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The detection of structure in visual displays
Acta Psychologica 0 North-Holland
40 (1976), 115-125 Publishing Company
THE DETECTION Christopher
IN VISUAL
DISPLAYS
D. FRITH
Inst. of Psychiatry,
Received
OF STRUCTURE
London
University, Denmark
Hill, London
SE.5, England
May 1975
The structural complexity of visual displays was investigated by measuring the time observers took to pick out the structured quadrant in a display with three random quadrants. The structured quadrant was composed of a basic subunit which was repeated with the various transformations (reflection, rotation and counterchange) used in the production of symmetry. When the subunit formed l/4 of the structured display reflection was detected most rapidly, with plain repetition most slowly and rotation intermediate. The addition of counterchange made reflection as difficult to detect as rotation. It is suggested that observers detect structure by searching for corresponding small details. Rotated and reflected details are easily recognized as corresponding, but counterchanged details are not. The type of symmetry rule determines the distance apart of corresponding details, those that are close together being discovered more quickly. Mirror reflection, in particular, has the property of generating displays in which many of the corresponding details are very close together. Thus stimuli which might be thought identical in information content can be markedly different in subjective complexity.
This study grew out of a dissatisfaction with the commonly used measures of complexity applied to visual displays. Complexity has usually been identified with information content (e.g. Vitz 1966), i.e. the number of independently determined elements in the display. There are two disadvantages to this definition. The first, which is a minor matter of technique, is that in most of the methods used for constructing the visual displays information content is confounded with amount of contour (Frith and Nias 1974). The second, which is a major disadvantage, is that this definition of complexity misses out structural complexity. Definitions of complexity based on information theory essentially describe different kinds of randomness. For example stimuli may be constructed with many or few independent elements. However since the elements are independent each of these stimuli is random to a
116
C. D. Frith/Detection
of structure in visual displays
specifiable degree. By this definition the most complex stimulus is one that is most random. Such a stimulus is complex in the sense that to completely specify the stimulus it would be necessary to specify every one of its elements. Such a stimulus might be said to be structureless. On the other hand, one can imagine a stimulus which can be specified completely by specifying a small proportion of its elements and a rule by which the rest might be generated with certainty. Such a stimulus would have a large amount of redundancy and low information content, yet it could be subjectively very complex. Applying different rules would not change the redundancy or the information content in the usual sense, but might well change the subjective complexity. Information theory has been widely used to describe different kinds of randomness, but not different kinds of redundancy. It might be possible to specify the structural rule in information theory terms as Newell and Simon (1963) have for problem solving and Leeuwenberg (1971) has for certain visual patterns. However this goes beyond the purpose of the present study which was to discover whether different structural rules are associated with different degrees of subjective complexity. In order to investigate structural complexity in visual displays we require a definition of structure. Garner (1962) has defined structure as ‘the totality of relations between events’. Essentially a stimulus that has structure is one that is not random. Hence if in a random stimulus the elements are determined independently of one another, in a structured stimulus the elements must be to some extent determined by one another. In other words, there is some rule by which all the elements of a structured stimulus can be generated from a subset of its elements. There are various parameters that might relate to the complexity of such a stimulus: (1) the number of independent elements in the original subunit (information content), (2) the number of times the rule was applied (repeats), (3) the type of rule, (4) the rigidity with which the rule was applied (partial repetition). The subjective complexity of such a stimulus could be defined as the difficulty of recognising it as structured rather than random, without necessarily being able to specify the rule or the basic subunit to which it applied. Using partial repetition Julesz (1962) and Pollack (1973) have shown that the number of independent elements in the original subunit (which Julesz calls depth) is an important determinant of complexity in this sense. Julesz (1971) has also studied the effects of the type of rule
C. D. FrithlDetection
117
of structure in visual displays
applied and has shown that mirror symmetry about an axis is more easily perceived (and hence less complex) than repetition about an axis. The result is supported by Deregowski (197 1) who showed that patterns with mirror symmetry were easier to remember than patterns with repetition about an axis. The present study attempts to extend these findings to other kinds of symmetry, i.e. rotation and counterchange.
