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 UNIVERSITY OF ILLINOIS 
 URBANA, ILLINOIS 
 
 Report No. 1^2 
 
 SYNTACTIC DESCRIPTIONS OF PICTURES AND 
 GESTALT PHENOMENA OF VISUAL PERCEPTION 
 
 R. Narasimhan 
 July 25, 1963 
 
 This work was supported in part "by the 
 Atomic Energy Commission Contract No. AT(ll-l)-10l8 
 
?r?*4L 
 
 
 Table of Contents 
 
 Page 
 
 1. Introduction „ „„<,„„.„ . . . „ „ „ „ . . . . . . . . . 1 
 
 2. The Basic Syntactic Model ................. 3 
 
 3„ The Gestalt-Qualitat of Visual Perception ......... 7 
 
 k. The Extended Syntactic Model ................ 10 
 
 5. Ambiguous Figures ..................... l4 
 
 6. Some Further Implications of The Syntactic Model ...... 21 
 
 References . . „ . . „ . . . . . . . „ , . . . . . . . . . . 25 
 
 Appendix 1 . „ . . . „ . . . . . „ . . . . . „ . . . . . „ „ 26 
 
Digitized by the Internet Archive 
 in 2013 
 
 http://archive.org/details/syntacticdescrip142nara 
 
1. Introduction 
 
 We have advocated elsewhere [7,8] a model- -called the Syntactic Model- - 
 for the analysis and description of pictures. This model was originally 
 developed to answer a very specific problem, namely, that of identifying 
 patterns that occur in bubble chamber negatives. Towards this end, a variety 
 of specific algorithms have been developed and a computer program is currently 
 being written to implement the model in this case. A novel, parallel- 
 processing computer- -called the Pattern Articulation Unit--is also under 
 fabrication to carry out the specific computations involved in the algorithms 
 in an especially efficient manner. 
 
 The Syntactic Model itself is, however, much more general in scope. 
 Briefly, it is a descriptive scheme based on assigning a hierarchic system of 
 labels to the points which make up the picture. The labeling algorithms 
 make implicit use of the underlying syntax which characterize the class of 
 pictures being described. Central to the descriptive scheme, then, is the 
 notion of a class of pictures and a set of grammar rules which characterize the 
 syntax of the patterns that occur in the pictures of that class. 
 
 For example, in the specific context, cited earlier, of bubble chamber 
 negatives, the class sought to be described is the class of pictures composed 
 of line-like elements (or, more informally, pictures which look like road maps). 
 The particular grammar rules are to a large extent specified by the underlying 
 physical process which gives rise to these pictures. Another useful class of 
 pictures for study would be the class of hand -printed letters (or, more 
 generally, hand-printed alpha-numeric characters). Although these look like 
 road maps too, clearly, the grammar rules for their efficient description need 
 not be the same as in the previous instance. However, because of this basic 
 similarity in appearance, a large number of the labeling algorithms devised for 
 the earlier class can be equally well applied to the class of hand-printed letters 
 
 The PAU and the associated computer are being designed and built 
 in this Laboratory by a group led by Dr. B. H. McCormick. 
 
 See below in Section 2 for a more detailed description of this model, 
 
 -1- 
 
A third familiar class of pictures can be defined as follows: each 
 picture is composed of a configuration of two-dimensional fields, the boundaries 
 of each field being some well-defined geometric figure, say, a circle, square, 
 triangle, other types of polygons, etc. A generalization of this class would 
 permit the "interiors" of the individual fields to be either all black or all 
 white. A straightforward extension of the labeling algorithms set up for the 
 road-map-like pictures can be made to apply to this wider class also. 
 
 Our principal concern, however, here, is not with the construction 
 of algorithms for application to specific classes of pictures. Rather, our 
 interest is in a meta-theoretic study of the potentialities of descriptive 
 schemata such as the one referred to earlier, in modeling the process of visual 
 perception. As a starting point towards such a study, we shall consider in 
 the following pages the ability of the Syntactic Model to cope with some of 
 the phenomeno logical features which have been emphasized by the Gestalt 
 school of psychologists as pre-eminently characterizing the visual perception of 
 data. In particular, we shall examine two such features --both extensively 
 studied and discussed in the literature: (l) the "spontaneous" organization of 
 entities in the visual field into "wholes and subwholes" according to qualitatively 
 discernible principles; (2) the occurrence of ambiguous (sometimes also called 
 reversible) figures and the visual phenomena associated with them. 
 
 It must be emphasized here that our concern at this stage is a well 
 circumscribed one: attempting to characterize in a purely functional manner the 
 above Gestalt features within the framework of a coherent descriptive scheme 
 for processing visual data. In the context of the Syntactic Model (for 
 descriptions of classes of pictures) mentioned earlier in this section, we shall 
 formulate this problem as follows: Is it possible to extend the labeling schemata 
 in a natural way so as to incorporate in the resulting descriptions of pictures 
 the same kinds of organization of data that are characteristic of the visual 
 process? Moreover, can the visual phenomena associated with ambiguous figures 
 be characterized within the framework of this extended Syntactic Model in a simple, 
 intuitively meaningful way? 
 
 -2- 
 
An affirmative answer to both these questions would, in effect, imply 
 that a computer program processing visual data according to this model would, 
 anthropomorphically speaking, "see" the data organized (and/or ambiguous) 
 exactly as required by the Gestalt principles. We shall outline in the sequel 
 a specific extension to our basic Syntactic Model and exhibit a set of computer- 
 processed outputs based on this extension which bear out the above assertion. 
 
