Perception of Symmetry in Patterns Constructed
from Two Kinds of Elements
著者
journal or
publication title
volume
page range
year
URL
MASAME KEN
Tohoku psychologica folia
44
59-65
1986-03-31
http://hdl.handle.net/10097/62634
Tohoku Psychologica Folia
1985, 44 (1-4), 59-65
PERCEPTION OF SYMMETRY IN PATTERNS
CONSTRUCTED FROM
TWO KINDS OF ELEMENTS
By
KEN MASAME (J{Jt fm)
(Tohoku University)
The effect of elements on the perception of symmetry was examined by using patterns which
were constructed from two kinds of elements. SUbjects were 12 undergraduates and reaction
times were measured. Two kinds of elements were similar and the experimental situation was
expected to allow subjects to find "low resolution symmetry" easily. Nevertheless, it was more
difficult to find "low resolution symmetry" than to find normal "full symmetry". The results
showed the wholistic configural structure of pattern is symmetrical and the corresponding
elements are mutually mirror-imaged are necessary for the instantaneous perception of symmetry.
Key words:
pattern.
perception of symmetry, low resolution symmetry, pattern structure, dot
It is well known that symmetry, one of characters of forms, can be noticed very
easily. Many studies have been carried out about this matter (e.g. Barlow & Reeves,
1979; Masame, 1983, 1984; Royer, 1981). Usually, dot patterns have been used in
these studies. Main advantage of using dot patterns is that the characteristics of
pattern organization are emphasized rather than the characteristics of pattern components (Uttal, 1975).
What is investigated in the studies about the perception of symmetry is such
symmetry as the wholistic structure of patterns. Obviously, wholistic structure
emerges from the array of elements. Then, we can raise a question about this matter,
namely, whether we perceive emergent symmetry independently of the features of its
elements, or not. Royer (1981) studied the perception of symmetry with dot patterns
and diagonal line patterns, and concluded that the actual time spent processing
symmetry information is largely independent of the configurational elements.
In the case of patterns constructed from some kinds of elements, Palmer (1982).
proposed the new concept of symmetry which was called "low resolution symmetry".
It is such symmetry as follows. Its overall, configural structure is symmetrical in that
for each element on one side there is a corresponding element on the other side related
1.
Department of Psychology, Faculty of Arts & Letters, Tohoku University, Kawauchi, Sendai 980,
Japan.
60
K. Masame
by reflection in one line, but the shapes of the corresponding elements are not identical
(Palmer, 1982, p-122).
With spatial filter, Julesz & Chang (1979) demonstrated the low-band channels
have considerably stronger perceptual weight than the high-band channels in the
perception of symmetry. According to this and Royer's findings, it seems to be able
to perceive symmetry in spite of the difference of features of elements at least under
certain circumstances.
In this study, the patterns constructed from two kinds of elements were used and
the possibility of the perception of "low resolution symmetry" was explored. The
degrees of the dissimilarity between the features of elements seem to hava strong effect
for finding of "low resolution symmetry". Then, two kinds of circles which had the
same average density as a whole were used as pattern elements so that there was little
difference of easiness to perceive each element. These matters were expected to allow
the finding of "low resolution symmetry" to be more easy.
METHOD
Subjects: Subjects were 12 Tohoku University undergraduates, all possessmg
normal or corrected-to-normal vision.
Apparatus: Two projector-type tachistoscopes presented the stimuli and the
fixation point on the translucent screen with circle window (9 cm in diameter). The
subjects observed the screen at a distance of 57.3 cm from the chis rest. The electric
stimulator was used to control the time course of the fixation point and the stimuli.
Two micro-switches were placed side by side and used as the reaction keys for the left
and right hands.
Stimuli: There were four pattern-conditions. At each pattern-condition, both
symmetrical and random (asymmetrical) patterns were constructed from 72 dots in
imaginary 12 X 12 matrix. As shown in Fig. 1, there were two kinds of pattern
elements, namely center-meshy and center-blank dots. Fig. 1 shows sample patterns
of each pattern-condition.
