Determinants of the Bourdon effect

Transcription

1 Perception & Psychophysics 1980,28 (1), Determinants of the Bouron effect G. 1. N. ROZVANY an R. H. DAY Monash University, Clayton, Victoria 3168, Australia The Bouron illusion is the apparent inwar bening of straight, collinear eges in a soli figure consisting of two elongate triangles meeting at their apexes. This effect was investigate in five experiments. In the first an thir experiments, it was shown that the apparent bening is greatest when the apical angles are about 12 eg an the axis of the figure is oriente at about 22 eg from the vertical. The secon experiment was a control involving visual acuity for angular epartures of two lines from collinearity an serve as a basis of selection for subjects in Experiments 3, 4, an 5. Experiments 4 an 5 showe that the illusion occurs strongly in a soli ("fille in") figure but is notably smaller in outline figures of the same size an shape. It tens to be negative in outline figures with bounaries forme by continuous an broken lines. The relationship between the Bouron illusion an the "negative" Zollner illusion is consiere. Although the contours AB an BC in Figure 1 are collinear, they appear to be isplace inwar towar the points 0 an E. In consequence, the straight ege, ABC, appears to be bent inwar about B. As far as is known, this compelling effect, which was first escribe by Bouron in 1902, has not been systematically stuie. The five experiments reporte here were the first in a series esigne to o so. Two aspects of the Bouron illusion suggest that it might be ifferent from a number of geometrical illusions of irection. First, the apparent irections of the collinear eges are isplace towar those of their opposite eges, which meet at an obtuse angle. For the most part, illusions of irection are oppose to the irection of the inucing lines or contours. The Zollner illusion an its numerous erivatives are cases in point. However, there are some notable exceptions in figures in which the angle between inucing an inuce contours is about 5 eg (Aam, 1964; Oyama, 1975; Wallace & Crampin, 1969). Uner this conition, the test or inuce line is apparently isplace towar the inucing line. Thus, one of the issues raise by the illusion in Figure 1 is whether it is essentially the same as these "negative" Zollner effects. Secon, there are scattere references to figures similar in shape to that shown in Figure 1 but consisting of lines only (Luckiesh, 1965; Sanfor, 1897; von Kries, cite in von Helmholtz, 1909). Curiously, the illusion reporte in these outline figures is opposite to that reporte in the soli Bouron figure; i.e., the collinear line appears to ben outwar about its center, not inwar as in Figure 1. As far as is known, there are no other instances of one irection of illusion in a soli or "fille in" figure an the opposite irection in an outline figure of the same shape. If this opposition between the irections of The assistance of R. Kreymborg is gratefully acknowlege. the illusion in soli an outline figures of the same shape was confirme experimentally, an important question concerning the role of contours an lines in the generation of illusions of irection woul be pose. Five experiments are reporte. Experiments 1 an 3 were concerne with the effect on the Bouron illusion of orientation «(1') of the figure relative to the vertical an of the inner apical angles (f3). (See Figure 3.) Experiment 2 was a control for Experiments 1 an 3, an was concerne with visual acuity for angular epartures from collinearity as a function of line orientation. The ata from this experiment were also use in the selection of subjects in Experiments 3, 4, an 5. In Experiments 4 an 5, the size an irection of the illusion in soli an outline figures were investigate. GENERAL PROCEDURE Subjects Subjects of both sexes were recruite from among acaemic staff, research assistants, technical personnel, an grauate stuents. In pilot stuies for Experiments 2 an 3, some subjects exhibite consierable inconsistencies, owing, presumably, to poor motivation or failure to learn the tasks involve. Therefore, subjects in Experiments 3, 4, an 5 were selecte on the basis of their performance in the