 Before doing this, however, it is first necessary to describe in 
 greater detail the basic Syntactic Model as well as the Gestalt features one is 
 trying to characterize. Sections 2 and 3 are concerned with these matters. 
 In Section k we describe our extended model. A few computer-processed output 
 pictures exhibiting the above Gestalt features are given in Appendix 1. 
 Section 5 is concerned with a. discussion of the ambiguous figures and of how 
 the visual phenomena associated with them follow as a natural corollary to the 
 processing details implicit in the Syntactic Model. In the last section we 
 shall consider some of the implications of the Syntactic Model and their 
 relevance to known empirical results connected with visual perception. We shall 
 also draw attention to a few problems explicitly suggested by the model which 
 seem worth experimental investigation. 
 
 2. The Basic Syntactic Model 
 
 For the sake of definiteness, let us restrict our consideration to 
 pictures consisting of black and white points. Figure 1 illustrates a picture 
 of this class. The Syntactic Model would now seek to describe this picture by 
 assigning a hierarchic system of labels to every point in it. The labels 
 assigned form a hierarchy in the following sense: the procedure for labeling 
 divides into a series of well-defined levels. At each level, the labeled outputs 
 from the lower levels serve as the input to the current level of labeling. What 
 particular labels are assigned at each level would, of course, depend on the 
 particular class of pictures being (or sought to be) described. 
 
 -3- 
 

 
 
 
 
 
 
 
 
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 -h- 
 
As a specific example, consider the picture illustrated in Fig. 1 
 again and let the syntax used be that pertaining to the description of the class 
 of hand-printed letters. At the lowest level, each point is assigned one of 
 the labels, black or white. In the next level all black points connected 
 together are assigned a distinct connectivity label. At the third level, 
 labels are assigned to each point to signify what type of primary road it forms 
 a part of; (The four primary roads are North-South, East -West, Right Diagonal, 
 Lef t -Diagonal. ) Using the road segments so formed and grammar rules defining 
 the syntax, at the next level, higher order phrases are formed. The names 
 of these phrases are now assigned to the corresponding points as labels. This 
 process is continued till, at the highest level, the names of the phrases are, 
 respectively, the names of the letters. These are thus assigned as the highest 
 level labels to the points constituting the respective letters. 
 
 To illustrate how this labeling scheme would work, consider the three 
 
 points labeled P, Q, R in Fig. 1. In the table below are listed the various 
 
 labels assigned to the three points at the different levels. In writing down 
 
 the table entries, the following notation has been used: I., (j = 1,2,...) denotes 
 
 J 
 the connectivity labels, all points connected together being assigned the same 
 
 label, I._ . The road labels used are: N (North -South): E (East-West): 
 ' jl " ' 
 
 A (Right Diagonal); B (Left Diagonal). 
 
 -*■* 
 
 We have tacitly assumed here that the "figure" in the field 
 is defined by the black points. There is, of course, 
 no justification for this assumption. The figure could 
 as well be defined by the white points. In certain 
 circumstances, both sets of points could simultaneously 
 define figures independently, thus giving rise to 
 ambiguities in further processing. This is a crucial 
 point and we shall return to it again in Section 5 below 
 where we discuss ambiguous pictures. 
 
 The name 'phrase' is used merely as a suggestive terminology. 
 
 Phrases at all levels need not be linear strings; in fact, 
 they will not be. Distinct phrases should be thought 
 of as representing certain well-defined 'primitive' 
 graphs . ( See next footnote . ) 
 
 -5- 
 
Q R Remarks 
 
 Level 1: 1 1 1 Black = 1 
 
 White = 
 
 Level 2: I I I Connectivity 
 
 Level 3: A N A Names of 
 
 primary roads 
 
 Phrase names 
 
 Last Level: ABA Names of 
 
 letters 
 
 In the case of hand-printed English alphabets, these intermediate phrase 
 
 levels may, of course, be empty, or they may exist for some letters and 
 
 not for others. These details, which are for the most part optional, 
 
 do not play anything more than an incidental role in processing particular 
 
 pictures. 
 
 The notion of phrases, which represent intermediate level groupings, is, 
 however, of some importance. Its significance and plausibility can 
 perhaps be made clear by means of the following example: Consider an 
 alphabet consisting of the five characters shown below: 
 
 □ H Q / ^ V 
 
 Let their names be SI, S2, S3, S4 and S5, Let G / \. /\ 
 be referred to as a square, a right slash, a left slash and a cross. 
 Then, clearly, an efficient description scheme for the five characters is 
 to say that SI consists of a square, S2 of a square and a dot, S3 of a 
 square and a right slash, Sk of a square and a left slash, S5 of a 
 square and a, cross. The square, the right and left sla.shes and the cross, 
 which are groupings of the primary roads N, E, A, B are examples of 
 phrases. It is evident that their introduction simplifies the description 
 of this particular class of pictures. It is our view that in the 
 context of visual processing of data,, although, in many cases, these 
 phrase structures may be arbitrary (i.e., optional), in some cases they 
 may be obligatory. In the latter event, the subgroupings should be 
 actually perceived as such. 
 
 Labeling of the type indicated in the table is most readily realized with 
 the help of the Pattern Articulation Unit referred to earlier. Extensive 
 work using hierarchic labeling algorithms has been done with a parallel 
 processing simulator that has been written for the IBM-7090 computer 
 [9] • Some processed outputs using this simulator are given below in 
 Appendix 1. For a more detailed description of labeling schemata of the 
 type exemplified in the table, see [8] . 
 
