Spatial data handling systems generally use either topological or gridimage data structures. It makes little sensefor these

systems to be incompatible.

Manipulating Data Structuresin Pictorial InfonnationSystems

Margaret Chock N1 t I EAlfonso F. Cardenas

Allen Klinger

UCLA

The collection and processing of digital image databased on photographs, drawings, and maps is currentlyundergoing a period of rapid growth. Industry, univer-sities, and governmental agencies are producing an ever-increasing volume and variety of such data. In recentyears a number of image data handling systems have beendeveloped to store and retrieve this two-dimensional im-age data.

Problems facedin the image processing field

In 1977 there were several hundred systems and pro-grams for spatial data handling. ' However, very few ofthese can be considered generalized systems, that is, sys-tems flexible enough to handle the variety of data andoperations representative ofa large portion ofthe users ofsuch data. Furthermore, many of the systems have fol-lowed independent paths in the development of datamanagement techniques, and this has resulted in widevariations from system to system in' a number of areas.

Logical image data structure. As we will see below, themajor alternative image data structures can be broadlyclassified as either topological or grid structures. Each im-age system usually implements one of the two structures,but not both. In the few systems that do use both, one isclearly dominant and receives information from the otherfor only a single type of processing. Each of the structureclassifications has its own strengths when it comes torepresenting certain types of data and permitting the cost-effective implementation of certain image data process-ing operations (more details will be given later).These dif-ferences between the structure types mean that a large setof images, which we will define as an image data base, is

not transferable or portable from one system to anotherunless it has the same logical data structure. An imagemust be unloaded, converted to the new structure, andthen loaded onto the new system-an awkward and ex-pensive process.

Internal physical representation and organization ofimage data. The number of bits in a pixel and the arrange-ment of pixels into records varies from system to system.How this file is organized and searched differs, although afrequently used method of organization is to set up a se-quential file on tape with several records grouped into aphysical file.The physical arrangement of coordinate lists has still

greater variation. Several systems have a pair of points oneach physical record, along with various sorts of appli-cation-dependent information. Sometimes lists of log-ically connected points have common associated infor-mation stored in a record, together with the end points ofthe list; the intermediate points may even be kept on a dif-ferent type of storage device. A third general method ofstoring the coordinates is to store redundant lists byassociated features-for example, the common border oftwo adjacent countries stored with the information foreach country.

Higher-level file organizations, such as the invertedstrategies widely used in generalized data-base manage-ment systems, or GDBMS, for nonimage data have notbeen applied to image systems except for the indexing ofpoint lists by end point. These higher-level file organiza-tions have the potential in image systems to allow easiersub-image access and to improve access time performancein retrieving large numbers of images. Although thispotential has not been exploited, a few of the newer imagesystems are exploring GDBMS as a possible aid to imageprocessing.

0018-9162/81/1100-0043S00.75 (3 1981 IEEENovember 1981 43

POINT(x, y)

ORDINARY LINE SEGMENT(xi, Yl)

(X2, Y2)

POINT LIST(x1, y1)

/ (X2, Y2)(x3, y3)

(xe, yn)

DIME LINE SEGMENTFROM NODE (x1, y1)

RIGHT R LEFTPOLYGONI POLYGON

TO NODE (X2, Y2)

ARC OR CHAINFROM NODE (x1, yj)

(x2, Y2)(X3, Y3)

RIGHT LEFTPOLYGON POLYGON

TO NODE (xn. yn)

Figure 1. Points, segments, and chains.

Figure 2. Cartographic networks (rivers and coasts).

Figure 3. Cartographic polygons.

Image data definition language. Few systems have anysort of data definition facility that is understood by boththe user and the system itself. Normally the user obtainsdata structure information from a manual, while the sys-tem follows a set of file-accessing procedures. Thus, auser, or an application program written in any program-ming language (Fortran, PL/l, etc.), needing access toimage data is bound to a particular image system. If accessto images residing in other image systems is desired, allimage retrieval instructions in the application programhave to be reprogrammed, or the user has to be retrained.This is an expensive and tedious process. The need for aprecise, common data definition language is well estab-lished for conventional, nonimage data-base manage-ment systems.2