Method Subjects The Ss were five men and five women, years.’
all student
volunteers,
aged between
20 and
30
Stimuli Each stimulus consisted of white. This matrix was divided having structure (symmetry). content/contour, (2) number of
Information
a matrix of 80 X 80 squares each of which could be black or into four quadrants, three having no structure and the fourth The stimuli varied along three dimensions: (1) information repeats/size of subunit, (3) symmetry.
content/contour
Both the random and the structured quadrants had two possible levels of information content/contour. High information/high contour was achieved by setting the probability of each square in the random. quadrants and in the basic subunit of the structured quadrant being black or white to 0.5. Thus the colour of each square was independent of the others. Low information/low contour was achieved by having the probability of each square being black or white depending on the colour of the surrounding squares, so that black squares tended to be next to black squares and white next to white squares (p = 0.9). Thus the number of independent elements of which the stimulus was composed was reduced. The method for controlling information content/contour has been described in greater detail elsewhere (Frith and Nias 1974; Frith 1974).
Number
of repeats/size
of subunit
The structured quadrant was made by generating a random subunit as described above and then repeating it. There were two levels of repetition. The 40 X 40 matrix either consisted of a 20 X 20 subunit repeated four times or a 10 X 10 subunit repeated 16 times.
’ 1 would supported
like to thank Axe1 Schild and Dorothea Huber for testing the subjects. in part by a grant from the Bethlem-Maudsley Research Fund.
This study
was
118
C. D. FrithlDetection
of structure
in visual displays
b
a 16 repeats
16 repeats high contour 180’ rotation
hi gh contour PIain repetition
e
f
16 repeats h igh contour r epetition + counterchange
Fig. 1. Examples
16 repeats high contour 180’ rot. + counterchange
of the stimuli.
C. D. FrithlDetection
of structure in visual displays
d 16 repeats low contour mirror reflection
C
16 repeats low contour 9o” rotation
g
4 repeats high contour 90 rot. + counterchange
h 4 repeats high contour mirror refl. + counterchange
Fig. 1. (cont’d).
120
C. D. EZith/Detection of structure in visual displays
Symmetry As the subunit was repeated various simple transformations were performed upon it. The transformations used were those giving the basic types of symmetry used in decorative designs (Christie 1910). As in decorative design the transformations were applied in such a way as to achieve ‘double infinite rapport’ (Weyl 1952), i.e. a transformation rule was applied consistcntly throughout the plane surface. The transformations were: plain repetition across a horizontal and vertical axis, mirror reflection across a horizontal and vertical axis, 180” rotation about the intersection of the horizontal and vertical axis, 90” rotation about this axis. In addition, counterchange (reversing the colour of the black and white squares) across a horizontal and vertical axis was superimposed upon the four previously described transformations giving a total of 8 different kinds of symmetry. The stimuli were generated by a computer program (Frith 1974) which drew them on microfilm in a format suitable for 2 X 2 slides. Examples of the stimuli are shown in fig. 1. Although the symmetrical stimuli were generated using only the 8 transformations described above the application of these rules often results in more than one type of symmetry being present in the same stimulus. Stimuli generated by 180” rotations have plain repetitions along the horizontal or vertical axis. Stimuli generated by 90” rotations have 180” rotations along the diagonals, as do stimuli generated with two mirror reflections. When counterchange is added this only affects rows and columns and the transformation along the diagonals remains unaltered (as in a checkerboard). Thus plain repetition + counterchange has plain repetitions along the diagonals, 180” rotation + counterchange has 180” rotations along the diagonals, and 90” rotation + counterchange and mirror reflection + counterchange have 180” rotations along the diagonals.
Procedure The stimuli were back projected onto a ground glass screen giving a picture of 20 cm square. This was viewed freely by the subjects at a distance of roughly 50 cm. The S had as much time as he wished to decide which was the structured quadrant. He indicated his choice by pressing one of four buttons placed at the corners of a square corresponding to the four quadrants of the stimulus. Each button press initiated a 1 set delay followed by presentation of the next stimulus. In addition to the 32 slides described above there were two slides (high and low information content) in which all four quadrants were random. There were four practice slides with one quadrant structured for which the correct answer was explained to the S if he did not find it for himself. The main series of 34 slides was presented in the same order for all Ss. This order was balanced for information content, repetitions and symmetry, but higher order interactions between these variables would be confounded with order effects, if any. Ss were given the following instructions: ‘You will see a number of black and white abstract designs. Each display is divided into four quadrants. As you see in the following examples one of these quadrants will be structured symmetrically while the other three are random. I want you to decide as quickly as possible which of the four quadrants has symmetrical structure, and then to press the corresponding button on the response panel. Try to make a decision in every case as well as you can. If you really cannot decide then guess. You must press a button in order for the next picture to be displayed.’
