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Shape constancy is the process by which individuals perceive the true nature of an object as opposed to the image the object casts on the retina. Previous research has demonstrated that individuals tend to regress to the true shape of the object when matching shapes to slanted stimuli. 167 university students completed an image-matching task where they matched ellipses to a circle that was perceived from increasing distances. As predicted, results indicated that participants tended to "regress to the real"; that is, they tended to choose ellipses that were more reflective of the true shape of the circle than the increasingly elliptical image that was cast onto the retina. Suggestions for future research include the utilisation of more complex and unfamiliar objects, as well as a systematic investigation of the relationship between perceived slant and shape constancy.
An imperative goal of any perceptual system is to construct a stable percept-or mental impression of a perceived object-from sensory input that reflects the constantly changing external world. The visual system is particularly susceptible to these frequent variations in the environment, given that the image projected onto the retina is altered with any change in the orientation of an object (Goldstein, 1995). Shape constancy is one instance of the perceptual system's attempt to create a stable internal representation of an object. The term refers to the ability of individuals to perceive the true shape of a distal stimulus, or an object in the environment, despite changes in the shape of the proximal stimulus, or the shape that the distal object projects onto the retina (Levine, 2000). Should a percept be constructed that is based purely on the retinal image, individuals would experience a considerable amount of confusion whilst interacting with their environment; for instance, a door that is being opened would appear to be changing from its original rectangular shape to a trapezoidal one. In view of the fact that shape serves as one of the most essential clues to the identity of objects, it is difficult to underestimate the convenience that shape constancy affords individuals (Pizlo, 1994).
To understand the process by which shape constancy is achieved, a description of how shape information is represented by the visual system is first necessary. The frontal plane projection is the plane onto which the front view of a scene is projected and corresponds to the image projected onto the retina (Levine, 2000). If an image of an uninclined square is presented to an observer who views the square straight on, their frontal plane projection will be a regular square. However, if the square is tilted or laid flat on a surface such that it is inclined about a horizontal axis to the normal to the observer's line of sight, the observer's frontal plane projection will be a foreshortened version of the square (Levine, 2000). More precisely, the retinal image will be a square whose long axis (an imaginary line running parallel to the square lengthwise) appears to recede away from the observer, or a trapezoid (Howard, 2012). It is thus apparent that the shape of the retinal image undergoes continuous change as the slants of objects and the angles from which they are viewed are altered.
However, individuals do not perceive these raw sensory representations of objects; slant is automatically taken into account in the construction of a percept. In an illustration of this idea, Beck and Gibson (1955) asked participants to match a tilted triangle (the test triangle) to one of two other triangles: one that gave an identical retinal image to the test triangle and one that was physically identical to the test triangle. Beck and Gibson found that when they isolated participants from cues to slant (i.e., by asking participants to view each triangle monocularly and through a narrow aperture), participants selected the triangle that was identical to the frontal plane projection of the test triangle. When participants were permitted cues to slant (i.e., when the participants were allowed to view the stimuli binocularly and were able to freely shift their gaze), they chose the other triangle (Beck & Gibson, 1955). Cues to slant are therefore considered by the perceptual system when an internal representation of a distal object is being created, thereby producing a percept that differs somewhat from the retinal image (Levine, 2000).
A number of other studies have substantiated the findings of Beck and Gibson (1955) by demonstrating that when permitted cues to slant, individuals have a tendency to select an image that is more like the actual shape of the test object than the image it projects onto the retina (e.g., Nelson & Bartley, 1956). The perceptual system, in other words, automatically makes an adjustment for the slant of the distal stimulus (Levine, 2000). In particular, individuals will select a shape that lies intermediate between the frontal plane projection and the actual shape (Levine, 2000). The tendency of the perceptual system to distort the proximal stimulus in this way has been referred to as phenomenal regression to the "real" object; it can be viewed as the propensity of individuals to "pull back" towards the shape of the distal stimulus (Thouless, 1931). This phenomenon is what underlies the ability of individuals to perceive the shapes of objects as being constant despite changes in slant and viewing angle (i.e., shape constancy).
