance tendency are discussed. No previous investigation has assessed both the effects of size information on distance judgments and the effect of distance information on size judg­ ments for varying retinal images. The purpose of the present study was to investigate these variables in a single experimental setting in which cue reduction was assured. The majority of the studies in this area focus on size or distance judgments under familiar size in­ structions or with off-sized familiar objects. Several studies (Fitzpatrick, Pasnak, & Tyer, 1982; Gogel, 1968; Gogel & Mertens, 1967) have shown that the judged size of a familiar object corresponds very well to its real size, and judged distance corresponds to the actual distance at which that size would produce the given retinal size. In other studies (Baird, 1963; Park & Michaelson, 1974), an object is presented and the observer is told that it is the same size as a fa­ miliar object; distance judgments correspond quite well to the distance at which that object would pro­ duce the given retinal image. It is not clear what the effect would be if an instruc­ tion regarding an object's size was not associated with a familiar object. In this case, an observer would have to interpret the object in terms of the retinal image and cognitive information. Coltheart (1970) reported that subjects could do this very well; Park and Michaelson (1974), on the other hand, reported that size instruction had no effect on dis­ tance judgments. Since it is not possible to determine why these results differ, the present experiment was undertaken, in part, as an attempt to resolve this con­ flict.

A neglected problem: Kinetic size constancy

Size constancy in three-dimensional motion, “kinetic size constancy”, was investigated by measuring both perceived size and perceived distance under monocular and binocular viewing conditions. It was found that forward-motion facilitated a tendency to see an object with an approximately constant size and made it possible to perceive veridically the distance to the object (distance constancy). The size-distance invariance hypothesis, expressed in the form S'/ D'= Kθ n , was found to hold in the present experimental situation. In contrast to static size constancy, with kinetic size constancy there is no requirement for separate depth cues if a focal stimulus changes along its vertical and horizontal dimensions and this results in the perception of a shape.

A Study of the size-distance invariance hypothesis

Abstract The experiment described examined the Invariance Hypothesis (IH) in the form Perceived Size, S'/ Perceived Distance D' = k Actual Size S/ Actual Distance D where the spatial extent scaling constant (k) was eliminated from the final test equation by the subjects making three judgements: a match of the size variable to the size of the standard object; a match of the distance of the distance variable to that of the standard object; and a match of the size of the size variable to the size of the distance variable as set in the second match. A new design of the size variable in terms of its frontal aspect ratio (AR) provided support for the importance of aspect ratio for the accuracy of size estimation judgements.

Interrelation of the effects of binocular disparity and perspective cues on judgments of depth and height

The effects of binocular disparity (aniseikonia) and perspective cues operating together on judgments of depth and height were studied, both when these stimulus variables operated in the same direction and when they were in conflict. Both depth cues were effective upon the perception of depth and height. The effects of binocular disparity and perspective cues upon perceived depth were found to be additive. The effects of these depth cues upon perceived height showed some interaction in the sense that, operating together, the effect of the perspective cue was stronger than the separate effect of the perspective cue, both when binocular disparity and perspective cues operated in the same direction and when they were in conflict. This interactive effect increased with increasing strength of the perspective cues. The size-distance invariance hypothesis was confirmed under the present experimental conditions. By a causal analysis of inference, this invariant relation could be explained in the following way: both the perceived depth and the perceived height of the sides of the patterns were directly determined by binocular disparity and perspective cues, but the perceived height was also indirectly determined through change of perceived depth. A direct causal relation between perceived depth and perceived height was found.

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.

Did Ptolemy Understand the Moon Illusion?

