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Gestalt similarity principle, difference thresholdsand pattern
discriminability J
ALVIN G. GOLDSTEIN2UNIVERSITY OF MISSOURI, COLUMBIA
Perceptual group.ing within a visual array has been studiedas a
function of the difference limen between elements com-posing the
array. Two experiments are reported in which thearray elements
differed in size or in shape. Although there isa relationship
between perceptual emergenc e and amount ofdifference between
elements of the display as expected, therewas clear evidence that
above threshold differences betweenelements could not be used to
predict the emergence of apattern hidden in the visual array.
In 1957 Goldstein proposed an experimentandofferedsome
preliminary data relevant to the Gestalt psy-chology problem of
perceptual organization of visualstimuli. The present report offers
further data fromtwo experiments which confirm the earlier,
tentativeconclusion that perceptual emergence of a patternfrom its
background is not a simple linear functionof the amount of physical
disparity between the ele-ments composing the pattern and the
elements com-posing the background to the pattern.
If the Gestalt principles of perceptual organiza-tion are
considered as hypotheses, and thus are opento empirical test,
several difficulties arise when anattempt is made to devise a
suitable experiment.For example, the lack of experimental
investigationsof Gestalt principles has been attributed to the
factthat they are qualitative notions (Koffka, 1935, p, 166;Osgood,
1953, pp. 213-214), and therefore presumablyare not amenable to
empirical investigation. Hochbergand McAlister (1953) point out
that the principles,although of heuristic value are formulated in
sub-jective and qualitative terms making empirical studydifficult.
These seem weak arguments because thereare methods for studying
qualitative and subjectiveattributes of stimuli, and, just as
relevantly, thevast majority of "theoretical" statements in
psy-chology are not couched in quantitative terms, asituation which
in no way seems to reduce the amountof empirical research these
statements spawn. Onthe other hand, some progress has been made
inapplying empirical methods to the study of someGestalt principles
(Attneave,1955; Brunswick & Kamiya,1953; Bower, 1965, 1967;
Hochberg &. McAlister,1953; Hochberg &. Silverstein, 1956;
Knight, 1937;Rush, 1937). The concept "similarity," which isbasic
to the research reported here, has receivedattention from several
investigators but not neces-sarily in relation to its significance
for Gestalt psy-chology. In the broadest sense, implications of
theconcept of similarity are fundamental to every area
of psychology and to science in general (Attneave,1950, 1951;
Noble, 1957). Moreoever, the Gestaltprinciples-more commonly called
"laws"-are notprecisely stated. Granting this imprecision,
certainimplications still appear to follow from a combinationof the
written principle plus the meaning inherent inthe numerous
demonstrations offered by the earlyadvocates of Gestalt psychology.
The implicationsrelevant to the "law of similarity" will be
developedduring the discussion which follows.
The principle of similarity has been stated as" .•. a tendency
for like parts to band together ••. ' I(Wertheimer in Ellis, 1950,
pp, 71-81). Atoneextreme,this means that every object in our visual
world isan object because its internal elements "band together"and
emerge from a visual background to form ahigher level perceptual
unit. It seems plausible toassert that in order for an object to be
perceivedas a unit distinct from its surroundings, the ele-ments of
the object must be different psychologicallyfrom the elements of
the surroundings. Thus, in thelaw of similarity there is the clear
implicationthat "like parts" will band together and emerge asa
higher order visual form as a consequence of somediscrepancy
between object-elements and surround-elements. Demonstrations of
the Gestalt similarityprinciple are replete with examples of this
implica-tion. The question which develops from this reason-ing is:
How much psychological difference betweenthe object-elements and
surround-elements are neces-sary for perceptual emergence of the
object to takeplace?3
METHODThe measure of the dependent variable was obtained
from the responses to a visual display which closelyresembled
(but was not identical with) the formalaspects of the Ishihara
color vision test. It willbe recalled, that in each stimulus
display of thattest, numerous elements (circles) are distributedin
an apparently random manner. In reality, eachdisplay is composed of
two kinds of elements, thosemaking up the "hidden" figures (e.g.,
the number"2") and those making up the fabric of the
background(visual "noise" or interference elements). The
figureelements are, of course, a noticeably different huethan the
background "noise" elements. Keeping thisexample in mind, then, in
the present experiment, Swas presented with a display similar to
the one shownin Fig. 1 (top). This array is constructed from
two
Perception & Psychophysics, 1967. Vol. 2 (8) Copyright 1967.
