10. generalising spatial data and dealing with multiple representations

1 INTRODUCTION

‘Wherever there is life, there is twist and mess: thefrizz of an arctic lichen, the tangle of brush along abank, the dogleg of a dog’s leg, the way a line hasgot to curve, split or knob. The planet ischaracterised by its very jaggedness, its randomheaps of mountains, its frayed fringes of shore . . .Think of a contour globe, whose mountain rangescast shadows, whose continents rise in bas-reliefabove the oceans. But then: think of how it really is.These heights aren’t just suggested; they’re there . . .What if you had an enormous globe in relief thatwas so huge it showed roads and houses – ageological survey globe, a quarter of a mile to aninch – of the whole world, and the ocean floor!Looking at it, you would know what had to be leftout: the free-standing sculptural arrangement offurniture in rooms, the jumble of broken rocks in acreek bed, tools in a box, labyrinthine ocean liners,the shape of snapdragons, walrus . . . The relief

globe couldn’t begin to show trees, between whoseoverlapping boughs birds raise broods, or thefurrows in bark, where whole creatures, creatureseasily visible, live out their lives and call it worldenough.’ (Dillard 1974: 141–3)

A Highway Department studies how to widen andstraighten a road that runs through towns andvillages in a river valley. A property owner decidesto develop land that has restrictions by the state onconstruction within 100 metres of waterways. Aplanning board attempts to rationalise acommunity’s haphazard zoning code to minimisefuture conflicts between adjacent land uses. Afarmer buys a new, larger tractor and needs to revisehow he or she ploughs and intercrops in hilly terrain.

All of these are real-world analogues of whatcartographers call map generalisation. Althoughthey concern physical forms and processes on thelandscape, these decisions also involve abstractionsfamiliar to users of GIS, such as categoricalcoverages, curve geometries, proximity buffers, and

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10Generalising spatial data and dealing with multiple

representations R WEIBEL AND G DUTTON

Functions for generalising spatial data are of fundamental importance in GIS because of avariety of requirements for scale-changing as well as thematic reduction and emphasis.Following a brief introduction, section 2 discusses what generalisation is, what itsobjectives are, and why it is important. In section 3, the distinction is developed betweenprocess-oriented and representation-oriented approaches to generalisation, first discussingthe latter in the context of multiple representations and multi-scale databases. Section 4provides an introduction to the range of conceptual models of process-orientedgeneralisation, outlining the nature and relationships of data models, operators, objectives,and controls. Section 5 sketches the requirements for a successful digital generalisationsystem, including elements of data modelling, structure and shape analysis, generalisationalgorithms, knowledge-based methods, human-computer interaction, and qualityevaluation. The chapter concludes with a brief look at some operational generalisationsystems, recently developed and still evolving.

spatial autocorrelation. Were the people describedabove to make use of GIS to help solve theirproblems, they would quickly see that in making andmanipulating 2-dimensional representations of theirproject worlds they would be making cartographicdecisions, and furthermore that their systems wouldnot be of very much help in the process.

This chapter describes what generalisation ofspatial data is, why it is necessary, some techniques forperforming it in the digital domain, and what toolscurrently exist to support it, providing pointers tosome of the recent research literature. More detailedsurveys of generalisation techniques have beenpublished, notably by McMaster and Shea (1992) andWeibel (1997), who focus on algorithmic methods.This topic is discussed from the perspective of dataquality by Veregin (Chapter 12). Compilations ofrecent research are provided by Buttenfield andMcMaster (1991), McMaster (1989), Molenaar(1996a), Müller et al (1995), and Weibel (1995a). Fordiscussions of generalisation in the context ofparticular applications see, for example, Larsen(Chapter 71), Meyers (Chapter 57), Wilson (Chapter70), and Yeh (Chapter 62).

2 DESCRIBING GENERALISATION

Our world presents us with an infinite regress of detailhaving neither beginning nor end. Digital computers,being primitive machines with limited memory forand no real understanding of facts, must be coaxedand prodded artfully to do anything useful with datadescribing the planet, its regions and phenomena. AsDillard thoughtfully observes, if we try to model theworld it is impossible not to generalise spatial data,whether we intend doing so or not.

2.1 Generalisation in conventional cartography

In conventional cartography, map generalisation isresponsible for reducing complexity in a map in ascale reduction process, emphasising the essentialwhile suppressing the unimportant, maintaininglogical and unambiguous relations between mapobjects, and preserving aesthetic quality. The mainobjective then is to create maps of high graphicalclarity, so that the map image can be easily perceivedand the message the map intends to deliver can bereadily understood. This position is expressed by theconcise definition which equates map generalisationto ‘the selection and simplified representation ofdetail appropriate to the scale and/or the purpose ofa map’ (ICA 1973: 173).

Scale reduction from a source map to a targetmap leads to a competition for space among mapfeatures caused by two cumulative effects: at areduced scale, less space is available on the map toplace symbols representing map features, while at thesame time, symbol size increases relative to theground it covers in order to maintain size relationsand legibility. Figure 1 illustrates the spatial conflictsthat arise from reduction of available map space andenlargement of symbol sizes. These can be resolvedby simplifying symbolism, by selecting only a subsetof features to depict, and by displacing somefeatures away from others (e.g. moving buildingsaway from streets).

However, note that map scale is not the onlyfactor that influences generalisation. Map purpose isequally (and perhaps even more) important. A goodmap should focus on the information that is essentialto its intended audience. Thus, a map for cyclists willemphasise a different selection of roads than a maptargeted at car drivers. Map purpose also influences

R Weibel and G Dutton

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Fig 1. Competition for space among map features as a consequence of scale reduction.

(a)

(b)

(c)

directly the selection of the appropriate map scale,as spatial phenomena and processes should bestudied at the level of scale at which they are mostrelevant (Dikau 1990). Other factors that controltraditional map generalisation are the quality of thesource material, the symbol specifications (e.g. thewidth and colour of line symbols to depict roads,political boundaries, etc.), and technicalreproduction capabilities (SSC 1977). Thecombination of these factors is termed the ‘controlsof generalisation’.

2.2 Generalisation in digital systems

In digital cartographic systems and GIS, generalisationhas gradually assumed an even wider meaning. It canbe understood as a process which realises transitionsbetween different models representing a portion of thereal world at decreasing detail, while maximisinginformation content with respect to a givenapplication. Figure 2 shows how transitions take placein three different areas along the database and mapproduction workflow; the terminology used here wasoriginally developed for the German AmtlichesTopographisch–Kartographisches Informations system(ATKIS) project (Grünreich 1992), but has since beenadopted by other authors. Generalisation takes place:

● as part of building a primary model of the realworld (a so-called digital landscape model orDLM) – also known as object generalisation;

● as part of the derivation of special-purposesecondary models of reduced contents and/orresolution from the primary model – also known

as model generalisation (also termed ‘model-oriented’, or statistical (database) generalisationby different authors; cf. Weibel 1995b);

● as part of the derivation of cartographicvisualisations (digital cartographic models orDCMs) from either primary or secondary models– commonly known as cartographic generalisation.

The next section takes a closer look at the scope andthe objectives of these three generalisation types.

2.2.1 Object generalisation This process takes place at the time of defining andbuilding the original database, called the ‘primarymodel’ in Figure 2. Since databases are abstractrepresentations of a portion of the real world, acertain degree of generalisation (in the sense ofabstraction, selection, and reduction) must takeplace, as only the subset of information relevant forthe intended use(s) is represented in this database.Although seen from the perspective of generalisationhere, this operation is sufficiently explained bymethods of semantic and geometric data modelling(which define the relevant object classes and theirattributes and relations), as well as samplingmethods (which define the sampling strategy anddesired resolution and accuracy), combined withhuman interpretation skills (e.g. if photogrammetricdata capture is used: see Dowman, Chapter 31).

2.2.2 Model generalisationWhile the process of object generalisation had to becarried out in much the same way when preparingdata for a traditional map, model generalisation isnew and specific to the digital domain. In digitalsystems, generalisation can affect directly not onlythe map graphics, but also the map data. The mainobjective of model generalisation is controlled datareduction for various purposes. Data reduction maybe desirable to save storage and increase thecomputational efficiency of analytical functions.It also speeds data transfer via communicationnetworks. It may further serve the purpose ofderiving datasets of reduced accuracy and/orresolution. This capability is particularly useful inthe integration of datasets of differing resolutionand accuracy as well as in the context of multi-resolution databases (Goodchild and Longley,Chapter 40). While model generalisation may also beused as a preprocessing step to cartographicgeneralisation, it is important to note that it is notoriented towards graphical depiction, and thusinvolves no artistic, intuitive components. Instead, itencompasses processes which can be modelled

Generalising spatial data

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Fig 2. Generalisation as a sequence of modelling operations(after Grünreich 1985).

object generalisation

model generalisation

cartographic generalisation

ëReality’

Primarymodel (DLM)

Secondarymodels (DLM')

Cartographicproduct (DCM)

completely formally (Weibel 1995b); these may,however, have aesthetic consequences for subsequentcartographic generalisation.

2.2.3 Cartographic generalisationThis is the term commonly used to describe thegeneralisation of spatial data for cartographicvisualisation. It is the process most people typicallythink of when they hear the term ‘generalisation’.The difference between this and model generalisationis that it is aimed at generating visualisations, andbrings about graphical symbolisation of data objects.Therefore, cartographic generalisation must alsoencompass operations to deal with problemscreated by symbology, such as feature displacement(cf. Figure 1), which model generalisation does not.The objectives of digital cartographic generalisationremain basically the same as in conventionalcartography (see above). However, technologicalchange has also brought along new tasks with newrequirements (Kraak, Chapter 11) such as interactivezooming, visualisation for exploratory data analysis,or progressively adapting the level of detail of3-dimensional perspective views to the viewingdepth. The concept of cartographic generalisationthus needs to be extended. On the other hand, typicalmaps generated in GIS are no longer complex multi-purpose maps with a multitude of feature classesinvolved, but rather single-purpose maps consistingof a small number of layers. Furthermore, maps andother forms of visualisations are often presented bymeans of a series of different partial views in a multi-window arrangement, particularly in exploratorydata analysis (Anselin, Chapter 17). Together withthe capabilities of interactive direct manipulationthese new forms of cartographic presentationspartially alleviate (but by no means eliminate) someof the generalisation problems, or at least make themless salient for many GIS users.