C. D. FrithfDetection
of structure in visual displays
121
Results The reaction times (measured by a LINC-8 computer) showed a marked positive skew and there was also a strong relationship between means and standard deviations across the different stimuli. Therefore the analysis of variance was carried out on a logarithmic transformation of the RTs to the 32 structured stimuli combining correct and incorrect responses. The analysis was a 2 X 2 X 2 X 4 within subject design (information, repetition, counterchange and symmetry respectively). There was a small main effect of information/contour (Univariate F(1,9) = 4.96, p GO.05) such that patterns made high information subunits took longer to detect. There was a significant interaction between repetition and symmetry (Multivariate F(3,7) = 7.46, p GO.01). With 16 repeats the structured quadrant was found quickly whatever
1.f
1.6
1.4
1.::
p1.c
4
2
repeats +
counterchange
2
.4 +
g0.e
\
.d *
\
s
\
2
. .
.
.
..-
.
\
.‘. .
.
\
0.6
. .
\
..\ \. \ . . 16 repeats \ \
\
0.4
Rep.
I80’
Refl.
9o” symmetry
Fig. 2. Effect
of symmetry
and repetition
I+ repeats
on reaction
time.
122
C. D. FrithlDetection
of structure
in visuql displays
type of symmetry was involved. With four repeats mirror reflection was found quickly, simple repetition was found slowly, if at all, and 180” and 90” rotations were intermediate. There was also an interaction between counterchange and symmetry (Multivariate F(3,7) = 7.42, p 90.01) such that counterchange made structure slightly more difficult to find for all types of symmetry except mirror reflections which was made very much more difficult to find. All these effects are illustrated in fig. 2. The number of errors made to each stimulus closely related to the reaction times, many errors going with long reaction times. For the two stimuli associated with the longest reaction times (four simple repetitions, high information content, with and without counterchange) there were so many errors (8 and 6) that performance did not differ from chance. The reaction times associated with these stimuli were of the same order as those associated with the stimuli in which all four quadrants were random.
Discussion This study has confirmed the finding that structure produced by mirror reflection is more easily perceived than that produced by simple repetition. It has also revealed that structure produced by rotation is of an intermediate difficulty level. Imposing counterchange (reversing black and white) makes all types of structure slightly more difficult to see and destroys the advantage of mirror reflections over rotations. Why should the addition of counterchange have a more drastic effect when associated with mirror reflection as opposed to rotation? A possible explanation is provided by consideration of the secondary types of symmetry present in the stimuli. When counterchange is added to some other symmetry transformation the stimulus still contains repeated subunits that do not involve counterchange. Plain repetition + counterchange has plain repetitions along the diagonals, and 180” rotation + counterchange, 90” rotation + counterchange and mirror reflection + counterchange all have 180” rotations along the diagonals. Thus, even if an observer cannot recognise that a counterchanged subunit is the same as the original subunit, in every case there are other kinds of repetitions available for him to detect, although these occur less frequently than in the stimuli without counterchange. In the case of plain repetition + counterchange and 180” rotation + counterchange, the secondary symmetry is the same as for repetition and 180” rotation without counterchange and so one would expect only a slight increase in detection time. For 90” rotation + counterchange the secondary symmetry is 180” rotation but since 90” and 180” rotations are detected with equal ease it is reasonable that the addition of counterchange to 90” rotations should make only a small difference to the time to detect structure.
C. D. FrithfDetection
of structure in visual displays
123
However the addition of counterchange to mirror reflection results in a secondary symmetry of 180” rotation which is more difficult to detect than mirror reflection. The finding that mirror reflection + counterchange is no easier to detect than 180” rotations suggests therefore that observers pay attention only to the secondary symmetries when counterchange is present and find difficulty in recognising that a counterchanged unit is the same as the original subunit. Another transformation with which observers have similar difficulty involves changing the size of the original subunit. Julesz (1971) has shown that dilating the portion of the stimulus to one side of the axis of reflection hinders the detection of symmetry. The second main finding of this study was that mirror reflection was easier to detect than rotation which was in turn easier to detect than plain repetition. A plausible explanation is provided by the observers’ reports as to how they carried out the task. If the structured quadrant was not immediately apparent then the observer chose some outstanding detail (such as a white cross on a black ground) and searched for repetitions of this detail. A quadrant containing such repetitions was chosen as the structured one. The important point about this strategy is that only a small detail of the stimulus is used and not the repeating subunit as a whole. It seems reasonable to suppose that the ease of finding repeated details will depend on their distance apart. With plain repetition all the repeating details are exactly one subunit’s width apart. However with mirror reflection details close to the axes of symmetry are very much closer to their reflected counterparts. Similarly with rotational symmetry details close to the axis of rotation will be very close to their rotated counterparts. Since the area round the axis of symmetry (the intersection of horizontal and vertical axes) is smaller than the area round the axes of reflection (the horizontal and vertical axes), there will be more corresponding details that are close together for mirror reflection than for rotation and there will be more corresponding details that are close together for rotation than for plain repetition. Thus the ease of finding these three kinds of structure can be explained in terms of the distance apart of corresponding details. This hypothesis would also account for the superiority of 16 over four repetitions since the corresponding details in the 16 repetition structures are closer together because the basic subunit is smaller. The failure for there to be an effect of symmetry with 16 repetitions might indicate that for all types of symmetry the corresponding details
