Interactive on-line perception of line patternsEDWARD L. MOROFSKY

Biomedical Computer LaboratoryWashington University School ofMedicine

St. Louis, Missouri 63110

and

ANDREW K. C. WONGBiotechnology Program, Carnegie-Mellon University

Pittsburgh, Pennsylvania 15213

A pattern perception system, PPS, has beenimplemented on the 360/67 time-sharing system withthe capability of analyzing, representing, comparing, andclassifying complex line patterns. Patterns are input tothe system as digitized arrays and are subject to tracingby several heuristic methods based on junctioncharacteristics. The trace yields a set of component lines.The representation is a structured pattern description interms of these components and distinguishes thetopological structure of the pattern as a whole from theprimitive features (straight segments, curves, angles) thatconstitute each line component of the pattern. Thechoice of a reference component about which to clusterthe description is the determining factor in the structureobtained, and a simplicity criterion is advanced toidentify a plausible first choice for this role. Thetopological structural description acts as the initialdiscriminator in the comparison or matching of patterns.Since the topological description is orientation, size, andfeature invariant, such information need not be retrievedfrom the primitive feature portion of the descriptionunless the initial comparison is positive. This form ofrepresentation facilitates the identification oftransformationaily related patterns and eliminates theneed for normalization of patterns. The comparison oftopological structures begins at the reference component(Levell) and proceeds from level to level (componentlevels are determined by their relationship to thereference). The level-by-level comparison is used toextract embedded sub patterns and serves as the basis forscene analysis in PPS. This organized structuralrepresentation is referred to as the perceived pattern andis the product of the constructive aspect of perception.Al! further processing achieved by PPS is accomplishedthrough the use of this representation. Resultingdescriptions can be reduced by compressing multipleexamples of component interrelationships to theirgeneral recursive rule of formation. Such a reduction ofrecursive patterns to their common generative form is aprerequisite for efficient classification, i.e., patternsformed by or containing a random number ofapplications of some simple interrelationship are moreeasily recognized as similar when the commongeneration rules have been isolated. This process resultsin two different levels of pattern description-theunreduced specific description with all of its peculiaritiesand the reduced description of the general class of whichit is a member. It is the general descriptions that arestored in a pattern universe as a memory of knownpatterns. Unknown input patterns are comparedparallelly with those contained in the pattern universeand are either classified as members of a pattern universeclass or used as the basis for the formation of a newclass. Many of the methods used in PPS were based onfindings in perceptual psychology, e.g., hierarchicalrepresentation and sequential comparison. The manner

Behav. Res. Meth. & Instru., 1973, Vol. 5 (2)

in which such concepts were incorporated into PPS andtheir further influences on the functioning of the systemwill be discussed.

A pattern perception system, PPS, has beenimplemented in the APL computer language (Falkoff &Iverson, 1969) on the 360/67 time-sharing system withthe capability of analyzing, representing, comparing, andclassifying complex line patterns. The representationalstructures and processing methodologies of PPS weredesigned with the explicit objective of incorporatingsome known and hypothesized characteristics of humanperception. This paper contains an elementarydescription of the principal system components alongwith the specific psychological evidence which served asthe motivating influence on the design. The implicationsof these decisions in terms of system efficiency andperformance are discussed. Complete technical systemdescription can be found in Morofsky and Wong (1971),Morofsky (1972), Wong and Morofsky.! Morofsky andWong,2 and Wong and Morofsky.f

The initial goal of PPS is the analysis of the inputpattern into its constituent line components and thegeneration of a structured description of therelationships among these components. The descriptionis hierarchical with relationships defined betweencomponents of adjacent levels as well as the same level.The first level component serves as the reference aboutwhich the description is clustered. The resultingdescription is embodied in a tlexible representationalstructure designed to facilitate the processing involved inthe comparison and identification of line patterns and inthe analysis of scenes. The design criteria of PPS result ina decreased efficiency in routine classification tasks, butallows a flexibility of representation and processing thatmore nearly parallel human performance in complexperceptual tasks.