2.3 Motivations for generalisation

The discussion above has already alluded to some ofthe reasons for generalisation. Extending Müller’s(1991) discussion of requirements for generalisation,it is possible to develop a more detailed list ofmotivations.

1 Develop a primary database: build a digital modelof the real world, with the resolution and contentappropriate to the intended application(s), and

populate it (object generalisation):● select objects;● approximate objects.

2 Use resources economically: minimise use ofcomputing resources by filtering and selectionwithin tolerable (and controllable) accuracylimits:● save storage space;● save processing time.

3 Increase/ensure data robustness: build clean, lean,and consistent spatial databases by reducingspurious and/or unnecessary detail:● suppress unneeded high-frequency detail;● detect and suppress errors and random

variations of data capture;● homogenise (standardise) resolution and

accuracy of heterogeneous data for dataintegration.

4 Derive data and maps for a range of purposes:from a detailed multi-purpose database, derivedata and map products according to specificrequirements:● derive secondary scale and/or theme-specific

datasets;● compose special-purpose maps (i.e. all new

maps);● avoid redundancy, increase consistency.

5 Optimise visual communication: developmeaningful and legible visualisations:● maintain legibility of cartographic

visualisations of a database;● convey an unambiguous message by focusing

on main theme;● adapt to properties of varying output media.

Examination of the above list reveals that classicalcartographic generalisation mainly relates to task 5(visual communication) and to a lesser extent also totask 4, while tasks 1 to 3 are more specific to the digitaldomain (object generalisation, model generalisation).In task 5, an aspect of cartographic generalisationgermane to a GIS environment is that output may begenerated for media of varying specifications, such ashigh-resolution plotted maps or low-resolution CRT(cathode ray tube) views, requiring consideration ofthe resolution of the output media when composingmaps for display (Spiess 1995).


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3 GENERALISATION AND MULTIPLEREPRESENTATIONS

3.1 Generalisation: process-oriented vsrepresentation-oriented view

The above discussion has implicitly taken a process-oriented view of generalisation, understanding it asthe process of transforming a detailed database intoa database or map of reduced complexity atarbitrary scale. As was already mentioned,generalisation is a complex process, and indeed,satisfactory implementations of all thetransformation operations (and their interactions)necessary to achieve comprehensive automatedgeneralisation largely remain to be developed.

An alternative – or complementary – approach isto develop multi-scale databases. We term thisapproach the ‘representation-oriented view’, becauseit attempts to develop databases that integrate singlerepresentations at different fixed scales into aconsistent multiple representation. An example mayhelp to illustrate the concept. Consider a set of fourmaps of the same region, drawn at scales 1:1000,1:25 000, 1:100 000, and 1:250 000. In a particularsettlement, dwellings may be represented by theirdetailed footprints at 1:1000. At 1:25 000 buildingsare now represented by simplified rectangularshapes; some building polygons may even have beenaggregated. At the next smaller scale, 1:100 000,built-up areas are depicted as tinted blocks definedby the street network and urban boundaries, thus aretransformed into larger, less regular polygons.Finally, the 1:250 000 scale map shows onlyaggregations of blocks, tinting entire cities as onepolygonal feature, and transforming smaller townsinto point symbols. At still smaller scales, allsettlements might be depicted as point symbols.Were all of these maps to be digitised into a GIS,some way would be needed to encode and associatethese transformations, in which features grouptogether, acquiring different topologies as well asnew symbolism. There are still many open problemsregarding how such representational issues shouldbe handled. This section reviews some of thepertinent research efforts, but starts by examiningthe concept of multiple representations.

Analogous to the concept of views in tabulardatabases, the term ‘multiple representations’ issometimes encountered in discussions of spatialdatabases (Buttenfield and DeLotto 1989;Devogele et al 1997; Kidner and Jones 1994). It isused to describe a number of different things,

including alternative graphical depictions, scale-filtered versions of digital data, changes in databaseschema, and hierarchical data structures. Multiplerepresentations are often associated with specificdisplay scales, but also may tailor data to serveparticular thematic or analytic purposes. In bothrespects they are intimately related to generalisation.

The most common form of multiple (scale)representations are topographic map andnavigational chart series. National mapping agenciesand private map producers normally publish maps atdifferent scales, whereby each scale serves as a basisfor the compilation of the next smaller one, forminga map series. When map series are updated, usuallythe large-scale representations are modified first,then the changes are propagated manually throughthe other scales. In describing the difficulties thisentails, Charles Schwarz of the US National OceanService wrote:

‘The problem of multiple representations is that it isdifficult to maintain consistency. One of the mostimportant concepts in database management is thatit is preferable to keep only a single copy of a dataitem, so that consistency is automatically insured.The alternative is controlled redundancy, where oneattempts to exercise control procedurally. This isdifficult to enforce.’ (quoted in Buttenfield andDeLotto 1989: 77)

3.2 Implicit multiple representations:generalisation by preprocessing

Several methods to deal with ‘controlled redundancy’– that is, to enable consistent matching of featuresbetween different levels of scales – have beenproposed. One possible approach is to preprocess thespatial data and compute and store the results ofgeneralisations from a single database for subsequentinteractive on-the-fly retrieval across a range of scales.A series of implicit (‘latent’) multiple representationsis thus stored and the need for explicit representationsof scale transitions avoided. Oosterom (1993) andOosterom and Schenkelaars (1995) describe a set of‘reactive data structures’ to accomplish this using theobject-oriented DBMS Postgres to store spatialdata, indices, and procedures (see also Oosterom,Chapter 27). One data structure, the binary linegeneralisation (BLG) tree, encodes results fromDouglas-Peucker line simplification (Douglas andPeucker 1973) to allow retrieval of linear objects atany level of precomputed detail. Another structure,


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the Reactive tree (based on R-trees), stores collectionsof points, polylines, and polygons indexed byminimum bounding rectangles (MBR) and by somemeasure of their ‘importance’ such as perimeter orarea. When zooming in or out, a roughly constantnumber of objects is selected for display according totheir importance. The third data structure, theGAP-tree, is called upon to fill the gaps betweenregions caused by omitting less important areas. TheGAP-tree contains (precomputed) alternativetopologies for the omitted polygons by merging theareas they cover with a similar or dominant (mostimportant) neighbour. The importance of an areacan, for instance, be expressed as a function of its sizeand an application-specific weighting factor (e.g. anurban area may be more important than a grasslandarea). Note that this approach requires completetopology for all areal features to be known in order tobuild the GAP-tree, as well as extensive analysis andpreprocessing of all geometric data. For furtherdetails, see Oosterom (Chapter 27).

3.3 Explicit multiple representations: multi-scaledatabases

Rather than deriving implicit multiplerepresentations by preprocessing, one might wish tobuild multiple representations by integrating existingmono-scale representations and by modellingexplicitly the transitions between scales. Accordingto Devogele et al (1997), the design of such multi-scale databases entails three types of problem:

1 Correspondence between abstractions: databaseschemata translate phenomena of the real worldinto abstracted instances of databases, byfocusing only on relevant parts of thesephenomena; integration of abstractions thusrequires methods for schema integration on thesemantic level.

2 Correspondence between objects of differentrepresentations: data models are required todescribe the links between corresponding objectsof the different representations.

3 Defining the matching process between objects: inorder to identify corresponding (homologous)objects, two sets of geographical data must besearched for objects that represent the samereal-world objects; methods for this purpose aresubsumed under the term ‘data matching’.

Devogele et al (1997) concentrate on the first andlast problems, schema integration and datamatching. In their research, they aim at developingmethods for building a multi-scale database fromtwo road databases available at the French InstitutGéographique National (IGN), BDCarto andGéoRoute, for purposes of road navigation.While the first database relates to a mapping scale of1:100 000, the second contains more detailed roaddata for urban areas. Since the two databases employdifferent definitions of feature classes and theirattributes, schema integration is required in a firststep to arrive at a common schema that allows thetwo individual schemata to be related and thefeature classes matched. In a second step, theindividual objects of the two databases are matched,involving the matching of entire roads, as well asindividual crossroads and sections. Road matching isachieved by comparing semantic information(attributes such as road number), and crossroadmatching by a combination of topological andmetric criteria. Section matching is carried out intwo steps: first by semantic criteria (sectionsbelonging to the same road are identified), andsecond by a metric search using the Hausdorffdistance (for a definition of Hausdorff distance see,for example, Huttenlocher et al 1992).

A significant part of the research on multi-scaledatabases has focused on the second of the aboveproblems, the design of data models and datastructures to encode the correspondence relationsbetween the individual representations. Most of thework was inspired by the largely hierarchical nature oftransitions between scales. Extending a classificationproposed by Beard (1991), such hierarchical relationscan be found in four fundamental data domains: thedomains of spatial primitives (geometric componentsof entity abstractions, such as points, lines, andpolygons); features (real-world referents, such asbuildings, rivers, and political units); attributes; andthe spatial domain.

In the primitive domain, emphasis of hierarchicalmultiple representations is on the manipulation ofdetail of spatial primitives. Examples include theBLG-tree described above (Oosterom 1993) and theequivalent ‘simplification tree’ of Cromley (1991),both of which precompute the order ofdisappearance of vertices on a line using theDouglas-Peucker line simplification algorithm. In thefeature domain, a great variety of hierarchies existwhich lend themselves to multiple representations.