Condition I: Patterns in this condition were made by one kind of dots. Half
of all were constructed from center-meshy dots, and others from center-blank dots.
Condition II: At each pattern in this condition, one half-pattern was made by
only center-meshy dots and another half-pattern was made by only center-blank dots.
Condition III: Each half-pattern was constructed from two kinds of dots. In
symmetrical patterns of this condition, the dots which showed symmetrical correspondence mutually were the same kind of dots.
Condition IV: Each half-pattern was made by two kinds of dots. In symmetrical patterns, the dots which exhibited symmetrical relation were the different kinds of
dots mutually.
For each pattern-condition, 10 symmetrical and 10 random patterns were prepar-
Condition I
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62
K. Masame
ed. The size of patterns was 5.3 X 5.0 visual angle. The patterns appeared white
against a blackg-round. The luminance of patterns was about 90 nit on average.
Procedure: Excepting the difference among the pattern-conditions stated above,
the procedure was the same in each condition.
One trial was constructed as follows. After a varbal "ready" signal was given by
the experimenter, the fixation point was presented for 750 msec. The fixation point
was followed immediately by the stimuli which were presented for 2 sec.
The task given to the subjects was to judge whether each presented pattern was
symmetrical or random, independently of the kinds of dots. The subject was told to
rest the index finger of each hand on a micro-switch and push one switch if the
presented pattern was symmetrical, the other if it was random. Rection times were
measured to the millisecond by an electronic timer which was activated simultaneously
with the stimulus presentation and was stopped by the subject's pressing of the
micro-switch. Half of the subjects responded to symmetry with the preferred hand,
half with the non-preferred one. The subject was instructed to respond as rapidly as
possible, but to try to avoid errors.
One session was made up of 20 trials and four sessions were given for each subject.
Pattern-condition was held constant during one session. Before each session, the
subject was given the information about the pattern-condition which would be used in
the session.
0
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RESULTS
Reaction times: Table 1 shows the mean of 12 subjects' median reaction times
(RTs). 3-way analysis of variance of RTs (pattern-condition x judgment X subject)
was performed. It showed only the effect of pattern-condition was significant
(F(3, 33) = 11.918, p < .01) and the effect of judgment and the interaction of them were
not significant.
For futher analysis, sign-rank test was performed on each pair of patternconditions. Significant differences were shown at the pairs of I-II, I-IV, II-III, and
III-IV (each Roman numerals indicated the numbers of pattern-conditions; T+ =0,
p<.Ol; T+ =0, p<.Ol; T- =9, p<.05; T+ =2, p<.Ol, respectively). The
Table 1.
Mean of median reaction times CRT) and error rate CER) on each
pattern-condition.
~
Judgment
I
II
III
IV
Symmetry
RT
ER
513.3
7.5
622.6
10.0
546.0
3.3
595.2
5.0
(%)
Random
RT
ER
534.5
6.7
626.1
19.2
570.2
13.3
604.7
11.7
(%)
(msec)
(msec)
Effect of Elements on the Perception of Symmetry
63
difference between II and IV was not significant (T - = 21, P >.1). The difference
between I and III was not reached significant, but it showed the trend toward
significance (T+ = 16, .05<p<.I).
To varify whether a perceptual effect was identical for both two kinds of dots or
not, U-test of RTs for each suject was carried out for the results of Condition 1. For
all subjects, the difference of RTs between symmetrical patterns constructed from
center-meshy dots and ones from center-blank dots was not significant. From this
matter, it can be concluded that a perceptual effect of both kinds of dots was almost
identical.
Errors: Table 1 also shows the mean error rate at each pattern-condition. 3-way
ANOV A showed that the effect of pattern-condition and the effect of judgment were
both significant (F(3, 33)= 3.346, p <.05; F(I, 11)= 11.406, p <.01, respectively).
Table 1 shows the trend that more errors occured for random patterns than for symmetrical patterns at each pattern-condition.
DISCUSSION
In respect to the differences of easiness for the judgment of symmetry among
pattern-conditions, introspective reports almost coincided with all subjects. Namely,
the judgments in Condition I and III were easier than ones in Condition II and IV.
