APPARENT SIZE AS A DETERMINER OF FIGURAL AFTER-EFFECTS. I

K olehmainen , K. Apparent size as a determiner of figural after-effects. I. Scand. J. Psychol ., 1968, 9, 230–236.—Apparent size as a determiner of figural after-effects (FAE) was studied by presenting the inspection figures in drawings which appeared three-dimensional because of gradient-effects. Significant FAEs were found. It is argued that apparent size does not determine FAE directly but an apparent decrement in the size of the test figure is connected to an after-effect in third-dimension.     

Figural after-effects and apparent size

Sutherland (1954) obtained results which suggest that when the retinal size of test and inspection figures is equal, the direction of the FAE may be determined by the relative apparent sizes of the two figures. Other investigators have reproduced this result when exactly the same conditions were used: when the conditions were changed the result was not obtained. In the present paper these results are discussed and an attempt is made to determine why the effect is not obtained with small variations in the experimental conditions. It is further shown that some FAE phenomena cannot be explained by the two main existing theories; these phenomena could be explained if some analysis of the stimulus is being performed before the stage of the nervous system at which the process underlying FAEs occurs. Some recent physiological evidence (Hubel and Wiesel, 1959) supports this hypothesis. If this hypothesis is correct, it is likely that further work on FAEs determined by apparent size may help to throw light on the physiological mechanisms underlying size constancy, and some further experiments are suggested.     

Illusions of brightness, length, and now size: comparable effects derived from the Craik-O'Brien-Cornsweet distributions

Analogous illusions of brightness, line length, and object size occur when stimulus distributions follow the Mach function. Similarly, analogous illusions of brightness and length are produced by stimulus distributions that follow the Craik-O'Brien-Cornsweet function. In Exp. 1, object size is studied using Craik-O'Brien-Cornsweet stimuli composed of 12 clip-art representations of candles, swords, forks, screwdrivers, or pens. Despite their equal dimensions, the three objects next to the taller gradient were judged larger than the three adjacent to the shorter gradient. In Exp. 2, variations of the sword and screwdriver figures having three separations of their constituent objects were used. The illusion produced in Exp. 1 was replicated and, for the figures composed of screwdrivers, increasing separation reduced the hypothesized mis-estimations. The relationship of these Craik-O'Brien-Cornsweet size illusions to their brightness and length counterparts mirrors the relationships previously reported for Mach stimuli; moreover, these findings converge to suggest that the visual system registers size of objects with a frequency code and that illusions of size appear when interactions among neurons disrupt this code.     

Gradients of distortion seen in the context of the Ponzo illusion and other contours

It is suggested that the spatial distortion evident in the Ponzo figure is a special case of a more general illusion in which a gradient of attenuation appears within areas bounded by angular brackets. The magnitude of this gradient is measured in five lines seen against a number of angular contexts. A similar gradient appears also in the presence of single oblique lines. Accordingly, it is suggested that the distortions seen in the figures usually referred to as “the angle illusions” depend upon the presence of contours which do not necessarily define angles. The implications of these findings for certain existing theories which suggest that some illusions depend upon apparent-distortion of angular size and that they contain features usually associated with two-dimensional perspective projections of typical three-dimensional scenes are discussed.     

Satiation or availability? Effects of attention,memory, and imagery on the perception of ambiguous figures

The prolonged-inspection technique has been used to demonstrate effects of satiation on the perception of ambiguous figures. We propose that the inspection phase, in which subjects view an unambiguous version of the stimulus prior to observing the ambiguous figure, does not create neural fatigue but rather provides a context in which the alternative percept is apprehended and gains perceptual strength through processes such as imagination or memory. The consequent availability of the alternative organization drives the perceptual phenomena that have been thought to reflect satiation. In Experiment 1, we demonstrated that (1) preexperimental exposure to the target figures and (2) allocation of attention to the-inspection figures-were both necessary in order to obtain results similar to those predicted by the satiation model. In Experiment 2, we obtained similar results, finding that effects of prior inspection were greater the greater the amount and availability of information regarding the alternative percept during the inspection phase. Subjects who generated visual images of the noninspected alternative during inspection yielded results comparable to those from subjects to whom both versions were presented isuaily.     