Human pattern perception involves an interactionbetween the encoded representation of the visual sceneand an internal representation of known pattern classesand concepts stored in memory. These representationsare in a continuous state of refinement and decay asfiner distinctions are drawn or as old concepts are nolonger useful. Therefore, the visual input is used toupdate and expand continually the memory storage ofknown patterns, and these pattern classes are, in turn,used to analyze and classify the visual scene. An essentialprerequisite of such interaction is an efficientlyorganized memory storage. It must facilitate retrieval ofspecific classes and accommodate the modification,addition, and deletion of classes. The memory storage ofpatterns must also be responsive to changingrepresentations or refinements of a class over time.

The possible interactions between an unknown inputpattern description and the system memory of known

139

(a)

(c)

then completed. In the third type of reconstruction(Fig. 1d), the S builds a structure around a subpatternwhich resembles a meaningful pattern. It was thennecessary to ask whether memory does in fact influencethe decomposition of an unknown pattern into ameaningful subpattern or if a representation in terms ofa meaningful subpattern is the later product ofhigher-level processes on an ordinary decomposition ofType B or C. We decided on the latter interpretation.reasoning that a pattern or subpattern cannot in fact berecognized before it is represented in some encodeddescription. In the words of Merleau-Ponty (1962),"Before any contribution by memory, what is seen mustat the present moment so organize itself as to present apicture to me in which I can recognize my formerexperiences." This view is in contradiction to thecommonly held opinion that familiar patterns are easierto see, which gains support from the word-frequencyeffect or the inverse relation between the frequency ofoccurrence of a word in print and the viewing timerequired for its identification. However, the apparentrapidity with which familiar patterns can be identifiedmay well be due to a partial match in which the missingportions of the percept or representation are filled in bythe observer (Robinson, 1969). This led us to theestablishment of two initial trace strategies in PPS-thecontinuity trace (Fig. 1b) and the outer boundary trace(Fig. Ic).

Once components have been obtained, one mustdecide upon the relational structure and the relations tohe used A representation will be the most importantresult of a pattern analysis and must contain, in explicitform, defining relational invariants of a pattern class andbe of such a form that identifiable subpatterns can beextracted or added with minimal disruptions of theoriginal description. Since various alternativedescriptions are possible, the goal of the specificdescription is to organize the pattern components into astructure which contains their meaningfulinterrelationships. The core of the specificdescription isa hierarchical description suggested by the demands ofefficient processing and the results of retinalstabilization studies (Evans, 1968; Heckenmueller. 1969:Pritchard, Heron, & Hebb, 1960), in which the image ofa visual target is stabilized on the retina. These studiesshow that fragmentation of patterns occurs with retinalstabilization. Perceived patterns break up into parts,some or all of which may disappear. Complex patternsseem to remain visible for a longer time. The linescomprising a complex figure behave independently ofeach other, and each separate element of the figuredisappears and regenerates as a unit. The nature of theresponse to the physiological strain imposed by retinalstabilization provides insight into the manner in whichpatterns are analyzed and processed. It has beenobserved (Mackay, 1970) that the effects of thestabilized retinal image are transferred between eyes.indicating the presence of central as well as peripheral

Fig. I. Pattern of (a) with components obtained by acontinuity trace (b), by an outer boundary trace (c), and in (d)by isolating a familiu subpattem ''8.'' Representation of (d) isheld to be a later product of (b) or (c).

pattern classes, or PU, define the basic implementedcapabilities of PPS. Reduction of the search space ofpossible pattern matches, PU, to a subset containingonly those classes that are potential matches is the firststep. This reduction is based on partial cues, anotherhuman characteristic. Instead of matching the unknownwith each potential pattern class in turn, PPS attemptsto synthesize or replicate, in oarallel. e-ach notentialpattern class. The number of replications is continuallydecreased as the necessary essential components fail tobe located in the input. This process eliminates the needto segment a complex scene before classifying theindividual subpatterns and reduces scene analysis to aserial application of the simple pattern identificationroutine.

DESCRIBING PATTERNSIN PPSThe first choice to be made in the analysis of a line

drawing is the method of decomposing the pattern intocomponents. The method chosen will affect the types ofstructures obtained and the relations involved. A studyby the psychologist Djang (1937) served as the startingpoint for component definition in PPS. The Ss in thisstudy were asked to reconstruct meaningless patternsthat had previously been presented to them and toindicate the perceptual units involved. The resultsseemed to indicate three main types of processing asshown in Fig. I. The pattern is built up from linesegments that close or terminate at junctions with othercomponents (Fig. 1b), much like one might draw thepattern without breaking contact between pencil andpaper for each component, and no backtracking orretracing is allowed. The second type is exactly thesame, except that an enclosingboundary, if one exists. ischosen as a component (Fig. lc) and all inner lines are

140 Behav. Res. Meth. & lnstru., 1973, Vol. 5 (2)

Fig. 2. The pattern "apple-3" is shown with labeledcomponents and the resulting linkage field of component pairswhich is the basis of the pattern description in PPS.

