representation and matching pictorial structuresgrauman/courses/spring2007/...control theory...

67IEEE TRANSACTIONS ON COMPUTERS, VOL. c-22, NO. 1, JANUARY 1973

[4] K. D. Senne and R. S. Bucy, "Digital realization of optimaldiscrete-time nonlinear estimators," in Proc. 4th Annu. PrincetonConf. Syst. Sci., 1970.

[5] R. S. Bucy and K. D. Senne, "Digital synthesis of non-linearfilters," Automatica, vol. 7, pp. 287-298, 1971.

[6] E. C. Tacker and T. D. Linton, "Digital and hybrid simulationof a discrete-time optimal nonlinear filter," in Proc. 4th HawaiiInt. Conf. Syst. Sci., 1971, pp. 465-467.

[7] -, "Digital and hybrid simulation of a Bayes-optimal non-linear filter," Studies in Digital Automata, Louisiana StateUniv., Baton Rouge, Air Force Office of Scientific ResearchContract F-44620-68-C-0021, Tech. Rep. LSU-T-TR-40, Sept.1970.

[8] R. E. Mortensen, "Mathematical problems of modeling sto-chastic nonlinear dynamic systems," J. Statist. Phys., vol. 1, no.2, 1969.

[9] C. W. Helstrom, "Markov processes and applications," in Com-munication Theory, A. V. Balakrishnan, Ed. New York:McGraw-Hill, 1968.

[10] R. S. Bucy, M. J. Merritt, and D. S. Miller, "Hybrid computersynthesis of optimal discrete nonlinear dynamic systems," inProc. 2nd Symp. Nonlinear Estimation Theory and Its Applica-tions (San Diego, Calif.), 1971.

[11] ,"Hybrid synthesis of the optimal discrete nonlinear filter,"Stochastics, vol. 1, Jan. 1973.

[12] D. S. Miller, Ph.D. dissertation, Dep. Elec. Eng., Univ. South-ern California, Los Angeles, 1972.

Edgar C. Tacker (S'59-M'64) was born in Savannah, Tenn., onSeptember 26, 1935. He received the B.S. degree (with distinction) inelectrical engineering from the University of Oklahoma, Norman, in1960, the M.S. degree in electrical engineering from New YorkUniversity, New York, N. Y., in 1962, and the Ph.D. degree fromthe University of Florida, Gainesville, in 1964.

IN 01!31,11~5~Q~N, ~0 His industrial experience includes two:1_ i 5years as a Systems Engineer with Bell Tele-

8 phone Laboratories, Inc. He is presently anAssociate Professor in the Departments ofElectrical and Chemical Engineering, Loui-siana State University, Baton Rouge. He hasdeveloped graduate courses in applied func-tional analysis, systems science, and digitaland hybrid computation at LSU and MichiganState University, East Lansing. His currentresearch interests are in the areas of stochastic

control theory and multilevel system theory, with emphasis on com-putational aspects. He has applied these theories to problems involv-ing the control of chemical processes and interconnected electricalenergy systems.

Dr. Tacker is a member of Tau Beta Pi, Pi Mu Epsilon, and EtaKappa Nu.

Thomas D. Linton was born in Frost, Ohio,on November 9, 1944. He received the B.S.

i degree in electrical engineering from the Uni-versity of Arkansas, Fayetteville, in 1967, andi% the M.S. degree in systems science fromMichigan State University, East Lansing,in1969.He is presently working toward the Ph.D.

degree in the Department of Electrical Engi-neering, Louisiana State University, BatonRouge.

Mr. Linton is a member of Eta Kappa Nii and Phi Kappa Phi.

The Representation and Matching of Pictorial StructuresMARTIN A. FISCHLER AND ROBERT A. ELSCHLAGER

Abstract-The primary problem dealt with in this paper is thefollowing. Given some description of a visual object, find that objectin an actual photograph. Part of the solution to this problem is thespecification of a descriptive scheme, and a metric on which to basethe decision of "goodness" of matching or detection.We offer a combined descriptive scheme and decision metric

which is general, intuitively satisfying, and which has led to promis-ing experimental results. We also present an algorithm which takesthe above descriptions, together with a matrix representing the in-tensities of the actual photograph, and then finds the describedobject in the matrix. The algorithm uses a procedure similar todynamic programming in order to cut down on the vast amount ofcomputation otherwise necessary.

One desirable feature of the approach is its generality. A newprogramming system does not need to be written for every newdescription; instead, one just specifies descriptions in terms of acertain set of primitives and parameters.

There ate many areas of application: scene analysis and descrip-tion, map matching for navigation and guidance, optical tracking,

Manuscript received November 30, 1971; revised Mav 22, 1972,and August 21, 1972.

The authors are with the Lockheed Palo Alto Research Labora-tory, Lockheed Missiles & Space Company, Inc., Paln Alto, Calif.94304.

stereo compilation, and image change detection. In fact, the abilityto describe, match, and register scenes is basic for almost anyimage processing task.

Index Terms-Dynamic programming, heuristic optimization,picture description, picture matching, picture processing, represen-tation.

INTRODUCTIONTllHE PRIMARY PROBLEM dealt with in thisT paper is the following. Given some description of

a visual object, find that object in an actual photo-graph. The object might be simple, such as a line, orcomplicated, such as an ocean wave, and the descriptioncan be linguistic, pictorial, procedural, etc. The actualphotograph will be called the "sensed scene," a two-dimensional array of gray-level values, while the objectbeing sought is called the "reference."

This ability to find a reference in a sensed scene, or,equivalently, to match or register the images of twoscenes, is basic for almost any image processing task.Application to such areas as scene analysis and descrip-tion, map matching for navigation and guidance, optical

1EEE TRANSACTIONS ON COMPUTERS, JANUARY 1973

tracking, stereo compilation, and image change detec-tion is direct and obvious.There are two basic approaches to solving the image-

matching problem as defined above.If we possess a precise description of the noise and dis-

tortion process which defines the mapping between thereference and its image in the sensed scene, we can em-ploy statistical decision theory techniques to derive animage-matching procedure which optimizes some objec-tive criterion (e.g., minimum error, or minimum risk,in determining the best embedding of the reference inthe sensed scene). A typical outcome of such an analysisis the use of a correlation-like matching procedure. How-ever, in most practical problem situations, the requirednoise and distortion model is not available, nor is itfeasible to attempt to construct one. For example, wemight consider all human faces to be perturbed versionsof some single ideal or reference face. However, to at-tempt to define completely a valid noise and distortionmodel for this situation would be a hopeless task.A second and more general approach to the image-

matching problem bypasses the need for a noise and dis-tortion model by accepting an embedding metric with-out requiring its justification as being equivalent to aminimum error (or minimum risk) procedure. In fact,without a noise and distortion model, there is no the-oretically valid way to derive or predict the error per-formance of a selected procedure prior to its actualapplication. Our primary concern in this paper is withthis latter case.We offer the following two sets of criteria for an em-

bedding metric not theoretically derived on the basisof error performance. First, it must be successful inapplication (i.e., its observed error performance mustbe acceptable), intuitively satisfying (so we can havesome confidence in its ability to deal with as yet untriedapplications), and general enough so that it can be em-ployed over a wide range of problems without significantmodification. Second, it must be possible to specify acomputationally feasible decision algorithm which se-lects a suitable embedding based on the given em-bedding metric. (The combination of embedding metricand corresponding decision algorithm will be called anembedding model.) In the remainder of this paper, wewill present an embedding metric and correspondingdecision algorithm, present examples of the applicationof this embedding model to a number of distinct prob-lem areas, and show how this embedding model is rele-vant to the problem of scene representation as well as toimage matching.