 -6- 
 
Such a scheme of labels assigned to each point in the picture 
 constitutes a complete description of the picture- -for example, that it 
 consists of three distinct (i.e., disjoint) hand-printed letters, namely 
 two A' s and a B. Clearly, even at a more local level, the labeling scheme 
 provides a complete set of intuitively significant descriptions. Considering 
 the three points P, Q, R, although they are all disjoint, the labels assigned 
 show that P and R are similarly situated in a certain intuitively meaningful 
 sense and that both of them differ in this respect from A. It is also worth 
 noting that the processing based on labeling schemata, as indicated above, is 
 intrinsically independent of the positioning of the picture in the 'visual' 
 field. It is also independent of the size of the total picture so long as 
 this size is not too small for the resolution of the underlying mosaic of 
 points. By incorporating equivalence relationships in the grammar rules, 
 recognition of figures in the field can also be made, to a, large extent, to 
 be independent of their orientation. Thus, "transposition," one of the 
 central problems in modeling visual perception, , is taken care of in a basic 
 way by labeling schemata. 
 
 3. The Gestalt -Qualita't of Visual Perception 
 
 It is a matter of common experience that the visual field is not a 
 chaotic patchwork of various colors and brightness but consists of structured 
 units, certain areas belonging together and forming shaped regions distinguishably 
 segregated from other areas. One can give a variety of examples to demonstrate 
 this tendency for spontaneous organization of visual data: perhaps the best 
 known is that associated with a large number of dots, lines, squares, etc., which, 
 apparently distributed at random in the visual field, take on various phenomenal 
 groupings. It was emphasized originally by the Gestalt psychologists that this 
 tendency for spontaneous organization is an intrinsic characteristic of the visual 
 process and requires investigation and study. A comprehensive exposition of 
 this view may be found, for instance, in Kohler's book on Gestalt psychology [5]. 
 
 -7- 
 
Our immediate interest here is not in the Gestalt theory per se or in 
 its wider psychological implications "but in the so-called "principles of 
 organization" first enunciated by Wertheimer. (A somewhat condensed translation 
 of his original paper may be found in [l]; see also Dember [4].) After drawing 
 attention to the fact that a collection of figures in the visual field is, 
 perceptually, more than chaotic and unstructured, he pointed out that the way 
 in which the parts are seen, in which groupings occur and subwholes emerge, is 
 not completely arbitrary but is subject to well-discernible, albeit qualitative, 
 organizing principles. He characterized several properties of figures in terms 
 of which the resulting organization could be described. Of these, for our 
 present purpose (since we are not considering either movement or depth vision), 
 the properties of major significance are proximity, similarity, good continuation 
 and closure. We shall describe briefly the import of each one of these by means 
 of suitable examples. (Figures 2, 3, ^ f 5 are taken from Dember [^].) 
 
 Proximity : Other factors being constant, subgroups tend to be formed 
 from parts which are spatially close together. Such immediate organization 
 based on the proximity of elements, moreover, tends to be highly stable. 
 This is illustrated in Figs. 2a and 2b. In 2a, the squares are perceived 
 as organized into horizontal lines; in 2b, the same elements are seen 
 organized into vertical lines. 
 
 Similarity : Where elements are dissimilar, organization will be 
 determined by similarity relationships among the elements. In Fig. 3> 
 for instance, although the squares form an equally spaced grid, the 
 dark squares and the light ones are seen organized into vertical lines. 
 Under certain circumstances, similarity might play a more decisive role 
 in the resulting organization than proximity. 
 
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Good Continuation ; This principle is concerned with the manner 
 in which an existing organization tends to affect its extension to 
 newly introduced elements in the field. Referring to Fig. 4., for 
 example, given the organization of the shaded circles, to extrapolate, 
 the principle of good continuation would demand choice of c rather 
 than of a or b although all the three are equally close to the last 
 shaded circle. In fact, even if c were missing, the choise would he 
 on d rather than a or b. 
 
 Closure : This organizing principle is illustrated in Fig. 5- The 
 dots are seen as forming two separate enclosed regions rather than as one 
 smooth figure-of-eight curve. 
 
 It must be emphasized that, in all the foregoing, the claim is not that 
 those indicated are the only organizations perceived. The point made is that these 
 organizations occur, so to speak, spontaneously and remain stable; to "see" any 
 other organization requires great effort and despite this the resulting figure 
 tends to be unstable. 
 
 k. The Extended Syntactic Model 
 
 Before explaining the extension, we have to introduce an operation on 
 pictures which we shall term 'smearing.' By smearing, we mean a local spatial 
 extension of the set of points which constitute a picture. This operation is 
 most simply realized as follows: replace each point in the picture by a 
 neighborhood of points, say, by a circular area with the original point as the 
 center. The resulting picture will clearly be a certain "fuzzy" enlargement of 
 the original input picture. Figure 6 illustrates this smearing operation carried 
 out on some representative pictures. 
 
 -10- 
 
FIGURE 6. a 
 
 FIGURE 6.b 
 
 
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 INPUT 
 
 FIGURE 6.c 
 
 SMEARED OUTPUT 
 
 FIGURE 6' EXAMPLES OF SMEARING OPERATION 
 
 (SMEARED AREA SHOWN LIGHTLY SHADED) 
 
 -11- 
 
 UNIVERSITY OF 
 ILLINOIS LIBRARY 
 
To be sure, for actual implementation in a processing algorithm, this 
 definition has to be made more precise. It must be specified in quantitative 
 detail to what extent (i.e., how much in spatial area) each point is to be 
 smeared. However, we shall not attempt any such quantitative characterization 
 at this stage for two good reasons: (l) we do not have any plausible criterion 
 at present on which to base such a quantitative measure; (2) for the purposes of 
 our present exposition, all that we need are the qualitative implications of such 
 a smearing operation, as we shall see presently. 
 