control experiment (Experiment 2), in which the task was that of juging whether lines were collinear. Thus, whereas the number of subjects in Experiments I, 3, 4, an 5 was preetermine for the particular experiment, that in Experiment 2 accumulate until the maximum was reache with the completion of Experiment 5. Apparatus A Data General Eclipse S 200 computer was interface with a Tektronix cathoe-ray storage-type enhance moule isplay terminal. The keyboar of the terminal was fitte with a cover with suitable openings that expose only the four keys to be use. An aluminum viewing tube 20 cm in iameter an 40 cm long, was place in front of the isplay, with its axis normal to the screen an at a istance of 5 ern from it. This arrangement resulte in a circular fiel of view about 22 em Copyright 1980 Psychonomic Society, Inc $00.850

2 40 ROZVANY AND DAY in iameter. A rubber mask that fitte the face was fixe at the observer's en of the tube to control istance an to prevent the subject from tilting his hea. At the screen, I em subtene a visual angle of eg. The results of each experiment, together with relevant particulars of the subject, were printe up on a secon terminal an store in a file on the computer isk for statistical processing. Processing was carrie out automatically by a separate routine. Stimulus Figures The basic figure is shown in Figure I. All figures were light on a ark groun. The luminance of the figures was approximately 14.6 cm' an that of the backgroun approximately 3.1 cm'. The raial istance of each ege from the central apex to the outer en of the figure, which was constant throughout, was 10.5 em (13.13 eg). All the other figures shown in Figure 2 were erive from that shown in Figure I. Proceure In all experiments, the subject was require to rotate simultaneously two lines or eges in a series of steps in opposite irections until they appeare to be collinear (see Figure 2A). Rotation was achieve by pressing appropriate keys on the console. It was possible to rotate the eges in small steps to the left an upwar or to the right an ownwar in either irection, as shown in Figure 2A. When the subject was satisfie that the c E A Lli I B ";G'~V (~i~ )~"'P'~", 1. E -y Experiment 1 Experiment 2,:1' Experiments 4 an 5 11 F Experiment 4 i I, I, "I, <.J o a varies Jt' S ' Experiment 3.. I, "" ' 'I 'I v~ ' Experiment 5 A B o Figure l. The Bouron illusion. The eges AB an BC are collinear but appear to ben inwar about B towar D an E, respectively. Figure 2, The stimulus figures use in the five experiments. The symbols a, 13, v., an Y refer, respectively, to the orientation of the long axis of the figure relative to the vertical, the internal apical angles of the figure, an the ifference between the apparent an physical collinearity in angular terms after an ajustment (the score) an before an ajustment (the starting misalignment). lines or eges were collinear, other keys were presse, which generate the next conition. Both the sequence of conitions an the initial misalignments (Yi in Figure 2A) were ranomize by the computer. At the beginning of the session, each subject was given stanar instructions to rea an was later invite to ask any questions about the task. Two practice trials were unertaken before the series of experimental trials. The score throughout was the ifference in egrees between apparent an true collinearity of the two eges or lines. EXPERIMENT 1 The purpose of Experiment 1 was to investigate the effect of the angle (0') of the figure relative to the vertical an the size of the internal apical angles (~) on the apparent collinearity of the eges AB an Be, shown in Figure 1. It was expecte that, like other illusions of irection, the effect woul be greater for oblique orientations of the figure than

