Identification of Symmetry: Effects of Stimulus Orientation and Head Position

Home , Orientation (geometry)

Perception & Psychophysics 1982,32 (5), 443-448 Identification of symmetry: Effects of stimulus orientation and head position

CELIA B. FISHER Fordham University, Bronx, New York

and

MARC H. BORNSTEIN New York University, New York, New York

It has been argued that the perceptual advantage of symmetry depends upon the essentially symmetrical properties of the visual system. According to this explanation, the ease of identifi cation of symmetries about different axes of orientation should decrease with increasing dis tance from the vertical: Reaction times to vertical symmetry should be faster than those to diagonal symmetry, which in turn should be faster than those to horizontal symmetry. Previ ous research demonstrating this pattern of responding employed stimuli with linear axes. In the present study, the subjects viewed tachistoscopically presented symmetrical and asymmetrical dot patterns (which had no explicit axes) in one of three head positions: upright, 45 deg left, and 45 deg right. The subjects' performance failed to support the structural explanation: Identifi cation of symmetry is equivalently fast for vertical and horizontal; vertical and horizontal show strong advantages over obliques, and this general advantage follows retinal coordinates. Find ings are discussed in light of alternative theories of symmetry processing.

Experimental investigators since Mach (1897) have ceptual advantage over other symmetries (e.g., repeatedly observed that, in visual perception, sym Bornstein, Ferdinandsen, & Gross, 1981; Deregowski, metrical patterns hold advantages over asymmetrical 1971; Fisher, Ferdinandsen, & Bornstein, 1981; ones: They are preferred, they are detected, discrim Julesz, 1971; Palmer & Hemenway, 1978; Rock & nated, and identified more easily, and they are re Leaman, 1963; Szilagyi & Baird, 1977). Indeed, membered better (e.g., Arnheim, 1974; Attneave, Julesz (1971) found that symmetries are detected 1955; Garner & Sutliff, 1974; Julesz, 1971). Mach fastest only when symmetrically projected to the vi and, more recently, Corballis and Roldan (1975) sual system; however, his finding was limited to high argued that these advantages for processing sym spatial frequency patterns. metry reflect the fact that, structurally, the visual Second, with regard to nonvertical symmetries, system is itself essentially symmetrical and therefore Mach's (1897) explanation predicts an increasing that visual sensitivity to symmetry reflects either sym advantage for patterns whose orientation of sym metrical projection to a more or less symmetrical vi metry is nearer to vertical. According to the struc sual system or symmetrical representation leading to tural explanation, symmetries about nonvertical axes homotopic mapping in the brain. would be identified only after they were mentally Three predictions for symmetry perception follow aligned or rotated to the anatomical vertical. Corballis from this structural position. The first is that sym and Roldan (1975) have offered strong support for metries along the vertical should be most easily per this prediction. In three separate experiments using ceived, because they are congruent with the bilateral dot patterns with an explicit axis of orientation, they symmetry of the visual system. In fact, in measures found that response times to identify symmetrical of preference, detection, and recognition, vertical patterns increased linearly with increasing angular symmetry has typically been found to have a per- displacement from the vertical: Identification times for vertical symmetry were shorter than those for diagonal symmetry, which in turn were shorter than The research and preparation of this report were supported by those for horizontal symmetry. However, these re the Fordham University Research Council, the Spencer Founda sults may be constrained by the stimuli that were tion, and BRSG Grant RR07062 awarded by the Biomedical Re used, since Palmer and Hemenway (1978), who used search Support Grant Program, Division of Research Resources, bilaterally symmetrical closed polygons having no National Institutes of Health. We thank Marjorie Melendez for help with data analysis. Requests for reprints should be sent to explicit axis but rotated in different orientations, Celia B. Fisher, Fordham University, Department of Psychology, found that subjects identified horizontal faster than Dealy Hall, Bronx, New York 10458. diagonal.