 The basic Syntactic Model, it will be recalled, consisted in assigning 
 a hierarchic system of labels to each point in the picture. These labels were 
 to be assigned in a well-defined order, as described earlier in Section 2: 
 first the labels black, white; next the connectivity labels; then in increasing 
 order the phrase names till the highest level (as defined by the grammar for the 
 class under consideration) is reached. At this stage, the original picture can 
 be decomposed into subpictures, each subpicture consisting of all those points 
 which have been assigned the same highest level label. Visualize these sub- 
 pictures as being present on separate replicas of the original field* The 
 extension to the model now consists in iterating this labeling scheme independently 
 on the subpictures, after smearing them. The process ends when on two successive 
 cycles the same highest level labels are assigned to the points of the original 
 picture (i.e., the first input picture). Schematically, then, the extended model 
 can be represented as shown below: 
 
 
 
 
 
 Smear 
 
 New Subpictures 
 
 
 
 } 
 
 r 
 
 
 ^ 
 
 
 
 
 Input 
 Picture 
 
 Label Subpictures 
 
 
 Highest level 
 
 labels to input 
 
 picture unchanged 
 1 
 
 No 
 
 1 W 
 
 
 
 Yes 
 
 
 
 
 
 
 Stop 
 
 ■12- 
 
In the very first cycle there is only one subpicture, namely, the input 
 picture. 
 
 Although the model seems complex in terms of the description given 
 above, conceptually it is really very simple and straightforward, given the basic 
 hierarchical labeling scheme. The only new aspects to the model are its recursive 
 characterization and the operation of smearing. The crucial point to bear in 
 mind is that smearing is restricted to the collection of points with the same 
 highest level label in each cycle. It might be wondered that the processing 
 suggested by the model could become very complicated in cases where several 
 subpictures are generated in each cycle. For instance, if in each cycle, each 
 subpicture decomposes into two subpictures, the number of independent subpictures 
 to be labeled would go up exponentially. This is true in principle. In fact, 
 this observation suggests some new problems for study concerning the visual process 
 which one might not have thought of a priori. We shall return to these later 
 in this paper. For the moment, however, it is sufficient to note that in 
 practice, for instance in all the examples illustrated in the previous section, 
 the iteration terminates after the second cycle and also only one subpicture is 
 labeled in each cycle (i.e., only one subpicture forms the figure; the other 
 constitutes the 'ground' and so is ignored). 
 
 It is not difficult to verify that an iterative, hierarchical labeling 
 carried out as suggested by the model will, in effect, result in organizations 
 conforming to the Gestalt principles. Smearing, being a purely local, neighborhood 
 operation, will clearly be influenced by proximity considerations. The 
 separation into subpictures conforms to the similarity principle. In fact, it 
 is plausible to argue that, at every level, an operational meaning for similarity 
 is the assignment of common labels. If we recall now that a picture is a set of 
 labeled points, it is readily seen that, at each cycle, the processing implied 
 by the model amounts to the following: Step 1. decompose the picture into 
 similar subpictures; Step 2. form pictures according to proximity. 
 
 -13- 
 
In the language of the Syntactic Model, the principle of good continuation 
 would he formulated in terms of phrase structures . Qualitatively one -would say 
 that given a picture, new elements introduced into the field tend to be incorporated 
 into the picture so as to preserve the underlying phrase structure. This is 
 naturally hound to be a very context-dependent operation. It seems quite 
 plausible that at least a good part of the closure phenomenon is characterizable 
 on similar considerations. However, other psychological factors having to do 
 with the stability in the visual field of simply connected domains might play a 
 determining role. We do not wish to prejudge the issue at this stage. 
 
 To demonstrate the algorithmic feasibility of the model, we give in 
 Appendix 1 some actual computer outputs. These have been obtained using the 
 parallel processing simulator referred to earlier and exhibit the organization 
 achieved in the input data when processed according to the recursive syntactic 
 schemata outlined in this section. The close conformity to the Gestalt principles 
 in the "perceived" organizations should be considered as a convincing demonstration 
 of the intrinsic potentialities of syntactic labeling schemes to serve as 
 explanatory models for visual perception. 
 
 5. Ambiguous Figures 
 
 So far, we have been concerned with the perceptual organization of elements 
 in the visual field into structured subpictures. But a much more remarkable 
 feature of the visual process is that certain stimulus configurations tend to 
 give rise to multiply -perceived organizations. These are the so-called ambiguous 
 figures, sometimes also referred to as reversible figures when the alternatives 
 are two in number. A variety of such patterns have been discussed in the 
 literature. In this section we shall see that the occurrence of ambiguous 
 figures is most readily comprehended in terms of the Syntactic Model. We shall 
 see further that some of the visual phenomena associated with these figures in fact 
 verify some of the results one would be led to infer from the model. 
 
 ■lk- 
 
Let us recall, to begin -with, that a Syntactic Model is a hierarchic 
 labeling scheme where, at each level of the hierarchy, labels are assigned to the 
 input elements of that level by structuring them according to given composition 
 rules (i.e., the grammar rules associated with that level). Unless explicit 
 constraints are built into the model to avoid all ambiguities, clearly, situations 
 can arise where a given set of input elements admit of more than one grammatically 
 valid structuring. Moreover, in general, this can arise at any level of the 
 hierarchy. It would perhaps be instructive to consider a few illustrative 
 examples from a Syntactic Model with which everyone is familiar, namely, that 
 for the natural languages. Consider discourse in English, to be specific. 
 
 The standard model for describing (or equivalently, analyzing) the 
 flux of English discourse is to label it into phoneme sequences, morpheme sequences, 
 phrases, sentences and so on, hierarchically, according to well-defined syntactic 
 rules. It is a common experience that ambiguities in labeling often arise. We 
 give some examples below. 
 
 The following two valid morpheme sequences are easily verified as 
 arising from the same (except for the final-cj underlying phoneme sequence: .. 
 
 The good candy came any way. 
 The good can decay many ways. 
 