Image data processing language. No two major imagesystems have the same user language for defining partic-ular image processing operations such as polygon overlayor point-to-line distance. Furthermore, major systemsdiffer widely in the kinds of image processing operationsthat they support, as we will see later. This, too, restricts auser or program in any programming language to a partic-ular image system, and, once more, the application pro-gram has to be modified, or the user has to be retrained, ifimages residing in one system are to be reproduced in adifferent system.The proliferation of individual systems, the growing

amount of image data being generated, the expandingcommunity of users, and the ever-increasing need to shareand make such resources readily accessible and cost-ef-fective mean that solutions to the problems listed aboveare becoming increasingly urgent. Some of them havealready been pointed out by Haralick,3 but the imagedata management field has not yet produced any imagedata definition or image data manipulation standard tohelp resolve this system incompatibility problem. Thenumeric (nonimage) data management field sufferedthrough the same types of problems for a number ofyears, until Codasyl suggested its 1971 DBMS standard.4Today this standard is endorsed by the majority of avail-able DBMS, although there are some major exceptions tothe endorsement. Also running counter to the standard isa recent wave of alternative relational DBMS architec-tures that are now on the market.Any road toward a standard, or toward more general-

ized systems, or toward easier and more cost-effective ac-cess to the image data bases of different systems musthave as its base an understanding of the similarities anddifferences among computing systems with respect todata definition and data manipulation capabilities. Thisarticle looks at the data structures of existing major sys-tems and outlines the data manipulation capabilities ofthese systems as a way of providing some of the informa-tion necessary to arrive at this understanding.

Data base structures ofpictorial information systems

Pictorial information systems reviewed. In order tofind potential standards for logical and physical datastructures and for data definition and data manipulation

COMPUTER44

languages, we have studied a set of pictorial informationsystems that can define multiple attributes over the samespatial area and that together exhibit a wide range offunc-tions (see box below). AGS,5 GADS,",6 GEO-QUEL,7and IMAID8 are either defined as conventional data-basemanagement systems or are built upon them. IBIS,9-12ODYSSEY,1" 3 SYMAP,1"14 and CGIS1"10"15"16 areamong the best known cartographic systems. BASIS'7 isincluded as an example of a multiple-variable grid cellsystem. POLYVRT,13"18-20 which has had longer use,is a predecessor to ODYSSEY, and KANDIDATS,",2'STANDARD,"122 NIMS,",23 and WRIS",24 are includedas additional, well-documented examples.

Classification by data structure. As stated previously,two-dimensional digital data structures can be separatedinto two broad classifications-topological or grid struc-tures. These classes include the particular structures usedin various combinations by cartographic systems.

Topological data structures are a family of orderedpoint sets, including isolated points, line segments orpoint pairs (the basic structures for GEO-QUEL andIMAID), and lists of points outlining geographicalfeatures (used in AGS), as shown in Figure 1.

In the simplest systems, the data is stored in what A. H.Schmidt describes as "cartographic spaghetti' '25-lists ofpoints outlining geographical features with no explicitrelationships among the features. A good example isWorld Data Bank II, which was started in 1971 to providegeodetic base data for thematic maps. In it, each chain islabeled with its continent, country, and feature typenames, as well as the level of detail depicted. Such listscan be branched to form networks, shown in Figure 2, orclosed to form polygons as in Figure 3. The basic objectsof GADS and WRIS are regions bounded by just suchclosed lists. STANDARD and CGIS utilize both regionsand networks.The US Census Bureau's DIME structure26 augments

segments with directionality (where a segment runs"from" one point "to" another) and names the regions(census tracts or counties) on their left and right sides.POLYVRT extends this structure by chaining all linesegments between branches or intersections to form pointlists, starting with a "from" node, ending at a "to" node,and having uniquely defined left and right polygons.ODYSSEY's basic structure is the "least common geo-graphic unit," a polygon formed by overlaying and cut-ting all chains bounding all types of regions in the database to obtain subregions within which all data values areconstant. NIMS uses the same chain structure, only withdifferent labeling.The second major class of data structures subdivides

the area of interest in an image into a rectangular grid. Adata record is used to represent each grid cell or pixel inmultiple-variable systems such as BASIS. A value fieldfor each type of data contains an average or represen-tative value for the cell, as shown in Figure 4. These fieldsare predefined at the time the data base is established.BASIS includes empty fields of fixed format, most ofwhich will later be filled with permanent data, and a fewof which will be kept as work spaces. Other grid systemsconcentrate on the two-dimensional variation ofvalues of

a single variable. Matrix systems such as SYMAP store allor most of the grid in memory at once, while imagesystems such as IBIS and KANDIDATS store resolutioncells ofan image in raster-scan order, usually with an 8-bitvalue field for each cell (see Figure 5).Polygons are by far the most widely used structures. In

fact, they are the only objects in three of the 14 systemsand are important structures in six of the others.POLYVRT and ODYSSEY primarily use line segmentsand chains to form polygon boundaries. Simple point lists