\~'ith component (l 1), the apple outline, acting as reference theaverage hierarchical level is 2, while vt th t hc "3" as referencethe average hierarchical level would be 2.4. ThE' simplicl ty cri r­err cn ·...auld therefore indicate the apple outline as the reference.

3

4

2

5

18

Fig. 3. The eight possible bearings of the directed linesegments that are used to approximate the line components inPPS.

variation in the structured description (due to indecisionas to the choice of reference) may be viewed as anindication of the instability of the organization of theperceived pattern. A pattern that can be represented byhierarchical structures of equal stability or simplicity isconsidered to be an ambiguous pattern. The perceivedpattern may then shift from one representation toanother. While the above scheme offers a method ofmeasuring the relative complexities among variousrepresentations of the same pattern, the problem ofranking different patterns according to their complexityin agreement with human judgments of difficulty ofreproduction remains unsolved. It requires a weightingof the feature primitives on each level in terms of thenumber of levels used and the types of relations amonglevels as a contribution to the total complexity of thefigure.

Each component is individually analyzed intoprimitive features, namely, curved segments of bothpositive and negative curvature, straight segments, andangles. This is accomplished on the bearing stringrepresentation introduced by Freeman (1961), whichapproximates a component by a series of directedsegments having one of the eight possible bearings shownin Fig. 3. Each component is described as a sequence ofprimitive features, Le., straight and curved segments ofvarious lengths, curvatures, and bearings. The mainobstacle in analyzing components having multiplefeatures is in deciding where the segmentation pointsbetween features occur and ensuring that the resultingfeatures have some resemblance to those which humanobservers see. The segmentation points are determined insequence as the features are synthesized. Eachcomponent of the hierarchy is tagged with a double levelof description. The first simply indicates whether thecomponent is closed and which primitive components itcontains. A hash-coded representation in terms of thetype, sequence, and dimensions of the features is alsogiven. A hash table index is calculated, and the data canbe retrieved from the hash table by the use of the index.Numerical vectors, matrices, and characters may all behashed in this manner. It is the hash-code index which is

2 1

11 Four compo nen t pairs for the four junctions., ,/' cont a i ncd in the reference - all are relations.. between the first level and the three comport-3 ent s on level two. ~

3

1 1 Three coraponent pairs describing relations of1 .....- second level components - (2 2) and (2 3)

pof nt i ne vp...·ards to the third level component1 (3 1) with component (2 1) terminating.

o - Component (3 1) has no relations with higherlevel components - it t ermt r.at es , as does (2 1).

1 1

1 1 2

1 1 2

1 1 2

2 1 1

2 2 3

2 3

3 1 0

factors. Thus. neural adaptation, as well asphotochemical adaptation, is involved. Thefragmentation is not haphazard, but occurs in such away as to retain a meaningful pattern. In the words ofone of the investigators (Evans, 1968), " ... we havedemonstrated that fragmentation phenomena are notsolely a function of retinal stabilization and thehypothesis that the partial perception of patternsreflects the partial and variable activation of a perceptualhierarchy seems to be supported." The hierarchicaldescription employed by PPS begins at the componentor components on Level I, with all other componentsassigned levels determined by their relationship to thisfirst level. When the first level is occupied by onecomponent, it is referred to as the reference component.All components sharing a junction with the reference areassigned hierarchical Level 2, and, in general,components are assigned a level of one more than thelowest level component with which they share acommon junction. This process is indicated in Fig. 2,where the components have been labeled in this manner.The choice of a reference component naturally is theprime determinant of the structured description afterthe decomposition has been performed. A simplicitycriterion, which selects the component that, when actingas reference, results in a hierarchical structure having thelowest average hierarchical level, is proposed to identifya plausible first choice for this role. The susceptibility to