AN EMBEDDING METRIC

To introduce the generic form of our embeddingmetric, and establish its intuitive validity, let us firstconsider the following process. Assume that the refer-ence is an image on a transparent rubber sheet. Wemove this sheet over the sensed image and, at each pos-sible placement, we pull or push on the rubber sheet to

get the best possible alignment between the referenceimage on the sheet and the underlying sensed image.We evaluate each such embedding both by how good acorrespondence we were able to obtain and by how muchpushing and pulling we had to exert to obtain it.

Let us now consider a discrete version of the aboveprocess which is both more precise and more reasonablefrom an implementation standpoint. In a specific appli-cation, we might have some information on the rangeof permissible distortions that can occur between thereference and sensed images. For instance, some subsetof the items appearing in the sensed image might alwaysretain their internal shape even though their relativepositions might be subject to change with respect totheir locations in the reference scene. Further, wherechange of relative position is possible, we might be ableto bound the extent of such change; and, finally, wemight like to assign variable "costs" to the differenttypes of change of relative position or relative change insome nongeometric attribute.To achieve these capabilities, we replace the rubber

sheet by a reference image which is composed of a num-ber of rigid pieces (components) held together by"springs." A rigid piece of the reference image can be assmall as a single resolution cell, or as large as the entirereference image, and corresponds to a single coherententity in the reference image. The springs joining therigid pieces serve both to constrain relative movementand to measure the "cost" of the movement by howmuch they are "stretched." (Typically, the springs willbe highly nonlinear in their behavior.) In determiningthe cost of an embedding, we measure the "tension" oneach spring (the tension can be a function of directionas well as stretch or even a relative change in somelocally defined attribute), and also make a local evalua-tion of how well each coherent piece is embedded as anindependent entity.The above model permits two interesting dichotomies.

The first dichotomy is the separation of "syntactic" and"semantic" information. The semantic information,which is application dependent, is embodied in thespecific partitioning of the reference into coherentpieces, the placement and cost functions assigned to thesprings, and the cost functions associated with the inde-pendent embedding of the coherent pieces. The syn-tactic information, which is relatively independent ofthe particular application, defines the class of descrip-tions which the algorithm can process. These data areembodied in the limits set on reference decomposition(e.g., number and maximum size of pieces, etc.); in theformats which must be employed to specify the globalconstraints and costs; and in the form of the embeddingmetric which evaluates "global" fit. The separation ofsemantic and syntactic information is essential to per-mit application of the model to a broad range of prob-lem areas without the necessity of making significantchanges in the implementation.The second dichotomy is the separation between the

68

FISCHLER AND ELSCHLAGER: PICTORIAL STRUCTURES

local and global evaluation functions. The global evalu-ation function, associated with the relative positioningof the coherent pieces as described previously, hasstrong syntactic controls on its form to permit its inte-gration directly into the decision algorithm. This is im-portant because the global evaluation produces the mostsevere combinatorial problems. A local evaluation func-tion, associated with how well a given coherent piece isindependently embedded, is easily changed from prob-lem to problem (based on problem-dependent considera-tions) without requiring any change in the core algo-rithms. Thus, the form of a local evaluation functioncan be a (conventional) correlation function togetherwith a pictorial reference component, or a procedurebased on linguistic concepts together with a formaldescription of a reference component,' or even a seriesof guesses in'serted interactively by a human evaluator.The decoupling of the local evaluation functions fromthe core algorithms provides a great deal of flexibilityin' making changes or improvements in the evaluationfunctions for a given problem, as well as when switchingfrom problem to problem. Further, because of the aboveseparation, the performance of the algorithms (bothlocal and global) can be independently evaluated in adirect and intuitively obvious manner. Such an evalua-tion then permits iterative improvement in performanceby selective alteration in the problem-dependent options.We are now in a position to present formally the pro-

posed embedding metric. Let the reference be composedof p components (i.e., p coherent, or primitive, pieces).For 1

IEEE TRANSACTIONS ON COMPUTERS, JANUARY 1973

global (intercomponent) constraints, and, if acceptable,then evaluate the embedding metric for the given selec-tion. Obviously, such an approach is completely imprac-tical even for small pictures. For example, a 50X 30 SM(M = 1500) and a 5 X 5 RM (N = 25) would require morethan 1054 selections and evaluations, a hopelessly largenumber. If we assume that the coherent and relationalconstraints provide us with P = 6 nonoverlapping com-ponents, each component sequentially constrained tostay within w = 10 locations referenced to the locationof the previously placed component, then we would stillbe required to perform on the order of 1500 X 105= 1.5 X 108 evaluations. Assuming 10-3 s per evaluation,we would require 1.5 X 105 s or approximately two daysof computation time. It is thus obvious that a moreeffective technique is required.

Dynamic ProgrammingExpressed in formal terms, the evaluation of the em-

bedding metric for a typical picture results in a non-linear, integer programming problem with local optimadifferent from the global optimum (i.e., no particularregularity, such as unimodality). The only availableclass of computational procedures for finding the globaloptimum under the above conditions (other than the ex-haustive search techniques discussed earlier) is usuallydesignated by the generic name dynamic programming.DP is a multistage or iterative optimization proce-

dure which can be described in general terms as follows(see [6] and [7]). We wish to find

min G(X) = E h(Xi) (3)X iEI

where X= {X1, X2, , xp4, each xi, 1


table forfk and yk*. The number of lookups required forthe construction of this kth table will be proportional tothe number4 of its rows- [AMD(G)j] and (for each row)the constrained number of feasible locations of the-vari-able being eliminated (denoted Wk, whereWk


responding locations of the embedded components aredetermined from Y [see (20)].7

Given the restriction that the hi in (3) are independentof all xj forj > i [this is consistent with the embeddingmetric as presented in (2) ], then dynamic programmingcan be viewed as a procedure for finding the shortestpath through a graph. We define this graph in the fol-lowing way. The nodes of the graph are arranged in pcolumns, where each node in the ith column is labeledby the values of the variables corresponding to a uniqueset of embeddings for the first i components; there areas many nodes in the ith column as there are uniqueembeddings of the first i components. The length of abranch between a node in column i -1 (with label Xi1)and a node in column i (with label Xi) is hi(Xi). Wedelete branches with infinite length.To determine the shortest path from the root node

(a single node placed in column zero) to some node incolumn p, we can proceed as follows. In the ith column,for each node, sum all the branch lengths correspondingto the label of the node. We now determine that set ofvariables (xi) which do not appear in any hj for j> i,and call this set of variables Zi (the variables in Zi cor-respond to components in columns ji). We now place the nodes in the ith column intosets, such that, for each set, the nodes are identical intheir labels except for the variables in Zi. For each suchset, we retain the node with the shortest path lengthfrom the root node, and delete all the other nodes in theset as well as those nodes in columnsj>i which branchfrom deleted nodes. It is this pruning process whichgives DP its computational advantage over completeenumeration. After the above set of operations is carriedout through the Pth column, we select the node definingthe shortest path through the tree, and thus the lowestcost embedding for the P components. The LEA differsfrom DP in that in the sequential determination of theshortest path, a maximum of only mi nodes will be re-tained in the ith column (mi is the number of permissiblelocations for embedding the ith component). In pro-cessing the ith column, the nodes are grouped into setssuch that, for each set, the nodes are identical in theirlabels for xi. For each such set we then proceed as in theDP case. Thus, at the ith iteration we save only the mi"best" current embeddings, such that every possible