November 1981 45

are important in AGS, but they are only secondary struc-tures in SYMAP. IMAID performs simple image-proces-sing operations to convert images to line segment format.Thus, for purposes of further discussion, BASIS, IBIS,KANDIDATS, and SYMAP are classified as grid systems,with the others falling under the topological heading.

Figure 4. Rectangular grid cells.

tf i l ! i I i 1-

Figure 5. Raster-scan ordering of grid cells.

Table 1.Data-base flexibility.

TEMPORARILY INDEPENDENTSYSTEM FIXED EXPANDABLE EXPANDABLE IMAGES

GADS XGEO-QUEL X

CGIS XWRIS XNIMS X

STANDARD XPOLYVRT XODYSSEY X

AGS XIMAID XBASIS XSYMAP X

IBIS XKANDIDATS X

The accuracy of the two-dimensional data representa-tion is a function of both the data structure's resolutionand its basic category. Topological structures provide asuperior representation of objects that are either legallydefined or are smaller than the level of resolution. Suchobjects include counties or real estate parcels whoseboundaries are defined as straight lines between survey-ors' landmarks. They may also be cities or rivers on small-scale maps whose areas, widths, and deviations are small-er than the resolution of their computer representations.

Objects that are less clearly defined are better repre-sented by grids of adequate resolution. If a transition isgradual, as in the case of a boundary between a stand ofpine trees and one that is half-pine, half-oak, topologicalnotation requires imposition of a sharp boundary, whichmay distort reality. However, the grid can show thisgradual change, with built-in visual error bounds in theform of rectangular cell edges.

Table 1 is an indicator of a system's data-base elas-ticity-the degree to which new images can be added toan existing data base. As shown in the table, GADS andSTANDARD data bases are not expandable. A GADSdata base can be replaced with a more detailed one torepresent more regions and new attributes, but the typesof information in a STANDARD data base are built intothe system. NIMS and BASIS are somewhat expandable,allowing users to add temporary data for display pur-poses. New images can be added to the permanent dataof GEO-QUEL, CGIS, WRIS, ODYSSEY, AGS, andKANDIDATS; however, any permanent data forPOLYVRT, SYMAP or IBIS must come in the form ofindependent images.

It is not possible for ordinary users to add permanentdata to their own data bases in GADS, NIMS, STAN-DARD, AGS, BASIS, or CGIS; this function must beperformed by experts with a knowledge of the internalworkings of these systems. Thus, users can only generatetheir own multiple-variable image data bases in GEO-QUEL, WRIS, ODYSSEY, and KANDIDATS. In thelatter three cases, the entire data base is rewritten when animage is added, with WRIS being restricted by the totalnumber of polygons the system can handle andODYSSEY by resolution problems. The independent im-ages of IMAID, POLYVRT, SYMAP, and IBIS canreflect data from multiple sources which have been pre-combined, though only IBIS supplies the combining facil-ities. Limitations on the label size of the polygons and onthe number of gray-levels for a grid cell may restrict theamount of source information that can be carried by thecombined images. The total data-base size is also an im-portant limitation for most of the systems; only ODYS-SEY, AGS, IBIS, and KANDIDATS are reportedcapable of handling data bases equivalent to more than1000 polygons.

Data manipulation and retrieval capabilities

Other than input, editing, and output, Table 2 showsall of the specific data manipulation operations that wewere able to identify for the major systems. Few of theavailable references list their fundamental data manipu-