 Ambiguities at the phrase structure level are much more readily come by. The 
 following, due to Chomsky, is probably as famous as any: 
 
 They are flying planes . 
 
 It is important to note two points here: (i) that ambiguous constructions can 
 occur; (ii) that often the ambiguity can be resolved by explicitly exhibiting 
 the preferred sense by bracketing. For instance, the following bracketing, in the 
 example above, makes the intended sense unambiguous: 
 
 (They) (are (flying planes) ) . 
 
 These examples are quoted by J. S. Bruner in [3] where he attributes 
 them to G. A. Miller. 
 
 -15- 
 
Chomsky has, however, shown that for the description of English sentences 
 this type of immediate constituent analysis is not wholly adequate and has 
 extended the Syntactic Model "by an additional level which he has called the 
 transformational level. Certain sentence constructions are now to be described 
 by giving their transformational "history" from specific underlying kernel 
 sentences o Some ambiguous constructions are most readily resolved by making use 
 of this device. Consider, for example, the following sentence: 
 
 Visiting relatives can be a nuisance . 
 
 One can quite simply indicate the preferred connotation by saying, the above 
 sentence is to be viewed as a transform of the sentence 
 
 Visiting relatives are a nuisance . 
 
 The other sense can be derived from the underlying construction 
 
 Visiting relatives is a nuisance.. 
 
 To go back to ambiguous pictures, it is our contention that within the 
 framework of the Syntactic Model for describing pictures that we have been out- 
 lining, the occurrence of ambiguous pictures and their resolution should be 
 construed in a manner quite analagous to the linguistic examples considered above. 
 Let us try to substantiate this claim by considering three specific examples. 
 
 It will be recalled that in the labeling scheme, at the very lowest 
 level, points are assigned the labels ; black; white. In all our discussions so 
 far we have tacitly assumed that the figure is composed of the black points and 
 have been concerned with their subsequent labeling exclusively. It is clear 
 that a figure could equally well be defined by the white points and, in particular 
 instances, both sets of points could define figures and hence be eligible for 
 labeling at all higher levels. In such situations ambiguities are likely to arise 
 and we suggest that ambiguous pictures based on the figure-ground relationship are 
 of this type. A well-known example is the picture consisting of a vase and two 
 profiles illustrated in Fig. J. 
 
 -16- 
 
FIGURE 7- VASE 6 2 PROFILES 
 
 FIGURE & A TRIPLY AMBIGUOUS FIGURE 
 
 -17- 
 
Another type of ambiguity is illustrated in Fig. 8. This picture, 
 which we have constructed, is triply ambiguous. It can be viewed as two 
 equilateral triangles, or as two parallelograms, or as two hour-glass -like 
 figures. We shall consider this picture in greater detail presently, but, for the 
 moment, suggest that the type of ambiguity illustrated here is somewhat analagous 
 to the phrase -structure -level ambiguity in the language model. 
 
 Finally, we have constructed in Fig. 9« a > a n ambiguous picture which 
 is a variant of the original "My wife - My mother-in-law" picture introduced by 
 Boring [2]. This variant, except for its 'streamlined' aspects, has the same 
 structural ambiguity as Boring's original picture. We suggest that ambiguities of 
 this type are most readily comprehended (and hence resolved) by considering the 
 picture as transforms of certain underlying unambiguous pictures. Figures 9-b and 
 9»c show the underlying pictures in terms of which the ambiguity implicit in Fig. 9» a 
 can be resolved. It is our view that the ambiguity associated with the well-known 
 reversible cube is also best understood along these lines. 
 
 We have seen earlier that in certain cases --especially at the phrase 
 structure level- -the preferred construction can be explicitly exhibited by 
 auxiliary brackets. By analogy it would seem that the same kind of resolution 
 should be possible with pictures. Recalling that according to Gestalt principles 
 similar figures tend to be organized together (see Section 3)> it is easy to check 
 this conjecture. In Fig. 10 we have redrawn the ambiguous picture of Fig. 8 
 but explicitly imposing a preferred phrase structure for two of the lines. It 
 is evident that this imposed organization is consistent with only one of the three 
 possible "readings," namely, that into two parallelograms. Comparing Figs. 8 and 
 10, it does seem that in the latter the two -parallelograms aspect is much more 
 stable. That the same arguments can be extended even when the ambiguous picture 
 consists of dots instead of lines is verified by comparing Figs. 11. a and 11. b. 
 
 -18- 
 
FIGURE 9.a 
 
 FIGURE 9.b 
 
 FIGURE 9.c 
 
 FIGURE 9= PORTRAIT OF TWO WOMEN 
 
 -19- 
 
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 -20- 
 
6. Some Further Implications of the Syntactic Model 
 
 As was mentioned at the start of this paper, our ultimate goal is the 
 construction of a phenomenalogical model in terms of which known psychophysical 
 phenomena associated with the visual process could he adequately described and 
 studied. As a first step towards this end we have been concerned here with two 
 aspects of the visual process which have received great attention in the psychological 
 literature: the Gestalt qualitat of the data in the visual field and the occurrence 
 of ambiguous figures. Our point of departure was a, certain Syntactic Model for 
 picture processing which was originally developed to answer a very specific problem 
 in pattern analysis and description. In the foregoing pages, we have shown that a 
 very simple extension of this model does provide an adequate and intuitively 
 plausible basis for an understanding of these two aspects of the visual process. 
 In this last section, we should like to consider some of the implications and 
 secondary features of a Syntactic Model such as the one we have proposed and 
 see to what extent they conform to results obtained in studies on visual perception. 
 