3 THE BOURDON EFFECT 41 for either the vertical or horizontal ispositions (see Day & Dickinson, 1976; Robinson, 1972). Although no preictions were mae about the effect of variation in {3, it was assume that if the effect is a manifestation of the negative Zollner illusion, it woul be maximal for an a value of about 5 eg or less, as shown earlier (Aam, 1964; Oyama, 1975; Wallace & Crarnpin, 1969). Conitions, Subjects, an Proceure The stimulus pattern is represente in Figure 2B. There were five values of a-o (collinear ege vertical), 22.5, 45, 67.5 an 90 eg (collinear ege horizontal)-an three values of ~ 5, 12.5, an 20 eg. Thus, there were 15 conitions in all. The initial misalignment, Yi' was ranomize within the range of 0 (collinearity) to -3.6 eg. Negative initial values were aopte, since, on the storage-type cathoe-ray isplay use in this experiment, the value of Y coul be increase very rapily by simply aing lines to the top ege of the figure, thus reucing the apparent misalignment. However, to ecrease y, it was necessary to erase the entire figure an reraw it. This latter proceure require at least 20 times as much time as the former. With the negative initial value, the subject coul use the fast comman moe for most of the trials an the slow negative moe for the relatively rare occasions when there was an overshot. Since this asymmetry of both Yi an the control moe is open to criticism, symmetrical values of about 0 an an ientical proceure for both positive an negative changes of y were use in later experiments. It can be note that no bias ue to asymmetry was foun in comparing the outcomes of the first an later experiments. There were eight subjects, each of whom participate twice uner each conition, resulting in 30 trials in all. The angular misalignment of the two eges was ecrease in steps of.4 eg. The score for each conition was the mean ifference in egrees between physical an apparent angular alignment base on the two trials. Mean angular misalignments (y) for the five values of a are plotte separately for the three values of {3 in Figure 3. It can be observe that, as expecte, the illusion was greater when the figure was oriente obliquely. It was also notably greater at 22.5 an 45 eg when {3 was 12.5 eg than when it was at either 5 or 20 eg. These ifferences among the three values of {3 were not apparent at orientations of 0, 67.5, an 90 eg. An analysis of variance with repeate measures on the factors a an {3 showe that the ifferences between the means for both factors were significant [Fa(2,14) = 13.6, p <.001; F~(4,28) = 29.0, p <.001]. The interaction between these two factors was also significant [Fa~(8,56) = 3.95, p<.001]. Two points can be mae about these outcomes. First, the Bouron effect, like the Zollner an Poggenorff illusions (Robinson, 1972), is greatest when the feature to be juge is obliquely ispose. Secon, on first consieration, the occurrence of a significantly greater effect for an internal apical angle of 12.5 eg suggests that the illusion is not a special instance of the negative Zollner illusion. The negative Zollner is greatest for angles between ;- >-... C QJ E c =; 0 0 ~ L -10 '- :J c ~ Orientation Figure 3. Magnitue of the Bouron illusion in egrees as a function of orientation (a) of the figure relative to the vertical an the internal apical angles (m (Experiment I). inucing an test lines of about 5 eg an, accoring to Oyama (1975), is almost negligible at 10 eg. However, the ata from Experiments 4 an 5 below have le to a moification of this view. The point is taken up again in the iscussion. 45 EXPERIMENT of Figure (a') The purpose of the secon experiment was twofol; first, to establish whether variations in the magnitue of the effect as a function of figure orientation is attributable to variations in visual acuity an, secon to provie a basis for the selection of subjects for Experiments 3, 4, an 5. Both the Zollner an Poggenorff illusions are greater when the property exhibiting illusory istortion is obliquely oriente. It is likely that in each case this is ue to poorer visual acuity for both straightness an iscontinuity of oblique lines-the oblique effect (Appelle, 1972). In other wors, the illusory istortion is greatest when visual resolving power for the relevant object property is poorest. The subject's task in Experiment I involve visual acuity for angular epartures from collinearity. While this figure has not been traitionally use in the measurement of visual acuity, it is essentially an acuity-base task. It is therefore reasonable to assume that it also exhibits the oblique effect. One purpose of the secon experiment was to test this assumption.