Behav. Res. Meth. & Instru., 1973, Vol. 5 (2) 141

1)~ 14 345 ~'J~

1 154 !.~ l!.S :-q:-I

1 1 2 ) l5~ 66 J4S lOS

1 2 3 154 66 345 79~

2 1 1 77 2 106 ,:!1J9

2 2 3 77 2 1166 ]!.6l

2 3 -5 5 1120 400

) a 0 -85 0 911 7;,8

feature code of (1 1) ~ 154

2 x 7 x 11 = 154

closed x conv~x curve x concave curve

indicatin~ that the reference is closed and contains

bot h cor-vex and concave curved segnents , tb..... exact

~izc ilnd seoquence of which is contained in the hash

tabl" retrievable hy the index 198.

junction CO<!l' describing the relation of c""'P0nents (1 1) and

(2 1) is equal to 14.

2 x 1 = 14 ....hich indicates thnt the apole st('m (2 1)

has .:'1 T-juncticn ..-ith the apple outline

(1 1) and lies outs t de of (l 1).

Fig. 4. The description, D, of the "apple-3" drawing. Thefour-column linbp field of Fig. 2 has been augmented by afeature c:ode, junctioa c:ode, and two hash codes in Columns 5,6, 7, .... 8, respecti¥eIy.

stored in the description. A hash code is preferable to alist label in that a unique code can always be obtainedfrom identical data without matching the entry datawith all data previously stored in search of a commonlabel. Thus, if one wishes to collect all known patternshaving a closed reference component, it is not necessaryto search the detailed description of each reference, buta simple examination of the partial features code issufficient.

Each row of the specific description, D, describes acomponent and its relation to another component withwhich it shares a common junction. This relation iscontained in a junction code and describes the type ofjunction and the relative position between the twocomponents, which are referred to as a component pair.A complete description of the pattern of Fig. 2 is shownin Fig. 4.

OPERATIONS ON REPRESENTATIONSThe representation of the perceived pattern serves not

only to structure the visual field in a meaningful way,but also, by its very construction, to lend itself to moreefficient processing. The data structure of PPS can beextended or compressed by the insertion or deletion ofcomponent pairs as long as the resulting structuresatisfies the requirements of a description (Wong &Morofsky"). The first operation to be considered is thecomparison of two descriptions with the objective ofspecifying the degree of their resemblance, if any.

The structure of the descriptive representations willobviously affect the type of matching algorithms that

142

can be considered. This raises the familiar issue ofwhether visual recognition is a parallel, one-step processor a serial one. Experimental studies. in which the timetaken by a S to recognize different patterns is measured,have tended to support the serial recognition viewpoint.The S is asked to scan a group of patterns, searching fora previously encountered pattern. It was found (Norton& Stark, 1971) that the S takes longer to recognize thepreviously encountered pattern than to reject anunfamiliar one. It was also found that the S takes longerto recognize complex patterns than to recognize simpleones. Both results are to be expected if patterns arematched serially.

Pattern matching in PPS begins at the referencecomponent and proceeds to greater levels of thehierarchy as long as a match is maintained. Variousdegrees of correspondence are available ranging fromtopological equivalency to identity. This simplematching procedure is utilized in classifying an unknowninpu t pattern as a member of a known class in thememory or pattern universe, PU. A sample PUcontaining five pattern classes is shown in Fig. 5. The PUcontains the defining representations of known patternclasses in an extendable array of 10 columns. The rowsof the PU are grouped into cells, each of whichrepresents a pattern class. A pattern class address vector,PeA, gives the row indices of the PU at which eachpattern class cell begins. A pattern class name vector,PeN, is used in conjunction with PeA and contains thehash-coded class name corresponding to each classaddress of PeA. The PCA and PCN for the sample PUare also given in Fig. 5. The first six columns of each cellare equivalent to the corresponding columns of thedescription D. The seventh column contains therecursive label, which is used in representing patternscontaining recursive relations and will be discussed later.Column 9 indicates whether or not the component isessential to the class definition, while Column 8 registersthe frequency of component presence during learning,thus providing a means of changing the status of thecomponent as a result of experience (Wong &Morofsky").

If an element of Column 9 of the PU is 1, then thecorresponding component of Columns 1 and 2, say (i j),is essential and must be present in an unknown D if theunknown pattern is to be classified as a member of thepattern class. If Column 9 is 0, the component (i j) isnonessential and may be present in the D, but itspresence is not necessary. It can be seen from Fig. 5 thatin the pattern apple, the apple outline is essential to theclass and the stem is not. Assignment of the stem asnonessential means that it will be seen as part of theapple when present rather than as a component externalto the apple. This is an important concept for discerningobjects embedded in a scene. An additional component,attached to an identified object and not correspondingto a nonessential component at its connection level. isconsidered to be external to the pattern.