7The yi defined in (16) clarify the presentation of the LEA. How-ever, in a computer implementation one need Inot calculate these yi,which are arravs, each element of which is a sequence of locations.Rather, it is only necessary to compute a more restricted funiction Zidefined by

Zi (Xi) = Xi-lwhere xi- is that value which minimizes the previous equiation

These zi are arrays, each element of which is a single locatioiirather than a sequence of locations. Then in the compuitations in-volving the Si, if Si depends on more than the two rightmost loca-tions of y_ (xi-,)*xi, the additional locations may be retrieved fromthe Zk, 1


YSM

44 5 2 8

3 7 5 1 3

2 8 1 5 7

1 4 3 2 4

1 2 3 4 -_z

C1 (1, 1)

c2 (1,1)

C3 (1, 1)

C4 (1,1)

4Q-L C2

2 3

= CI =36C2 4

=C3 =5=C4 =3

I(z Y) = I SM(z,Y) Cifor I i - 4

Spring definition when (i, j) = (2, 1) or (i,j) - (4,3)

Xi - Xj =(Zi - Zj J _ yj) gi (xi- X)1,0 02,0 1

otherwise

Spring definition when (i,j) - (4, 1) or (i,j) = (3,2)

xi-=xj- (zi- zi Yi Yj) g.i(Xi-x.)0,1 00,2 1

otherwise

(b)

Evaluation of g2

x2 x1 61 s2z2 Y2 z1Y1 I1 12 g21 9224 14 1 2 0 3

3 4 1 4 1 4 1 6

2 4 4 4 0

4 4 2 4 4 4 1

3 4 2 4 0 6

2 3 1 3 1 1 0 2

3 3 1:3 1 3 1

2 3 1 3 0 4

4 3 2 3 1 1 1 3

3 3 5 1 0

22 1 2 2 3 0 5

3 2 1 2 2 1 1 4

2 2 5 1 0

4 2 2 2 5 3 1

32 1 3 0 4

Evaluation of 93

x3 x2 x s3

z3 33 z2 Y2 zlyl 13 g32 g2 g32 3 2 4 1 4 0 0 3 3

3 3 3 4 1 4 4 0 6 10

4 3 4 4 3 4 2 0 6 8

2 2 2 3 1 3 4 0 2 6

2 4 4 1 3

3 2 3 3 2 3 0 0 4 4

3 4 0 1 6

j4 2 4 3 2 3 2 0 3 5

4 4 2 1 6

2 1 2 2 2 0 5

2 3 1 3 2 1 2 5

3 1 3 2 1 2 3 0 4 7

3 3 3 1 4

4 1 4 2 3 2 1 0 4 5

4 3 1 1 3

Evaluation of g4 = G

x4 23 xl 94Z4y4 Z y33 1 Y 6g43 g41 S4 14 g3 G

1 3 2 3 1 4 0 0 0 4 3 7

3 3 1 4 1 0 1 4 10 15

2 3 3 3 1 4 0 2

4 3 3 4 1 2

3 3 4 3 3 4 0 0 0 2 8 10

1 2 2 2 1 3 0 0 0 5 6 11

3 2 2 3 1 5

2 2 3 2 2 3 0 0 0 2 4 6

4 2 2 3 1 0 1 2 5 8

3 2 4 2 2 3 0 2

1 1 2 1 1 3 0 1 1 1 5 7

3 1 1 2 1 0 1 1 7 9

21 31 12 0 0

41 32 1 0

31' 4 1 3 2 0 0 0 1 5 6

(c)

Fig. 1. An example illustrating the operation of the linear embedding algorithm. The definitions of x, gij, I, are given on pagesz and y are the components of x; that is, x = (z, y). (a) The sensed image. (b) The reference description. (c) Linear embedding algorithm.

73

x= (z Y)

1,42,43,44,41,32,33,34,31,22,23,24,21,12,13,14,1

SM (Zty)

5288751381574324

(a)

-[ (2, 3), (3, 3), (3, 2), (2, 2)]

-I (3, 2), (4, 2), (4, 1)(3, 1)]


ponents, or perhaps by someone guessing at what a"good" embedding might actually look like.) Now, em-ploying the LEA (or DP) to place and evaluate thecumulative cost of placement of the components se-quentially, we can eliminate from further considerationany of those placements whose costs exceed the boundestablished by our best trial embedding. It should benoted that this technique is valid only if the cost asso-ciated with the embedding of each component is non-negative. However, this can almost always be the casefor the class of problems we are discussing in this paper.A heuristic embellishment of the above branch-and-

bound technique would be to use some fraction (say[k/N]') of the bound at the kth stage of an N-stageprocess as the threshold for eliminating a possible se-quence of embeddings.

Scale and Rotation (S&R) ConsiderationsIn attempting to match or register two images, we

frequently are faced with the problem of unknown rela-tive scale and orientation. While such variations areconceptually indistinct fromn any of a host of unwantedvariations between the reference and the image, they(S&R) can serve as a vehicle for clarifying some im-portant issues pertaining to the way the LEA is em-ployed.As noted in earlier sections, the embedding process is

carried out at two levels. First, the components of thereference are searched for as independent entities. Theparticular processes by which these searches are exe-cuted are not a direct issue of concern here; the im-portant point is that, regardless of the search mecha-nism, the outcome of the search for any individual com-ponent is presented to the LEA by a tabulation calledthe local evaluation array [L(EV)A]. Each entry in theL(EV)A corresponds to a possible embedding in theimage of the associated reference component, indexed bythe variables used to define the embedding. The entryconsists of a number related to the probability that the-component is actually present at the "location" specifiedby the indexing variables, and each entry can also con-tain the values of attributes of the component as mea-sured at the indexed location. The LEA has no knowl-edge of the component beyond what is presented to itin the L(EV)A for that component. The purpose of theLEA is to integrate global or structural knowledge withthe information provided in the L(EV)A's to find thebest overall embedding (or embeddings) of the referencein the image. The acceptability of the final embeddingselected by the LEA will thus be dependent on tlhe qual-ity of the information presented in the L(EV)A's,where the extent of this dependence is related to therelative importance of local (component definition) ver-sus global (intercomponent) information for the particu-lar problem. Thus, it is the responsibility of the localevaluation function, in attempting to gather evidenceabout the presence of some given reference component,to be able to deal with the various noise and distortion

Fig. 2. Reference description of a squiare.

processes (such as S&R) which might be encountered.To the extent that these same noise and distortion pro-cesses affect the global or structural relationships be-tween the reference components, the LEA provides themachinery necessary to deal with the resulting problems.

Ability to deal with variations at the global level isaccomplished by defining "attributes" which measure(or estimate) these variations, and then making the"spring" parameters functions of these attributes.Thus, in the case of S&R, if a component Pi has scale

and rotation attributes Si and 01, the springs (vectors)attached to P1 would be (conceptually) scaled as a func-tion of S1, and rotated as a function of 01. The followingexample illustrates some of the above comments.

Problem

Given a two-dimensional region in which there are krandomly oriented and positioned line segments, findthe four-line segments which best approximate a square.Each line is specified by a four-tuple of the type (x, y,0, 1) where the x, y coordinates locate the center of thesegment, 0 specifies the orientation, and I the length ofthe segment. To simplify this example, we will ignorethe detection problem and assume that the given valuesfor each segment are known with probability one. Weassign a cost Ci for each unit of positional disparity be-tween the sides of a candidate square, and a cost C2 foreach degree of rotational disparity between the sides(i.e., sides should meet at right angles).