4 42 ROlVANY AND DAY As pointe out above, some subjects in pilot stuies ha exhibite consierable variation in their jugments of collinearity because of obvious ifficulties in performing the task. For this reason, performance on the acuity task serve as a basis for inclusion in Experiments 3, 4, an 5. The criterion for acceptance was a maximum absolute score of 1.2 eg or less an a mean absolute score of.6 eg or less. Subjects whose maximum or mean score exceee these values were also exclue from Experiment 2. A total of six subjects were so rejecte. Conitions, Subjects, an Proceure The stimulus pattern is shown ir. Figure 2e. Again, there were five values of a: 0 (vertical), 22.5, 45, 67.5, an 90 eg (horizontal). The initial misalignment (Yi) was ranomize over the range ±1.4 eg in step sizes (Ay) of.2 eg, There were 36 subjects, each of whom participate uner each conition once. The proceure an scoring were the same as for Experiment 1. The line thickness was.2 mm. The mean misalignments (y) for the five a conitions are shown in Figure 4 (lower, broken line). The mean values are small (y = -.028, -.100,.056,.129, an.067 eg for the ex conitions of0, 22.5, 45, 67.5, an 90 eg, respectively. An analysis of variance inicate that these mean misalignments were not significantly ifferent. However, if the signs are ignore, the absolute values of y for the same orer are.250,.433,.366,.328, an.244 eg (Figure 4; lower continuous line). The tren in the magnitue of these scores is similar to those for the Bouron effect (Figure 3), with greater errors for the oblique orientations of the figure than for the vertical horizontal. An analysis of variance showe that the ifference between these absolute values of y are significant [F(4,140) = 4.26, p <.005]. Further examination by the Newman-Keuls metho has shown that only the ifference between a = 22.5 eg an either a = 0 eg or ex = 90 eg was o ~. C G.l E c':!' 11\ r r... "3 en c «-1.0 Expt 1 18subjects) <,,.... "..., I " I... I ". ~ Expt 2 (36 subjects) 225 Figure 4. Upper: Magnitue of the Bouron illusion as a function of orientation (a) of the figure relative to the vertical (continuous line: Experiment 3; broken line: Experiment 1). Lower: Apparent collinearity of two lines as a function of orientation relatlye to the vertical (Experiment 2, continuous line: mean absolute values; brokenline: mean values) Orientation of Figure (c") 90 significant (p <.01). Thus, it can be conclue that, like other visual acuity tasks, the task of etecting angular epartures from collinearity exhibits the oblique effect (Appelle, 1972). This can be taken to inicate that the greater Bouroneffects for the oblique orientations of the figure foun in Experiment 1 are attributable in some part to poorer visual acuity for alignment when the figure is obliquely ispose. EXPERIMENT 3 In Experiment 1, the ranomize initial misalignments (Yi) were asymmetrical about zero for the reason pointe out earlier. In aition, an increase in y was generate faster than a ecrease. It is conceivable that these asymmetries of esign an ajustment coul have affecte the outcomes. The thir experiment was conucte in orer to check on the possibility of bias ue to asymmetry in Yi an spee of ajustment. A total of six subjects were exclue because they faile to satisfy the criteria of acceptance in Experiment 2. Conitions, Subjects, an Proceure In orer to maintain consistency with Experiment I, the value of (J was 12.5 eg when the leaing eges of the figure were in alignment (y = 0). For other values of y, the actual value of (J was therefore 1.2S eg+(yl2). Thus, ify = 1.4 eg, the final value of (J woul be (1.412) = 13.2 eg. There were 25 subjects selecte on the basis of a maximum angular acuity score of 1.2 eg an a mean acuity score of.6 eg or less in Experiment 2. The initial alignment was varie over the range ±2.80 eg with a step size of.4 eg. To facilitate comparison, mean angular misalignments are shown in Figure 4 (upper continuous line) with those for Experiment 1 (upper broken line). Although the mean for 22.5 eg is slightly less in Experiment 3, the means generally accor well with those of the earlier experiment. The slightly lower score in Experiment 3 at 22.5 eg is probably accounte for by the notably greater scores of two of the eight subjects in the first experiment. The essential similarity between the results inicates that the asymmetrical values of Yi an ajustment spees in Experiment 1 i not unuly bias the scores. An analysis of variance showe that, as earlier, the ifference between the means was significant [F(4,96) = 32.5, p<.001]. Further analysis using Newman-Keuls tests showe that all ifferences were significant at p <.01 level, with the exception of that between a == 0 an a == 67.5 eg (p <.05) an between a = 22.5 an a == 45 eg (not significant). All these outcomes accor with those for Experiment 1. EXPERIMENTS 4 AND 5 The Bouron illusion was originally observe in a soli figure like that shown in Figure I. In outline