124
C. D. FrithlDetection
of structure in v&al displays
were sufficiently close together to be perceived immediately. A strategy of detecting corresponding details might also account for Julesz’s (1971) finding that mirror symmetry was only detected when the 0 fixated the axis of symmetry, since this is where the corresponding details are close together. It would be predicted that pulling apart the two symmetrical halves should make mirror symmetry more difficult to detect even if fixation is still on the axis of symmetry. Some support for this prediction is provided by Corballis and Roldan (1974) who found a superiority for mirror reflection over repetition only when the two halves of the pattern were close together and not when they were apart. However the patterns they used were extremely simple (e.g. subunit matrix 2 X 3). A mechanism for detecting corresponding outstanding details would also explain why structure was more difficult to detect with high information/high contour subunits. Frith and Nias (1974) have suggested that it is the high contour rather than the high information that makes such stimuli complex because the 0 tends to perceive them in terms of ‘runs’ (discrete areas of black and white, Restle 1966) and there will be more such runs in a high contour stimulus. A detail (or feature) also tends to be a discrete black or white area and hence there will also be more details in a high contour/high information stimulus. A large number of details will clearly make the search for correspondence more difficult, since only a limited number of types of detail can occur. It may be difficult to pick one detail that stands out among the rest. There may be corresponding details in two areas by chance rather than as a result of structure. Finally there may be a subjective metric in terms of details or runs per unit distance which renders the corresponding details effectively further apart in a high information/high contour structure. The original aim of this study was to find some objective correlates of structural complexity (which is subjective). From the results it is clear that complexity is affected by the type of symmetry rule used to generate a stimulus from a basic subunit, by the size of the basic subunit and by the information content of the basic subunit. These effects can all be explained if it is hypothesised that observers detect structure in visual displays by searching for corresponding small details in different parts of the display. Details that are rotated or reversed will easily be recognised as corresponding, but details that are counterchanged (black and white reversed) will not. The distance apart of these
C. D. FrithlDetection
of structure in visual displays
125
corresponding details will be determined by the type of symmetry rule applied and by the size of the basic subunit, which in this study was confounded with the number of repetitions of the subunit. The density of the details will be determined by the information content of the basic subunit. It seems likely that the difficulty of finding corresponding details will depend on their distance apart and on the overall detail density. It is clear from these considerations that stimuli can differ markedly in subjective complexity without differing in information content in the usually accepted sense.
References Christie, A. H., 1910. Traditional methods of pattern designing. Oxford: Clarendon Press. (Reprinted by Dover, 1969). Corballis, M. C., and C. E. Roldan, 1974. On the perception of symmetry and repeated patterns. Perception and Psychophysics 16, 136-142. Deregowski, .I. B., 1971. Symmetry, Gestalt and information theory. Quarterly Journal of Experimental Psychology, 1971, 23, 381-385. Frith, C. D., (1974. A program for generating abstract designs varying in ‘information’ and symmetry. Technical report CDF/AZ, Psychology Department, Institute of Psychiatry. Frith, C. D., and D. K. B. Nias, 1974. What determines aesthetic preferences? Journal of General Psychology 91, 163-173. Gamer, W. R., 1962. Uncertainty and structure as psychological concepts. New York: Wiley. Julesz, B., 1962. Visual pattern discrimination. Institute of Radio Engineers Transactions of Information Theory IT-8, 84-92. Julesz, B., 1971 Foundations of cyclopean perception. Chicago: Univ. of Chicago Press. Leeuwenberg, E. L. J., 1971. A perceptual coding language for visual and auditory patterns. American Journal of Psychology 84, 307-340. Newell, D. A., and H. A. Simon, 1963. Computers in psychology. In: R. D. Lute, R. R. Bush and E. Galanter (eds.), Handbook of mathematical psychology, Vol. 1. New York: Wiley. Pollack, I., 1973. Depth of visual information processing. Acta Psychologica 37, 375-392. Restle, F., 1966. Run structure and probability learning: Disproof of Restle’s model. Journal of Experimental Psychology 72, 382-289. Vitz, P. C., 1966. Preference for different amounts of visual complexity. Behavioural Science 11,105~114. Weyl, H., 1952. Symmetry. Princeton: Princeton Univ. Press.