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Sets of features can nest within one another, forexample political territories or census geography.Network data, particularly hydrography and roads,may also be classified hierarchically, by orderingstream segments (Rusak Mazur and Castner 1990)and designating routes (Ruas 1995a). A relatedtechnique is to identify containment relationsbetween smaller and larger features. For instance, aset of buildings can be represented by a centroid of ablock or other feature that contains them. Featurescan also be grouped into ‘placeholders’ (e.g. a group ofbuildings that is turned into a single building or apolygon representing a built-up area at a smaller scale).Timpf and Frank (1995) have proposed the use of adirected acyclic graph to represent such transitions. Inthe attribute domain, the classical example ofhierarchies is categorical data which may have inherenthierarchy, such as land-use or soil classifications. Suchinherent relations can be formalised for storage andretrieval as hierarchies (Molenaar 1996b; Richardson1994). Finally, in the spatial domain, a number ofspace-primary data structures can be used to representspatial objects at varying levels of resolution, includingquadtrees (Samet 1990), pyramids, and sphericalquadtrees (Dutton 1989, 1997; Fekete 1990; Goodchildand Yang 1992). The use of such data structures ingeneralisation is discussed in more detail in section 5.2.

Clearly, the hierarchy levels used to representspatial objects in the four domains must be inharmony to achieve a good generalisation. Forinstance, when feature and attribute hierarchies areused to reduce detail by reducing the number ofobjects, the primitives that make up these objectsmust also be simplified. None of the existingtechniques for representing multi-scale relations hasundertaken to address the hierarchies in all fourdomains comprehensively, yet examples of acombined treatment of hierarchies exist. Thecombination of the BLG- and GAP-treesdocumented by Oosterom and Schenkelaars (1995)allows hierarchies to be linked in the primitive andfeature domains (cf. section 3.2). A prototypical GISthat links the hierarchies in the primitive, feature, andattribute domains has been described by Kidnerand Jones (1994). This testbed employs anobject-oriented database (OODB), as well asobject-oriented programming (OOP) techniques, toconstruct class hierarchies of objects and methodsthat allow variants of cartographic elements to bestored, manipulated, and accessed for query anddisplay. The system is intended to handle multi-source,multi-scale, and multi-temporal versions of spatial

data, incorporating processing histories and othermetadata specific to point sets, polylines, polygons,triangulated irregular networks (TINs), and rasterimages managed by the GIS. An enhancement of thissystem, now named GEODYSSEY (Jones et al 1996),relies more heavily on metadata and assertions aboutspatial relations to match multiply-representedfeatures, both exactly and probabilistically. The systemcan determine if two representations are similarenough to delete one, and will invoke simplificationprocedures to satisfy queries to which the featuredatabase provides no suitable match. Topologicalrelations and assertions are respected, and can bederived from geometry if necessary.

Finally, while it is easy to find evidence ofhierarchical relationships between multiple scales, itis also true that features can change their shapegradually between scales, making it unfeasible tomodel such transitions in a purely hierarchicalfashion. To deal with smooth shape modificationsand displacements, Monmonier (1991) hasdescribed methods for interpolating (linear)features from two or more representations digitisedat different scales, conflated to matchcorresponding critical points along them. Recently,some GIS vendors have added rubber sheetingtools to their systems; these are primarily designedfor map conflation (e.g. for building transportationdatabases), but may also have applications in therealm of map generalisation.

3.4 Multiple representations of terrain

Terrain surfaces are an important component ofmany GIS applications, and the need often arises tosimplify their structures for analysis or display. Untilrecently, most digital terrain models (DTMs) wereelevation grids having fixed resolution. Manyenvironmental modelling applications utilise suchdata, which may be resampled to suit the scales andpurposes of inquiry. But as Dikau (1990) observes,different types of geomorphological complexity andprocesses exist at different scales, and all cannot easilybe captured in a single DTM, and may be obscureddue to resampling operations. Most non-raster-basedGIS model terrain using triangular irregular networks(TINs). The requirement to construct TINs atdifferent resolutions is as common as it is for handlingplanimetric data. A number of solutions have beenproposed for the analytic construction ofmulti-resolution TINs (De Floriani and Magillo,Chapter 38). Early methods for building


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hierarchical triangulations (De Floriani et al 1984)started with a coarse triangulation of highlysignificant points such as local extremes, to which lesssignificant points are progressively inserted to yieldfiner levels of resolution, subdividing the initialtriangles while maintaining their edges. This approachallows the hierarchical TIN to be represented as a treestructure, but a problem is that skinny triangles maybe formed: this may be alleviated to some extent byusing more sophisticated splitting rules(Scarlatos and Pavlidis 1991), or by employing theDelaunay criterion (Boots, Chapter 36) whensubdividing coarser triangles (De Floriani andPuppo 1995). As triangle edges of coarser levels ofthe hierarchy remain unchanged, however, skinnytriangles may still form and show up as distinctartefacts on surface displays (De Floriani andPuppo 1995). Such adverse effects can only beavoided effectively by optimising the triangulationindependently at each level of resolution (e.g. byconstructing a full Delaunay triangulation at eachlevel). This implies a departure from the simpletree structure and building more complex directedacyclic graphs (Berg and Dobrindt 1995), but thesurface will be approximated more consistently ateach individual level.

One problem that hierarchical TINs mustovercome is the elimination of verticaldiscontinuities that occur when new vertices areadded along edges of a coarser triangulation. Thisnecessitates retriangulation in the vicinity of theadded points and complicates data management.An alternative approach, called ‘implicit TINs’(Jones et al 1994), attacks this problem by notstoring any triangles at all; instead, each surface-specific point is labelled with a detail level. Thisparameter may be derived in a number of ways,most commonly via a full triangulation from whichthe least significant vertical deviations are identifiedand these vertices successively removed. When asurface having a certain degree of detail is requiredfor use, all points with greater or equal importanceto the criterion are retrieved and triangulated, on thefly, by a Delaunay triangulation which takes intoaccount linear constraints such as surface breaklines(constrained Delaunay triangulation). Asconstrained Delaunay triangulation is a relativelyfast operation (especially when points are spatiallyindexed), this just-in-time approach to generatingmultiple terrain representations is more flexible than

hierarchical TINs and may prove workable in anumber of applications. Similar implicit or onlinetechniques have been presented by Puppo (1996) andMisund (1997) to build TINs of variable resolution.Variable resolution TINs are needed, for instance, inflight simulation where resolution decreases withincreasing viewing distance or in other applicationswhere some regions may be in the focus of interestwhile others are not (Misund 1997).

4 CONCEPTUAL MODELS OF GENERALISATION

Following the discussion of multiple representationsin the previous section, the remainder of this chapterwill adopt again the process-oriented view ofgeneralisation. To that end, it first examines themodels that have been developed in the literature todescribe conceptually the processes necessary toderive generalised datasets or visualisations fromdetailed databases.

4.1 Conceptual frameworks of the generalisationprocess

In order to understand, much less to render, acomplex and holistic process such as generalisationamenable to automation, conceptual frameworksneed to be developed. Such theoretical models mustbe capable of describing the overall process and mustat the same time identify essential processcomponents and steps. McMaster and Shea (1992)review several conceptual frameworks proposed in theliterature, and then go on to present a comprehensivemodel of digital generalisation which extends asimilar framework proposed by Brassel and Weibel(1988), specifying details for model componentswhich were previously defined only in general terms.The model of McMaster and Shea summarised inFigure 3 decomposes the overall process into threeoperational areas: first, consideration of thephilosophical objectives of why to generalise; second,cartometric evaluation of the conditions whichindicate when to generalise; and third, selection ofappropriate spatial and attribute transformationswhich provide techniques on how to generalise.Resolving generalisation is then seen as an attempt toanswer each of the three questions in turn, wherebyeach one forms a prerequisite for the subsequent one.


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The discussion of the philosophical objectives(why to generalise) of McMaster and Shea (1992)uses similar arguments to the ones raised in ourreview of motivations for generalisation above.

The second area of the McMaster and Sheamodel, cartometric evaluation (when to generalise) isessentially equivalent in scope to the key steps in theframework of Brassel and Weibel (1988), calledstructure recognition and process recognition.Spatial and holistic measures are employed tocharacterise the shape and structure of the source data by quantifying the density of feature clustering,the spatial distribution of features, the length,sinuosity, and shape of features, and more. Thesemeasures then serve as parameters in evaluatingwhether critical geometrical conditions are reachedwhich trigger generalisation, such as congestion(crowding) of map objects, coalescence of adjacentobjects, conflicts (e.g. overlap), imperceptible objects(e.g. objects that are too small to be clearly visible),

etc. Process recognition, as specified in the Brasseland Weibel model, is served by transformationcontrols to help select appropriate operators,algorithms, and parameters to resolve the criticalgeometrical conditions. Points not explicitlymentioned in the McMaster and Shea model, butwhich are nonetheless of utmost importance togeneralisation, are the identification of topological,semantic, and proximity relations, as well as the establishment of priority orderings among features.Examples of cartometric evaluation and structurerecognition are provided in section 5.3.

Finally in the third area, spatial and attributetransformations (how to generalise) consisting of alist of 12 generalisation operators are identified(originally proposed in an earlier paper by Shea andMcMaster in 1989), subdivided into ten operatorsperforming spatial transformations – simplification,smoothing, aggregation, amalgamation, merging,collapse, refinement, exaggeration, enhancement,


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Fig 3. The conceptual framework of digital generalisation by McMaster and Shea (1992).