Figurai vs. configural effects in the filled duration illusion

Patterns varying in form goodness and size were presented for 15, 30, and 45 msec. The experiment included three independent groups of subjects. Half of the first group were presented size variations with good figures, while the other half were shown size variations with poor figures. Half of the second group were presented goodness variations with small figures, while the other half were shown goodness variations with large figures. A third group experienced variations in both goodness and size. The major findings were: (1) poor figures and large figures were judged “longer” than good or small figures when varied within a session; (2) this effect vanished when the different levels of size or goodness were presented to separate groups of subjects; (3) the magnitude of the difference in temporal estimation was the same for size and goodness when each was varied in isolation; (4) when size and form goodness were varied orthogonally in the same session, both dimensions produced reliable changes in temporal estimation. These data are discussed in light of current theoretical explanations of the filled duration illusion.     

The hidden face of Kanizsa's triangle: apparent movement of subjective figures in three-dimensional space

Several demonstrations on the apparent movement in depth of subjective figures are presented. They include: (a) apparent rotational movement as a result of shape invariance or rigidity; (b) apparent rotational movement with three-dimensional subjective figures not accompanied by a brightness gradient; and (c) apparent rotational movement by kinetic occlusion.     

Stimulus size matters: do life-sized stimuli induce stronger embodiment effects in mental rotation?

Against the background of the embodied cognition approach this experiment investigated the influence of motor expertise on object-based vs. egocentric transformations in a chronometric mental rotation (MR) task using images of either the own or another person’s body as stimulus material. The present study aimed to clarify two issues: (1) whether stimulus size (life size vs. small) is able to induce embodiment effects and (2) which role self-awareness processes play when using stimuli of the own body. The same design was conducted twice using both small stimuli (Study 1) and life-size human figures (Study 2). Using life-sized figures in Study 2 resulted in an explicit advantage of self-related stimuli and improved performance for motor experts compared to non-motor experts in both object-based and egocentric transformations. In conclusion, these results suggest that life-sized figures do indeed induce stronger embodiment effects in MR.     

Illusion decrement and transfer of illusion decrement in real- and subjective-contour Poggendorff figures

The reduction in illusion magnitude with visual inspection and the transfer of such illusion decrement to a noninspected figure were examined in real- and subjective-contour Poggendorff figures. For both types of figures, illusion magnitude decreased significantly, and in a similar manner, during a 5-min inspection period. Postinspection tests showed that inspecting either a real- or subjective-contour figure resulted in a reduction in illusion magnitude for the other, noninspected figure. These findings suggest that real- and subjective-contour Poggendorff figures share a similar global organization and are thus probably processed in a similar manner. These characteristics make subjective-contour figures a useful tool for separating illusion-producing mechanisms into structural and strategy components.     

A further investigation of apparent size and retinal size as determinants of the figural after-effect

A figure which is more distant from the eye than another but subtends the same visual angle is usually seen as the larger. This phenomenon is called perceptual size constancy. Experiments have been reported which show that sometimes the apparent and sometimes the retinal sizes of the stimulus figures determine the direction of the figural after-effect. These experiments are reviewed and two further experiments are reported. In the first experiment two types of stimulus figure (discs and annuli) which subtended a visual angle of 1° 36' resulted in figural after-effects, the direction of which would have been predicted by the retinal sizes of the figures. In the second experiment larger figures were used which subtended a visual angle of about 4° and which were the same as those used by Sutherland (1954). In this experiment the after-effects were generally in a direction which would have been expected if apparent size determined the direction of the after-effect. In the interpretation of the results attention is drawn to the “Central Tendency Effect” which has been observed in size judgements of stimulus figures of varying size. Two hypotheses are suggested; one is that the true figural aftereffect has been obscured by the “Central Tendency Effect” in successive judgements, and the other is that time error in successive judgements of size is essentially a figural aftereffect. Some supportive evidence for the latter hypothesis is reported. It is concluded that apparent size is not a critical determinant of the figural after-effect.     