40 (1976), 115-125 Publishing Company
THE DETECTION Christopher
IN VISUAL
DISPLAYS
D. FRITH
Inst. of Psychiatry,
Received
OF STRUCTURE
London
University, Denmark
Hill, London
SE.5, England
May 1975
The structural complexity of visual displays was investigated by measuring the time observers took to pick out the structured quadrant in a display with three random quadrants. The structured quadrant was composed of a basic subunit which was repeated with the various transformations (reflection, rotation and counterchange) used in the production of symmetry. When the subunit formed l/4 of the structured display reflection was detected most rapidly, with plain repetition most slowly and rotation intermediate. The addition of counterchange made reflection as difficult to detect as rotation. It is suggested that observers detect structure by searching for corresponding small details. Rotated and reflected details are easily recognized as corresponding, but counterchanged details are not. The type of symmetry rule determines the distance apart of corresponding details, those that are close together being discovered more quickly. Mirror reflection, in particular, has the property of generating displays in which many of the corresponding details are very close together. Thus stimuli which might be thought identical in information content can be markedly different in subjective complexity.
This study grew out of a dissatisfaction with the commonly used measures of complexity applied to visual displays. Complexity has usually been identified with information content (e.g. Vitz 1966), i.e. the number of independently determined elements in the display. There are two disadvantages to this definition. The first, which is a minor matter of technique, is that in most of the methods used for constructing the visual displays information content is confounded with amount of contour (Frith and Nias 1974). The second, which is a major disadvantage, is that this definition of complexity misses out structural complexity. Definitions of complexity based on information theory essentially describe different kinds of randomness. For example stimuli may be constructed with many or few independent elements. However since the elements are independent each of these stimuli is random to a
116
C. D. Frith/Detection
of structure in visual displays
specifiable degree. By this definition the most complex stimulus is one that is most random. Such a stimulus is complex in the sense that to completely specify the stimulus it would be necessary to specify every one of its elements. Such a stimulus might be said to be structureless. On the other hand, one can imagine a stimulus which can be specified completely by specifying a small proportion of its elements and a rule by which the rest might be generated with certainty. Such a stimulus would have a large amount of redundancy and low information content, yet it could be subjectively very complex. Applying different rules would not change the redundancy or the information content in the usual sense, but might well change the subjective complexity. Information theory has been widely used to describe different kinds of randomness, but not different kinds of redundancy. It might be possible to specify the structural rule in information theory terms as Newell and Simon (1963) have for problem solving and Leeuwenberg (1971) has for certain visual patterns. However this goes beyond the purpose of the present study which was to discover whether different structural rules are associated with different degrees of subjective complexity. In order to investigate structural complexity in visual displays we require a definition of structure. Garner (1962) has defined structure as ‘the totality of relations between events’. Essentially a stimulus that has structure is one that is not random. Hence if in a random stimulus the elements are determined independently of one another, in a structured stimulus the elements must be to some extent determined by one another. In other words, there is some rule by which all the elements of a structured stimulus can be generated from a subset of its elements. There are various parameters that might relate to the complexity of such a stimulus: (1) the number of independent elements in the original subunit (information content), (2) the number of times the rule was applied (repeats), (3) the type of rule, (4) the rigidity with which the rule was applied (partial repetition). The subjective complexity of such a stimulus could be defined as the difficulty of recognising it as structured rather than random, without necessarily being able to specify the rule or the basic subunit to which it applied. Using partial repetition Julesz (1962) and Pollack (1973) have shown that the number of independent elements in the original subunit (which Julesz calls depth) is an important determinant of complexity in this sense. Julesz (1971) has also studied the effects of the type of rule
C. D. FrithlDetection
117
of structure in visual displays
applied and has shown that mirror symmetry about an axis is more easily perceived (and hence less complex) than repetition about an axis. The result is supported by Deregowski (197 1) who showed that patterns with mirror symmetry were easier to remember than patterns with repetition about an axis. The present study attempts to extend these findings to other kinds of symmetry, i.e. rotation and counterchange.