Digital generalisation

Philosophical objectives(Why to generalise)

Cartometric evaluation(When to generalise)

Spatial and attribute transformations(How to generalise)

Theoreticalelementsreducing complexitymaintaining spatial accuracymaintaining attribute accuracymaintaining aesthetic qualitymaintaining a logical hierarchyconsistently applying rules

Application-specificelementsmap purpose and intended audienceappropriateness of scaleretention of clarity

Computationalelementscost effective algorithmsmaximum data reductionminimum memory/storage usage

Geometricalconditionscongestioncoalescenceconflictcomplicationinconsistencyimperceptibility

Spatial and holisticmeasuresdensity measurementsdistribution measurementslength and sinuosity measuresshape measuresdistance measuresGestalt measuresabstract measures

Transformationcontrolsgeneralisation operator selectionalgorithm selectionparameter selection

Spatialtransformationssimplificationsmoothingaggregationamalgamationmergingcollapserefinementexaggerationenhancementdisplacement

Attributetransformationsclassificationsymbolisation

and displacement – and two operators for attributetransformations – classification and symbolisation.The definition of a useful set of operators is ofparticular interest in the conceptual modelling ofgeneralisation, and deserves further discussion in thefollowing two sections.

4.2 Generalisation operators

The overall process of generalisation is oftendecomposed into individual sub-processes (Hake 1975).Depending on the author, the term ‘operator’ may beused, or other terms such as ‘operation’ or ‘process’.Cartographers have traditionally used terms such as‘selection’, ‘simplification’, ‘combination’ and‘displacement’ to describe the various facets ofgeneralisation, an example of which is the definition ofgeneralisation by the ICA (1973) given in section 2.1.A detailed list of terms occurring in traditionalcartography has been provided by Steward (1974). Inthe digital context, a functional breakdown intooperators has obviously become even more important,as it clarifies identification of constituents ofgeneralisation and informs the development of specificsolutions to implement these sub-problems. Figure 4illustrates some of the generalisation operators used inthe discussion of section 4.3 (Table 1) for a simplemap example. Three levels of scale are shown, eachone at 100, 50 and 25 per cent, respectively. Theappropriate reduction is highlighted by a doubleframe. Naturally, given the holistic nature of thegeneralisation process, this reductionist approach istoo simple, as the whole can be expected to be morethan just the sum of its parts, but it provides a usefulstarting point for understanding a complex of diffuseand challenging problems.

Shea and McMaster’s (1989) typology is the firstdetailed one which also attempts to accommodatethe requirements of digital generalisation, and spansa variety of data types including point, line, area,and volume data. Still, closer inspection of this setof operators reveals that some fundamentaloperators are missing (e.g. selection/elimination) andthat the definitions of some operators are perhapsnot sufficiently clear (e.g. refinement) or overlapping(aggregation, amalgamation, merging). Even worse,cartographers may use different definitions for thesame term or use different terms for the samedefinition, as a recent study by Rieger and Coulson(1993) has shown. This has led other authors (e.g.Plazanet 1996; Ruas and Lagrange 1995) to extend

this classification by adding operators and byrefining definitions of existing ones. Thecomposition of a comprehensive set ofgeneralisation operators is still the subject of anongoing debate; it is hoped that having it wouldassist the development of adequate generalisationalgorithms as well as their integration intocomprehensive workflows.

No matter what set of operators is defined,however, the relationship between generalisationoperators and generalisation algorithms ishierarchical. An operator defines the transformationthat is to be achieved; a generalisation algorithm isthen used to implement the particulartransformation. This also implies that operators areindependent of a particular data model (e.g. vectoror raster). Algorithms are linked to a specificrepresentation, usually the one that is best suited toimplement an operator for a given purpose. Formost operators, a number of algorithms withdifferent characteristics have been developed. Inparticular, a wide range of different algorithmsexists for line simplification in vector mode. Notealso that operators often are phenomenon-specific,as Figure 5 shows. Generalisation algorithms may bephenomenon-specific and must take into account theparticular shape properties and semantics of thereal-world features in producing a generalisedversion. Also, the selection of operators will varydepending on the feature classes and scales.

4.3 Relations between operators, data, andgeneralisation objectives

Available conceptual models of cartographicgeneralisation such as the ones referred to abovetend to stop short of describing how differentoperators come into play for map elements andspecific purposes. This section attempts to synthesisesome of these concepts, illustrating howgeneralisation operators (procedures), operands(data), and objectives relate to one another.

We have attempted to integrate the diverse andoften conflicting operator sets proposed in theliterature into a combined list (Table 1). Note thatthis typology is solely meant to support ourdiscussion and is not intended as yet anotherproposal of the ultimate set of generalisationoperators. There is, for instance, some debate overwhether a distinction should be made betweensimplification (by weeding redundant points from a


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135

Fig 4. Application of map generalisation operators (cf. discussion in section 4.3, Table 1).

Map at original scale Displace

Collapse

Eliminate

SimplifyAggregate

Generalised for 50% reduction

Generalised for 25% reduction

50% scale

50% scale

50% scale

25% scale

25% scale

25% scale

Scale reduction involvesshrinking areal symbolswhile maintaining mostline weights. To achieve

this, several differentgeneralisation operators

may need to be used

In this example, the first stageof generalisation does not altermost map symbols drastically,but many types of changes are

needed to prevent conflicts.

The second generalisation stagerequires some simplification, but

mainly additional elimination,aggregation, and typification.


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line) and smoothing (by modifying coordinates on aline to plane away small irregularities), ascartographers normally do not make a consciousdistinction between the two operations whensimplifying the shape of a map object (Plazanet1996; Ruas 1995b; Weibel 1997). One of the criteriathat guided our choice of operators was that eachoperator should possibly be valid for all common data types including points, lines, areas, fields(usually raster data), and hierarchies (trees andrecursive tessellations). This contrasts with Shea andMcMaster’s (1989) typology, where some operatorsare only applicable to certain data types. In Table 1,basic examples are given for each operator, and noteis made of whether the operator may altertopological relations or affects the attribute domain.For some of the operators alternative terms found inthe literature are also given.

Table 1 focuses on the ‘how to’ aspect ofgeneralisation, categorising some functions thatmight exist in a process library (Brassel and Weibel1988). Yet selection of such operators is also shapedby the objectives or ‘whys’ of generalisation. To

achieve these objectives, each situation should beevaluated cartometrically to determine ifcommunication goals are being met (Brassel andWeibel 1988; McMaster and Shea 1992). Table 2describes this process in terms of simple rules thatmay be applicable depending on the generalisationobjective(s). Terminology for ‘cartometric criteria’ istaken from a larger set described by McMaster andShea (1992: 42–51), and can be described as:

1 Crowding: excessive feature density attributable toscale reduction;

2 Conflict: symbolism for features which overlap orcannot be distinguished;

3 Consistency: uniformity of symbolism and valueclassification across a map;

4 Perceptibility: maintaining legibility when featuresor symbols are shrunk.

Lastly, generalisation operators can be related to thefundamental data domains introduced in section 3.3,by discriminating between those that: (1) select ormodify spatial primitives; (2) select or modify features;(3) transform the attribute domain; or (4) transformthe spatial domain. This is useful because it helps to

Table 1 Relations of generalisation operators and data (operands).

TYPE OF SPATIAL DISTRIBUTIONOPERATOR Points Lines Areas Fields Hierarchies

Eliminate/ Weed based on Eliminate minor Eliminate small areas Recode less significant Ignore nodes withSelect attributes or priorities branches or sub-polygons values to null few children

Simplify Weed to min. Eliminate minor Remove islands Collapse category Shift to lower levelneighbour distance segments or and concavities definitions of detail

inflections

Smooth Make distribution Reduce angularity Soften concavities Average or convolve Average at nodesmore uniform and crenulations variations of tessellation

Aggregate/ Combine similar Simplify intersections Delete edges between Interpolate to larger Derive lower levelsAmalgamate/Merge neighbours similar features cell size from higher ones

Collapse Replace by area Combine nearly Shrink to point Merge similar Redefine orsymbol or convex parallel features or medial axis categories reorganise hierarchyhull

Displace Disperse from each Increase separation of Move away from (not normally attempted) Move data to lessother and larger objects parallel lines linear elements occupied neighbours

Enhance/ Impute, randomise, or Impute or emphasise Complicate boundaries, Emphasise differences, Extrapolate to levelsExaggerate densify distributions changes in direction impute inclusions equalise histogram of higher resolution

Note: Table entries are suggestive only and are not intended to be exhaustive. Underlined entries may require/result in topological transformations.Italic entries require reference to attributes or change their domain.


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identify the point at which operators get applied, andidentifies what types of side-effect they may have.

Knowing which data domains are targeted by agiven procedure helps users (and applications) toselect procedures from a process library (algorithmsavailable to implement operators). The content andstructure of the database must be appropriate for agiven operator to work, and the manner in which anoperator functions is highly dependent on what hooksdata models and data structures provide for handlingcartographic primitives, features, attributes, and spaceitself, as well as what types of constraintgeneralisation must satisfy (cf. sections 5.2 and 5.4).Clearly, it may be necessary to take several of theseactions together, even if one approach is primary. Inpractice, operations from more than one domain willbe invoked to generalise a given digital map for astated purpose. Operations in different domains havemany close relationships, and can be combined in anumber of natural and effective ways. As a simpleexample, aggregation of class values in the attributedomain of a categorical land-use map to formsuperclasses – e.g. aggregating ‘deciduous forest’ and‘coniferous forest’ to ‘forest’, or ‘residential area’ and‘industrial area’ to ‘built-up area’ – will have an effecton the geometry of the primitive domain (somepolygon boundaries will disappear) and on the featuredomain (new and larger regions will be formed).