More evidence on size modification in spatial axes systems of varying complexity

Pictorial space can be conceptualized as aggregate space (where figures compete for limited available space) or as axial space (where space is infinite and exists independently of figures). That these two kinds of space concepts follow a developmental sequence was tested by investigating size regulation mechanisms in 7- to 12-year-old children's figure drawings. An earlier longitudinal study had shown that the more figures were drawn and the more complex the spatial axes system, the smaller the figures. Two studies confirmed that object-driven size reduction was the size regulation mechanism in younger children, whereas axes-driven size reduction was the only factor regulating figure size in 12-year-old children. Size reduction occurred in a gradual fashion in younger children, whereas size reduction was more pronounced in crossed axes systems in older children. In addition, 7-year-old children showed a dynamic and fluid interaction between internal and external task demands for size regulation.     

Carry-over effects in face recognition: Processing mode or attentional window?

This study investigates whether or not the dominant processing mode (global or local) in a Navon task is carried over to a face recognition task when the dominant processing mode (configural or featural) in an encoding phase is manipulated. In Experiment 1, Navon figures that were equal in size to a facial photograph were prepared. Participants performed better on the face recognition task after reading large letters in the Navon figures than after reading small letters when configural processing was required in the encoding phase. In Experiment 2, Navon figures that were equal in size to the parts of a face were prepared. The performance after reading large letters did not differ from that after reading small letters. This suggests that both the dominant processing mode in Navon tasks and the size of Navon figures should be considered when discussing the effects of Navon tasks in face recognition.     

Visual transformation of size.

To investigate human visual identification of different-sized objects as identically shaped, matching reaction times were measured for pairs of simultaneously presented random figures. In three experiments, reaction time for correct reactions to test pairs of figures of the same shape and orientation consistently increased approximately linearly as a function of the linear size ratio of the figures. In the second experiment, where this ratio was defined for control pairs as well as for test pairs, reaction time for correct reactions to control pairs showed a similar increase as a function of size ratio. The results suggest that the task was performed by a gradual process of mental size transformation of one of the members of each pair of figures to the format of the other one.     

On the notions of indiscernibility and indeterminacy in the light of the Galois–Grothendieck theory

We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to \(K\) -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry.     

How to keep a reversible figure from reversing: teasing out top-down and bottom-up processes

The nature of processes underlying our perception of reversible figures was examined through two experiments investigating the effects of prior exposure conditions on an observer's report of figural reversal. In experiment 1, observers were adapted over several minutes to an unambiguous version of a rotating Necker cube prior to the presentation of the standard ambiguous figure. Results indicated that adaptation produced an immediate bias to perceive the ambiguous figure in the opposite configuration (ie reverse bias) and to reduce reports of reversal over the test period. The introduction of a brief delay between the adaptation and test periods revealed that this bias is a highly transient effect and is only clearly evident when the adaptation and test figures are matched in size. In experiment 2, observers were primed with an unambiguous figure for a few seconds prior to the presentation of the standard ambiguous figure. In this case, the obtained bias strongly favored the observer's reporting the ambiguous figure to be in the same configuration as the adapting figure (ie positive bias); and neither introducing a delay period nor changing figure size had any effect. We conclude that these experiments reveal the distinct roles of transient, retinally localized neural processes as well as more stable, global processes under specifiable conditions.     

Body Type Preferences in Asian and Caucasian College Students

While there is an extensive literature on gender differences in body image, little has focused on ethnic group differences in men's body image. College students ( N = 466) from a prestigious New England university indicated their current and ideal figures. Compared to Caucasians (N = 289), Asians (N = 92) reported smaller current figures. Both Caucasian and Asian women rated their current figure as larger than their ideal. Caucasian males reported no discrepancy between their current and ideal figures. However, Asian males rated their current figures as smaller than ideal. The effect of ethnicity on body satisfaction depended upon gender. For women, the ideal was thinner than current figure regardless of actual size, producing a discrepancy between current and ideal figures for both Caucasian and Asian women. Conversely, Asian and Caucasian men identified a similar ideal, producing a discrepancy between current and ideal figures only for Asian men.     