 1. Any syntax analysis is necessarily a sequential processing scheme. 
 
 In the hierarchic labeling model, for instance, the labeling process at 
 any level, in general, has to wait for the completion of the labeling 
 process in the preceding levels. This would imply that if the analysis 
 is time-limited, only the initial stages of labeling could be realized. 
 The known results from tachistoscopic studies on organization of visual 
 data would seem to be entirely in conformity with this expectation. 
 They seem to add up to the following observations: perceptual 
 organization takes time; that it is a temporal process. There is a 
 primary level of perception at which no grouping occurs. Further- 
 more, there is a direction to this developmental process. Organization 
 proceeds from the simple to the complex. (See, for example, the 
 experiments of Krech and Calvin quoted by Dember [k] and those of 
 Oberly, Bobbit, etc., quoted by Vernon [10].) It should be of 
 considerable interest to make tachistoscopic studies using pictures of the 
 type illustrated in Fig. 9 (see below under (3) for further related 
 discussion) . 
 
 ■21- 
 
A second factor that plays an essential role in the labeling scheme is 
 the grammar „ We have defined a grammar as "being associated with 
 a class of pictures and as something given prior to the labeling. 
 This would seem to imply that before a picture can be labeled it 
 must be assigned to some specific class of pictures. We suggest 
 that this is entirely in keeping with the notion of 'set* as used 
 in the psychology of perception. 
 
 Actually, going a step further, we should like to point out that a 
 Syntactic Model for visual perception provides a very fruitful basis 
 to resolve the conflict between empiristic and organizational 
 theories in regard to form perception (see, e.g., the comprehensive 
 review by Zuckerman and Rock [ll]). Structural linguists distinguish 
 between 'obligatory' and 'optional' rules in syntax analysis. It 
 would seem entirely appropriate to introduce (or, equivalently, 
 look for) the same types of distinctions in the labeling schemata. 
 Labeling rules which apply quite independently of the input picture 
 classification are precisely those which one would characterize as 
 being intrinsic to the process itself (i.e., as the innate organi- 
 zational features )j on the other hand, rules based on grammar 
 associated with particular classes would be the optional ones and would 
 presumably depend on past experience, in so far as grammar is a measure 
 of achieved learning based on prior exposure to the particular class of 
 pictures or on knowledge of the process which generates the pictures. 
 
 It is not necessary to suppose that this assignment to a class of pictures 
 is a rigid procedure which determines subsequent labeling once and for all. 
 It is much more reasonable to assume that classification is also a dynamic 
 procedure and that, in fact, there is bound to be a considerable amount of 
 feedback between labeling and classification. For our immediate purpose 
 all that we argue is that, at any given level, grammar -dependent labeling 
 necessarily presupposes some classification of the input picture at that 
 level. 
 
 Parenthetically, it may be remarked here that we do not believe that, in actual 
 perception, labeling is always carried through to its completion over all the 
 hierarchical levels. It is extremely likely that labeling is terminated as 
 soon as the description, sufficient for the purposes on hand, has been 
 achieved. A good part of the occasional "MISREADING" of a picture is 
 understandable along these lines . 
 
 -22- 
 
3„ The remarks on decomposition into subpictures in Section k show 
 that processing according to the syntax model could become fairly- 
 complex if the original configuration in the visual field cannot 
 he described in terms of a single figure and ground. It should be 
 highly instructive to study to what extent this is borne out in 
 actual perception o Figure 12, although quite straightforward in its 
 organization, indicates that its visual comprehension does require 
 great effort. Tachistoscopic studies on similar pictures should 
 throw considerable light on the sequential nature of the organization 
 process. 
 
 If one accepts the plausibility of a syntactic scheme — in some such version 
 as we have indicated in this paper- -as a metatheoretically appropriate framework 
 for the description and study of the visual process, it would seem that for the 
 next step in the development of a model it is necessary to be able to answer 
 questions of the following kind: How much of the labeling is done in parallel 
 and how much serially? Does scanning the visual field play an intrinsic role 
 in labeling? If so, at what level? At any given instant, is it possible for 
 different parts in the visual field to have reached different levels in the 
 labeling hierarchy? Is it possible to label simultaneously non-overlapping 
 fields using different grammars? Can this be done even if the fields overlap? 
 
 Such visual perceptual situations as these occur rather familiarly 
 while viewing motion pictures. In some of the more sophisticated 
 productions, quite often the credit titles are shown superimposed 
 on the initial segment of the main picture sequence. 
 
 -23- 
 
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 -2U- 
 
References 
 
 1. D. C. Beardslee and M. Wertheimer: Readings in Perception, 
 
 D. Van Nostrand Co., Inc., (1958). 
 
 2. E. G. Boring: A New Ambiguous Figure, Am. J. Psychology, 
 
 i£, (1930), kkk-h5. 
 
 3. J. S. Bruner: Neural Mechanisms in Behaviour, The Brain and the 
 
 Human Behaviour, Vol. 36, Proc. Assoc. Res. Nervous and Mental 
 Disease, (Baltimore, 1958), Pp. 118-43. 
 
 k. W. N. Dember: The Psychology of Perception, Henry Holt and Co., (i960). 
 
 5. W. Kohler: Gestalt Psychology , Mentor: MD279, (19V7). 
 
 6. R. K. Rice and R. Narasimhan: Bubble Chamber Scanning Program: LABEL, 
 
 Digital Computer Laboratory, File No. 5^-2, June 1963, University 
 of Illinois. 
 
 7- R. Narasimhan: A Linguistic Approach to Pattern Recognition, 
 
 Digital Computer Laboratory, Report No. 121, July 19&2, University 
 of Illinois. 
 
 8. R. Narasimhan: A Programming Language for the Parallel Processing of 
 
 Pictures, Digital Computer Laboratory, Report No. 132, January 1963, 
 University of Illinois. 
 