A more complicated case of pattern classification

Behav. Res. Meth. & Instru., 1973, Vol. 5 (2)

~feat UTe co dv

lunction code

recursive l::lhel

154 14 0 798 60 .4 ~ 469

0 0 -85 0 0 788 J1 1 -5 3 1623

-5 1623

~-5 0 .6 0 207

2 102 66 0 379

Fig. S. Sample PU representing the pattern 102 42 0 379 2 22

classes, apple, "3," tree, house, and ship.02 2 102 42 379

2 102 66 0 379

1 -3 6 0 .9 2061 1

2 51 6 0 . 3 0 933

7854 42 0 2893 1

2 1 7854 42 0 289

~2 3 51 42 0 1 589

3 1 51 42 0 1 589 1 1

2 1 21 6 0 616

PCA"- 1, 3, 4, 7, 13

PC;..- 716, 97, 42, 456,698

occurs when more than one known pattern occurs in adescription of an input pattern. A description containingmultiple patterns is referred to as a scene. Theclassification of the constituent patterns of a scene isnaturally a more difficult problem, since it involves boththe segmentation of the scene into separate patterns andtheir assignment to pattern classes. Normally, thissegmentation must be accomplished before classificationcan begin. However, PPS performs both the separationand classification simultaneously by using theanalysis-by-synthesis approach. That is, an identifiablepattern is synthesized or constructed from componentscontained in D until a definite classification ismade-this being the first step in the analysis of D intoits constituent patterns. Beginning with the referencecomponent of D, all possible matching pattern classes ofthe PU are synthesized. level by level. using the availablecomponents of D (initially only essential components).Pattern classes of the PU are eliminated when one oftheir essential components fails to find a match in D. Allsurviving pattern classes have a match in D according tothe degree of correspondence specified. After a patternclass has been found to have its essential componentsmatched in D, the nonessential components of the classare matched with the remaining components of D. Allpreviously unmatched components of 0 that correspond

Behav. Res. Meth. & Instru .. 1973. Vol. 5 (2)

to nonessential components are added to the previouslyidentified subpattern. If all components of thedescription are not contained in the first synthesis, theremaining components are regrouped into a newdescription and a second synthesis is begun. This processis continued until all components have been identified orfound not to match any of the pattern classes in the PU.Thus. descriptions containing one pattern and thosecontaining multiple patterns are treated in the samemanner. and no special preprocessing is required.

The suggestion (Mackay. 1970) that analysis ofcomplex scenes might well be advantageouslyaccomplished by a process of internal replication-withthe internal specification serving as a compactdescription of the pattern-has been utilized for sceneanalysis in PPS. The search space of possible patternmatches. PU, is reduced to a subset containing onlythose pattern classes which might possibly besynthesized from the reference of D. This reduction isperformed according to the feature codes of thereference components and the levels of essentialcomponents. This replicating procedure is particularlyuseful. since it is unaffected by transformations thatleave the pattern invariant and requires no modificationwhen going from single pattern to complex scene. Such a"matching response" is much more general than that of

143

q l

Fig. 6. A simple vertically recursivepattern with labeled components is shownalong with the linkage field before and aftercompression to the recursive form. The S inColumn 5 of the compressed linkage field

1 1 2 1 indicates simple vertical recursion.

2 1 3 1

3 1 4 1

4 1 5 1

5 1 6 1 ;> S

6 1 7 1

7 1 8 1 9 8 0

8 1 9 1

9 1 8 1

simple imitation and makes particularly helpful the useof essential and nonessential pattern components. Suchessential and nonessential components or relations giveone the ability to differentiate the defining componentsand relations of a given class from those that may occurbut whose presence is not necessary. For example. a treemust have branches but mayor may not have leaves.Roth are instances of the class tree.