COMPUTER46

lation operations, thus, the set may be incomplete forseveral systems. For example, KANDIDATS and IBISboth have access to large libraries ofprograms that proba-bly include operations not listed here. Output or datadisplay operations for each system are shown in Table 3.Some of these operations are performed on gridded

data-either digitized photographs in the case of KAN-DIDATS and IBIS, or samples of a numeric variable forSYMAP. The scattered point operations can be performedon either class of data. Line operations are executed on

lists of x,y coordinates. Region operations are performedon connected sets of grid cells or on closed coordinate-listboundaries. The operations on region attributes are per-

formed by GADS, GEO-QUEL, and IMAID, based on

relational systems in which each region is represented by a

set of domains containing such data as population or

average rent. Most of these systems produce some form ofsimple map and several generate such conventional com-puter output as reports, tables, and graphs as well. How-ever, we do not examine data input and editing capabil-ities in this article.Each system seems to perform only a small percentage

of the total number of functions shown in Table 2. Thegrid systems do appear to perform a larger number of op-erations per system, on the average. This may be due tothe difficulties involved in manipulating topological data.Operations on topological data tend to require the manip-ulation of varying numbers of variable-length lists ofpoints-something that is difficult to do in most general-purpose programming languages. Many algorithms in-

Table 2.Data manipulation operations.*

KANDI- ODYS- POL- STAN- GEO-DATS IBIS SYMAP BASIS IMAID AGS SEY YVRT NIMS DARD WRIS CGIS QUEL GADS

OPERATIONS ON IMAGESEDGE OPERATORS GCLUSTERING GCOVARIANCE GAVERAGE GRID CELL VALUES G GPOINT CLASSIFICATION G GHISTOGRAMS OF GRID CELL VALUES G G GTHRESHOLDING G G GTEMPLATE MATCHING GOPERATIONS ON SCATTERED POINTSINTERPOLATION GTHEISSEN POLYGONS GCONTOURS G G P PPROJECTION CHANGE G G P P POPERATIONS ON LINESNEAREST POINT ON A LINE PCENTER OF A LINE PGENERALIZATION P PINTERSECTION OF NAMED LINES P PPOINT-TO-LINE DISTANCES P PLINE LENGTHS P P P POPERATIONS ON REGIONSPOLYGON OVERLAY (INTERSECTION) G G G G P P P P P PCROSSTABULATION OF OVERLAYS G PFIND ADJACENT POLYGONS P PAGGREGATION P p p pPOINT-IN-POLYGON P P PAREA P P P PCENTROID p p pOPERATIONS ON REGION ATTRIBUTESRELATIONAL OPERATIONS P P P

*P represents data in polygon tormat; G represents data in gridded format.

Table 3.Data display operations.

KANDI- ODYS- POL- STAN- GEO-DATS IBIS SYMAP BASIS IMAID AGS SEY YVRT NIMS DARD WRIS CGIS QUEL GADS

DIGITIZED PHOTOGRAPHS X XREGION MAPS: GRAY OR COLORED X X X X X X X X XREPORTS, TABLES, LISTS, GRAPHS X X X X X X X X"THREE-DIMENSIONAL" MAPS X XLINE AND POINT MAPS X X X X X X X X X X

Noeme1914November 1 981 47

volve a search for line segments or chains likely to intersect,followed by tests for and calculations of intersections.The operations in Table 2 rarely allow the user a choice

of procedures to be followed; the parameters usually in-clude a map or image to be processed, numeric variablesto be used in predefined arithmetic expressions, andsometimes the name of a point, line, or region. NIMS,POLYVRT, and SYMAP each have a small number offunctions with user-specified options. GEO-QUEL,GADS, IBIS, and KANDIDATS allow definition of logicor arithmetic operations on region attributes or pixelvalues. BASIS and SYMAP are designed to incorporateuser-written Fortran programs at certain points in pro-cessing. Additionally, IMAID and CGIS have user pro-gram interfaces.

Most of the systems can operate on multiple images, forinstance, more than half of them can overlay polygons.Covariance calculations, interpolation (in SYMAP), andcrosstabulations of regions are performed on pairs oftwo-dimensional variables. KANDIDATS (and possiblyIBIS and BASIS) has routines with multiple-variable in-put. GADS, GEO-QUEL, and IMAID can perform a va-riety of operations on attributes of regions, with GADSbeing limited to two domains at a time. GEO-QUEL andIMAID, on the other hand, can use several domains.There is a growing need to combine data from different

types of sources. These sources include digitized satelliteand aerial photographs, stereo photographs used to findrelative elevation (for use in contour maps), numericalvalues representing any arbitrary variable, such as eleva-tion or population density (either at nodes of a regulargrid or at isolated points to be interpolated to the grid),and lists of coordinates representing points, lines, andregion boundaries.Combining topological data from these different sources