 9. J. H. Stein: PAX, an IBM-709O Program to Simulate a General Purpose 
 
 Pattern Recognition Computer, Digital Computer Laboratory, 
 File No. 513> January I963, University of Illinois. 
 
 10. M. D. Vernon: A Further Study of Visual Perception, Cambridge Univ. 
 
 Press, (1952). 
 
 11. C. B. Zuckerman. and I. Rock: A Reappraisal of the Roles of Past 
 
 Experience and Innate Organizing Process in Visual Perception, 
 Psych. Bull., 5K (1957), 269. 
 
 -25- 
 
Appendix 1 
 (in Collaboration With J. P. Fornango) 
 
 We give here two examples of input pictures processed according to the 
 extended Syntactic Model (i.e., the recursive labeling scheme) described in 
 Section K. The illustrations shown are actual outputs from an IBM-7090 computer. 
 The Syntactic Model was simulated using PAX,, a general purpose parallel processing 
 simulator that has been written for this computer [9]. (For a detailed account of 
 the nature of computations involved in parallel processing and for the system 
 organization of a parallel processing computer, see 18],) 
 
 The design of the simulator limits the extent of the input 'visual 1 
 field to a mosaic of 72 x J2 points. As will be seen from the two input pictures 
 shown (Figures 13 .a and 13.e), this resolution is not fine enough for a proper 
 delineation of the squares and diamonds which make up the organizations in the 
 field. Hence, in the first cycle of recursion, we used a rather ad hoc labeling 
 scheme to separate out the subpictures (shown in Figs. 13.b and 13. d, respectively). 
 More general labeling algorithms can be constructed to identify squares, circles, 
 triangles and other familiar geometrical figures. A labeling scheme based on these 
 could, of course, be used if the resolution of the input field were sufficiently 
 fine. 
 
 In smearing the subpictures, the quantitative measure used was to replace 
 each black point by a set of nine points, viz., the original point and its eight 
 immediate neighbors in the mosaic. 
 
 For the second cycle in the recursion, these two new subpictures should 
 have been labeled using a recognition program for alphanumeric characters. We 
 did not have such a program readily available to us. So the labeling was done 
 using a scheme that has been devised for processing bubble chamber pictures 
 (for details, see [6]). This labeling algorithm is set up to convert the input 
 picture into a labeled graph. It accomplishes this by first thinning the roads in 
 the input picture suitably and then assigning directional labels to the road segments 
 
 -26- 
 
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 SUBHCTUHCS AFTER FWOT OfCLE 
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 Ml Ml Ml HI 111 
 
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 Ml III XII III 
 
 Ml MX UK MX 
 
 Ml XXX MI XIX IXX 
 
 III 1AK III 
 
 Ml XII III 
 
 111 
 III 
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 111 IIX IIX 1X1 
 
 XXX III XXI 
 
 xn xn in 
 
 -27- 
 
 Cft( HOC LUP CO 
 
 OOA noo COO 
 
 ooo cno run 
 
 000 CrtC cw 
 
 oon boo cod in 
 
 OOP coc con 
 
 )0i rt c r-pr pi' 
 
 sss sss sss sss 
 jSS sss sss sss 
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 SSS SSt 00" nun 9PP OOP DOC 
 
 sss s-.s SSS SS 
 
 ') 
 
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 sss 
 
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 sss 
 
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 a 
 
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 inir 
 
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 SSS SiS sss sss sss -ss 
 
 ,-»i S . . S55 iSS SS 1 . SSS 
 SSS SSS SSS SiS sss sss 
 
 "ii poo "tor 
 
 S'.S .SS SSS SSS SSS SSS SSS SSS 
 
 SSS SSS S',S sss sss sss sss sss iino oon POO 
 
 SSS SSS SSS jSS SSS SSS SSS SSS it n 
 
 tioo cou 30ii ijun oo*> non 
 
 nop noo oon 
 
 oon ono onu oon i op nop nnP doo 
 
The directional labels assigned as N, E, A, B, as explained in the tabulation in 
 Section 2. Junctions, bends, etc., where two or more road segments meet, are 
 identified by the multiple labels assigned to them. In the computer outputs 
 shown, the following code has been used: 
 
 E,A: 3 
 
 A,B: 
 
 E,N,B: k 
 
 E,N: 5 
 
 N,B: 2 
 
 A,N,B: 8 
 
 E,Bs 9 
 
 E,A,N: 7 
 
 E,A,N,B: U 
 
 A,N: 6 
 
 E,A,B: 1 
 
 
 Points not assigned any of these labels are referred to as 'nulls' and are shown in 
 the outputs by asterisks (*). A region in the field consisting entirely of nulls 
 would be interpreted as an undifferentiated 'black' area. 
 
 The separation into 'Figure' and 'Ground' after the second labeling cycle 
 is clearly evident in Figs. 1^ and 15. Further smearing and labeling does not 
 generate any new subpictures and so the processing ends here. 
 