MEMORY AND THE GENERAL CLASSThe specific description, D, of an inpu t pattern

contains all of the information needed to specifyuniquely the given pattern. Such a description can beused to reconstruct the pattern, to answer inquiriesabout its structure, or to compare different patterns.The pattern classes stored in the PU are generaldescriptions of groups of patterns sharing some commoncharacteristics. The reduction of specific descriptions isaccomplished by compressing multiple examples ofcomponent interrelationships to their general recursiverule of formation. Recursive patterns are composed,wholly or in part, of components exhibiting a distinctiveseries of repeating structural relations. Theirrepresentations present unique opportunities for a morecompressed description and generality of pattern classrepresentation. The binary tree structure, for example, isdistinguished by the branching relation, which can beconsidered a simple vertical recursion, i.e., similarbranching recurs indefinitely from one level to the next.Compound recursion in depth refers to a recurringsequence containing more than one relation. A verticallyrecursive pattern is identified, from an examination ofits description D, by isolating an interconnected series ofcomponent pairs pointing from lesser to greaterhierarchical levels and having a repetitive series of

144

structural connections. The basic set of componentswhose structural relations are repeated is called asubuniverse, SU, and its identification is the first step inrecognizing a recursive pattern. Obviously, the originaldescription must be structured in such a manner that therecursive relations are present. This requirement is onlyfulfilled by a proper component set and choice ofreference.

The objective of efficient recursive pattern descriptionis to compress the recursive portions of D into a singlerelation (in simple vertical recursion) or a reduced set ofrelations (in compound vertical recursion). Compressedrepresentations of recursive patterns save considerablespace and achieve generality of pattern class description.Two basic types of recursion are treated by PPS, vertical

2 H

8 1 1 H

Fig. 7. A horizontally recursive pattern with eight first-levelcomponents. The compressed linkage field is given with the Hrepresenting horizontal recursion.

Behav. Res. Meth. & Instru., 1973, Vol. 5 (2)

and horizontal. Vertical recursion involves componentsof differing hierarchical levels which can be telescopedinto a single set of defining relations. Horizontalrecursion involves components of equal hierarchical levelwhich are all similarly related. one to the other. Anadditional column is inserted into the description ofcompressed recursive patterns to indicate whichcomponent pairs exhibit recursive connections and whatspecific type of recursion is involved. These labels areindicated in Figs. 6 and 7. A detailed system for therealization of recursively connected subuniverses,including recursive rules for the compression of adescription formulated as rewriting rules. and theexpansion of the resulting compressed representation arepresented in Wong and Morofsky.!

The organization of the PU into pattern classes mustsatisfy two main criteria. First. each pattern class mustbe broad enough to encompass the various patterns thatare members of the class and display some degree ofdivergence in their respective descriptions. Second, eachpattern class must be adequately selective so that eachinput pattern can be classified into a unique patternclass. These two criteria can be viewed as theembodiment of a pair of partially conflicting goals, sincethe first requires an abstraction or generalization of thecommonly shared characteristics of all the members ofthe same pattern class and the second requires aseparation of pattern descriptions belonging to differentpattern classes based on characteristics that are uniqueto each class. Of course, the classification of unknownpatterns mav be based on various degrees of similaritybetween the input description and the pattern class,depending on (a) the objectives of the classification and(b) the number and similarity of pattern classes in thePU.

When the pattern class "apple" is formed with asufficiently low threshold on the weighting factors tomake both the apple outline and stem essentialcomponents, the pattern class is very selective. That is, itmakes fewer mistakes in classifying nonappledescriptions as apples.

However. selectivity decreases. The pattern of (c) mightwell be classified as an apple, since its structure matchesthat of the pattern class and the features of the appleoutline, although distorted, also match. It might beconsidered as a caricature of an apple and would surelybe seen as such by many human observers. However,without the stem, as in (d), its resemblance to an apple ismuch less. even though the two outlines of (c) and (d)are in exact correspondence. But if (c) is classified as anapple, (d) must also be classified as such since the appleoutline is the only essential component. Another patternclass might also exist with an essential outline as theonly component, such as the pattern class "red bloodcell," which also matches (d). Thus, the classification of(d) as an apple or a red blood cell would be uncertain,i.e., selectivity is decreased by the high threshold.