Solution

Consider a single "local evaluation array" consistingof the given list of four-tuples (x, y, 0, 1). We can con-sider x, y to be the "location" indexing variables, and0, 1 to be attributes. All entries have unit probability,entries with zero probability are deleted. The "descrip-tion" of a square is shown schematically in Fig. 2. Each(spring) vector is rigidly attached to its line segment ata fixed angle of 45°. Costs (C1) associated with (x, y) dis-parity between the end of a vector and the center of thenext line segment are circularly symmetric (i.e., the"cost" function increases with distance from the tip ofthe vector) about the tip of the vector. We also assess acost (C2) proportional to the difference in measured

74


(attribute value) orientation of more or less than 900for sequential line segments.The general form of the LEA, with orientation ad-

justed springs, and spring costs augmented by attribute(S&R) differences, is adequate to deal with the prob-lem as posed. A minor difficulty arises from the fact thatthe orientation of a line segment is actually two valued(i.e., 0 and 0+1800). If we list each line segment twicein the local evaluation array, once for each of its twoorientations, then the LEA can be applied withoutmodification.We can handle squares of differing size by using the

line-segment-length attribute in the same manner as theorientation attribute (except that double entries are notrequired here). Spring stretching is augmented by acost proportional to the difference in length attributefor sequential line segments. That is, when the LEAexamines a new line segment as a possible additionalside for a square already partially formed, it comparesthe length of the new line segment with the length of theline segment in the partial square to which the new seg-ment will be attached. The spring between the new andthe old line segments then is stretched (over and aboveany stretching due to angular and positional disparity)by an amount proportional to the difference in theselengths.

In the above example note that, because each entryin the local evaluation array had either zero (oo cost)or unit (0 cost) probability associated with its occur-rence, the size of this array could be reduced to listingonly those few coordinate combinations associated withthe feasible (nonzero probability) occurrence of a com-ponent (line segment). This procedure can be used inother situations where it is reasonable to reduce all lowprobability entries in the local evaluation array to zero.

PICTORIAL REPRESENTATION

A central problem in much of the work concernedwith the computer processing of pictorial data is that ofrepresentation. Since we cannot manipulate the realworld object (itself) within the computer, we attempt toconstruct a representation (or model) which can be usedin place of the actual object and which has the following(somewhat overlapping) properties.

Complete: Any question of interest which could beresolved by reference to the actual object should also becapable of being resolved by reference to the represen-tation.

Compact: The representation should be free of infor-mation redundant to the purposes for which it will beused. This is necessary to minimize computer storagerequirements.

Transformable: Much of the information contained ina representation will be implicit rather than explicit inform. The ability to manipulate easily the representa-tion to extract required information is essential. Forexample, if we represent a picture by an intensity matrixor raster, then a count of the number of isolated objects

appearing in the picture would be implicit informationwhich could be extracted from the representation afterconsiderable processing. However, if the representationconsisted of the contours of the object appearing in thepicture, then the required count could be obtainedrather simply.

Incrementally Changeable: If we observe a slightchange in the real world object, it should be a relativelysimple and straightforward task to alter the representa-tion. Further, from the standpoint of image matching,a small change in the real world should require only asmall change in the representation.

Accuracy and Simplicity of Translation: Given a realworld object, it should be relatively simple to derive anaccurate representation of the object.Over the past ten years or so, much of the work con-

cerned with pictorial representation has been restrictedto the domain of line type drawings, and the use of for-mal linguistic methods (see [8 ]- [10 ]). Very little successhas been achieved in attempts to extend this work toscenes of terrains, cloud covers, human faces, etc.,which can only be described meaningfully in terms ofpicture components which are not line elements, butwhich are regions with colors, textures, shadings, etc.8

Perhaps the most serious failing of the linguistic (andsimilar) techniques occurs with respect to the "transla-tion" property. These techniques build a representationby constructing a hierarchy based on picture primitives,assembled into linear expressions employing specifiedrelational forms, and satisfying a set of syntax rules. Theproblem arises from the fact that (usually) the onlydirect correspondence between the actual object and itsrepresentation occurs at the level of the primitive ele-ments (typically points, intensities, and lines), while inpractice there are pieces of a picture that are too in-volved or complicated to describe in terms of theseprimitives. Theoretically, the description is possiblesince the matrix representing the picture is finite. How-ever, such a description would be so complicated that,aside from the difficulty of composing it, there would bea considerable likelihood of error and inaccurate repre-sentation.

In the previous portions of this paper we have pre-sented a representational scheme for pictures, and wereprimarily concerned with its application to imagematching. We will now show that the representationalscheme has wide general applicability, and avoids manyof the problems of the linguistic approaches. First wenote that it is a hybrid type of representation in that itinvokes symbolic (numerical) elements as well as allow-ing actual picture segments to be part of the representa-tion. The ability to intermix picture segments and sym-bolic data in the same representation greatly simplifies

8 Specialized systems have been developed, highly tailored tospecific problems, which are exceptions to this assertion; e.g., seeKelly [11]. A number of papers, including Bledsoe [15], [161 and

* Goldstein and Harmon [17], effectively consider the problem of faceidentification based on feature measurements obtained manually.

75


the translation problem. Where a pictorial concept isdifficult to describe symbolically, we can use an actualpiece of the picture as part of the description. A secondaspect of our representation that simplifies the transla-tion problem is the fact that the components (picturepieces, local evaluation arrays, etc.) and the relationalforms (springs) are two-dimensional rather than one-dimensional entities. We thus avoid the problem of hav-ing to construct a one-dimensional model for a two-dimensional structure.

Let us now examine some of the other representationalattributes. Incremental changeability follows directlyfrom ease of translation (although the inverse relation-ship would not necessarily hold). Transformability withrespect to image matching has certainly been estab-lished; the fact that the representation is already intwo-dimensional form, with metric, geometrical, andtopological relationships explicitly and quantitativelyexpressed, implies that transformability for many otherapplications is more than adequate.

In many respects, compactness and transformabilityare antithetical since data in explicit form are usuallymore extensive than the equivalent implicit information.This is the case with our representation. It requires con-siderably more storage than might be required for alinguistic representation.The one area where the linguistic approach has an

obvious advantage is with respect to completeness. Alinguistic representation can treat nonpictorial informa-tion (e.g., relations between items in a picture and otheritems not visible, but perhaps implied or normallyassociated with the pictured items) in a way that wouldbe extremely difficult in our representation. This addi-tional capability could, of course, be achieved by ap-pending the necessary linguistic machinery to our cur-rent scheme, although the final result might well be amixture of two representations rather than one inte-grated representation.

EXPERIMENTAL RESULTS

In order to evaluate the practical implications of thetechniques presented in this paper, we have initiated aprogram involving experiments on a variety of line typedrawings and gray-level imagery. Over 400 experimentshave already been performed with the following generalresults.

1) On well-defined imagery (i.e., relatively noise-freeand unblurred -pictures), the embeddings produced bythe LEA were almost always in agreement with the bestembedding as predetermined by human evaluators.Where the few deviations did occur, they were reason-able, and usually related to the crude component de-scriptions employed.

2) On noisy imagery (course resolution, additiverandom and coherent noise), the fall in performanceparalleled the difficulty human evaluators had in locat-

ing suitable embeddings. Where the components werediscernible in the image, the embeddings were usuallycorrect; those components which were significantlyaltered by the noise were sometimes missed, but thesubstitution error was usually in close proximity to thecorrect embedding location, and, even in error, thecorrect embedding almost always had a score close tothe best score.