As the results of sign-rank test showed, these introspective reports were consistent with
the median RT data for each subject.
For symmetrical patterns in Condition I and III, each element on one side and its
symmetrically corresponding element on the other side were identical. Against this,
they were mutually different for symmetrical patterns in Condition II and IV. Two
kinds of elements used in this experiment were similar, and a perceptual effect was
(a )
Fig. 2. Two vertically symmetrical patterns constructed from triangular elements. The
mutually corresponding elements on two side are (a) identical, and (b) mirror-imaged. It
is more difficult to notice vertical symmetry in pattern (a) than in pattern (b). Pattern (a)
looks oblique symmetry (right side up) rather than vertical symmetry.
64
K. Masame
almost equal for both kinds of elements. In spite of these matters, there was
significant difference between Condition 1.111 and Condition II.IV. Therefore, it
can be concluded that pattern elements have relatively strong influence on the judgment of symmetry.
Maybe this seems to be slightly inconsistent with the findings of Royer (1981).
Royer used the patterns which constructed from one kind of elements. From these, it
seems to be important for the judgment of symmetry that each element on one side and
its symmetrically corresponding element on the other side are identical. However, as
shown in Fig. 2, strictly speaking it is necessary for finding symmetry easily that these
mutually correspoding elements are rather mutually mirror-imaged than identical.
The results of Royer (1981) seem to show that the detection of symmetry is largely
independent of elements when the above condition about the correspondence of
elements between two sides is fulfilled.
In this experiment, although the significant differences were shown among
pattern-conditions, these differences seemed to be relatively small. The largest
difference was shown between Condition I and II, and it was about no msec. These
relatively small differences were caused by the relatively high similarity between two
kinds of elements and the long pattern presentation of 2 sec which allowed subjects to
use various strategies for the judgment of symmetry. According to the introspective
reports, almost all subjects judged whether the presented pattern was symmetrical or
random through the outline shape of top of the pattern. In this experiment, information like this seems to be little influenced by the difference of element shapes. Under
the tachistoscopic presentation, an available information and strategy will be
restricted, so that to find symmetrical structure in the patterns of Condition II and IV
is supposed to be more· difficult in such circumstance. About this matter, futher
examination is expected to carry out in future.
This experimental condition seems to allow the subjects to find "low resolution
symmetry" very easily. Nevertheless, there were significant differences between RTs
for normal "full symmetry" and ones for "low resolution symmetry". Although the
further examination under the tachistoscopic presentation will be necessary for the
sufficient conclusion, it can be concluded as follows in the meantime. We can find
symmetry independently of the shapes of elements (such as low resolution symmetry)
through the various mental manipulations. However, it is necessary for the percetion
of symmetry that each element on one side and its symmetrically corresponding
element on the other side have mutually mirror-imaged shapes. In other words,
symmetry can be perceived instantaneously only when the pattern is strict symmetry
on the whole.
REFERENCES
Barlow, H.B. & Reeves, B.C. 1979 The versatility and absolute efficiency of detecting mirror symmetry
in random dot display. Vision Research, 19, 783-793.
Effect of Elements on the Perception of Symmetry
Julesz, B. & Chang, J-J. 1979
Symmetry perception and spatial-frequency channels.
65
Perception, 8, 711-
718.
Masame, K. 1983
Detection of symmetry in complex patterns: Does symmetrical projection to the visual
system necessary for the perception of symmetry? Tohoku Psychologica Folia, 42, 27-33.
Masame, K. 1984 Detection of symmetry in relatively simple patterns. Tohoku Psychologica Folia, 43,
42-48.
Palmer, S.E. 1982 Symmetry, transformation, and the structure of perceptual system. In J. Beck (ed.),
Representation and organization in perception. Hillsdale, NJ: Erlbaum, pp.95-144.
Royer, F.L. 1981 Detection of symmetry. Journal of Experimental Psychology: Human Perception
and Performance, 7, 1186-1210.
Uttal, W.R. 1975 An autocorrelation theory of form detection. Hillsdale, NJ: Erlbaum.
(Received November 15, 1985)