Given an input stereotype, D, the PU can be searchedfor the set of all pattern classes that have a specifiedrelation to the stereotype. An indefinite number of suchsets might be formed by varying the degree ofcorrespondence on different hierarchical levels. Forexample, one may form the set of all pattern classes ofthe PU that are identical to D on the first level and thatare topologically equivalent on all higher levels. Thesame method may be used in forming a class fromamong a group of unknown patterns or in determiningthe configurational pattern which defines an unknownconcept. If Pattern I is selected as the stereotype andPatterns 2-6 are presented along with an indication ofwhether they share in an unknown resemblance toPattern I, a commonly shared concept among PatternsI, 2, and 6 is formed. When these patterns are compared,it is seen that they match in topological equivalence, theleast degree of correspondence in PPS, Such techniquescan be used to measure the acquisition of simpleconcepts of form. i.e., those in which the commonattributes are dependent on actual stimuluscharacteristics.

QHowever, the class is not very general. since it wouldclassify (a) as an apple but not (b), which is missing thestem. Thus, a low threshold tends to increase theselectivity and decreases the generality of a patte "\ class.

If the class "apple" is formed with a sufficien highthreshold. then only the apple outline is made essentialand both (a) and (b) would be classified as apples. This"idicates that a high threshold increases generality.

SUMMARYPPS describes complex line patterns in terms of the

relationships among its components (structural) and theprimitive features contained within each of thecomponents. The structural description is size and

soYES

(d)(c)(b)(a)

Behav. Res. Meth. & Instru .. 1973. Vol. 5 (2) 145

REFERENCESrole of past experience in the visual perception of

rms. Journal of Experimental Psychology, 1937,20,

rotation invariant and is used as the initial discriminatorin comparisons and classifications, i.e.. if structures donot correspond, there is no need to further comparefeatures. The feature description is dual level inproviding an easily accessible partial description and anexhaustive description. This type of description lendsitself to efficient processing, especially when multiplerepresentations are more or less possible. Given suchdescriptions, a variety of comparisons among patternsare possible including the detection of embeddedpatterns. The buildup of pattern classes is accomplishedby recording the occurrence of the various relations untilthe defining intersection of characteristics emerges. Suchtechniques are applicable to many familiar psychologicalstudies of the interactions between stimulus structureand learning, e.g., are forms with a less ambiguousstructure remembered more easily than those withseveral ambiguous representations?

Djang, S. Tmasked f29-59.

Evans. C. R. Fragmentation of patterns occurring withtachisto opic presentation. Institute of Electrical E!1&ineeringConfere ce Publication, 1968. 42, 250-256.

Falkoff, ~. D., &. Iverson. K. E. APLI360: User's manual.Watson Research Center, IBM, 1969.

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Freeman. H. Techniques for the digital computer analysis ofchain-encoded arbitrary plane curves. Proceedings of theNational Electronics Conference. 1961, 17,421-432.

Heckenmueller, E. G. Stabilization of the retinal image: A reviewof methods, effects and theory. In R. N. Haber (Ed.),Information processing approaches to l'isual perception. NewYork: Holt, Rinehart &: Winston. 1969.

Mackay, D. M. Perception and brain function. In F. O. Schmitt(Ed.), The neurosciences. New York: Rockefeller UniversityPress, 1970.

Merleau-Pontv, M. The phenomenology of perception. London:Routledge &: Kegan Paul, 1962.

Morofsky, E. L. Computer perception of complex line patterns.(Doctoral dissertation, Carnegie-Mellon University) AnnArbor. Mich: University Microfilms, 1972. No. 72-29,862.

Morofskv, E. L., &: Wong, A. K. C. Computer perception ofcomplex patterns. Second International Joint Conference onArtificial Intelligence, Advance Papers of the Conference,British Computer Society, 1971,248-257.

Norton, D., &: Stark, L. Eye movements and visual perception.Scientific American, June 1971, 224, 35-43.

Pritchard, R. M., Heron, w., &: Hebb, D. O. Visual perceptionapproached by the method of stabilized images. CanadianJournal of Psychology, 1960, 14. 67-77.

Robinson, J. S. Familiar patterns are no easier to see than novelones. American Journal of Psychology, 1969,82,513-522.

NOTES1. Wong, A. K. C., &: Morofsky. E. L. Recognition and

representation of recursive and quasi-recursive line patterns.Unpublished manuscript.

2. Morofsky, E. L., &: Wong, A. K. C. Isolating and identifyingobjects in line drawings. Unpublished manuscript.

3. Wong, A. K. C., &.Morofsky, E. L. Formation and updatingof classes of line patterns. Unpublished manuscript.

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