On structural grounds, evidence for mental rota whether stimuli without explicit axes would yield re tion is not in itself sufficient to demonstrate that the sponse patterns consistent with the hypothesis that visual system is singularly sensitive to vertical sym- the bilateral symmetry of the visual system princi .metry: when observers view symmetries with their pally underpins the perception of symmetry in vi heads upright, reaction-time differences to nonverti sual patterns. To do this we reexamined the roles of cals could just as well reflect mental alignment of stimulus orientation and head position in symmetry symmetries with gravitational vertical. In order to identification of dot patterns that lacked explicit axes demonstrate that the specialty of visual symmetry is a and whose orientations were thus defined solely in product of the bilateral symmetry of the visual sys terms of symmetrical organization. In our study, the tem, a third prediction must be fulfilled, viz., the subjects failed to meet predictions that derived from pattern of visual sensitivity to symmetry posed in the Mach's (1897) structural explanation of symmetry second prediction must be retinally rather than en identification. vironmentally determined. Corballis and Roldan's (1975) study also provided evidence on this point: METHOD when subjects tilted their heads 45 deg left or right, Subjects latencies to identify symmetry (characterized by an Thirty-six subjects, ranging in age from 17 to 22 years, were advantage for vertical over oblique and oblique over randomly assigned to one of three head-position groups: upright, horizontal) were aligned to retinal coordinates more 45 deg right, and 45 deg left. For the three groups of 12 subjects, closely than to environmental coordinates. there were 4 and 8, 7 and 5, and 6 and 6 men and women, re In several ways, Corballis and Roldan (1975) spectively. All subjects possessed normal or corrected-to-normal vision. present strong support for Mach's (1897) structural explanation of identifying symmetry. Unfortunately, Stimuli and Apparatus the nature of the stimuli used in their study-12 dots Four symmetrical and four asymmetrical 16-dot patterns were that were symmetrical or repeated about a strong used (see Figure I). Each pattern was constructed such that the distance from its center to a circular perimeter of eight dots spaced linear axis-raises a minor question concerning the at 45-deg steps from 0 to 315 deg was 2 cm. For the symmetrical generality of their findings but also detracts from the patterns, four dots were randomly distributed to the right of the strength their findings lend to the generality of vertical meridian inside the perimeter, and then each half-pattern Mach's structural explanation. Specifically, the pres was reflected about the vertical axis. For the asymmetrical pat terns, all eight inner dots were randomly distributed within the ence of an explicit axis enables identification of pat perimeter. In the experimental situation, patterns subtended ap tern orientation prior to the detection of stimulus proximately 3 deg ofvisual angle. symmetry. Corballis and Roldan themselves recog The stimuli were presented in a Gerbrands three-field tachisto nized this possibility when they observed that the scope and were viewed monocularly with the right eye. The sub presence of a linear axis could influence perceptual ject's head was oriented upright or at 45-deg tilts left or right by a rotatable head piece attached to the viewer portion of the tachisto judgments otherwise typically employed in perceiv scope. Both the preexposure field (an asterisk) and the stimulus pat ing symmetry. Indeed, a review of their data argues terns were observed through a circular mask. The preexposure field against the possibility that any general processing was illuminated for 750 msec, and then the stimulus was presented strategy for symmetry could be derived on the basis immediatelyfor I,OOOmsec. The onset ofthe stimulusstarteda clock. A microphone positioned close to the subject's mouth tripped a of stimuli that have explicit axes of orientation. voice key that stopped the clock when the subject responded. Specifically, responses were not special to symmetry per se; rather subjects responded similarly to both Procedure symmetrical and asymmetrical patterns and to The subjects were informed that the purpose of the experiment instructions to look for symmetry or for repetition was to test how fast they could identify patterns as being either symmetrical or asymmetrical. To explicate the notion of symmetry (Corballis & Roldan, 1975; Corballis, Zbrodoff, & before the test patterns were presented on the tachistoscope, the Roldan, 1976). subjects were shown a small number of paper-and-pencil training In brief, there are data to support a structural ex patterns with axes drawn in and "symmetrical pattern" was de planation of symmetry identification, but the gen fined for them as a pattern whose two halves were exact mirror images of one another. To familiarize subjects with the task, they erality of this explanation may be jeopardized by were given a series of practice trials with eight such training limitations in the stimuli used to support the ex patterns. No training pattern was used again in testing. The sub planation. In the present study, we sought to test jects were instructed that on these and subsequent test trials they