Since the programmed version of the algorithm is stillevolving, and some of the discussed features have notyet been implemented (e.g., the "attribute" feature isnot operational as yet), most of the experiments wereinformal in nature. However, for the purposes of thispaper, two sets of controlled experiments were run andare described below.

Image-Matching Experiments Using FacesThe majority of the experiments we have run to date

had human faces as their subject. Reasons for this selec-tion include the following.

1) The availability of a set of digitized gray-scalepictures containing faces.

2) A single reference (face) could be tested on all thefaces in the data set. In the case of, say, terrain pictures,a separate reference (or, at best, a unique compositionof standard reference components) is necessary for eachpicture.

3) Our familiarity with faces and their components(eyes, nose, mouth, etc.) facilitates evaluation of per-formance as noise and distortion are introduced.The data set used in the face experiments consisted of

15 human faces,9 both men (some with beards) andwomen, digitized to approximately 16 true gray levels,and each face typically was contained in a picture fieldof from 2000 to 3000 resolution elements. Using a refer-ence as shown schematically in Fig. 3(a), with com,ponents as described in Fig. 3(b) and (c), almost 300formal and informal experiments were performed. Ineach experiment, additive (truncated) Gaussian randomnoise with zero-mean and standard deviation of either 0,10, or 15 units was added to each resolution element(relative to a pseudogray scale of 64 units for the noise-free pictures). In some of the informal experiments,coherent noise consisting of randomly placed lines wasalso inserted [see Fig. 4(a)].With no more than two or three exceptions, when the

reference was restricted to hair, eyes, and sides of face,correct embedding was achieved. These results aregratifying in view of the simple component descriptionsemployed, and the equivocation displayed by the re-sulting L(EV)A's. (See examples shown in Fig. 4.)Two series of formal experiments were run on the

I These data were obtained from the Staiiford Artificial Intelli-gence Laboratory and are a subset of the data employed in the ex-periments described by Kelly [11].

76


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VALUE(X)=(E+F+G+H)-(A+B+C+D)

Note: VALUE(X) is the value assigned to theL(EV)A corresponding to the location Xas a function of the intensities of locationsA through H in the sensed scene.

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HAIR WAS LOCATED AT (6, 18)L/EDGE WAS LOCATED AT (18, 10)R/EDGE WAS LOCATED AT (18, 25)L/EYE WAS LOCATED AT (17,13)R/EYE WAS LOCATED AT (17, 21)NOSE WAS LOCATtD AT (22,18)MOUTH WAS LOCATED AT (24,17)

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L(EV)A for eye. (Density at a point is proportional toprobability that an eye is present at that location.)

(a)

Fig. 4. Examples of image-matching experiments using faces. (a) Successful embedding under coherent nioise.

78


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(d)

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81


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19 A+"*-U 111114A8 ZlZ+ lZb= 'WAL4SX42' lZ?2 '9 >+'4-'l C ,7R 5 (;A (O Z +XIZi=*Glfl A *:*Z,2r *' t ) t )~ 1\ _ ) 1ZI

2 1 115 AAX XL- IC 1= i= 1 + ) ++ 1. )

22 S t4Z11AA1,+f ==;g A=++ z=61 =z23 X-FtAXSSlISx.4-1 X,+ ) i1 1 --* +A( !SZl6139'M24 IEM1 X Std XX' I9) XX(.eZ)S+H:VXEII 4X#*? +Ai25 IZ1Z e" AI1-itIP+ A)ZI I.I AZX)++3'-4)X2?6 P'14A)A APX 8AXt *\ Z) (*4+14 +_A1M)27 1i )1*=ve/+ )=f )A+4*) ?.)A Z+1 =0Z A28 X 1 )IgpWO+'#iAfX- Y91 XRI+ XI-A+ IZM29 %L)P'1I+r1XZZlZ1A)1 A+l+= + +a1 13C 6 Z-Z)1K 4+XtL ml CZ eZX= + I 1X=31 1 W f;Y1)= i+ + )ti Z ====3X3 2 Z+L'. Z== J 1 1XZ'l +Z+= + 7ZZ=)33 MXA + I 1'f1'A XX l4Z1A1Xm'M34 A) +4A = 1 IX + M 4Z X=1-61A35 1 + - I _ A )M I m1@@1

12345o78Q')1234567031234567itOl23456789(


HAIR WAS LOCATED AT (8, 20)L/EDGE WAS LOCATED AT (20, 11)R/EDGE WAS LOCATED AT (20, 27)L/EYE WAS LOCATED AT (18,15)R/EYE WAS LOCATED AT (18, 23)NOSE WAS LOCATED AT (23,18)MOUTH WAS LOCATED AT (25,18)

123456759C1234557P8n12345675C012345A 75)^.

L(EV)A for L/EDGE. (Density at a point is propor-tional -to probability that L/EDGE is present atthat location.)

(e)

Fig. 4 (continued). (e) Successful embedding under random noise.

82


12 i4-rr 7 3C' 1? i4'r,,;7>lt4.1234546751'12 1456 710i'6hfVVYi;flE4.44f * *.eeswtienortngVI*

_2 _*IEVWWYfl6Me9*f6Owe*tfIt(t(itj.#,1eiguv.1i H9bUi?iwt* ent*ieifiri?ts e*e.4wx3e4 3flM ti etinX ZIttt ZvtrtftF9 X4t.t et44w5 '8 '1eX)k14t#4'fI 94v17 IVE)FIRSSSI,SSRSm17.fefscXXIf;4*ueXes

_T )(teu0g8ES sSg s0 w,Ao6e ;- IWtSISSSIhhhAHS1SESIR P3@JiX4i- --"

IL *&ff*MiHS"'RHuh0AX X =/*UInsmvXAtXX4A'sA13 *fIfEm 1 14) I=,+7vsErXs I-X1Ax An14 t**4:*4"lAA V W XZ Z4 7X * +) I z "ELjv5gjg 44 4.-3

I2f- 9" 'AA X L XA A YI 4) le I Ii X ILXAXI Ai A XN< S

16 *i"+IShIelGt:wX.X l)t)+ ++X..1xAIh Zhix7AAHXe;q

l 7 F'-M K Afo Ai= r . L I1 Xk61 +I 1Z7lllll X 7 Z Z7e

1EfI'1A5X3IRs813'IX)AZNSSS#t.t #S11mHm'YIX YI1i I15 **4XASISSffiIx V*(4'XVSSXKKKX IK IAM1PI-S14AZfEfE&Sfl.Y XXXfit'SSsZ?6X&-XX)4

3 2 tffAAXiv. :X il ) Z9EN IF X XZ AAA4

4: !4 Hai*>ti e1 4 VI i i:" A '1, et.L Ia=1 Y_tM/ZXX24 X X4X FMSOW4A X_f;x. "'A.x 4E1 f 131 0Jt XXX-AX\ Z

12?4Fl'7i.670

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35 XX(X tf!I9SSUUVit'PAKKKxYKLAW*fESW9*3VSRS.X

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Original picture.