5 ELEMENTS OF A GENERALISATION SYSTEM

Whether generalisation functionality is implementedas an ad hoc set of tools made available in a toolbox,or represents a sub-system of a larger GIS orcartography system, or forms a stand-alonegeneralisation system is not in itself important.(See Openshaw and Alvanides, Chapter 18, for asimilar view with regard to the implementation ofspatial analytic functions.) What matters is that thenecessary elements required to solve a given class orseveral classes of generalisation problems are madeavailable in a way which enables the system or user toinvoke the right actions. This section attempts toidentify the elements that need to be present in anidealised (not yet available) comprehensivegeneralisation system. Discussion of these elements willserve as a review of selected existing techniques andwill highlight critical issues requiring additionalresearch. The systems-oriented approach helps toidentify the interrelations between the various elements.

5.1 An idealised generalisation system

The following discussion is based on twoconstraining assumptions. First, the discussion herewill be restricted to functions for generalisation inthe narrow sense. That is, we assume that basicgraphics functions needed for map production

Fig 5. The set of appropriate generalisation operators varies depending on the feature classesand scales.

Culture

Hydrography

simplification,exaggeration,aggregation,elimination

Small scaleMedium scaleLarge scale

simplification,aggregation,elimination,collapse


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(cartographic symbolisation, projections, zooming,etc.) will be available to the envisaged ideal system,or will be supplied by a carrier system (e.g. a GIS).Second, we assume that a human (user) will beinvolved in the generalisation process in somecapacity, interacting with the system. Userinvolvement may range from close to zero (invoking‘batch’ modules) to a constant stream of interactions(fully interactive mode of operation, with no built-inmachine ‘intelligence’). In all cases, users will alwaysbe involved, even if the involvement is restricted tovisual evaluation of results. That is, the more thesystem relies on user interaction, the moreresponsibility is put on the user. Cartographicexperts will obtain better results than novices.

The next question we have to ask is what softwareparadigm is used to build the system. A look at priorresearch in digital cartographic generalisationreveals that neither purely algorithmic methods(Leberl 1986; Lichtner 1979) nor knowledge-basedtechniques such as expert systems (Fisher andMackaness 1987; Nickerson 1988) have been capableof solving the problem comprehensively. While theformer suffer from a lack of flexibility (since they areusually designed to perform a certain task) and fromweak definition of objectives, the development ofthe latter was impeded by the scarcity of formalisedcartographic knowledge and the problemsencountered in acquiring it (Weibel et al 1995).

More recent research has therefore concentrated onsystems that attempt to integrate different paradigmsinto a single coherent approach. Workbench systemsdesigned to support research on more complex,contextual generalisation operators such asaggregation and displacement today use acombination of algorithmic (deterministic) andknowledge-based techniques commonlyimplemented on the basis of object-orientedtechnology. Examples of this class of researchsystems are MAGE (Bundy et al 1995; Jones et al1995) and Stratège (Ruas 1995a; Ruas and Plazanet1997). Another paradigm from artificial intelligenceresearch is that of autonomous agents, which is juststarting to be applied to generalisation (Baeijs et al1996). If we consider how a system could be used ina production environment to solve actualgeneralisation problems, we find that the decisionsupport system (DSS) paradigm, a strategy oftenused to solve ill-defined problems, may be anappropriate approach to take. A particular approachin this vein has been termed amplified intelligence(Weibel 1991). As visualisation and generalisationare essentially regarded as creative design processes,the human is kept in the loop: key decisions defaultexplicitly to the user, who initiates and controls arange of algorithms that automatically carry outgeneralisation tasks (Figure 6). Algorithms areembedded in an interactive environment and are

Table 2 Rules for achieving map design objectives.

CARTOMETRIC CRITERIAGENERALISATION Crowding Conflict Consistency PerceptibilityOBJECTIVES

Reduce/Maintain Enforce radical Displace or eliminate Apply tolerances and Weed detail toGraphic Complexity law where practical overlapping symbols thresholds uniformly perceptual limit

Maintain/Standardise Respect map Displace less accurate Generalise uniformly Do not represent Spatial Accuracy accuracy standards or critical features within a given feature features that cannot

class be distinguished

Maintain/Standardise Streamline attribute Do not construct Always use the same Limit no. of valueAttribute Accuracy classification overlapping symbol symbol for a given classes more as

classes attribute within a map features shrink

Maintain/Standardise Use minimum Maintain figure/ground Use distinct but related Be judicious when Aesthetic Quality appropriate symbol rels., use compatible colours and line styles using multi-variate

sizes colours, textures symbolism

Reduce/Maintain Combine related Eliminate minor features Use same value Ensure that the Attribute Hierarchy feature classes by size or attribute classification everywhere classification conveys

for a feature class enough information

Note: Table entries are suggestive only and are not intended to be exhaustive.


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complemented by various tools for structure andshape recognition giving cartometric information onobject properties and clustering, spatial conflicts andoverlaps, and providing decision support to the useras well as to knowledge-based components. Ideally,interactive control by the user reduces to zero fortasks which have been adequately formalised and forwhich automated solutions could be developed.

In a system such as Figure 6 depicts, algorithmsserve the purpose of implementing tasks for whichsufficiently accurate objectives can be defined. Thisincludes cartographic generalisation operators suchas simplification, aggregation, or displacement;functions for structure and shape recognition,including shape measures, density measures, anddetection of spatial conflicts; and modelgeneralisation functions.

Knowledge-based methods can be used to extendthe range of applicability of algorithms and codeexpert knowledge into the system. This initiallybuilds on methods for knowledge acquisition; forinstance, machine learning may help to establish aset of parameter values that controls the selectionand operation of particular algorithms in a givengeneralisation situation (Weibel et al 1995). Second,procedural knowledge and control strategies areneeded: once the expert knowledge is formalised, itcan be used to select an appropriate set andsequence of operators and algorithms and to

establish a strategy to solve a particulargeneralisation problem.

An ideal system builds on a hierarchy of controllevels. The human expert makes high-level designdecisions and evaluates system output. Knowledge-based methods operate at an intermediate level and areresponsible for selecting appropriate operators andalgorithms and for conflict-resolution strategies.Finally, algorithms are the workhorses at the lowestlevel, forming the foundation of everything else.

In summary, the following main areas – which willbe discussed in the remainder of this section – need tobe addressed to implement a comprehensivegeneralisation system based on the above assumptions:

● data representations and data models;● structure and shape recognition;● generalisation algorithms, including model

generalisation;● knowledge-based methods;● human–computer interaction;● generalisation quality assessment.

5.2 Data representations and data models

Most generalisation algorithms available today arerelated to operators such as selection, simplification,or smoothing which are context-independent,treating map objects largely independently oftheir context. Few solutions are available for

Fig 6. The concept of amplified intelligence for map generalisation.

Generalisationsystem

Data modelsStructure recognitionGeneralisation algorithmsKnowledge-based methods

User

Holistic reasoningVisual perception

Quality assessment

Graphical user interface

Decision support

Procedural knowledge

Map


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context-dependent operators such as aggregationor displacement which the spatial context(spatial relations of objects, object density, etc.)triggers and guides to completion. Various authorshave argued that the scarcity of available context-dependent generalisation algorithms is caused by thefact that commonly used spatial data models areunable to provide adequate support of such complexfunctions, in particular those requiring arepresentation of proximity relations betweendisjoint objects (Bundy et al 1995; Dutton 1984;Ruas and Lagrange 1995; Weibel 1997). In recentyears, research has therefore started to exploitalternative data models. The problem needs to beaddressed at two levels, involving representations forgeometric primitives as well as complex data models.

5.2.1 Representations for geometric primitivesAdequate data structures must be available forrepresenting geometric primitives (points, lines,areas), including methods such as polygonal chains(or polylines), mathematical curves, and rasters.These primitive representations must be capable ofcapturing the shape of the modelled featuresaccurately and in a compact and expressive way.

In vector mode generalisation, polylines are by farthe most commonly used representation scheme forgeometric primitives. Regardless of its popularity, thepolyline representation also imposes impediments onthe development of generalisation algorithms (Fritschand Lagrange 1995; Werschlein 1996), essentiallyrestricting the design options to simplification (vertexweeding) and smoothing (vertex modification). Thefact that a polyline is simply a sequence of pointsimplies that it is difficult to model entire shapes such asa bend of a road properly or compactly.Complementary representations to polylines aretherefore being investigated. Work by Affholder(reported by Plazanet et al 1995) on geometricmodelling of road data is an example of fitting therepresentation scheme more closely to the object thatneeds to be represented. Affholder models roads by aseries of cubic arcs, leading to a more compact andalso more realistic representation of these manmadefeatures which offers potential for the development ofnew algorithms.

Parametric curves based on curvature can beusefully exploited for shape analysis as critical pointssuch as inflection points show up as extremes(Werschlein 1996). The magnitude of these extremesexhibits the size of the shape that is associated withthe critical point and thus allows prioritisation.

Wavelets (Chui 1992) are a relatively untried butpromising approach to generalisation of bothsurfaces (Schröder and Sweldens 1995) and lines(Fritsch and Lagrange 1995; Plazanet et al 1995;Werschlein 1996). They either require a rasterrepresentation or, for vector data, that its geometry befirst transformed into a function (e.g. a parametriccurve). A geometric basis function, the ‘motherwavelet’, is then applied to fit the representation overdoublings of resolution. Wavelet coefficients can beanalysed to determine critical points and shapes, andthey can also be filtered to yield generalised versionsof the original feature. It is also possible to eliminateentire shapes selectively by setting the coefficients ofthe wavelets supporting a particular shape to zero(Werschlein 1996).

5.2.2 Complex data modelsComplex data models let one integrate primitivesinto a common model (e.g. a topological vectordata model) and record their spatial and semanticrelations. While the search for alternative primitiverepresentations is mainly guided by the requirementsof representing and analysing shapes, research intocomplex data models is driven by the need tosupport context-dependent generalisation. Improvedcomplex data models must: allow representation ofrelevant metric (proximity), topological, andsemantic object relations within and across featureclasses; enable object modelling (includingdifferentiation between primitives and features,complex objects, and shared primitives); and permitthe integration of auxiliary data structures such astriangulations, uniform grids, or hierarchicaltessellations for computing and representingproximity relations.