Figure 1. Examples of the four symmetrical patterns in the vertical, 4S-deg-right, horizontal, and 4S-deg-left orientations, and an asymmetric pattern. IDENTIFICATION OF SYMMETRY 445 were to call symmetrical patterns "Bill" (or "Ben") and asym The ANOV A using retinal coordinates also yielded metrical patterns "Ben" (or "Bill"). (The two names were bal a significant symmetry x orientation interaction anced in the groups and across subjects.) The subjects were then [F(3,99)= 11.37, p .001]. Tests of simple main ef given 64 feedback practice trials using test stimuli. Immediately < following these practice trials, the subjects received 128 test trials. fects indicated a significant effect of orientation for Each of four symmetrical and four asymmetrical patterns was symmetry [F(3,99) = 29.30, p < .001], but not for shown twice in each of the eight orientations rotated from 0 (verti asymmetry [F(3,99) = LSD, p > .05]. Sheffe tests in cal) to 31S deg in 4S-degsteps. Order was random. dicated that the subjects' pattern of responding fitted At the end of the experiment, trials on which the subjects had erred were rerun without the subjects' knowledge so that total data an "oblique effect" rather than a "mental rota sets of correct responses for each subject were available. Data on tion" function: identification of symmetries about 16 trials for each of the four major orientations of symmetrical the two main orthogonals was significantly faster and asymmetrical patterns for each subject were thus gathered. than identification of symmetries about the two diagonals [Fs(3,99) = 23.06, 12.06, and 14.84, ps < RESULTS AND DISCUSSION .001, for head upright, tilted right, and tilted left, re spectively]. Palmer and Hemenway (1978) found Mean reaction times for symmetry and asymmetry similar results with closed polygons that also lacked for each orientation for each head-position group explicit axes. In addition, for all head positions, were analyzed in two separate 3 (head position) x 2 Tukey's a posteriori tests (0 = .05) failed to yield sig (symmetry) x 4 (orientation) ANOVAs, one or nificant differences between vertical and horizontal ganized by environmental and one by retinal coor patterns or between left and right diagonal ones. No dinates. Table 1 gives the results in terms of gravita other significant or meaningful main effects or inter tional coordinates. The two analyses are logically actions emerged from either the retinal or environ identical for the main effects of head position and mental coordinates analyses. symmetry and for their interaction. In either anal Error rates for all conditions are given in Table 1. ysis, there was no main effect for head position. In Although planned comparisons failed to yield any both, the main effect for symmetry was highly sig significant differences among the means, the pat nificant [F(1,33) = 106.32, p < .001]. Across all three terns of the error data and latency data were sim head positions, the average latency to identify sym ilar: for each head position, errors were positively metrical patterns (mean = 1,280 msec) was substan correlated with reaction times (rs = .74, .57, and .54, tially shorter than that for asymmetrical patterns for head upright, tilted right, and tilted left, re (mean = 1,572 msec). spectively). The fact that latencies and errors are cor Comparison of the two analyses for orientation related suggests that differences in latencies were not demonstrated that the subjects' responses were con the result of a speed-accuracy tradeoff. sistent with a retinal rather than an environmental The failure to find an advantage for the vertical framework. When identification latencies were ana over the horizontal in symmetry detection differs lyzed with respect to retinal coordinates, there was from the results of previous studies. Between-pattern a significant main effect for orientation [F(3,99) = analyses on latencies and errors demonstrated that 5.04, p < .001], but no head position x orientation properties unique to any of the four symmetric pat interaction emerged. In contrast, the effect of orien terns had not biased the major analyses toward tation was not significant when the data were ana vertical-horizontal equivalence. A split-plot ANOVA lyzed in terms of environmental coordinates; rather, with head orientation as the between-subjects factor as would be expected if orientation sensitivity were and orientation and pattern as the within-subjects retinally determined, there was a significant head factors was performed on response times to the four position x orientation interaction [F(6,99) = 3.92, symmetric patterns oriented vertically and horizon p < .001]. tally with respect to retinal coordinates (see Table 2).

Table 1 Mean Reaction Times and Errors for Symmetry and Asymmetry as a Function of Orientation at Each of Three Head Positions Orientation Clockwise From Gravitational Vertical Odeg 45 deg 90 deg 135 deg Head Position Pattern Type RT Errors RT Errors RT Errors RT Errors .5 1318 3.6 1181 1.1 1302 3.3 Upright (0 deg) Symmetrical 1160 Asymmetrical 1631 3.3 1659 3.2 1644 3.5 1593 3.2 1.4 1424 Right (45 deg) Symmetrical 1502 5.2 1348 3.5 1377 1.9 Asymmetrical 1645 2.9 1715 2.9 1681 4.3 1757 5.0 2.7 1229 3.5 Left (45 deg) Symmetrical 1257 5.4 1090 1171 1.9 Asymmetrical 1391 4.3 1377 4.6 1426 4.7 1375 2.7