5 THE BOURDON EFFECT 43 figures of the same shape, the illusion is claime to be in the irection opposite to that in Figure 1. That is, the collinear lines opposite to those forming an obtuse angle appear to ben outwar at about the center point. However, while this irection of the effect has been reporte from time to time (Luckiesh, 1965; Sanfor, 1897; von Kries, cite in von Helmholtz, 1909), it has not been shown experimentally. The main purpose of Experiment 4 was to compare the irection an magnitue of the illusion in soli an outline figures. The scope of the experiment was extene by constructing the outline figures of continuous an broken (ashe) lines. While the inclusion of these two types of lines was mainly exploratory, it was thought that the broken test lines might be more conucive to the illusion than continuous lines. In the interests of a complete esign, four combinations of continuous an broken lines were inclue as shown in Figures 2E an 2F. Since the effect with line figures was small, Experiment 5 was conucte to establish whether or not this was ue to the absence of enclosing arcs at the ens of the figures (see Figure 5). Apart from this slight ifference, the proceures for Experiments 4 an 5 were essentially the same. For this reason, the two experiments are escribe together. Conitions, Subjects, an Proceure The stimulus figures are shown in Figure 2E an 2F. In Experiment 4, there were five figures-the soli figure an four line-figures with open ens. Of these, one consiste of continuous. 40 >... c: OJ E c:.~ "0 Vl r. L. <:I "5 0\ c: < , <, EXpt!rlment 5 -. "" " Conition 1 I" ( Expertment 4!,f Experiment 5 Figure 5. Magnitue of the Bouron illusion for a soli figure an for figures forme by lines (Experiments 4 an 5). r f, " f, r. f r I f, i) lines, one of broken (ashe) lines, an the remaining two of continuous an broken lines along one or the other contour. Each broken line consiste of 60 elements,.8 mm long. All lines were again.2 mm thick. The figures in Experiment 5 were the same, except that the ens were complete by arcs of the same raius as those forming the ens of the soli figure. For all figures, a was 22.5 eg an (3 was 12.5 eg, the combination that prouce the greatest effect in Experiment I. The criterion for the selection of subjects was the same as for Experiment 3. There were 14 subjects in Experiment 4, an 7 in Experiment 5. The proceures for presentation of the figures an for arriving at tile scores were the same as before. The mean scores for the two experiments are shown in Figure 5. It can be seen that the graphs for the two experiments are similar, suggesting that neither the relatively small effects with outline figures nor the negative irections for two conitions in Experiment 4 are attributable to the absence of enclosing enlines. In both experiments, the illusion was notably greater for the soli figure. The illusions in the outline figures was slightly negative in both experiments when one of the bouning lines was continuous an the other broken. An analysis of variance of the ata for Experiment 4 showe that the ifference between the means was significant [F(4,52) = 30.2, p <.001]. Further analysis using the Newrnan-Keuls proceure inicate that the ifference between the illusion with the soli figure (Conition 1) an each of the other conitions (2-4) were significant at p <.01. Those between Conition 5 an Conitions 3 an 4 (the negative effects) were also significant, both at p <.01. None of the other ifferences achieve significance. An analysis of variance for Experiment 5 also showe that the ifference between the means was significant [F(4,24) = 16.0, p <.001]. Since the ata for this experiment were strikingly similar to those of Experiment 4, a etaile analysis was not consiere necessary. DISCUSSION In summary, the Bouron illusion of irection is markely greater in a soli figure than it is in an outline figure of the same shape an, in the former, achievesa maximum of about 3.0 eg when the internal apical angles are about 12.5 eg an the axis of the figure is incline at about 22.5 eg to the vertical (Figures 3 an 4). When the figure is vertical or horizontal, the effect is not only much reuce but is also about the same in magnitue for internal acute angles between 5 an 20 eg. Finally, the illusion exhibits a tenency to reverse its irection, i.e., the collinear lines appear to ben outwar when one long bounary!s a continuous line an the other, opposite to it, IS broken or ashe. Among the most intriguing outcomes of these experiments are the relatively large illusion of irection in the soli figure, the figure in which this illusion was