As a consequence of these requirements the maindata model should be an object-oriented extensionof the basic topological vector model (as opposed tolayer-based). Data models of this kind are nowbeginning to appear in some commercial GIS.Integrated auxiliary data structures for proximityrelations are not yet available in commercial systems,but research is under way in that direction.

Data structures for proximity relations arecommonly based on tessellations (see Boots,Chapter 36 for a comprehensive review oftessellations in GIS). Space-primary tessellationsuse regular subdivision of space and can be used asa simple mechanism to assess spatial conflict within


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a fixed resolution, usually relating to the resolutionof the target map (Figure 7). They can also beturned easily into hierarchical data structures. Bydiscretising space in a hierarchical fashion, verticesand entire primitives can be coalesced or eliminatedwhen several are found to occupy the same location(a ‘chunk’ of space). Encoded features can haveaddresses that indicate where and how big they are,allowing access both by location and resolution.Generalisation often proceeds in such methods byaliasing the positions of points or grid cells to somemedian location (see Figure 8). Alternatively,detected overlaps or coalescing primitives can beresolved by displacement. Quadtrees (Samet 1990)and pyramids are commonly used to partition mapspace hierarchically; conventional approaches indexplanar coordinates using rectangular subdivision.Their use in geoinformation processing, however,has been principally limited to multi-resolutionimage reconstruction. Spherical quadtrees (Dutton1989; Fekete 1990; Goodchild and Yang 1992)enable planetary indexing of global geographicalcoordinates by partitioning the facets of regularpolyhedra into forests of triangular quadtrees. A linegeneralisation method via hierarchical coarseningusing a triangular quadtree structure – thequaternary triangular mesh (QTM) – has beenpresented by Dutton and Buttenfield (1993) and

Dutton (1997). This is illustrated in Figure 8 inwhich the ‘level’ of generalisation denotes theresolution (doubling of scale) of each hierarchicalencoding: level 16 corresponds to 150 m, level 12 to2.5 km resolution.

Most approaches to represent proximity relationsbetween spatial objects accurately, however, haveconcentrated on the use of object-primarytessellations including Delaunay triangulations orVoronoi diagrams (Jones et al 1995; Ruas 1995a;Ruas and Plazanet 1997; Ware et al 1995; Ware andJones 1996; Yang and Gold 1997). The data modelsused by Ruas (1995a) and by Bundy et al (1995) areboth based on Delaunay triangulations. Bothapproaches concentrate on the support of methodsfor detecting and resolving spatial conflicts(e.g. feature overlap or coalescence), and both usethe space subdivision scheme as a means to computeproximity relations, compute displacement vectors(if needed), and keep track of displacements.Beyond these similarities, however, the two datamodels take a different approach.

Ruas (1995a; see also Ruas and Plazanet 1997)subdivides map space according to the hierarchy ofthe road network. Within each of these irregulartiles, conflict detection and resolution again takesplace, starting at level 1 and proceeding to finerlevels. A local, temporary Delaunay triangulation is

Fig 7. Space-primary assessment of spatial conflict between a river and a road using alternative tessellations:(a) rasterising to a rectangular grid; (b) rasterising to a triangular grid.

(a) (b)

then built within each partition to negotiate spatialconflicts there. The triangulation connects thecentroids of the small area objects and point objectsfalling within the tile, as well as projection points onthe surrounding roads forming the tile boundary.The edges of the triangulation are classifiedaccording to the types of object they connect. Thusin Figure 9, edge e1 denotes an edge connecting two buildings; e2 connects two vertices on a road; and e3connects a building and a road. If the shape of abounding road is changed or buildings are enlargedor moved, the triangulation is used to determine anyconflicts that might have arisen. Displacementvectors are then computed from the distancesbetween objects and displacement propagation isactivated using distance decay functions. This isillustrated in Figure 10, in which a road (a) ismodified, leading to overlap (b). Displacementvectors are calculated (c) and buildings are rotated


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Fig 9. Local Delaunay triangulation between buildings andadjacent roads (after Ruas 1995a).

e1

e2

e3

Fig 8. Line simplification via hierarchical coarsening using a quaternary triangular mesh (QTM).

Input line Generalised Source data Level 16

307Points

Points along a vector that fall within a cell clusterbecome represented by their median location 292 Points 95% retained

Level 12Level 13

113 Points 37% retained 74 Points 24% retained

and realigned with the modified road (d). (For thesake of clarity only the road centreline is shown inthis figure; the symbol width of the road would betaken into account when computing thedisplacement vectors.)

In the triangulated data model developed byresearchers at the University of Glamorgan (Bundy etal 1995; see also Jones et al 1995; Ware et al 1995;Ware and Jones 1997) the triangulation forms the coreof the data model. Rather than connecting centroids ofmap objects, a constrained Delaunay triangulation ofall the vertices of all map objects is built (Figure 11).The resulting simplicial data structure (SDS) is

represented through a set of relations which are storedby pointers corresponding to the entity relationshipsillustrated in Figure 12. Since the SDS comprises allthe geometric information of the original objects, allgeneralisation operations are carried out directly onthe SDS. The target application for the MAGE systembuilt around the SDS is the generalisation of large-scale topographic map data of the Ordnance Survey ofGreat Britain. To that end, a palette of generalisationoperators has been developed including objectexaggeration (enlargement), object collapse(constructing the centreline of road casings), operatorsfor areal object amalgamation, and buildingsimplification using corner flipping of triangles.

5.3 Structure and shape recognition

As discussed in section 4.1, structure and shaperecognition (cartometric evaluation) are logicallyprior to the application of generalisation operators(Brassel and Weibel 1988; McMaster and Shea 1992).They can determine when and where to generaliseand inform the selection, sequencing, andparameterisation of a set of generalisation operatorsfor a given problem. Because cartographic data tendnot to be richly structured, parts of features (e.g. a


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Fig 10. Displacement of buildings after simplification of a road(after Ruas 1995a).

(a)

(b)

(c)

(d)

Fig 11. A sample section of the constrained Delaunaytriangulation forming the simplicial data structure (after Ware etal 1995).

Fig 12. Entity relationships in the simplicial data structure (afterJones et al 1995).

is-composed-

ofbelongs-to

is-composed-

of

belongs-to(left and right)

belongs-to(not modelled)

is-composed-

of

Object

Triangle

Edge

Vertex

1

n

2

m

3

2

hairpin bend on a road or an annex of a building)are rarely coded explicitly. Likewise, littleinformation is normally stored on shape propertiesof map features. Structure and shape recognitiontherefore aims at enriching the semantics of sourcemap data, and deriving secondary metric, topologic,and semantic properties including shapecharacteristics, object density and distribution,object partitioning, proximity relations, relativeimportance (priority) of map objects, and logicalrelations between objects.

In recent years, research in this area hasintensified. First attempts at cartographic linecharacterisation were made by Buttenfield (1985).Recently, an approach has been presented byPlazanet (Plazanet 1995, 1996; Plazanet et al 1995)which generates a hierarchical segmentation ofcartographic lines according to a homogeneitycriterion. The resulting tree structure is called the‘descriptive tree’. Figure 13 illustrates such a tree;the homogeneity of the individual sections is intuitivelyapparent. The homogeneity definition used to split upthe line is based on the variation of the distancesbetween consecutive inflection points which have beenpreviously extracted (Figure 14). While the objective ofsegmentation is mainly to obtain sections of the linethat are geometrically sufficiently homogeneous to betractable by the same generalisation algorithm andparameter values, further information is added to thedescriptive tree that characterises the sinuosity(and thus the prevailing geometric character) of each

line section. A variety of measures can be obtainedfrom the deviation of the cartographic line from atrend line formed by the base line connectingconsecutive inflection points. These measures arethen used to classify line sections according to theirdegree of sinuosity.

Analysis of complex situations involving disjointobjects such as buildings and roads in built-up areas can obviously benefit from data models such as thosediscussed in section 5.2.2. Proximity and adjacencyrelations can be assessed and possible overlapsdetected by direct analysis of the data model. Morecomplex relations involving many objects, however,require further processing. An example of such aprocedure has been presented by Regnauld (1997),who proposed the use of the minimum spanning tree(MST) to detect clusters of buildings of like shapeand alignment in order to form candidate sets foraggregation and typification operations.

In the area of terrain generalisation, Weibel (1992)has reported on the use of procedures forgeomorphometric analysis to drive the selection ofappropriate generalisation methods.Geomorphometric analysis is first applied at the globallevel, segmenting an entire DTM into homogeneousregions amenable for a particular generalisationmethod in an approach similar in nature to Plazanet’s(1995) technique for line segmentation. Next, structurelines (drainage channels and ridges) are automaticallyextracted from the DTM to form the so-called


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Fig 14. (a) Detected inflection points; (b) critical points retainedautomatically for segmentation.Source: C Plazanet, IGN France.

(a) (b)

Fig 13. An example of line segmentation into a descriptive tree. Source: C Plazanet, IGN France.

Trend line

‘structure line model’ (SLM) which is seen as a3-dimensional skeletal representation of the terrainsurface and used as a basis for the generalisationmethod termed ‘heuristic generalisation’. Thisprocedure generalises the SLM by modifying links inthe networks of channels and ridges and interpolates ageneralised DTM from the modified SLM (Figure 16(b) shows a result of this procedure).

5.4 Generalisation algorithms

In section 4.2, it was noted that generalisationalgorithms implement generalisation operators whichin turn define the spatial transformations necessary toachieve generalisation. Generalisation algorithms arethus at the heart of the generalisation system,‘making it happen’. As Figure 5 illustrates, however,generalisation algorithms tend to be phenomenon-specific because they must take into account theparticular shape properties and semantics of thereal-world features they aim to depict in a generalisedversion. Only careful analysis of the structure andshape of map objects – exploiting the resources of arich spatial data model – can give generalisationalgorithms the guidance they need.