Note -N = 12 for each head position. 446 FISHERAND BORNSTEIN

Table 2 Mean Reaction Times and Errors for Vertical and Horizontal Symmetries at Each of the Four Stimulus Patterns Stimulus Pattern 1 Stimulus Pattern 2 Stimulus Pattern 3 Stimulus Pattern 4 Head Position Orientation RT Errors RT Errors RT Errors RT Errors

Upright (0 deg) Vertical 1112 .17 1223 .33 1154 .00 1215 .00 Horizontal 1114 .08 1308 .42 1077 .00 1226 .58 . .50 Right (45 deg) Vertical 1372 1354 .25 1267 .17 1398 .50 Horizontal 1318 .33 1440 .33 1223 .17 1529 1.08 Left (45 deg) Vertical 1141 .17 1193 .67 1150 .33 1199 .75 Horizontal 1048 .17 1118 .67 1090 .33 1105 1.50 Note-At each head position, latency and error data are given in terms of retinal coordinates. The numbers assigned to the four stimulus patterns correspond to the order ofstimulus presentation (from left to right) illustrated in Figure 1.

The main effects of head tilt and pattern and the erence. These findings argue against major predic orientation x pattern interaction were significant tions by the structural explanation of symmetry iden [F(2,33)= 4.45, p < .025; F(3,99)= 6.10, p < .001; tification and thus limit the generality of that view. and F(3,99)=3.15, p < .05, respectively]. A posteriori The fact that reaction times for horizontal symme tests (a = .05) indicated that pattern type produced tries can approach those for vertical symmetries pro significant differences in reaction time when stimuli vides evidence against the prediction that only ver were oriented horizontally but not when they were tically symmetrical projections to the visual system oriented vertically: response times to horizontal pat are special. Moreover, the fact that horizontals are tern 3 were significantly faster than those to hori identified faster than obliques for all head orienta zontal patterns 2 and 4. All other differences among tions argues against the prediction that nonvertical patterns were unreliable. At each pattern, differences symmetriesare necessarilymentally aligned in a rota in reaction time to vertical and horizontal symmetries tionally ordered fashion to the anatomical vertical. remained insignificant. Palmer and Hemenway (1978) and Royer (1981) Errors were subjected to a similar analysis and have recently proposed different models of how yielded significance for the main effects of head tilt humans process symmetry. The former is charac and pattern and for the orientation x pattern in terized by a two-stage process that includes an initial teraction [F(2,33)= 4.26, p < .025; F(3,99)= 15.16, analysis of probable axis of symmetry followed by an p < .001; and F(3,99)= 8.91, p < .001, respectively]. evaluation of mirror identity about this axis, whereas Although the trends in the means are similar both at the latter speaks of an integral code for symmetrical vertical and horizontal orientations, the differences organization. Common to both theories is the as in response to pattern type were, as with the latency sumption of a hierarchical structure for processing data, reliable only when stimuli were oriented hori different types of symmetry, a structure character zontally: horizontal pattern 4 was significantly more ized by a vertical over horizontal advantage. Both difficult than horizontal patterns 1 and 3 (a = .01). In models, therefore, predict a vertical advantage for contrast with the results of the analyses of latencies, symmetry identification of the type found in most a posteriori tests indicated that the advantage for studies. In the present study, the subjects identified vertical over horizontal symmetry was significant for symmetry about the vertical and horizontal equally pattern 4 [F(1,33)= 165.57, p < .001]. Perhaps the quickly. Though these effects appear quite robust impression of diagonality imposed by the alignment holding over both head tilt and pattern type-it is an of dots in pattern 4 biased analysis of symmetry uncommon result, which may nevertheless be ex toward the oblique axis; although this configuration plicable in terms of current theory and our pro produces similar effects in both the vertical and the cedures. Previous investigators have been concerned horizontal orientations, a vertical advantage (atten with the effect of subject sophistication on detection uated by practice; see below) may have manifested latencies for different symmetries. For example, itself in increased horizontal error rates for this Corballis and Roldan (1975) found no effect on the pattern. orientation function to detect symmetry when trials We have found that when no axis of orientation is were blocked in terms of type of symmetry. Simi explicit in symmetrical stimuli of moderate com larly, Palmer and Hemenway (1978) found that la plexityand when speeded judgments of identification tencies to vertical symmetry continued to exceed are required, identification of symmetry can be those to multiple symmetries when subjects were in equivalently fast for vertical and horizontal, that structed to look solely for vertical symmetry. Finally, vertical and horizontal show strong advantages over Royer (1981) found that when specific hypotheses of obliques, and that this general advantage is relative symmetry were tested, a vertical over horizontal ad to retinal, rather than environmental, frames