Psychonomic Press, Goleta, Calif. 377
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Fig. 1. Complete pattern-recognition stimulus (Top). Embeddedin
this array is the "hidden" pattern (middle), composed of ele-ments
which differ markedly (most extreme ratio in Fig. 2) in sizefrom
the elements of the background (bottom).
378
sets of elements; one set is arranged in the nonrandom,"hidden"
pattern shown in the middle of Fig. l.This pattern is embedded in a
background of visual"noise" elements (Fig. I, bottom) which are
ran-domly distributed. In Experiment 1, the size (diameter)of the
pattern-elements was the independent variablesystematically
manipulated while the background ele-ments remained unchanged. In
Experiment 2, usingthese same background-elements, the shape of
theindividual pattern elements was systematically variedby reducing
the ratio of their vertical to horizontalaxes, thereby producing
figures progressively moreellipsoid.4 The most critical feature of
the methodnow becomes relevant: the psychological distancebetween
pattern-elements and background elementswas determined for each S
by means of a psychologicaldiscrimination procedure (paired
comparisons) in whichS was confronted with only two stimuli-one
patternelement and one background element-and had todecide whether
the stimuli were "same" or "differ-ent."
Thus, the purpose of the experiment was to measurepattern
discriminability as a function of the amountof psychological
distance between the elements of thepattern and the elements of the
background.
Stimuli and ApparatusAll stimuli were projected slides, white
figures on
a dark background.5 Two classes of stimuli were~sed,
corresponding to the two tasks which are de-
scribed in the next section. In the comparison trialseach
stimulus slide was composed of two elements;in the pattern
discrimination trials the stimulus (Fig. 1,top) was a matrix
composed of 78 background ele-ments and 17 pattern elements
(approximate ratio4.5:1). Projected image size of the individual
ele-ments in both classes of stimuli averaged 26 mm diam;separation
between contours averaged 5 mm (range3 to 10 mm in pattern
discrimination stimuli). Overallsize of the projected matrix was
approximately 33em sq.
A standard, 300 W 2 x 2 slide projector with anelectrically
operated shutter mounted in front ofthe lens was used to project
the stimuli upon a milkglass screen. Connected in series with the
shutterwas Ss' response key, an interval timer, and anelectric
clock. Closing Ss' key activated the intervaltimer which controlled
the 2-sec foreperiod betweenthe "ready" signal (given by E) and the
presenta-tion of the stimulus. S was instructed to close hiskey on
hearing the "ready" signal. Following theforeperiod, the timer
simultaneously opened the shut-ter and started the clock. Both
shutter and clocknow remained in this mode until S opened his
key,which stopped the clock and closed the shutter therebyending
the trial. Thus, S controlled the length ofthe time the stimulus
was visible to him and E mea-sured this duration from the clock.
Distance from Sto the rear projection screen was 183 em. The
center
Perception & Psychophysics, 1967, Vol. 2 (8)
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Comparison Threshold~.75 --------------
------------------------
Ecmpcrison Trials
~_.----_.>~ ......-1.00
50
.25 PatternJDiscriminationTrial..