A A ,AKWA 7 *'77411'7I t'vx/4At;?2 AX)ALA"Vr4?K t'A i X4"%3 AZX;0AKAi@ZZ* , ?\\wK*--AiA9l)'. Xii

'. erxu4#SSSetSwtflue**Sv-R ~tH 47e*;s ___9 tl8"'XtLlHSSStBS 'efllflfiS1dSf)ilSS4 el-+Sriz0

10 S*S6faSfl6kS+.B6&'1eiSASISvle1Sa*ntEtflL,lC SN(MhIHSSteHUSCS4GSWS@-1+=f'.Z±i%S12 4l"St41h5OS~LS: 11 7?XKHfft1l SiAI-C*1 3 USeXweISS*X#sY))XiI1-ZLVAWSESSNSxKzX8N0|SAV14 RISt*f11&1kkvlMZ 1 IY*I+'fSw51+Z1HtU1'15 XS'iE808SI\L1XAZ-+ AtS XSVRASX*N')16 *ISIAssixm 9Si e=)1271*?HSSX+ )1'tHU Z17 U,tR11*SZ: 1=- t+x vLsssrsIrazn,w7ev18 8leM ISE0SS? ZA.+ tEA"C4ZASSR#( 1=+t--&Y X19 4fSAttiS=SPHAahX~AXM?19#1# IE{AII*EF*F4I9) = f.S ^PYIS ^ a 1§11 X*'A,:A= EJ?C AJHN'vX l1I eNSRX' 6t -!'Z-IA4d 16 P 15


1234507b'd,1345678se 123456759012 345b73tf

2345 +11+

--++= )A649e1 -7 +A9**5q*i,"Y*Z =

I010 Ii wSf)ii oeZi** -a

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22 =166'iZK"48s1 *X)[email protected] 'v,6R'*-IZZLZX2Z22-1)6PSA

25 zSSAl + 1- Z 88#+25 1iSt I 1z= l __"+2 =- - )W+2R AOXI+-1).- += ++29 -AX)+ XA )=--)l3~~~~ ~~~~1YT2T- _ -

31 +X+)}+ -32 Y5) ++

34 Ad>X AZ+ I=35 -YtiZ ZZ14= 1)+

37 =+11)1*=)= = + ) Z Z xZ 1 1)38 ==1)+ - -+4+) IZXZZZZ1)-

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Original picture.

133457 ri,7 '1-, 71 11.7ZZ7AX 7I. 1..Z 11 1 I I1 .)++ 1)IIi I2 1177 A )1)))) + 1 j)))4 11) +

4 l)flh/1eXS77 1)1)1_1- += -+711l7^Y)1lt'7 Ii51YZ>7frlT72 Y7)7^;. r-- .-+ 4+# 11_Tf'Ft 7.UTT1T) 1-6 1 51 A?)4+,+-+*t YXJ'-+*- 171111J1Al7 1)JZ?iAxl+!7 =). 1JH *^.?1IX4, !F 1 1 }>+9s4j g s++)-W)AZZLT

I Xz JZ) I?I? ) I B ti ^' t G 4 !,10 XZ '£ J IIZ x 4' .-'Ai- F--*''s )1

l' I -lz =n,a1-''-*;4Ll : -'t- .; n-}-.TT 1I Zt^ / *X.Z hi:̂ i i i-i'fi if- Xt,Ytl'; 24 ,1 I Z I ) 4 1 t4- n ?V .J 4 4l1k.4 J.te'.:2)F -I

Ibt,1 ) + KAL^ ? *lE! f it I *I ) +) ,1w16 1 )'I I $8f +*1 7 )*.ut;HwI +' I1: 1

311 VP.s7 Ix /1==74 1 T? 177''-' ¼ H331o.)1111- **. j > 11 ++- )l ''"7--s} +

34 171 7 7 --

3751TT-i- -TV.'k7.i'4x 7i'.^.'>71 .1'

?? I ) ) z I t:q= !', "zha %'Z,R."1 IF ".]= ,,I7 11T) !1.1s8-IR JF= F +_ ii - r."~-3 XX1+ I J I I )y j Z1 )>- iZ v) I I7 f 7"> y fTi.

12345676og&034'LI -'34 12345678?0123456 '??O1 ()-X, )2= A=-= A- 1 + = 12 +=l I - + _=_= _ =3 I +-+= 2 X=1 = 1= XZ4 = : A 1 1-' I ++1 += Z +Z45 Z7 -- = I 1=A+ 1 ) X-iA= )A I

7Z +.x = =+=-Z I AN + 7 1.+ A7 + I I) 1 4 Wjatt46S66X Z -X1)-=1 A8 t 7Z +Z+XYYw88i.z*v vw*69"1= I0 +1 -1 + =-zi8I-5Z6hStai0Z = =

10 Z 1. .+7Xw06+UA6tU':6,64Ul 6*8ii^E -=1 1 * 1 - x*H6OYSZ0H66'6s36RwwI1V%= 112 -XZ1+1 1+ tRsUu6eeezdv+ 113 + 4 D AlX elE6VHM.m860S# I- +14 X) - o'A5a I*68EX?'5I4O6'a*.Zpi,Z +15 4 1 A.iesEeBm+vs0 mg".Zs*1-16 + 11)WE3sssaki*A\x + +Sl*3SSSli =Z17 Z1) - fY*10"'A1 11 )lM M70S,.IAA )1s 1= f£I66Rt'f - lx'11 16l9=19 )t 66RUAi,'X+ + - *ilggitifrl ) X=2C 4 1 +.f-4*lBI1 - 2 =Z X0-5-E 8Z+ All21 +1 ti=oSi-* = 6) 1541A687V*iX+=Z I22 1 *IlleiAS"m>.j ff= X.e9;*+z 123 + - - *10+.7 49"A9Si+) Zfl *SUI!=L-24 -x *=8s0*' + 1 M 3 -X= IhaS5 L X25 L=L86"= 1) +i= I#4661) 1=26 * 8* 1 E'31 111 I A Z1 Z Z -> )Xi=) X-M 1)

12345,795C12345t7h0C1?2345O7Q9c1234567890


HAIR WAS LOCATED AT (13,23)L/EDGE WAS LOCATED AT (25,13)R/EDGE WAS LOCATED AT (25,28)L/EYE WAS LOCATED AT (22,16)R/EYE WAS LOCATED AT (22,23)NOSE WAS LOCATED AT (27,20)MOUTH WAS LOCATED AT (29,19)

L(EV)A for eye. (Density at a point is proportional toprobability that eye is present at that location.)

(g)Fig. 4 (continued). (g) Successful embedding under random noise.

84


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2 z+=+++4 -+e+++,*++*++++#.....+...+...)P)2 ++++++ + +++,++ -++++-+++.-)*. . . . . . . . .4 .+.+....4.) P1111. 1 . P P P P P . . . . . .5 4+4*4pP) IP)) .S'V hA~5X P P P)P) P)IPX) P114

7 P P P Ati '4i,*@ 1R1 P P P P P P111 1A P P)))Z}1 /* *4*+6*~r') t))))P) IP1P1P9 PPP I l 1 ee*eti fi 7 P ) 1 P )1 Pil

IC PPP PPAt*ii*ti-iXt PXPIiliLl11I Iz Aiv)IIW+i9=@4++z*> I1!1 1 1 1_12 Z T)l*libi)+-+ZrfP21 1) 1 111 11113 =+-++lif*9XL-AZ17AAZ+14CI11 ).)1MIII14 2*e*)AePxiPX [email protected]===15 -+.M4LXN:-IAA2 Z%'AP) +9 .16 +X9I +1Z1P} =ZXZ 1 +>'*L---.---17 -XF1-44+4+ -++=--KA_+1 8 z VI PI1IMA XZ4-44XX4I Iq 19XXX X AAtAKAL 1 +WZ-20 +4MX.'NA5 AZMMXPP __ A_X t

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3Z 4'I:5\)7,.'"e Y 7 X A> a^^3, X4 K*^.,, #K^* *vl ^ tt** 5\

4 ~ St Ê -Y Y .: s X X . 8 1 )+x x z 1. X-Zs7î*5

itz'.7: i4 %; 74 1,c 144 7 ^92 54 t ,7 a9

L(EV)A for mouth. (Density at a. point is proportionalto probability that.mouth is presetit at that loca-tion.)