Ptolemy is often wrongly credited with an explanation of the moon illusion based on the size-distance invariance principle. This paper elucidates the two Ptolemaic accounts: one in the Almagest, based on atmospheric refraction, and the other in the Optics, based on the difficulty of looking upwards. It is the latter passage which has been thought to refer to size-distance invariance, but it is more probable that it refers to the idea that the visual rays are diminished by the force of gravity (i.e. that the retinal image is reduced in size). Alhazen was probably the first author to explain the illusion by the size-distance invariance principle, and Roger Bacon the first to explain the enlarged apparent distance of the horizon by the presence of intervening objects. Della Porta was the first to credit Ptolemy with these explanations, and this mistake was repeated by many subsequent authors.

Size-distance invariance and a distorted texture density gradient.

Summary The relationship was examined between judgments of relative distance and judgments of relative size made over a surface on which the packing density of the texture elements was progressively increased, from one end of the surface to the other along the S's line of sight. Significant positive correlations were obtained between distance and size judgments made by 32 Ss. This confirmed a weak version of the size-distance invariance hypothesis and supported a prediction contained in Gibson's theory of space perception.

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.

Distance judgments under different size-information conditions

Seventy-two Ss judged the absolute distance of a target presented without distance cues other than retinal size and assumed size. The method by which E communicated information about the size of a 3-in. target had a significant effect on the magnitude of the discrepancy between judged distance and the perceived distance required by the size-distance invariance hypothesis. In order of increasing effectiveness in producing distance judgments meeting invariance requirements were: size information in the form of verbally communicated metric units, size information communicated by labeling the target with the name of a familiar object, and size information in the form of a visual representation.

Possible stimulus hypothesis and visual space perception.

For any given retinal projection there is a family of stimuli whose members could each give rise to that projection when appropriately positioned with respect to the eye. Perception theorists often imply that this family of stimuli (and related stimulus positions) specifies the possibilities for perception but have not stated this explicitly. The hypothesis is referred to here as the possible stimulus hypothesis. More specific hypotheses are derived from it. They include Koffka's size-distance and shape-slant invariance hypotheses. It is shown that Koffka's hypotheses are only special cases of more general hypotheses named the size-distance-slant and shape-slant-tilt invariance hypotheses. Implications for perceptual constancy and for tests of invariance hypotheses are indicated. Explanations for the perception of objects in space should be more complex than Helmholtz and Koffka have indicated and Gibson's theory would be more precise and broader in scope if the possible stimulus hypothesis were recognized as an essential part of the theory.

The effects of perspective alterations on apparent size and distance scales

Ss made magnitude estimations first of the areas, then of the distances, of four circles presented at five distances within an enclosed box 9 ft long. There were three viewing situations: the box had parallel walls, converging walls, or diverging walls. The variations in perspective cues influenced the apparent distance scales: with converging and parallel walls, apparent distance grew as the 1.4 power of physical distance; with diverging walls, it grew as the .95 power. Apparent area was related to distance differently in the three conditions: with converging walls, apparent area increased with distance; with parallel and diverging walls, apparent area decreased with distance. Apparent area was thus not related to changes in physical distance as the apparent distance effects would predict. In each condition, the ratio of apparent area to apparent distance (S′/D′) was a monotonie increasing function of retinal angle θ, but the rate of growth varied among the three conditions. The failure of θ D′ to define a unique value of S′ across conditions indicates that the size-distance invariance hypothesis is inadequate to predict the outcome of this experiment.

大きさ-距離-不変項仮説の検討

大きさ-距離-不変項仮説の検討

The validity of the size-distance invariance hypothesis with cue reduction

The validity of the size-distance invariance hypothesis with cue reduction

Size-distance invariance in perceptual adaptation

Objects viewed through a facemask under water appear larger and closer than when viewed in air. Divers’ adaptation to this distortion was measured by obtaining estimates of the size and distance of an array of targets before and after a 20-min underwater dive. A negative correlation between size- and distance-adaptation scores indicated that most divers adapted to one dimension by counteradapting to the other. For example, some Ss adapted to size by increasing the distortion of apparent distance and some the other way around. The results were discussed in relation to the size-distance invariance hypothesis.