--P:~e~: tDiscriminationThreshold
Exper. I
S responded by releasing his key (thereby removingthe stimulus
from the screen and also stopping theclock) when he could locate
the pattern. He thenreported the orientation of the stimulus
pattern. Ifafter 15 sec of searching, S could not locate
thepattern, he was asked to guess at the orientation.As there were
six sets of comparison stimuli inExperiment I, an equal number of
matrices embody-ing these six size differences were presented to
S.Similarly. in Experiment 2. where there were fivesets of
comparison stimuli, there were also fivematrices. In both
experiments a matrix stimuluswas presented twice in counterbalanced
order to each S.
.03 .05 .07 .08 .09 .12
RATIO Of PAnERN ElEMENT TO BACKGROUNO ELEMENT
Fig. 2. Proportion of correct responses in comparison and
patternrecognition conditions. Each point based on 40
responses.
SubjectsTen men and 10 women Ss were tested in a re-
peated measures design in Experiment 1; the samedesign was used
in Experiment 2 with a differentgroup of 10 men and 10 women.
RATIO OF PATTERN ELEMENT TO BACKGROOND ELEMENT
Fig. 3. Proportion of correct responses in comparison and
patternrecognition conditions. Each point based on 40
responses.
.07
Exper. n
.05
Comparison Trials ...............
.04.03
~Po"ern DiscriminationJ
Triols
.01
-------- -- ----. --- -- --------- -.------ ~----
----p~~~;~.,DiscriminotionThreshold
25
1.00
t;
! so
!
ComporjsonThreshold 1
J5 --------------- - ------------.------------
I
RESULTSNumber of correct responses in both experiments
was not related to the sex of the S, and the data formen and
women have been combined and will betreated together.
It will be recalled that the goal of each experimentwas to
obtain data from the paired comparison trialswhich could be
compared to measures obtained in thematrix conditions. Essentially
the question was: Whatis the visibility of the embedded pattern
when itselements differ from background elements by psycho-logical
differences equivalent to those measured inthe comparison task?
This question can best be answeredif the paired comparison and
pattern discriminationmeasures were compatible. Le.• on the same
scale.One way to do this is to consider bOth measures asthreshold
measures. Thus. a difference threshold ob-tained in the comparison
trials could be comparedwith a pattern threshold in the pattern
discrimination
of the screen was approximately level with Ss' lineof sight.
Illumination in the room was low, but noattempt was made to keep
the room dark.
ProcedureIn this section a description of the two tasks com-
mon to both experiments will be given in the orderin which they
always appeared.
Comparison Trials. The psychological disparity be-tween the
elements of the pattern and the elementsof the background was
measured by the techniqueof paired comparisons using two stimuli
and twocategories of response, "same" or "different." IfS judged
the stimuli on a trial to be "different,"he had to specify, in
Experiment 1. which was thelarger stimulus, or, in Experiment 2,
which wasthe more elliptical ("egg-shaped"), By varying thephysical
disparity between the two comparison stim-uli in the ratios shown
on the abscissa of Figs. 2 and3, ascending and descending trials
were presentedso that every S judged each comparison on fourtrials,
but only the final two judgments were usedin the analysis.
Reference to the abscissa of Fig. 2shows that the six sets of
comparison stimuli werepresented to S (total trials =24) in
Experiment 1. andas shown in Fig. 3, five sets in Experiment 2.
Beforethe comparison trials, S was instructed to respondaccurately
and as quickly as possible by releasinghis key as soon as he could
make his judgment.Response time and verbal report were recorded by
E.
Pattern Discrimination Trials. As explained earlier,in the
pattern discrimination trials, S was underinstruction to find the
pattern (Fig. 1. middle) con-cealed within the matrix stimulus.