requires polygon overlay procedures. All intersecting linesegments must be found, the intersections must be com-puted, and the new segments (chains) need to be cataloged.A common problem is the formation of possibly signifi-cant "sliver" polygons with nearly congruent sides.These are selected and eliminated manually, or this can bedone automatically on the arbitrary basis of a length-to-

width ratio. As the number of merged images grows, thepolygons decrease in size. Maps displayed at the same res-olution get crowded, and the original precision used indigitizing the polygons becomes inadequate to distinguishthe smaller regions. Area measurements are less accurate,and there is greater risk of dropping a significant sliverpolygon. Additionally, the label for each polygon mustcontain or point to a growing amount of information.

Image data is usually converted to topological formatby manual methods. Areas of constant or nearly constantvalue in a photograph may be outlined on a digitizingtablet. IMAID uses a thresholding algorithm to extract abinary version of the image; edges in this thresholded im-age are then converted automatically to line segmentform. Topological data is converted to grid structure bycomputing line segment intersection with cell edges (inIBIS), or by interpolating scattered point values to a grid(in SYMAP).

In multiple-variable grid cell systems, all data values foran area are simultaneously available, but other grid cellsystems do not combine data so easily. Some matrix andimage systems have a few programs that concurrently ac-cept data from two images. One or both of these imagesmust be rubber-sheet stretched to fit a set of geographicalcontrol points. Currently detection of these points in eachpicture must be done manually. Once they are found,warping of the images to a common grid is done by spe-cialized optical equipment or by a large digital computer.Then the data from one image is overlaid onto or added tothe other's. The resultant image can be processed by thedesired programs and reinterpreted.

Table 4 lists the image retrieval characteristics of thereviewed systems. Data supplied to an operation may beuser-specified, such as point sets for a SYMAP display, orit may be an image with a predefined role in the system,such as a field from the BASIS file. The data base maycontain data for one or many areas. These may be ar-bitrary, or they may be organized as a set of complemen-tary maps such as 71/2-degree topographic quadranglesfor cartography. An area may be covered by one, two, orseveral variables, including political boundaries or single-

Table 4.Retrieval characteristics.

DISTINCT NUMBER OF NUMBER OF POINTERS DIRECTDATA REAL- OVERLAYS OVERLAYS TO TABLES ACCESS

SYSTEM SUPPLIER WORLD PER ACCESSIBLE BY WITHINAREAS AREA AT ONCE REGION IMAGE

GADS SYSTEM 1 1 1 YES YESGEO-QUEL EITHER INDEPENDENT MANY 2 YES YES

CGIS SYSTEM ORGANIZED MANY 2 NO NOWRIS EITHER ORGANIZED MANY 2 NO NO

STANDARD SYSTEM ORGANIZED 2 2 NO NONIMS BOTH 1 MANY 2 YES YES

POLYVRT EITHER INDEPENDENT MANY 1 NO YESODYSSEY EITHER INDEPENDENT MANY 2 NO NO

AGS EITHER ORGANIZED MANY MANY NO NOIMAID EITHER INDEPENDENT MANY 1 YES YESBASIS SYSTEM 1 MANY MANY NO NOSYMAP USER INDEPENDENT 2 2 NO NO

IBIS USER INDEPENDENT MANY 2 YES NOKANDIDATS EITHER INDEPENDENT MANY MANY NO YES

COMPUTER48

band digitized photographs. Most operations in most sys-tems can retrieve only one overlay at a time. A few, par-ticularly polygon overlay, can work on two images atonce, and the multiband structures ofKANDIDATS andBASIS allow the definition of simultaneous operationson several images. Some systems have facilities for tyingan overlay of polygon boundaries to tables of data foreach polygon. In addition to retrieval by area or retrievalby overlay, several systems allow direct access to objectswithin an overlay, at least from the user's point of view.

region. Each of these commands allows the definition oftemporary variables, calculations using arbitrary num-bers of image variables within a window which movesover the entire image area, and restriction of retrieval andcalculation to a set of logically defined regions. This newsystpm can perform any of the opera,tions in Table 2 usingone or two commands. E

Acknowledgment

This work was supported by US National Science Foun-dation Grant MCS 78-16754.Conclusions

The two image data structures in widest use are thetopological and grid structures that we have reviewed inthis article. Each has advantages and disadvantages. Ageneralized image data management system should allowthe user to select either, or both, structures via a standardhigh-level data definition language. Practical considera-tions will probably limit the topological choice to two orthree ofthe possible structures based on those in Figure 1,or to a way of automatically converting from one topo-logical structure to another. Standard or conversion pro-cedures are similarly required for gridded data.