The present study aimed to determine the extent to which individuals can perceive the shape of the retinal image of a circle which has been foreshortened to varying degrees. Given that a greater amount of foreshortening corresponds to an increasingly thinner retinal shape, progressively greater room for regression is present with increased foreshortening assuming that the shape of the distal stimulus remains constant. A relative measure of regression would indicate the proportion of regression occurring with the amount of foreshortening by considering the total amount of regression possible, and would therefore not be expected to change with the extent of foreshortening. It is thus anticipated that individuals will phenomenally regress to the distal stimulus such that the absolute amount of regression occurring will increase with distance, while the relative amount of regression taking place will remain constant across distances.
Participants included 167 university students undertaking the Visual Perception and Cognition course at the Australian National University. The study was conducted in groups of 3 and 4 participants; individuals in each group took turns observing the circle, with those not observing at any given time assisting with the measurement and recording of results.
The independent variable of this study was the degree to which the circle was foreshortened; this was manipulated by setting the distance between the circle and the observer to be 25cm, 65cm, or 105cm. The dependent variables were the judged shape ratio, or the ellipse that the observer deemed to be identical to the retinal image, and the retinal shape ratio, or a measure of the image that the circle projects onto the retina as a function of distance. The study had a within-subjects design such that each participant viewed the circle at each of the three distances.
An image of a regular circle on a white A4 sheet of paper served as the distal stimulus. Also utilised was a test booklet containing images of circles foreshortened to progressively lesser degrees (or "comparison ellipses"). Each page of the test booklet contained one ellipse and corresponded to a number that represented the judged shape ratio.
The sheet of paper was laid flat on a table at a distance 25cm away from the seated observer (this distance was measured from the bottom of the circle to the edge of the table). A measurement was taken of the observer's eye height, or the distance between their pupil and the surface of the table. The participant was presented with the ellipses in the test booklet at an angle perpendicular to their line of sight. They were asked to indicate the ellipse that best matched their view of the circle as the pages were turned by another student in either an ascending or descending sequence. This procedure was repeated four times for each of the three distances (25cm, 65cm, and 105cm), with an ascending sequence used for two of the trials and a descending sequence for the remaining two. If the observer indicated that the image of the ellipse being shown at a given time did not approximate their perception of the circle, a number of ellipses in the test booklet were skipped, after which stimuli were presented individually. The sequence in which the ellipses in the test booklet were presented across the four trials at each distance was randomised across participants.
To measure the absolute amount of phenomenal regression taking place at each distance, the difference between the mean judged shape ratio and the mean retinal shape ratio for each participant was calculated. Regression in relative terms was measured by calculating the Brunswick ratio, which considers the total amount of regression possible, for each participant at each distance. Overall averages of these measures across all participants were then computed.
The average amount of regression occurring in absolute terms was 0.12 (SD = 0.19), 0.28 (SD = 0.16), and 0.35 (SD = 0.19) for the distances 25cm, 65cm, and 105cm respectively. There was a significant difference in absolute regression between the distances of 25cm and 65cm, t(166) = -10.61, p < .05. Phenomenal regression in absolute terms also varied significantly between the distances of 65cm and 105cm, t(166) = -5.77, p < .05.
Mean regression in relative terms was 0.59 (SD = 0.59), 0.59 (SD = 0.35), and 0.56 (SD = 0.25) for the distances 25cm, 65cm, and 105cm respectively. There was no significant difference in relative regression between the distances of 25cm and 65cm, t(166) = .00, ns. Similarly, no significant difference was found in the relative amount of regression between the distances of 65cm and 105cm, t(166) = 1.79, ns.