Just prior to thefirst trial. S was thoroughly familiarized with
theshape of the pattern, and instructed that the "point"of the
pattern would be oriented to either the left,right, top, or bottom
of the projection screen. Usingthe apparatus described in the
preceding section,
Perception & Psychophysics. 1967. Vol. 2 (8) 379
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Table 1. Frequency and RT or Correct Responses in Comparison
Trials and Pattern Recognition Trials .in Experiment 1
Ratio of Pollern Element to Background Element.03 .05 .07 .08
.09 .12
Trials 2 2 2 2 2 1 2
Compari san Condition
Correct Freq. 10 11 15 19 20 19 19 20 20 20 20 19
Responses X RT 1.5 1.6 1.3 1.2 1.0 1.0 1.0 .9 1.0 .9 .9
.9(sec)
Pallern Recoqni tien
Correct Freq. 6 8 4 8 7 9 11 13 10 14 14 19Responses X RT 9.5
10.2 7.7 7.5 10.4 9.2 9.7 8.6 8.4 5.6 8.3 7.4
(sec)
Note: Chance level responding in comparison trials was 10
correct; in pattern recognition, 5 correct.
trials. Following this decision, the frequency of cor-rect
responses in the paired comparison and patterndisCrimination
conditions were analyzed in accordancewith the usual method of
determining thresholds.Since, in the paired comparison condition of
bothexperiments S was permitted to make "equal" judg-ments, all
such responses in the analyses were scoredas correct or incorrect
in proportion to the fre-quency of responses already in these
categories.It should be obvious that the responses in the
patterndiscrimination conditions can immediately be cate-gorized
either as correct or incorrect because S wasforced to make a
response even if he was guessing.
Figure 2 and 3 present the data of the two experi-ments in the
terms of the foregoing discussion. Speci-fically, chance level
responding in the paired com-parison condition is now taken as .50
(a response isnow either correct or incorrect), and, following
theaccepted convention, .75 is designated the "compari-son
threshold." For the curves representing thepattern condition data,
.25 indicates chance respond-ing (on each trial there were four
alternative orienta-tions of the pattern), and again following the
convention,.625 is designated as the "pattern threshold." Fromthese
graphs the relationship between the comparisonand pattern responses
can be seen. In Experiment I,
although the two stimuli are clearly perceived asdifferent in
the comparison task, the fact that thepattern discrimination curve
remains below its thresh-old suggests that the pattern does not
perceptuallyemerge from its background until the disparity be-tween
the pattern elements and the background elementsis very great. A
similar conclusion is also suggestedby the results of Experiment 2,
but here the patternnever emerges as a clear percept even though
thepattern elements are clearly seen as different fromthe
background elements in the comparison trials.
The response times, which were recorded on everytrial, offer
additional support to the conclusions justmentioned (Table 1 and
2). Tabulation and analysisof these data were restricted to RT of
correct re-sponses only, primarily because no coherent reasoncould
be discovered for looking at RT for incorrecttrials. As expected,
mean RT decreased in the pairedcomparison trials when the
discrimination task becameeasier, as indicated by the increased
number ofcorrect responses, a finding which offers little
newinformation. But even though the RT to the patterndiscrimination
trials also decreased as the pattern-background disparity
increased. the relative amountof this decrease was small and the
rather long RTsindicates that the pattern never reached the
figural
Table 2. Frequency and RT or Correct Responses in Comparison
Trials
and Pattern Recognition Trials in ElqIeriment 2
.01Ratio of Pallern Element to Background Element
.03 .04 .05 .07Trials
Comparison Condition
2 2 2 2 2
Correct Freq. 8 6 12 7 16 15 19 18 18 20
Responses X RT 2.5 2.3 2.6 2.8 2.6 2.1 2.1 2.2 2.0 1.8(sec)
Pallern Recognition
Correct
Responses
Freq.
X RT(sec)
11
12.5
6
12.4
10
11.4
4
12.9
8
11.8
5
12.4
9
11.4
9
11.0
7
12.6
10
8.8
380
Note: Chance level responding in comparison trials was 10
correct; in pattern recognition, 5 correct.
Perception & Psycbophysics, 1967, Vol. 2 (8)
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"emergence" level. Evidently, the Ss had to searchfor the
pattern; it did not appear to them as a figureon a ground.