 
 -28- 
 
IIX *** » 
 
 «IIX«I(I<' 
 XXXXXtXXII 
 XIIXKXXXXI 
 1>X >** * 
 
 XX< XII III XII HI (U Wfl NltS *** KM ■ *» 
 
 <ixx> <xxxaxXtx«xxt*iM«:XXXV*XIK«x«'XXXXlX>Xinx 
 
 XXXXXXXXXXXXXXXXXJiXXXXXXXXJMXXXXXXXXXXlt XI 
 XXXXX XXXXIIXX XX XXXXXXXXXIUXMXXIXXXXKIIX XX 
 • << XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX 
 X XXXXXX XX XX*XXXXXXXXXXXX*XinrXXX*XXXXX*M ** 
 XXXXXXX XKXXXXXX XX XX XXXXXXXXIXXlXUXXXXXV*' XX 
 XXXXXXXXX*X*XXXXXXXKXXXXrX*X*MaXXrXXKlXVXX XX 
 XXX XXX XXX ■<* XXX XXX X|I XXX XMX XXX XX 
 
 xxxxxxxx xxxxxxixxxmnxxxxxxi »i 
 
 (XXXXXXX XXXXXXXIXWXXXJIXXXXXIX X| 
 
 KXXXXXXX XXXKXXXXIXJKIXKXXXXXXI IX 
 
 xxx Hi XXK XXX XXX tiu xv* xx 
 
 (xxx ixKxxxxttfxxuxxxwxxxxx XI 
 
 ixxx xxxxxxxxxxxxxvxxxxxxi xx 
 
 (XXX X*|XXXX»XXIX*X*XK»XX Hi 
 
 (XX XIX XXX XXI XXX XXX «x 
 
 (XXX XXXXXIXXKXtXftXMX xx 
 
 <xkx xxixxxxxxxxxxixxx XX 
 
 XXXXXXXXIXI 
 
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 1 XXX XXV XXX 
 
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 ■ • ocaXXXx*! 
 
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 xxxxx 
 
 
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 Xf XXXX XX XXXXXXXXX XXXI 
 
 
 xttixxxxxxxx 
 
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 KXXXXXXftl 
 
 
 XXIXXD XXXXX 
 
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 XXXI XX, 
 
 XXXXXXXXX 
 
 XXX 
 
 XXIXXXIIRX 
 
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 ««»' "• 
 
 tfVJl 
 
 xxxxxx 
 
 XXXI'-""" 
 
 XXI 
 
 
 n»>: ■ ■>*// 
 
 XXX 
 
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 XXIXXXXXXX//X 
 
 
 
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 xxxaXRixxxixxxx 
 
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 XXXXXXX XX XXXXXIXXXXXXXXXXX 
 
 IIIIXXXXKXXMXXXXXXX 
 
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 HIIIIIXXXIXXXXXXXX 
 
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 IHIXXRKIXIKXXXXXXXX 
 
 XXXXXX XXXXXXXX 
 
 x»xxxx>«« 
 
 1***1 »XKXI XXXXXXXXX 
 
 IXIXIIXIIIXIXX 
 
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 XXIXXIKXIIXIX 
 
 
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 ■KIXKXXXXXXXX 
 
 
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 •IIIXXRRXXIIIHIX* 
 
 
 IKXXIXXII 
 
 XXXXXXXXXXXXX 
 
 
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 KXIXXXIkllXII 
 
 
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 lUI/lllMMK 
 
 
 IXXIXXXII 
 
 XXXXIXIXIIXttX 
 
 
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 above-. SUBPICTUKE3 AFTER SMEARING 
 
 FIG. 14 
 ( input as in 13a ) 
 
 below: AFTER SECOND CYCLE LABELING 
 left: GROUND right: FIGURE 
 
 •*«•»•»•>*••• 
 
 •••»•••»• 
 
 * 
 « 
 
 »»» 
 
 MM 
 W> It 
 
 HtHliliiflli 
 
 -29- 
 
XXX KXX III 
 
 MUMIUUU 
 
 IX XIX III 1X1 IXX XII IXM 
 IX1IXIIRXIIXXIXIIIIIXIIMXI 
 
 MKKIUUIMOIKIKIIll 
 
 IIXXIXKIII 
 
 XXX IXX XXX XIX XIX X' 1 
 IXXIIXXIXIIXXXIXXXXIIXK 
 
 XIXXXIXXIXXXXXXXXIIXX'IX 
 IIXIXXIXXXXXXXXXIXXXXKXI 
 
 IIIIXIXftlXXKXXXX 
 XXIIXIXllXXXIXXI 
 XIIIXXIXXXISXXXX 
 
 .•....<<...<■'. 
 
 M>u ..iKun 
 
 IXIkXIXIXXXIIXXKX'IHXIXIXH 
 
 IXUXXXXXXXXIXXXX'XXXXXXIX* 
 
 (XX«*IXIK1IIXI*'*XXXIXXKXX 
 
 XXX XXI XXX XXI IXK IXX UN 
 
 IXXIXIIXXXXI 
 
 II III "■ i 111 
 
 (XI'MXIIXXXI 
 
 fiuu . < ■ « lum 
 
 XKXXXXIIIKXXIXIX 
 
 lUii'iiinuu. 
 
 ■ ildimiiiin- 
 iliuiuiiinu. 
 IKXII 
 
 ■ XXIX 
 KKXXX 
 XXXIX 
 
 XXXIIXXXXI1XX 
 
 XXXXIXXXXIIXI 
 
 "iK.inuin 
 XXXXXXXXXXKXIXIXX 
 
 J 
 
 : 
 
 dim 
 
 IXXXXX 
 
 
 
 X 
 
 IIXIII 
 1XXKII 
 
 XXXII 
 XIKXX 
 XXXII 
 
 
 
 IXXIX* 
 
 XXI 
 
 IxKXXIIXX 
 
 IlilllU' 
 
 mil 
 
 "in 
 
 XXXIX 
 
 "in 
 
 XIIII 
 
 XXIII 
 XXXXI 
 XXIKX 
 
 obove: SUBPICTURES AFTER SMEARING 
 
 FIG. 15 
 (input at in 13c) 
 
 btlo«: AFTER SECOND CYCLE LABELING 
 left: GROUND right: FIGURE 
 
 LUEtfc£EFEEEE£EEc£eE£fcEEEE££t£c = = C = EEt: 
 
 LfitfcEtettt 
 
 kt£tlttEEtElllt f .E€tttLtlttE£c 
 
 -30- 
 
JUN 2 01969