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 com­posing 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 psy­chology 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 ele­ments composing the pattern and the elements com­posing the background to the pattern.

If the Gestalt principles of perceptual organiza­tion 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 sub­jective 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 psy­chology 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 neces­sarily in relation to its significance for Gestalt psy­chology. 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 ele­ments 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 surround­elements. Demonstrations of the Gestalt similarityprinciple are replete with examples of this implica­tion. The question which develops from this reason­ing is: How much psychological difference betweenthe object-elements and surround-elements are neces­sary 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

Fig. 1. Complete pattern-recognition stimulus (Top). Embeddedin this array is the "hidden" pattern (middle), composed of ele­ments 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 ran­domly distributed. In Experiment 1, the size (diameter)of the pattern-elements was the independent variablesystematically manipulated while the background ele­ments 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 "differ­ent."

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 ele­ments and 17 pattern elements (approximate ratio4.5:1). Projected image size of the individual ele­ments 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 presenta­tion of the stimulus. S was instructed to close hiskey on hearing the "ready" signal. Following theforeperiod, the timer simultaneously opened the shut­ter 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 mea­sured this duration from the clock. Distance from Sto the rear projection screen was 183 em. The center

Perception & Psychophysics, 1967, Vol. 2 (8)

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 embody­ing 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 psycho­logical 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 ob­tained 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 be­tween 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 stim­uli 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) con­cealed 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

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 19

Responses 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 cor­rect 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" judg­ments, all such responses in the analyses were scoredas correct or incorrect in proportion to the fre­quency of responses already in these categories.It should be obvious that the responses in the patterndiscrimination conditions can immediately be cate­gorized 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 experi­ments in the terms of the foregoing discussion. Speci­fically, chance level responding in the paired com­parison condition is now taken as .50 (a response isnow either correct or incorrect), and, following theaccepted convention, .75 is designated the "compari­son threshold." For the curves representing thepattern condition data, .25 indicates chance respond­ing (on each trial there were four alternative orienta­tions 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 thresh­old suggests that the pattern does not perceptuallyemerge from its background until the disparity be­tween 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 re­sponses 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 pattern­background 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)

"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 pattern­elements-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 com­posing the background. The facts from both experi­ments 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 conclu­sion 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 at­tempt 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 psycho­logical distance between pattern and background ele­ments alone, or is it related to the qualitative featuresof these two sets of elements? The former inter­pretation would suggest that perceptual grouping willoccur when stimulus elements differing in, e.g., bright­ness 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 interpreta­tion would suggest that some stimulus dimensionswere more "efficient" than others in producing per­ceptual grouping. In other words, it was intriguingto speculate that dimensions such as, say, bright­ness and size, would not be equally "potent" intheir effectiveness in making a pattern perceptuallyemerge. Thus, to obtain equal pattern visibility, dif­ferences between pattern and background elementswould have to be psychologically greater for onedimension than for the other. Obviously, one couldalso speculate that pattern emergence-figure group­ing-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 back­ground-to-pattern elements was tested. Future ex­periments 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 func­

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 stimulus­similarity: proximity vs. differences in brightness. Amer. J.

Psychol.. 1956. 69, 456-458.Knight, O. D. The role of the figure-ground relation in perceiving

and 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. Psy­chol., 1957, 57, 23-43.

Osgood, C. E. Method and theory in experimental psychology. NewYork: Oxford, 1953.

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Wertheimer, M. Laws of organization in perceptual forms. In W. D.Ellis (Ed.), A source book of gestalt psychology. New York:Humanities, 1950. Pp. 71-81.

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 essen­tially 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 dis­tances between the elements were arranged so that unequal proxi­mity between elements could not serve as a cue to the location ofthe pattern.

(Accepted for publication April 24, 1967.)

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