Obesity Bias in Children: The Role of Actual and Perceived Body Size

The aim of this study was to examine how children perceive their body size and whether their actual or perceived body size can explain their anti‐fat views. Four hundred and fourteen 5–6, 7–8 and 9–10‐year‐old children were read short vignettes depicting two characters, one possessing a positive and the other a negative quality. Following each vignette, participants were asked to pick the story characters among thin, average and obese figures. Obesity bias was defined as the attribution of the positive quality to the thin or average figure and the corresponding negative one to the obese. Body mass index determined children's actual body size. Perceived body size was determined with the use of Collins' (1991) figures of increasing size. The results showed that actual body size affected the accuracy of perceived body size. While the majority of average children were accurate at identifying their body size, most overweight and obese children tended to underestimate it. The accuracy of body size perception improved with age. Obesity bias did not relate to children's actual but to their perceived body size: Those who perceived themselves as heavier exhibited less bias. The implications of the findings are discussed in relation to children's developing identity, and suggestions are made for future research. Copyright © 2014 John Wiley & Sons, Ltd.     

Retinal projection or size constancy as determinants of the horizontal-vertical illusion?

To compare the influence of the projected retinal size and of the figure size on the perception of the horizontal-vertical illusion, the target size, the viewing distance, and the slant of an illusion figure were varied. In the first experiment the illusion produced by two figures of the same object size but of different retinal size was compared with that of two figures projecting the same retinal size but differing in object size. The illusion diminished when the size of the retinal projection was increased, whereas a change in figure size did not change the illusion. In Exp. II the illusion figure was tilted backwards which reduced the retinal projection of the 'vertical' figure limb. The illusion decreased and became negative as a function of the retinal projection, but this decrease was relatively small compared with the reduction of the retinal image. The results are interpreted as supporting a retinal origin as an explanation of the illusion. Although there is strong evidence for size-constancy scaling in a tilted figure, constancy scaling is considered of minor importance as a determinant of the usual illusion.     

Orientation-contingent tactual size aftereffects

A new contingent aftereffect of apparent size can be produced in the following way. A rectangular inspection block is oriented with its long dimension horizontal (or vertical). During an inspection (induction) period of 2 min, the subject alternately grasps the horizontal and vertical dimensions of the inspection block between the thumb and forefinger of a single hand, changing from one dimension to the other every 2 sec. After the inspection period, the hori zontal dimension of a square test block feels shorter (or longer) than the vertical dimension. Inspection blocks having larger ratios of width to height produce larger aftereffects. The aftereffect persists over delays of as much as 16 min between inspection and test.     

Are size illusions in simple line drawings affected by shading?

In a number of simple line drawings, such as the Müller-Lyer or Judd figures, we can experience strong distortions of perceived space-geometric illusions. One way of explaining these effects is based on the perspective information that can be read from the line drawings. For instance, the 'inappropriate constancy scaling' theory advocates that the inferred three-dimensional structure of the pictured object is used by the perceptual system to adjust the size of line-drawing components. Such a theory would predict that additional depth cues, for instance shading added to line drawings, should affect these illusions because they influence the three-dimensional appearance. We present here systematic measurements of the magnitude of length misjudgments in horizontal Müller-Lyer and Judd figures for three configurations: (i) pure line drawings, and with shading attached to (ii) the top, and (iii) the bottom of the figures. The latter two configurations are unambiguously interpreted as 'folded' structures with a horizontal edge behind the image plane or protruding from it, respectively. While we could not find any effect of shading in our experimental data, we did observe a length misjudgment in Judd figures that corresponds precisely to the asymmetry that can be observed in the Müller-Lyer illusion for inward and outward fins. This pattern of results is not consistent with notions of inappropriate constancy scaling but is fully coherent with the view that neural filtering mechanisms, which are affecting the perceived position of line intersections, are responsible for this type of geometrical illusions.