1 s4-. 7 -I , 1?'4 a 7 A Q-'v 2 34 7 u1 2 3 4 5j J7 j1 5t P _-K 4VZ4 -+.P = ) - 1+ Ii 1)2 +1XZ)+Z P=1 = Z I + -PZ A= * *t'1

A , + K I PP ' +A I PI.A4 P ) =v 1 *Z 1= = P +5 X 2z ) *t- 4-fE1X" 2 X 1=ZI +A 1 146 Z=-l.l- l P16R, A 17-0-- -ZAXX +1- PI7 Z-=-) A0XOU S*W-@wWSE@'P'U* P AlX 4-X 9A X -x P'4-EewefflemelzP-ZS) OP S9 1 Z A Ij 4U=9S=ROSaj19 ) Z13 - 1 PfHUIti.AAveB=.v x i=A * A11 P -eA-I:o1g6XQ1SIB ) X + +I*5P* 1 4 81 P0=..12 i1.AEi FtBXlsz= +-+. V'4110P) 11v) Z13 + X+Af XA9B4= OP) SOAIPI Li-E 'I14 1 P. -*'7 hh'. * 5- YX(1C 44 PtIA#+*e- LZLvAI-*vS A q16 All)XINA X)# .'1?U *VS-X Z =)I P17 P + z=1 )P==+-1+ 7 z = A 4 _Pd - = XZ-+ X )P44) I + A= A + K19 X + )XI = A7 Z - PS =+20 I PS PZ9I1 XI I9 I_______21 i6e+ t* '8P 641A1t -. 1-22 1P -tfigs'^.44 1 + 4+23 * - AIfU-'-e-i-o * PZ 1 p))24 + - P4 P'0SH'I-Pv'xv*lO Z =?5 14P-4OPK=E,I9I1.S 'M.1 ) -

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I Z k4 56 7- c l 2 5 70 -;) I 214'67 4OI2 34557j%(


HAIR WAS LOCATED AT (8, 19)L/EDGE WAS LOCATED AT (16,9)R/EDGE WAS LOCATED AT (16, 23)L/EYE WAS LOCATED AT (14,12)R/EYE WAS LOCATED AT (14,18)NOSE WAS LOCATED AT (18, 16)MOUTH WAS LOCATED AT (21,16)

(h)Fig. 4 (continued). (h) Successful embedding under random noise.

85


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l

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7

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o pr' oa' bA t y Ytt no seis p esn1 at tha loti on2 ) 5 x + + 1I Z I I I

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24 9'fl'JE"*;3t9,* >̂, =+ ZZ -C tvP+X f-71i; 0

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i

1 2 4 5iTpC 2 4 12 -! 7j) 1 2 :4F '7a,1t'5 h,7 7 }

L(EV)A for nose. (Density at a point is proportionalto probability that nose is present at that loca-tion.)

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A 1_ K Z7 A I 'Ai, I...A x--14) ) t77 A=I Z.

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FISCHLER AND ELSCHLAGER: PiCTORIAL STRUCTURES 89

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90


posed a rigid template which is correlated at the dif-ferent positions of the sensed scene in order to get thelocal evaluation array. The correlation is performed onlyat the indicated points of the template. Reproductiondifficulties make it hard to see the intensities of theseenclosed points. For "Vegetation 1," all the points areof intensity 40, for "Vegetation 2," 20. For "Urban," thepoints were randomly assigned intensities of 25 and 35,and so on for the other pieces.The terrain-matching experiments represent a con-

tinuing area of investigation. Our current efforts areprimarily directed toward obtaining a satisfactory setof primitives which can be used as the basis for referencecomponent description. In low-noise experiments, withlimited geometric distortion, the simple descriptions(i.e., ad hoc shape and texture components linked bysprings) produced correct embeddings. Experimentsunder more severe conditions remain to be performed.

Implementation DetailsIn all of the face and terrain experiments presented

in this paper, the springs were assigned the values

0g

gij(Xj -xi) = qt oo,

if A < row (xj-xi) < B andC < column (xj- xi) < Dotherwise.

The values A, B, C, and D were typically set by takinga number of sample pictures and determining the small-est box encompassing the variation in the relative posi-tion between the components i and j. A subroutine waswritten to perform this task and automatically set thederived parameters into the LEA.

In our current implementation, for a typical 35 X39(face) picture, we require 13 s to compute all theL(EV)A's, and 35 s to execute the LEA (these timesinclude picture input from a disk library, and storageof results on the disk). Most of the programming is inFortran, and the computer is-an IBM /360/40 (the addi-tion instruction on the 360/40 executes in 11.88 ,s).Total core and disk storage in bytes for all arrays isM(4f+2h) and NM(f+2h), respectively, where M, N,f, h are the number of resolution cells in the sensedimage, the number of L(EV)A's, the amount of coreneeded for a floating point number, and the amount ofcore required for a (small) integer. For a typical picturein the face experiments (M=1600, N=8, J=4, h=2),these requirements woi-k out to appr-oximately 32 Kbytes of core, and IOOK bytes of disk storage.

DISCUSSION

Many, though by no means all, visual objects can bedescribed by breaking down the object into a number ofmore "primitive parts," and by specifying an allowablerange of spatial relations which these "primitive parts"must satisfy for the object to be present.As an example, suppose we want to describe a frontal

view of a standing person. This visual object could be

decomposed into six primitive pieces: a head, two arms,a torso, and two legs. For this visual object to be presentin an actual picture, it is required that these six primi-tives occur (or at least that some significant subset ofthem occurs), and also that they occur within a certainspatial relationship one to the other-that is, the legsshould be next to each other, and below the torso; thetorso should be between and below the tops of the twoarms; and the head should be on top of the torso.

It may be noticed that in the previous two para-graphs, we implicitly separated the local aspects fromthe global aspects of the description; the local aspectsare the primitive parts of the picture, and the globalaspects are the spatial relations between these parts.While at first glance it does not seem unnatural to makethis separation, in practice there is a frequently encoun-tered difficulty, that is, the feedback between thWe localand the global.To illustrate this difficulty, let us go back to the ex-

ample of the view of a standing person. Any methodwhich detects torsos on a local level (that is, a methodwhich detects torsos without using any knowledge ofthe positions of nearby arms and legs) might very welldetect several torsos in a picture. In fact, the actual or"true" torso may be one of the weaker of the torsosdetected by the method; it may even happen that thetrue torso is not detected at all. What does determinethe position of the true torso is the position of the truearms, legs, and head. But, unfortunately, the reverse istrue. The positions of, say, the true arms depends onthe position of the true torso. Thus, the possible positionof each piece affects the possible position of each otherpiece, making for a circular type of dependency.

It seems that whatever the visual object is, wheneverwe try to separate the global and the local, the samecircular dependency occurs. Many times attempts torecognize visual objects described in such a way involvealternating between local and global analysis, heuristics,backup procedures, etc.One conceptual way of avoiding this circularity is to

evaluate simultaneously a complete interpretation of thepicture; e.g., in the example given above, we would lookat, and evaluate, complete configurations of head, arms,legs, torso, etc. The best complete interpretation couldthen be chosen. This approach, however, requires thatwe make an infeasibly large number of evaluations. Itwas just this computational problem that in the firstplace led to the decomposition approach.The implication of the above discussion is that, in

general, we cannot hope to decompose the global evalua-tion problem into a number of smaller independent prob-lems, but rather must use something akin to the simul-taneous evaluation, taking advantage of any reductionin total variable interdependency to reduce the requirednumber of such evaluations.