6 44 ROZVANY AND DAY originally but briefly mentione by Bouron (1902), an the slight effects with various forms of outline figure. As far as is known, this is the only instance so far escribe of a greater illusion ina soli figure, The observation raises the question of whether other "assimilative" illusions that are commonly associate with outline figures are greater when the figure is soli. The fining suggests that contours between extene regions of light an ark might interact in a manner ifferent from that of mere linesin generating some illusory istortions. Contrary to earlier reports (Luckiesh, 1965; Sanfor, 1897; von Kries, cite in von Helmholtz, 1909), the illusion in the outline figure with continuous lines forming the bounaries is not negative; i.e., the collinear lines o not appear to ben outwar, away from the figure. The illusion is in the same irection as in the soli figure, but markely smaller. However, the illusion is reverse but remains slight when one of the long bounaries is forme by a continuous line an the other by a broken line. This occurs irrespective of which bounary is continuous an which is broken. At this stage, the basis of the reversal is unclear. Clearly, a more etaile investigation of the effect of ifferent classes of lines in various combinations is calle for. Another issue to be consiere is whether the Bouron illusion is an instance of the "negative" Zollner illusion, the slight apparent tilt of a line in the same irection as another that meets it at a small angle. On first consieration, the two seem unrelate. The ata from Experiments 1 an 3 show that the Bouron effect is greatest when the angle between the two eges is about 12.5 eg. When the angle is 5 eg, the illusion at 22.5 eg from the vertical is much less. Aam (1964) showe that the negative Zollner illusion is maximal when the angle between the two lines is 2 eg, an Oyama (1975) showe that when this angle is 10 eg, the illusion is negligible. However, it is to be note that all experiments so far on the negative Zollner illusion have been conucte with figures in which the long test lines are vertical. As can be seen in Figures 3 an 4, the Bouron illusion is very slight when the collinear eges are vertical. In aition, there is no ifference in the illusion when the three internal angles vary between 5 an 20 eg for a vertical figure (Figure 3). Thus, while at first the Bouron an negative Zollner illusions seem to be ifferent effects, closer consieration oes not wholly support this view. Finally, it is to be note that the greater Bouron illusion for obliquely oriente figures is characteristic of most illusions of irection an alignment. Both the Zollner an Poggenorff illusions are greater when the figures are obliquely ispose (Robinson, 1972). Most forms of visual acuity eteriorate when the test elements are oblique (Appelle, 1972). The iscrimination of angular epartures from alignment is an acuity task, although it has not been commonly use as such. It is likewise poor when the two lines to be juge for their collinearity are oblique. It can be conclue, therefore, that the greater Bouron effect for the oblique orientation of the figure (Figure 1) is attributable in large part to poorer visual acuity with oblique contours. REFERENCES ADAM, J. A note on visual illusion of irection. Australian Journal ofpsychology, , ApPELLE, S. Perception of iscrimination as a function of stimulus orientation: The "oblique effect" in man an animals. Psychological Bulletin, 1972,78, BOURDON, B. La perception visuelle e espace. Paris: Reinwal, DAY, R. H., & DICKINSON, R. G. The components of the Poggenorff illusion. British Journal of Psychology, 1976, 67, LUCKIESH, M. Visual illusions: Their causes, characteristics an applications. New York: Dover, OYAMA, T. Determinants of the Zollner Illusion. Psychological Research. 1975,37, ROBINSON, J. O. The psychology of visual illusion. Lonon: Hutchinson, SANFORD, E. C. Experimental psychology. Lonon: Heath, VON HELMHOLTZ, H. Hanbuch er physiologischen Optik (Vo\. 3). Hamburg: Voss, WALLACE, G. K., & CRAMPIN, D. J. The effects of backgroun ensity on the Zollner illusion. Vision Research, 1969,9, (Receive for publication October 22, 1979; revision accepte March 25,1980.)