Countless generalisation algorithms have beendeveloped over the past three decades; thisdiscussion is restricted to algorithms for vector data.Raster-based algorithms are reviewed by Schylberg(1993); they are less common, but naturally lendthemselves to implementation of context-dependentoperators, as Figure 7 indicates. Most vectoralgorithms are intended to generalise point and lineprimitives using context-independent operatorssuch as selection, simplification, and smoothing(see McMaster and Shea 1992 for descriptions).Research in more recent years has beencharacterised by increasing interest in morecomplex context-dependent operators such asaggregation and displacement. Displacementalgorithms have profited from data models such asthe ones discussed in section 5.2, but also fromresearch in displacement propagation functions(Mackaness 1994). Examples of aggregationalgorithms include procedures for area patchgeneralisation described by Müller and Wang (1992)as well as the research at the University ofGlamorgan by Jones et al (1995).

Attention in research on generalisationalgorithms has also turned to the development ofalgorithms which are constrained by the particular

requirements and characteristics of specific featureclasses. Instead of generalising line or polygonprimitives, the focus is on the feature classes thatthese primitives purport to represent. That is,specific methods for generalising building outlines,traffic networks, or polygonal land-use maps aredeveloped. Such techniques may be based on moreprimitive algorithms, integrating them to build fine-tuned methods. An example of a system that hasemployed specialised algorithms at an early stage todevelop functionality for large-scale topographicmap generalisation is the CHANGE system whichintegrates two decades of research at the Universityof Hanover (Grünreich et al 1992). This systemincludes specific algorithms for generalisation ofroads (centreline generation, simplification,symbolisation), building generalisation (outlinesimplification, aggregation), and identification andediting of spatial conflicts. A sample output isshown in Figure 15. It represents the result of a fullyautomated procedure; interactive editing is usuallynecessary to clean up residual problems.

Other research has addressed the generalisationof road networks (Mackaness and Beard 1993;Thompson and Richardson 1995). Owing to thetopologic constraints of networks, these methods arebased on an analysis of the network structure usinggraph-theoretic algorithms. Techniques for terraingeneralisation have been proposed by Weibel (1992),who also summarises other approaches. A strategyis used that employs three types of generalisationmethods, two of which apply filtering techniques,while the third is based on an extraction of thenetworks of drainage channels and ridges(cf. section 5.3; see also Hutchinson and Gallant,Chapter 9). Figure 16 is based on an application ofthe third method and shows: (a) an original surface(7.75 × 5.5 km; 25 m resolution); (b) a generalisedsurface, resulting from the extraction andgeneralisation of the network of topographicstructure lines (channels and ridges); and (c) afurther modification of the automaticallygeneralised surface through interactive retouching toenhance prominent landforms using a DTM editordeveloped by Bär (1995). This editor offers a rangeof tools, most of which are implemented as localconvolution filters in the spatial domain and whichcan be controlled interactively.

Developing algorithms which can meet the needsof particular feature classes, scale ranges, and map


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Fig 15. An example of large-scale topographic map generalisation using the CHANGE system.Source: Grünreich et al 1992: courtesy of the Institute of Cartography, University of Hanover. Note that scale is only approximate.


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types requires that the constraints which govern aparticular generalisation task are defined accurately(Beard 1991; Weibel 1997). A good example of aconstraint-based algorithm is the procedureproposed by Berg et al (1995) for the simplificationof polygonal maps. Their algorithm satisfies fourconstraints:

1 all points on the simplified polygon boundary(chain) are within a prespecified error distancefrom the input boundary;

2 the simplified chain has no self-intersections;3 the simplified chain may not intersect other

chains of the polygonal map;4 all points of an additional point set lie to the

same side of the resulting polygon boundaries asbefore simplification.

Finally, the algorithms toolbox must also includemethods for model generalisation. Relatively littleattention has so far been paid to this segment ofgeneralisation, however. The volume edited byMolenaar (1996a) contains a selection of papers onthe topic. Weibel (1995b) discusses the requirementsof model generalisation and their differences fromthose of cartographic generalisation. Heller (1990)presents a method for filtering a grid or TIN DTMwhich can be used for model generalisation ofterrain models (see also section 3.4).

5.5 Knowledge-based methods

If a generalisation system were based solely on thedata models and algorithms discussed above, muchof the higher-level reasoning and decision strategieswould be lacking, making it necessary to relyentirely on the user for the provision of this missingknowledge. Knowledge-based methods have beenproposed as a way to overcome this reliance on theindividual user and to build more completelyautomated solutions. Knowledge-based methodswith a potential applicability to generalisationencompass expert systems (or knowledge-basedsystems) as well as machine-learning techniquesincluding methods such as inductive learning,case-based reasoning, genetic algorithms, orartificial neural networks (Carbonell 1990). Thepotential of these methods lies in two areas: inacquiring and representing human knowledgeexplicitly (e.g. inductive learning for knowledgeacquisition and rules of an expert system for

knowledge representation), and in complementingor replacing algorithmic techniques by use ofimplicitly encoded knowledge (e.g. knowledgewhich is latently contained in large sets ofexamples) as well as computational learningstrategies (e.g. genetic algorithms or neuralnetworks: see Fischer, Chapter 19).

Use of knowledge-based methods for the latterpurpose has been restricted to a few isolatedattempts to use genetic algorithms, neural networks,or case-based reasoning in generalisation, and is stillin an undeveloped state (see Weibel et al 1995 for areview). The former area, however, has receivedmore attention. Whatever the intended use ofknowledge-based methods may be, knowledgeacquisition (KA) is the key to success. This isparticularly true for expert systems, as they derivetheir power from the knowledge they contain andnot from the particular knowledge representationschemes and inference mechanisms they employ.Because of the scarcity of available formalisedcartographic knowledge, success of expertgeneralisation systems to date has been limited(with a few exceptions, such as that described byNickerson 1988), a situation which has sometimesbeen termed the ‘knowledge acquisition bottleneck’.

According to Armstrong (1991) cartographicknowledge takes three different forms. Geometricalknowledge describes the geometry (locations), shape,and distribution of cartographic objects. Structuralknowledge represents the structure of cartographicfeatures in terms of their geomorphological,economic, or cultural meaning, and thus relates tothe term ‘semantic knowledge’ used by other authors(e.g. Chang and McMaster 1993). Finally, proceduralknowledge is used to select the appropriategeneralisation operators, algorithms, and parametersettings required to perform a generalisation task. Itis the knowledge that is needed to control the flow ofoperations. While geometric knowledge is largelycontributed by methods for structure and shaperecognition (section 5.3), and structural knowledgecan be feature-coded into the database (or possiblyextracted by shape analysis), the acquisition ofprocedural knowledge is largely an open problem. Itsmain task is to find rules which relate generalisationoperators, algorithms, and parameter values to mapscale, map purpose, feature classes, and shapeproperties. That is, procedures are to be linked tostructure and semantics.


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Fig 16. Terrain generalisation.Source: DTM data courtesy of Swiss Federal Office of Topography.

Cartographic knowledge is different from otherknowledge types (e.g. the knowledge needed inmedical diagnosis) in that it is essentially graphicaland therefore hard to verbalise and formalise. It maybe acquired from different sources, necessitatingdifferent KA methods, which can be exploited incombination. Weibel (1995b) and Weibel et al (1995)discuss the potential of various KA methods andknowledge sources. The obvious source ofknowledge is the human expert (cartographer).According to McGraw and Harbison-Briggs (1989),methods for eliciting knowledge from expertsinclude interviews, learning by being told, andlearning by observation. In generalisation, directknowledge elicitation from experts has beenrestricted to projects linked to national mappingagencies (NMAs), such as those described byNickerson (1991) or Plazanet (1996). Text documentsform a second possible knowledge source. Apartfrom textbooks, written guidelines are available atNMAs, for example coding guides for digitisinghardcopy maps (USGS 1994). These textualdescriptions, often including positive and negativesample illustrations, may be used as a basis todevelop formal rules. In summarising an attempt tocast generalisation guidelines in use at OrdnanceSurvey of Great Britain into rules, Robinson (1995)observes that the resulting rules revealed that thewritten guidelines were incomplete and oftenvaguely specified. Maps as a third knowledge sourceembody cartographic knowledge in graphical form.It may be hoped that a study of the evolution offeatures across the scales of a map series can revealthe procedural knowledge that was used to create thegeneralisation. Practical experiments using this typeof ‘reverse engineering’ procedure have been usefulin establishing quantitative relations between scalessuch as the percentage of objects retained forspecific feature classes (Leitner and Buttenfield1995), but they have also demonstrated the difficultyof reliably identifying more complex proceduralknowledge such as the operators used to produce ageneralisation (Weibel 1995b). It is often impossibleto determine the operations that led to the resultfrom the result alone. Finally, process tracing ininteractive systems offers a method that couldcomplement KA from experts. Instead of elicitingknowledge directly from experts, interactions of theexpert with an interactive system are logged andlater analysed to extract rules. Thus, the system actsas a mediator which already achieves a first step oftranslating human knowledge into the ‘language’ of

generalisation systems. Use of this approach hasbeen proposed by several authors, including Weibel(1991) and McMaster and Mark (1991). Animplementation of this method to determineappropriate parameter values for line generalisationalgorithms is described by Weibel et al (1995) andReichenbacher (1995). The trace of interactions isanalysed using inductive machine-learningalgorithms in order to extract rules. Furtherexperiments using inductive learning have beencarried out by Plazanet (1996).