DISCUSSIONIf we take the principle of similarity at its face
value, so to speak, then in this study the
pattern-elements-which were known to be psychologicallydifferent
from the background elements-should haveemerged as a figure, t.e.,
as a higher order form,held together by their identity to each
other and theirdifference from the more numerous elements
com-posing the background. The facts from both experi-ments suggest
that supraliminal differences betweenbackground and pattern
elements is not a sufficientcondition for figural emergence.
Moreover, even whenthe pattern-background difference was most
extreme,(in this study) there was no evidence from the RTdata to
indicate that the pattern clearly emerged.To the contrary, the long
response times, and theverbal reports of the Ss indicate that the
pattern was"pieced together" instead of perceptually emergingas a
unit. It is encouraging to find evidence in arecent report (Beck,
1966) supporting this conclu-sion although the data were obtained
in an experimentusing a similar but not identical method and
altogetherdifferent stimuli. Beck concluded that [udged
similarityof figures (the "elements" of his study) is a
poorpredictor of perceptual grouping.
The most striking aspect of these experiments wasthe clear
difference between pattern and backgroundelements in the comparison
condition and the almostimpossible task of finding these same
stimuli whenthey were embedded in the matrix array. It appearedto
some observers as though an unusual interactionbetween the elements
was responsible for the apparentassimilation of the pattern
elements. This was especiallycompelling in Experiment 1. This
observation waslater tested in an experiment which showed
thatapparent visual size is systematically affected by thepresence
of adjacent stimuli (Goldstein,1961). Althoughthis finding may be
used to explain the results ofthe present experiment, it does not
appear to accountfor Beck's data (1966).
Although in the experiments reported here, no at-tempt was made
to evaluate the "potency" of thedimensions as perceptual
organizers, this researchrepresents two studies in a series of
investigationsaimed at deriving the rules by which
perceptualgrouping occurs. We hoped to answer the question:Is
perceptual emergence a function of the psycho-logical distance
between pattern and background ele-ments alone, or is it related to
the qualitative featuresof these two sets of elements? The former
inter-pretation would suggest that perceptual grouping willoccur
when stimulus elements differing in, e.g., bright-ness are a
certain psychological distance apart, and
Perception & psychophysics, 1967, Vol. 2 (8)
the size of this psychological gap would be exactlythe same for
hue, size, etc. The latter interpreta-tion would suggest that some
stimulus dimensionswere more "efficient" than others in producing
per-ceptual grouping. In other words, it was intriguingto speculate
that dimensions such as, say, bright-ness and size, would not be
equally "potent" intheir effectiveness in making a pattern
perceptuallyemerge. Thus, to obtain equal pattern visibility,
dif-ferences between pattern and background elementswould have to
be psychologically greater for onedimension than for the other.
Obviously, one couldalso speculate that pattern emergence-figure
group-ing-was a simple function of the number of justnoticeable
differences between pattern and backgroundelements irrespective of
the sensory dimension. Thedata from the present experiments could
not be usedto decide which of these speculations are veridical,not
only because a limited number of dimensions wereemployed, but also
because only one ratio of back-ground-to-pattern elements was
tested. Future ex-periments can be designed to help in deciding
betweenthese two hypotheses.References.Attneave, F. Dimensions of
similarity. Amer. J. Psycho!., 1950.
63.516-556.Attneave, F. Ability to verbalize similarities among
concepts and
among visual forms. Amer. Psycholoflist, 1951. 6, 270.
(Abstract)Attneave, F. Symmetry, information and memory for
patterns. Amer.
J. Psuchol., 1955, 68, 209-222.Beck, J. perceptual grouping
produced by changes in orientation
and shape. Science, 1966, 154, 538-540.Bower, T. G. R.