of ref- vantage for symmetry detection remained (with one IDENTIFICATION OF SYMMETRY 447 qualification-no significant difference emerged be specialty of vertical may be environmentally based. tween response times to detect whether vertical or The finding that response times to symmetries of horizontal symmetry was present in a stimulus that different orientations adhere to retinal, rather than had all symmetries). In the present study, the sub to gravitational, coordinates is incompatible with jects had extensive practice with the four types of Rock and Leaman's (1963) view that response to symmetry tested (including paper-and-pencil delinea symmetries of different orientations is phenome tions of the potential axes) and 64 practice trials with nally, rather than retinally, determined. Empirically, feedback for test stimuli. A review of the subjects' our study differed from theirs as follows: they looked performance on these tasks suggests a moderate prac at judgments of similarity (to a doubly symmetri tice effect: (1) Analysis of correct identification of cal form), whereas we tested symmetry detection; vertical and horizontal symmetry prior to the experi their subjects were instructed as to the top of the menter's delineation of the axis of symmetry revealed form, but ours were not; and their stimuli were that only 4 of our 36 subjects spontaneously identi holistic, whereas our were dot patterns. Any or all of fied the axis of symmetry of nonvertical stimuli. these factors could have contributed to the difference Thus, naive observers did not respond equally to ver in results. Our data do, however, suggest that a ver tical and horizontal symmetries in our patterns. The tical advantage may be phenomenally based, since subjects' performance on this introductory task the only condition to create a significant vertical could, however, be a function of a vertical bias, in effect was the practice trials for subjects with head herent within the lexical code, for the term "sym upright-the only condition in which retinal and metrical." (2) An analysis of responses to the 64 phenomenal frameworks were congruent. practice trials yielded the following means for la The present findings are inconsistent with the view tencies to vertical and horizontal symmetry: 1,358 that different types of symmetry must be processed in and 1,441; 1,519 and 1,579; 1,315 and 1,242 msec for relation to the symmetrical organization of the ner head upright, tilted right, and tilted left, respectively, vous system. Failure to support the structural model with only the upright condition yielding a statistically for symmetry processing parallels recent research in significant vertical advantage [t(11) = 2.6774, the coding of figural orientation. Mach's (1897) p < .02]. model predicts that a bilaterally symmetrical organ Why did we get an attenuation effect from prac ism should have more difficulty processing orienta tice in an upright condition, whereas others did not? tions along the horizontal dimension than along the Comparison with Royer's (1981)procedures are most vertical dimension. In recent years, however, equiva relevant here, since Palmer and Hemenway's (1978) lence in performance between left-right and up Experiment 2 was not designed to contrast vertical down problems has been demonstrated. For ex with horizontal and, as discussed previously, the ample, although young children have traditionally nature of Corballis and Roldan's (1975) stimuli been observed to confuse left-right stimuli presented severely limits generalization. In this regard, the dis simultaneously side by side (e.g., Rudel & Teuber, crepancy between Royer's findings and our own may 1963), their memory for left and right is often just as be tied to the number of alternative displays avail good as their memory for up and down when choice able. Over the course of testing, Royer's sophisti stimuli are individually presented (Fisher, 1979, cated subjects were exposed to nine different types of 1980; Fisher & Braine, 1981). Similarly, recent work symmetry and four different pattern types, whereas suggests that the inferior status of left-right, when our subjects could anticipate four types of symmetry compared with up-down, coding in adults may be and one pattern type. The limited range of stimuli in limited to the verbal encoding stage rather than to the our study may have increased the effectiveness of any perceptual encoding stage (Maki, Grandy, & Hauge, hypothesis adopted by the subject. Royer found (in 1979; Sholl & Egeth, 1981). Although the structural his Experiment 3) that when specific hypotheses of model is attractive in its simplicity, it has gained little symmetry are tested, the earliest stages of the hierar empirical support in both symmetry perception and chy, that is, vertical, show the least gain. In our orientation processing, which seriously calls into study, practice and stimulus certainty, together, may question Mach's (1897)explanatory position. have encouraged hypotheses biased towards nonver tical as well as vertical symmetries, thus lessening the REFERENCES vertical advantage and equating sensitivity between ARNHEIM, R. Art and visual perception. Berkeley: University of the principle orthogonals. 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