This study aimed to determine the extent to which individuals are able to perceive their retinal image and to ascertain how this ability varies with the degree to which the image is foreshortened. As anticipated, participants showed regression; in both absolute and relative terms, they selected a shape that was intermediate between their retinal shape and the actual shape of the distal stimulus. This result is consistent with previous research (e.g., Nelson & Bartley, 1954) that demonstrated a similar effect. In terms of how participants' ability to perceive their retinal shape differed with distance, participants showed increasing regression to the real in absolute terms, but not when considering the total amount of regression possible. That is to say, participants regressed to the real virtually the same amount at each distance when taking into consideration the total amount of regression possible.
The findings of this research make sense in view of the theory discussed earlier. The slant of an object, which was manipulated by situating the circle at increasingly farther distances, is implicitly considered by observers when they are making judgments regarding the shape of the object. The absolute results indicated that the difference between the retinal shape ratio and the judged shape ratio increased with distance. This is understandable as the image cast onto the retina became smaller (with increasing slant of the object) and the judged shape ratio also decreased with distance. The consistency of Brunswick ratios across the three distances, however, indicates that individuals will regress by the same proportion of total possible regression each time (from 56% to 59%). In effect, the participants can be said to have reached a perceptual compromise between the shape as displayed at an angle (the ellipse) and the actual shape of the object (the circle).
The results of this study underscore the limited ability of individuals to directly perceive the sensory image that is projected onto their retina, as well as the distortions the perceptual system makes to the sensory image. Rather than being a shortcoming of the perceptual system, these results simply reflect another demonstration of the system's aim to maintain a stable percept of the outside world. In reality, the orientation of objects to the observer is constantly changing, although the object itself remains essentially the same (e.g., an opened door may look trapezoidal, although the observer still perceives it to be rectangular in shape). It is therefore unsurprising that individuals tend to "regress" to the true shape of the object when perceiving it, as this confers a practical advantage. It is interesting to note that these findings also have implications for advocates of the structuralist approach to perception, which aimed to determine the mental elements of perception through asking observers to describe a distal stimulus in terms of the individual "sensations" it evokes (Edwards, 2012). The structuralists made a distinction between the conscious experience that perception of a distal stimulus produces and the actual object. The results of this study support this distinction. However, the fact that the participants could not directly perceive their retinal image calls into the structuralist tenet that an object can be described in terms of its constituent parts.
A consideration of the results must be tempered by acknowledging the limitations inherent in the methodology of this experiment. Firstly, insufficient opportunity may have been given for fine discrimination between comparison ellipses; some participants reported that the differences between successive ellipses in the test booklet were too large and did not afford them the opportunity to select a shape that matched exactly watch they saw. The results reported in this experiment may have therefore been inaccurate, with the judged shape ratio being either too small or too large, and thus distorting the measure of the difference between the retinal shape and the judged shape. Another limitation of the image-matching paradigm used in this experiment is that individuals may not have been consistent when selecting matching shapes. Previous studies (e.g., Lichte, 1952) have shown that as the tilt of the distal stimulus increases (i.e., as the circle becomes more elliptical), observers have a tendency to judge shape in terms of the projected image (Howard, 2012). This may have biased the results by underestimating the amount of phenomenal regression undergone. Finally, this study was conducted under the assumption that the distal stimulus was accurately perceived (i.e., the circle was perceived as increasingly elliptical with greater distance as opposed to an inclined circle). In the case of some individuals, this assumption may be unfounded, even when the observer is aware that the ellipse is in a frontal plane (Howard, 2012).
Overall, the results of the present study indicate that individuals tend to regress to the true shape of an object in a shape-matching paradigm, and that following from this, the ability of individuals to perceive their retinal image is limited. Future research would do well to investigate the specific conditions under which phenomenal regression is likely to be lesser or greater. Utilising stimuli that are more complex and unfamiliar than two-dimensional circles may assist in differentiating between the potential effects of object familiarity and true phenomenal regression. This would be particularly useful given that familiarity with the distal stimulus may have had a confounding effect on phenomenal regression. Future research that explicit asks participants to make judgments about the slant of the distal stimulus would assist in delineating the precise relationship between perceived slant and shape constancy, a topic on which the current state of research remains inconclusive.