Method Subjects The Ss were five men and five women, years.’
all student
volunteers,
aged between
20 and
30
Stimuli Each stimulus consisted of white. This matrix was divided having structure (symmetry). content/contour, (2) number of
Information
a matrix of 80 X 80 squares each of which could be black or into four quadrants, three having no structure and the fourth The stimuli varied along three dimensions: (1) information repeats/size of subunit, (3) symmetry.
content/contour
Both the random and the structured quadrants had two possible levels of information content/contour. High information/high contour was achieved by setting the probability of each square in the random. quadrants and in the basic subunit of the structured quadrant being black or white to 0.5. Thus the colour of each square was independent of the others. Low information/low contour was achieved by having the probability of each square being black or white depending on the colour of the surrounding squares, so that black squares tended to be next to black squares and white next to white squares (p = 0.9). Thus the number of independent elements of which the stimulus was composed was reduced. The method for controlling information content/contour has been described in greater detail elsewhere (Frith and Nias 1974; Frith 1974).
Number
of repeats/size
of subunit
The structured quadrant was made by generating a random subunit as described above and then repeating it. There were two levels of repetition. The 40 X 40 matrix either consisted of a 20 X 20 subunit repeated four times or a 10 X 10 subunit repeated 16 times.
’ 1 would supported
like to thank Axe1 Schild and Dorothea Huber for testing the subjects. in part by a grant from the Bethlem-Maudsley Research Fund.
This study
was
118
C. D. FrithlDetection
of structure
in visual displays
b
a 16 repeats
16 repeats high contour 180’ rotation
hi gh contour PIain repetition
e
f
16 repeats h igh contour r epetition + counterchange
Fig. 1. Examples
16 repeats high contour 180’ rot. + counterchange
of the stimuli.
C. D. FrithlDetection
of structure in visual displays
d 16 repeats low contour mirror reflection
C
16 repeats low contour 9o” rotation
g
4 repeats high contour 90 rot. + counterchange
h 4 repeats high contour mirror refl. + counterchange
Fig. 1. (cont’d).
120
C. D. EZith/Detection of structure in visual displays
Symmetry As the subunit was repeated various simple transformations were performed upon it. The transformations used were those giving the basic types of symmetry used in decorative designs (Christie 1910). As in decorative design the transformations were applied in such a way as to achieve ‘double infinite rapport’ (Weyl 1952), i.e. a transformation rule was applied consistcntly throughout the plane surface. The transformations were: plain repetition across a horizontal and vertical axis, mirror reflection across a horizontal and vertical axis, 180” rotation about the intersection of the horizontal and vertical axis, 90” rotation about this axis. In addition, counterchange (reversing the colour of the black and white squares) across a horizontal and vertical axis was superimposed upon the four previously described transformations giving a total of 8 different kinds of symmetry. The stimuli were generated by a computer program (Frith 1974) which drew them on microfilm in a format suitable for 2 X 2 slides. Examples of the stimuli are shown in fig. 1. Although the symmetrical stimuli were generated using only the 8 transformations described above the application of these rules often results in more than one type of symmetry being present in the same stimulus. Stimuli generated by 180” rotations have plain repetitions along the horizontal or vertical axis. Stimuli generated by 90” rotations have 180” rotations along the diagonals, as do stimuli generated with two mirror reflections. When counterchange is added this only affects rows and columns and the transformation along the diagonals remains unaltered (as in a checkerboard). Thus plain repetition + counterchange has plain repetitions along the diagonals, 180” rotation + counterchange has 180” rotations along the diagonals, and 90” rotation + counterchange and mirror reflection + counterchange have 180” rotations along the diagonals.
Procedure The stimuli were back projected onto a ground glass screen giving a picture of 20 cm square. This was viewed freely by the subjects at a distance of roughly 50 cm. The S had as much time as he wished to decide which was the structured quadrant. He indicated his choice by pressing one of four buttons placed at the corners of a square corresponding to the four quadrants of the stimulus. Each button press initiated a 1 set delay followed by presentation of the next stimulus. In addition to the 32 slides described above there were two slides (high and low information content) in which all four quadrants were random. There were four practice slides with one quadrant structured for which the correct answer was explained to the S if he did not find it for himself. The main series of 34 slides was presented in the same order for all Ss. This order was balanced for information content, repetitions and symmetry, but higher order interactions between these variables would be confounded with order effects, if any. Ss were given the following instructions: ‘You will see a number of black and white abstract designs. Each display is divided into four quadrants. As you see in the following examples one of these quadrants will be structured symmetrically while the other three are random. I want you to decide as quickly as possible which of the four quadrants has symmetrical structure, and then to press the corresponding button on the response panel. Try to make a decision in every case as well as you can. If you really cannot decide then guess. You must press a button in order for the next picture to be displayed.’