In this paper, we accomplish this through the follow-ing machinery. First, an embedding metric is presentedwhich sets the framework for evaluating how well any

91


composition of primitive picture pieces (parts of thedecomposed picture) matches the desired compositepicture. Second, a sequential optimization (dynamicprograming-type) algorithm is developed which takesadvantage of the decomposition to reduce drasticallythe computational requirements (our computationalrequirements grow linearly with the size of the picture,rather than exponentially). The contribution of thispaper is the simultaneous offering of the above two com-ponents and their suitability for application to a wideclass of pictorial objects.

In addition to the image-matching application, whichwas the center of most of the development in this paper,we have also attempted to establish the utility of therepresentational aspects of the embedding metric forgeneral picture description applications.The work presented here is a continuation of the

investigation described in [1] and [2], where Fischleruses sequential optimization for matching two-dimen-sional scenes, introduces the generic form of the em-bedding metric elaborated on here, and presents the con-cepts of coherent segmentation, arbitrary serialization,and sequential constraints. The relation of the heuristicembedding problem to formal decision theory is alsodiscussed. The only other paper in which sequentialoptimization is applied to a broad class of problems in-volving two-dimensional scenes is where Martelli andMontanari [4] present a metric and matched algorithmfor smoothing pictures. Kovalewsky [5 ] and Montanari[3] have applied dynamic programing to the detectionof (one-dimensional) line-like pictures. Reference [3] isan outstanding paper, in which Montanari providesmuch insight into the characteristics of sequential opti-mization. Both Kovalewsky [5 ] and Montanari [3]comment on the representational aspects associatedwith their optimization procedures. An embedding met-ric conceptually very similar to the one given in [1 J, [2 ],and this paper is discussed in a broad and interestingwork by Bremermann'0 [121 with respect to its poten-tial use in character recognition, speech recognition, andcontrol of effectors (e.g., manipulators).

ACKNOWLEDGMENT

The authors wish to thank 0. Firschein and J. Tenen-baum for many constructive suggestions relative to theorganization of this paper.

REFERENCES[1] M. A. Fischler, "The detection of scene congruence," Lockheed

Missiles & Space Company, Inc., Palo Alto, Calif., Rep. 6-83-71-2, Jan. 1971.

[2] M. A. Fischler, "Aspects of the detection of scene congruence," inProc. 2nd Int. Joint Conf. Artificial Intelligence (Advance Paper),Sept. 1971, pp. 88-100.

[3] U. Montanari, "On the optimal detection of curves in noisypictures," Commun. Ass. Comput. Mach., vol. 14, pp. 335-345,May 1971.

[4] A. Martelli and U. Montanari, "Optimal smoothing in pictureprocessing," in Proc. IFIP Congr. Amsterdam, The Nether-lands: North-Holland, 1971.

10 Other relevant publications by Bremerman) incltude [131 and[14].

[5] V. A. Kovalewsky, "Sequential optimization in pattern recog-nition and pattern description," in Proc. IFIP Congr. Amster-dam, The Netherlands: North-Holland, 1968, pp. 146-151.

[6] R. Bellman and S. Dreyfus, Applied Dynamic Programming.Princeton, N. J.: Princeton Univ. Press, 1962.

[7] U. Bertele and F. Brioschi, "A new algorithm for the solutionof the secondary optimization problem in nonserial dynamicprogramming," J. Math. Anal. Appl., vol. 27, no. 3, pp. 565-574,1969.

[8] 0. Firschein and M. A. Fischler, "Describing and abstractingpictorial structures," Pattern Recognition, vol. 3, pp. 421-444,Nov. 1971.

[9] A. Rosenfeld, Picture Processing by Computer. New York:Academic, 1969.

[10] W. F. Miller and A. S. Shaw, "Linguistic methods in pictureprocessing-A survey," in 1968 Fall Joint Comput. Conf.,AFIPS Conf. Proc., vol. 33. Washington, D. C.: Thompson,1968, pp. 279-290.

[11] M. D. Kelly, "Edge detection in pictures by computer usingplanning," in Machine Intelligence 6, B. Meltzer and D. Michie,Ed. New York: Elsevier, 1971, pp. 397-410.

[12] H. J. Bremermann, "Cybernetic functionals and fuzzy sets," inAnn. Symp. Rec. 1971 IEEE Syst., Man Cybern. Group,Oct. 1971, pp. 248-253.

[13] "Pattern recognition, functionals, and entropy," IEEETrans. Bio-Med. Eng., vol. BME-15, pp. 201-207, July 1968.

[14] -, "What mathematics can and cannot do for patternrecognition," in Pattern Recognition in Biological and TechnicalSystems, 0. J. Grusser, Ed. Heidelberg, Germany: Springer,1971, pp.31-45.

[15] W. W. Bledsoe, "The model method in facial recognition,"Panoramic Research, Inc., Palo Alto, Calif., Rep. PRI:15,Aug. 1966.

116] , "Man-machine facial recognition," Panoramic Research,Inc., Palo Alto, Calif., Rep. PRI:22, Aug. 1966.

[17] A. J. Goldstein, L. D. Harmon, and A. B. Lesk, "Identificationof human faces, "Proc. IEEE, vol. 59, pp. 748-760, May 1971.

Martin A. Fischler (S'57-M'58) was born inNew York,I- Y., on February 15, 1932. Hereceived the B.E.E. degree from the City Col-lege of New York, New York, in 1954 and theM.S. and Ph.D. degrees in electrical engineer-ing from Stanford University, Stanford, Calif.,in 1958 and 1962, respectively.

He served in the U. S. Army for two yearsand held positions at the National Bureau ofStandards and at Hughes Aircraft Corpora-tion during the period 1954 to 1958. In 1958

he joined the technical staff of the Lockheed Missiles & Space Com-pany, Inc., at the Lockheed Palo Alto Research Laboratory, PaloAlto, Calif., and currently holds the title of Staff Scientist. He hasconducted research and published in the areas of artificial intelligence,picture processing, switching theory, computer organization, andinformation theory.

Dr. Fischler is a member of the Association for Computing Ma-chinery, the Pattern Recognition Society, the Mathematical Associa-tion of America, Tau Beta Pi, and Eta Kappa Nu. He is currentlyan Associate Editor of the journal Pattern Recognition and is a pastChairman of the San Francisco Chapter of the IEEE Society on Sys-tems, Man, and Cybernetics.

Robert A. Elschlager was born in Chicago,Ill., on May 25, 1943. He received the B.S.degree in mathematics from the University ofIllinois, Urbana, in 1964, and the M.S. degreein mathematics from the University of Cali-fornia, Berkeley, in 1969.

Since then he has been an AssociateScientist with the Lockheed Missiles & SpaceCompany, Inc., at the Lockheed Palo Alto Re-

Q< search Center, Palo Alto, Calif. His currentinterests are picture processing, operating

systems, computer languages, and computer understanding.Mr. Elschlager is a member of the American Mathematical

Society, the Mathematical Association of America, and the Associa-tion for Symbolic Logic.

representation and matching pictorial structuresgrauman/courses/spring2007/...control theory...

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