5.6 Human–computer interaction

Assuming that any comprehensive generalisationsystem is likely to take at least a partially interactiveapproach, consideration must be given to thedesign of user interfaces for generalisation.Human–computer interaction (HCI) in GIS andcartographic systems has profited greatly from thewidespread availability of graphical user interfaces(GUI), but the specific requirements of generalisationmay necessitate the development of optimised HCImechanisms. Specific HCI mechanisms are neededduring several phases of the development and use ofgeneralisation systems: during algorithmdevelopment and testing, for selection and fine-tuning of generalisation algorithms and controlparameters, for the evaluation of results, forretouching, and more.

Beard and Mackaness (1991) discuss the problemof how the ‘cognitive responsibility’ of the designprocess is best shared between the generalisationsystem and the user, and how the general workflowcould be captured in the user interface. According tothe general user interface requirements forgeneralisation systems proposed by McMaster andMark (1991), the user interface should provide abroad set of generalisation operators, tools foridentifying map features, assistance in selectingparameters for algorithms, warnings aboutinconsistencies, and traces of generalisation actions.User feedback should include hypermedia-baseddocumentation and diagrams, graphical and numericmeasures of success, and highlighting of features orregions in need of generalisation. Chang andMcMaster (1993) report on a prototype system thatimplements parts of these elements, and developsspecific HCI mechanisms to support them. Thesystem was mainly intended for experimentationwith the different line generalisation algorithms


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described by McMaster (1987). Results of up to fouralgorithms can be displayed, and toleranceparameters of the algorithms can be controlled via aslider bar, effecting real-time generalisation. Theslider bar interaction technique was developedconcurrently in the MGE Map Generalizer systemdescribed by Lee (1995). Schlegel and Weibel (1995)developed a prototype system which was intended toillustrate some of the HCI requirements of ageneralisation system useful for production.Elements that were added to the design includedmultiple windows – a working window and twowindows to display the map at the source and targetscale, respectively – together with extensive featureselection functions (e.g. by selection via a histogramof shape measures), and full symbolisation withcorrect symbol size at target scale (necessary toassess the need for displacement). Finally, a novelinteraction technique termed generalisation byexample was proposed by Keller (1995). To specifytolerance parameters for a line generalisationalgorithm, the user draws a representative sampleline. The system picks up this sample and finds theparameter value(s) which can best reproduce theexample with the specified generalisation algorithm;the optimisation procedure uses a genetic algorithm.

5.7 Generalisation quality assessment

As is true for digital cartography in general,assessment of the quality of generalisation resultshas received relatively little attention in research sofar. The availability of a comprehensive palette ofevaluation methods and strategies, however, isindispensable for progress in generalisation research,making it possible to assist such diverse tasks as thecomparative appraisal of algorithms or entiresoftware systems, the development of built-inevaluation functions for genetic algorithms, or theselection of positive examples for the training ofneural networks (Weibel 1995b).

To date, evaluation has largely relied on visualassessment of the results obtained from a particularprocedure or system, for instance by comparingdigital results with a manually produced solution.This approach, however, is neither rigorous noralways possible, as the manual reference map maynot be available. More rigorous, intersubjective, andrepeatable methods are needed in digital systems.Quantitative assessment techniques can largely drawfrom structure and shape recognition methods

(cf. section 5.3), as a priori structure recognition issimilar to a posteriori assessment of results. Theformer analyses the structure of the objects in asource database, while the latter analyses thedifference between a source and a derived database.

In order to assess the geometric performance ofline simplification algorithms, McMaster developed avariety of geometric measures to analyse shapedistortion in terms of the difference between theoriginal and the simplified line (McMaster 1987).While this method is valid for entire lines,Mustière (1995) has proposed a series of measureswhich analyse a cartographic line for possible conflictswhich might arise due to symbol enlargement,suggesting, for instance, elimination or enlargementof a particular bend. Checks for topologicalconsistency such as tests for self-intersection,intersections between neighbouring lines, or pointcontainment violations caused by line simplificationare relatively easy to develop (Berg et al 1995). Ingeneral, quantitative assessment methods are weakwhen multiple objects are involved or the quality ofan entire map needs to be characterised. This area stillrequires additional research.

As generalisation involves subjective decisionsand aesthetic considerations, one cannot evaluate itsresults completely quantitatively, nor can qualityassessment simply consist of a series of atomic testsand measures. An integrated approach is needed tocapture the more holistic elements of generalisation.A methodology to integrate quantitative measureswith qualitative judgements by cartographic expertsin a consistent way has been proposed byEhrliholzer (1995, 1996). Using it, an assessmentprocess starts by carefully defining the relevantcriteria to be used in describing the quality of aparticular generalisation application. These criteriamay be measurable, such as the minimum size ofsmall areas, or qualitative and holistic, such as‘maintenance of the overall character of the map’.Application of these criteria will yield a ‘qualitydescription’ with interval/ratio values forquantitative measures and symbolic descriptions orkeywords for qualitative criteria. The two sets ofresults may then be integrated by transforming bothinto scores or ranks on a rating scale.

5.8 Digital generalisation in practice

Most commercial GIS today offer some generalisationfunctionality. Usually, however, generalisation


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capabilities in GIS are restricted to a few functions(e.g. line simplification, polygon aggregation, orvarious filters for raster data) which must be appliedthrough independent commands in a toolboxapproach (Morehouse 1995) or integrated to buildmore complex functions (Schlegel and Weibel 1995).Ruas (1995b) reviews the use of a general-purposeGIS (ARC/INFO) for the production of a database atscale 1:1 000 000 from a database at 1:100 000 at IGNFrance. Brandenberger (1995) reports on anexperiment of producing a 1:10 000 scale map fromdata captured at 1:1000 using another majorcommercial system (Intergraph MGE).

Special-purpose commercial generalisationsystems exist. The CHANGE system (Grünreich etal 1992), mentioned in section 5.4, builds on a suiteof batch modules controlled by parameter sets.Figure 16 shows a sample run, in which the(approximate scale) maps represent the results of afully automated procedure; following this first step,interactive editing is usually necessary to clean upremaining problem cases. Intergraph’s MGE MapGeneralizer product offers a palette of operatorsand algorithms embedded in an interactiveenvironment under full user control (Lee 1995).Both systems have recently been evaluated in asoftware test as part of the activities of theWorking Group on Generalisation of the OEEPE(Baella et al 1994; Rousseau et al 1995; Weibel andEhrliholzer 1995).

Commercial GIS and cartography systems canbe and are indeed used for the production ofgeneralised maps today, which certainly is animprovement over the situation a decade ago whenthis was largely impossible. However, thegeneralisation workflow in practice still involves agreat deal of interactive guidance and retouching(and essentially results in multiple representations ifgeneralisation output is committed to one GISdatabase), owing to limitations of availablegeneralisation capabilities. While generalisationfunctionality of current systems still needsconsiderable extension with respect to all of theelements of generalisation discussed above, perhapsthe most limiting factors to date are the ones thatform the foundations of a successful generalisationsystem: data representations and data models,generalisation algorithms, and structure and shaperecognition (Schlegel and Weibel 1995).

Despite these limitations, however, the presentsituation in the commercial sector gives rise tosubstantial hope for future improvement. Since thefirst release of Intergraph’s MGE Map Generalizerproduct in 1992 (Lee 1995), a growing number ofGIS vendors including, among others, ESRI andLaser-Scan have become aware of the relevance ofgeneralisation capabilities and have begun to extendthe range of tools for generalisation and toarticulate intentions to perform more long-termresearch and development (ESRI 1996; Hardy 1996;Woodsford 1995).

6 CONCLUSIONS

Generalisation is a highly complex process for whichno simple solutions exist. Yet, after a period ofrelative stagnation during the late 1970s and the1980s, generalisation has again attracted significantinterest in the GIS community and beyond. Thetopic is well represented at key GIS conferences andpursued by several international working groups. TheInternational Cartographic Association (ICA), theEuropean Organisation for ExperimentalPhotogrammetric Research (OEEPE), and theInternational Society of Photogrammetry andRemote Sensing (ISPRS) have all formedcommissions and working groups to coordinateinternational research efforts. Similar researchinitiatives are being pursued at the national level inmost of the larger industrialised countries.Additionally, the commercial sector is investing moreeffort in research and development in generalisation(see also Salgé, Chapter 50; Smith and Rhind,Chapter 47).

This situation has been caused by a confluence ofthree factors. First, there is an increasing demand forgeneralisation functionality by many types of GISusers, ranging from major national mapping agenciesto specialised application builders. Apart from the‘classical’ requirements of map production, theimportance of generalisation in digital cartographyand GIS is accentuated by continuing rapid growth ofthe number and volume of spatial databases and bythe need to produce data meeting specificrequirements and share them among different usergroups (see Rhind, Chapter 56). Second, as a


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consequence of the first factor these forces haveturned generalisation from a problem considered astoo hard to tackle into emergent solutions and marketopportunities, as technology suppliers (academicresearch and GIS vendors) react to these newdemands. The research community is finding arenewed interest in these issues, addressing them withnew conceptual approaches and more modernsoftware architectures. GIS vendors are respondingwith apparent commitments to extend and improvetheir systems’ generalisation capabilities. Third, thetechnological setting has matured; more powerfulenabling technologies have become available, reliable,and affordable. This last factor is of utmost importance as it has finally created a situation wherethe processing power, networking capabilities,software engineering technologies, and graphics andanalytical functions are available to approachrealistically the task of developing complexgeneralisation functionality (see Batty, Chapter 21;Coleman, Chapter 22). The next few years will showwhether the current high level of activity represents apersistent evolution or whether it merely marks apassing enthusiasm, to be tempered by the difficultyof the challenges facing the development ofgeneralisation technology. Given the fundamentalimportance of generalisation in the context of flexibleand distributed spatial data handling, however, weexpect that a lasting coalition of users, researchers,and vendors will form with a strong interest in andcommitment to developing workable solutions.

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