Phenomenal identity in infants. Psychon. sci.,
1965,3,323-324.Bower, T. G. R. Phenomenal identity and form
perception in an
infant. Percept. & Psychophys., 1967, 2. 74-76.Boynton, R.
M., & Bush, W. R. Recognition of forms against a
complex background. J. Opt. Soc. Amer .. 1956, 46,
758-764.Brunswick, E., & Kamiya, J. Ecological cue-validity of
'proximity'
and of other gestalt factors. Amer. J. Psuchol., 1953. 66,
20-32.Eriksen, C. W. Location of objects in a visual display as a
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tion of the number of dimensions on which the objects differ.J.
expo Psycho/., 1952,44,56-60.
Eriksen, C. W. Object location in a complex perceptual field.
J.
expo Psychol., 1953.45, 126-132.Eriksen, C. W. Partitioning and
saturation of visual displays and
efficiency of visual search. J. app/. Psycho/., 1955, 39,
73-77.Goldstein.A. G. Two proposed studies on configuration
perception.
In J. W. Wulfeck & J, H. Taylor (Eds.), Form discrimination
asrelated to military problems. Washington, D. C.: National
Acad.Sciences-National Res. Council. 1957 (Publication #561).
Goldstein, A. G. The relation of extraneous visual stimuli
toapparent size. Psycho/. Rec., 1961. 11, 257-263.
Hochberg, J., & McAlister, E. A quantitative approach to
figural"goodness". J. expo Psucnot., 1953. 46, 361-364.
Hochberg, J., & Silverstein, A. A quantitative index of
stimulus-similarity: proximity vs. differences in brightness. Amer.
J.Psychol.. 1956. 69, 456-458.
Knight, O. D. The role of the figure-ground relation in
perceivingand memorizing visual forms. 'lJnpublished doctoral
dissertation.Ohio State University, 1937.
KoUka, K. Principles of gestalt psyc!1.oI0flY. New York:
Harcourt.Brace, 1935.
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Noble, C. E. Psychology and the logic of similarity. J. gen.
Psy-chol., 1957, 57, 23-43.
Osgood, C. E. Method and theory in experimental psychology.
NewYork: Oxford, 1953.
Rush, Grace P. Visual grouping in relation to age. Arch.
Psycho/.,1937, 31, No. 217.
Wertheimer, M. Laws of organization in perceptual forms. In W.
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Notes1. This research was supported in part by the U. S. Air
Forceunder contract No. AF 18(600)1052, monitored by the
OperatorLaboratory, Air Force Personnel and Training Research
Center,Mather AFB, California.2. I would like to thank Barry
Dworkin for his critical reading ofthis paper.3. There have been
innumerable studies reported where S wasfaced with the task of
visually searching for a figure or objectwhich differed in hue, or
shape from others in his perceptual field(e.g. Boynton & Bush,
1956; Ericksen, 1952, 1953). It is difficultto evaluate the
relationship between those studies and the present
38~
one because of the differences in method, goal, etc. In any
event,most of the earlier studies concentrated on the. problem of
locatinga single item in a background of visual noise. whereas here
therelevant issue was the organization of several items into a
new,higher level percept.4, A third experiment was performed where
the independent variablewas the thickness of the elements'
contours. Results were essen-tially the same as found in the two
studies reported here.5. The prototypes, from which the slides were
derived, were labor;iously constructed in the following manner.
Original large scale,India ink drawings, carefully measured, were
reproduced andprinted in reduced size by the photo offset process
upon sheets ofglue-backed paper. These reprod uctions were used to
make thetwo-figure comparison slides and the multifigure pattern
recognitionslides. More than one prototype matrix (pattern
recognition array)was constructed for each experiment. In each
prototype the dis-tances between the elements were arranged so that
unequal proxi-mity between elements could not serve as a cue to the
location ofthe pattern.
(Accepted for publication April 24, 1967.)
Perception & Psychophysics, 1967, Vol. ~ (8)