C. D. FrithfDetection
of structure in visual displays
121
Results The reaction times (measured by a LINC-8 computer) showed a marked positive skew and there was also a strong relationship between means and standard deviations across the different stimuli. Therefore the analysis of variance was carried out on a logarithmic transformation of the RTs to the 32 structured stimuli combining correct and incorrect responses. The analysis was a 2 X 2 X 2 X 4 within subject design (information, repetition, counterchange and symmetry respectively). There was a small main effect of information/contour (Univariate F(1,9) = 4.96, p GO.05) such that patterns made high information subunits took longer to detect. There was a significant interaction between repetition and symmetry (Multivariate F(3,7) = 7.46, p GO.01). With 16 repeats the structured quadrant was found quickly whatever
1.f
1.6
1.4
1.::
p1.c
4
2
repeats +
counterchange
2
.4 +
g0.e
\
.d *
\
s
\
2
. .
.
.
..-
.
\
.‘. .
.
\
0.6
. .
\
..\ \. \ . . 16 repeats \ \
\
0.4
Rep.
I80’
Refl.
9o” symmetry
Fig. 2. Effect
of symmetry
and repetition
I+ repeats
on reaction
time.
122
C. D. FrithlDetection
of structure
in visuql displays
type of symmetry was involved. With four repeats mirror reflection was found quickly, simple repetition was found slowly, if at all, and 180” and 90” rotations were intermediate. There was also an interaction between counterchange and symmetry (Multivariate F(3,7) = 7.42, p 90.01) such that counterchange made structure slightly more difficult to find for all types of symmetry except mirror reflections which was made very much more difficult to find. All these effects are illustrated in fig. 2. The number of errors made to each stimulus closely related to the reaction times, many errors going with long reaction times. For the two stimuli associated with the longest reaction times (four simple repetitions, high information content, with and without counterchange) there were so many errors (8 and 6) that performance did not differ from chance. The reaction times associated with these stimuli were of the same order as those associated with the stimuli in which all four quadrants were random.
Discussion This study has confirmed the finding that structure produced by mirror reflection is more easily perceived than that produced by simple repetition. It has also revealed that structure produced by rotation is of an intermediate difficulty level. Imposing counterchange (reversing black and white) makes all types of structure slightly more difficult to see and destroys the advantage of mirror reflections over rotations. Why should the addition of counterchange have a more drastic effect when associated with mirror reflection as opposed to rotation? A possible explanation is provided by consideration of the secondary types of symmetry present in the stimuli. When counterchange is added to some other symmetry transformation the stimulus still contains repeated subunits that do not involve counterchange. Plain repetition + counterchange has plain repetitions along the diagonals, and 180” rotation + counterchange, 90” rotation + counterchange and mirror reflection + counterchange all have 180” rotations along the diagonals. Thus, even if an observer cannot recognise that a counterchanged subunit is the same as the original subunit, in every case there are other kinds of repetitions available for him to detect, although these occur less frequently than in the stimuli without counterchange. In the case of plain repetition + counterchange and 180” rotation + counterchange, the secondary symmetry is the same as for repetition and 180” rotation without counterchange and so one would expect only a slight increase in detection time. For 90” rotation + counterchange the secondary symmetry is 180” rotation but since 90” and 180” rotations are detected with equal ease it is reasonable that the addition of counterchange to 90” rotations should make only a small difference to the time to detect structure.
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However the addition of counterchange to mirror reflection results in a secondary symmetry of 180” rotation which is more difficult to detect than mirror reflection. The finding that mirror reflection + counterchange is no easier to detect than 180” rotations suggests therefore that observers pay attention only to the secondary symmetries when counterchange is present and find difficulty in recognising that a counterchanged unit is the same as the original subunit. Another transformation with which observers have similar difficulty involves changing the size of the original subunit. Julesz (1971) has shown that dilating the portion of the stimulus to one side of the axis of reflection hinders the detection of symmetry. The second main finding of this study was that mirror reflection was easier to detect than rotation which was in turn easier to detect than plain repetition. A plausible explanation is provided by the observers’ reports as to how they carried out the task. If the structured quadrant was not immediately apparent then the observer chose some outstanding detail (such as a white cross on a black ground) and searched for repetitions of this detail. A quadrant containing such repetitions was chosen as the structured one. The important point about this strategy is that only a small detail of the stimulus is used and not the repeating subunit as a whole. It seems reasonable to suppose that the ease of finding repeated details will depend on their distance apart. With plain repetition all the repeating details are exactly one subunit’s width apart. However with mirror reflection details close to the axes of symmetry are very much closer to their reflected counterparts. Similarly with rotational symmetry details close to the axis of rotation will be very close to their rotated counterparts. Since the area round the axis of symmetry (the intersection of horizontal and vertical axes) is smaller than the area round the axes of reflection (the horizontal and vertical axes), there will be more corresponding details that are close together for mirror reflection than for rotation and there will be more corresponding details that are close together for rotation than for plain repetition. Thus the ease of finding these three kinds of structure can be explained in terms of the distance apart of corresponding details. This hypothesis would also account for the superiority of 16 over four repetitions since the corresponding details in the 16 repetition structures are closer together because the basic subunit is smaller. The failure for there to be an effect of symmetry with 16 repetitions might indicate that for all types of symmetry the corresponding details