Existing systems differ widely with respect to data ma-nipulation operations that they support. Table 2 summar-izes the situation. Most of the operations shown in thetable should be provided in a generalized image data man-agement system. Obviously, many other operations havebeen reported or could be conceived, however, a set offundamental operators able to support the operations inTables 2 and 3 should also be able to support additionalimage processing capabilities. Then the extracted datacould be used by programs written in conventional pro-gramming languages or by generalized file managementsystems (Mark IV, ASI-ST, etc.).At UCLA we are developing a prototype for a pictorial

data-base management system, PICDMS, which may pro-vide the standards needed. The first version of PICDMS,which has already been implemented, stores digitized im-ages of an area with the same projection and resolution ina stack-a stack that expands as new images are added.This user view appears to the system as a set of records,each of which represents one grid cell. The data for an im-age is stored in a single field in each record, and a data dic-tionary keeps track of the current record format.Data definition consists of a stack definition command

(not yet implemented) that provides the data dictionarywith the number of rows and columns in each stack, thelength and width of each cell (say, in meters for a carto-graphic system), and appropriate coordinates for theorigin. The user supplies the definition, such as havingsingle-character or four-digit integer values, of new im-ages as they are added to the data base.The data manipulation language consists of a set of

standalone commands that specify what action is to betaken on the data base-add, replace, or delete an image,retrieve information (in the form of a raster map or lists ofa set of values), or calculate a minimum distance betweena point and a set of points which may constitute a line or a

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*This digest is available from the Order Desk, IEEE Computer Society,10662 Los Vaqueros Circle, Los Alamitos, CA 90720.

Margaret Chock is a graduate student andPhD candidate in computer science atUCLA. Her current research interests arein the theory and implementation of gener-alized access to two-dimensional multivar-iate data, and in modeling such entities ascomputer networks, health care systems,and VLSI chips using these capabilities.Chock is a member of the IEEE, ACM,

and the American Congress on Surveyingand Mapping. She received an MS in computer science fromUCLA in 1977, and has BA degrees in anthropology andmathematics from the University of California, Santa Barbara.

Alfonso F. Cardenas is an associate pro-fessor of computer science at UCLA, andis also a consultant in computer scienceand management. He has offered seminarsand consulted for IBM, Rand Corpora-tion, Arthur Young and Company, the JetPropulsion Laboratory, Petroleos Mex-icanos, Systems Engineering Laborato-ries, and other major organizations. Hisprofessional activities include data-base

management, management information systems, organizationand methods, systems analysis, software engineering, and pro-gramming languages. He is the author of many publications, in-cluding the books Data Base Management Systems and Com-puter Science.

Cardenas received a BS from San Diego State University in1964 and MS and PhD degrees in computer science from UCLAin 1966 and 1968, respectively. He is a member of ACM, theSociety for Management Information Systems and Sigma Xi,and is listed in Who 's Who in Computer and Data Processing,the Dictionary of International Biography, and American Menof Science.

Allen Klinger is a professor at the Com-puter Science Department of UCLA. Priorto joining UCLA in 1967, he was employedby the Rand Corporation, and he hassubsequently been a consultant to Rand,the World Bank, the System DevelopmentCorporation, and several other organiza-tions. He has held fulltime positions at ITTLaboratories, System Development Cor-poration, and the Jet Propulsion Labora-

tory. He has also been a consultant to Gateways Hospital, andnow consults with Memorial Hospital of Long Beach.

Klinger has published over 65 items in the last 10 years, in-cluding the edited book Data Structures, Computer Graphics,and Pattern Recognition. His research accomplishments dealwith the application of mathematical methods in a variety ofengineering contexts.

Klinger is a member of Tau Beta Pi, the Computer SocietyTechnical Committee on Machine Intelligence and PatternAnalysis, and has served as program chairman for the Third In-ternational Joint Conference on Pattern Recognition, and asprincipal investigator on research grants from governmentagencies. He received his BEE degree from Cooper Union, NewYork, in 1957, his MS from the California Institute of Tech-nology in 1958, and his PhD from the University of California,Berkeley in 1966.

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