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were sufficiently close together to be perceived immediately. A strategy of detecting corresponding details might also account for Julesz’s (1971) finding that mirror symmetry was only detected when the 0 fixated the axis of symmetry, since this is where the corresponding details are close together. It would be predicted that pulling apart the two symmetrical halves should make mirror symmetry more difficult to detect even if fixation is still on the axis of symmetry. Some support for this prediction is provided by Corballis and Roldan (1974) who found a superiority for mirror reflection over repetition only when the two halves of the pattern were close together and not when they were apart. However the patterns they used were extremely simple (e.g. subunit matrix 2 X 3). A mechanism for detecting corresponding outstanding details would also explain why structure was more difficult to detect with high information/high contour subunits. Frith and Nias (1974) have suggested that it is the high contour rather than the high information that makes such stimuli complex because the 0 tends to perceive them in terms of ‘runs’ (discrete areas of black and white, Restle 1966) and there will be more such runs in a high contour stimulus. A detail (or feature) also tends to be a discrete black or white area and hence there will also be more details in a high contour/high information stimulus. A large number of details will clearly make the search for correspondence more difficult, since only a limited number of types of detail can occur. It may be difficult to pick one detail that stands out among the rest. There may be corresponding details in two areas by chance rather than as a result of structure. Finally there may be a subjective metric in terms of details or runs per unit distance which renders the corresponding details effectively further apart in a high information/high contour structure. The original aim of this study was to find some objective correlates of structural complexity (which is subjective). From the results it is clear that complexity is affected by the type of symmetry rule used to generate a stimulus from a basic subunit, by the size of the basic subunit and by the information content of the basic subunit. These effects can all be explained if it is hypothesised that observers detect structure in visual displays by searching for corresponding small details in different parts of the display. Details that are rotated or reversed will easily be recognised as corresponding, but details that are counterchanged (black and white reversed) will not. The distance apart of these
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corresponding details will be determined by the type of symmetry rule applied and by the size of the basic subunit, which in this study was confounded with the number of repetitions of the subunit. The density of the details will be determined by the information content of the basic subunit. It seems likely that the difficulty of finding corresponding details will depend on their distance apart and on the overall detail density. It is clear from these considerations that stimuli can differ markedly in subjective complexity without differing in information content in the usually accepted sense.
References Christie, A. H., 1910. Traditional methods of pattern designing. Oxford: Clarendon Press. (Reprinted by Dover, 1969). Corballis, M. C., and C. E. Roldan, 1974. On the perception of symmetry and repeated patterns. Perception and Psychophysics 16, 136-142. Deregowski, .I. B., 1971. Symmetry, Gestalt and information theory. Quarterly Journal of Experimental Psychology, 1971, 23, 381-385. Frith, C. D., (1974. A program for generating abstract designs varying in ‘information’ and symmetry. Technical report CDF/AZ, Psychology Department, Institute of Psychiatry. Frith, C. D., and D. K. B. Nias, 1974. What determines aesthetic preferences? Journal of General Psychology 91, 163-173. Gamer, W. R., 1962. Uncertainty and structure as psychological concepts. New York: Wiley. Julesz, B., 1962. Visual pattern discrimination. Institute of Radio Engineers Transactions of Information Theory IT-8, 84-92. Julesz, B., 1971 Foundations of cyclopean perception. Chicago: Univ. of Chicago Press. Leeuwenberg, E. L. J., 1971. A perceptual coding language for visual and auditory patterns. American Journal of Psychology 84, 307-340. Newell, D. A., and H. A. Simon, 1963. Computers in psychology. In: R. D. Lute, R. R. Bush and E. Galanter (eds.), Handbook of mathematical psychology, Vol. 1. New York: Wiley. Pollack, I., 1973. Depth of visual information processing. Acta Psychologica 37, 375-392. Restle, F., 1966. Run structure and probability learning: Disproof of Restle’s model. Journal of Experimental Psychology 72, 382-289. Vitz, P. C., 1966. Preference for different amounts of visual complexity. Behavioural Science 11,105~114. Weyl, H., 1952. Symmetry. Princeton: Princeton Univ. Press.