1 Generalisation of Spatial Databases. William Mackaness

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1 1 Generalisation of Spatial Databases William Mackaness 1.1 The Importance of Scale in Geographical Problem Solving All geographical processes are imbued with scale (Taylor 2004 p214), thus issues of scale are an essential consideration in geographical problem solving. The scale of observation governs what phenomena can be viewed, what patterns are discernible, and what processes can be inferred. We are interested in viewing the precise detail of those phenomena, as well as the broad linkages across regional and global space. Choosing scales of analysis, comparing output at different scales, describing constructions of scale (Leitner 2004) are all common practices in the geosciences. We do this because we wish to know the operational scales of geographic phenomena, how relationships between variables change as the scale of measurement increases or decreases, and we want to know the degree to which information on spatial relationships at one scale can be used to make inferences about relationships at other scales (Sheppard and McMaster 2004). What is always apparent when viewing geographic phenomena is the interdependent nature of geographical processes. Any observation embodies a set of physical and social processes, whose drivers operate at a variety of interlocked and nested geographical scales (Swyngedouw 2004, p129). Both the scale of observation and of representation reflect a process of abstraction, an instantaneous momentary slice through a complex set of spatio-temporal, interdependent processes. Traditionally it has been the cartographer s responsibility to select a scale, to symbolise the phenomena, and to give meaning through the addition of appropriate contextual information. In paper based mapping, various considerations acted to constrain the choice of solution (the map literacy of the intended audience, map styles, the medium and choice of cartographic tools). Historically the paper map reflected the state of geographical knowledge, and was the basis of geographical inquiry. Indeed it was argued that if the problem cannot be studied fundamentally by maps - usually by a comparison of several maps - then it is questionable whether or not it is within the field of geography. (Hartshorne 1939 p249). Information technology has not devalued the power of the map, but it has driven a series of paradigm shifts in how we store, represent and interact with geographical information. Early work in automated mapping focused on supporting the activities of the human cartographer who remained central to the map design process. Current research is focused on ideas of autonomous design systems capable of selecting optimum solutions among a variety of candidate solutions delivered over the web, in a variety of thematic forms, in anticipation of users who have little or no cartographic skill. Historically the paper map reflected a state of knowledge. Now it is the database that is the knowledge store, with the map as the metaphorical window by which geographic information is dynamically explored. In these interactive environments, the art and science of cartography (Krygier 1995) must be extended to support the integration of distributed data collected at varying levels of detail, whilst conforming to issues of data quality and interoperability. 1.2 Generalisation At the fine scale, when viewing phenomenon at high levels of detail (LoD), we can determine many of the attributes that define individual features (such as their shape, size orientation), whilst at the broad scale, we see a more - 1 -

2 characteristic view - more particularly the regional context in which these phenomenon are situated (for example their gestaltic and topolgical qualities, and various associations among other phenomenon). For example Journey planning requires a broad scale view in order to gauge timeframes and alternate travel strategies, whilst a fine scale detailed map is required to reach the final point of destination. It is not the case that one map contains less or more information, but that they contain different, albeit inter related information. Thus maps are required at a range of scales, in a variety of thematic forms, for delivery across a range of media. The term map generalisation is often used to describe the process by which more general forms of a map can be derived from a detailed form. In the context of today s technology, a vision is of a single detailed database, constantly updated in order to reflect the most current version of a region of the world. For any given National Mapping Agency (such as the OS of Great Britain or the IGN of France) that region is defined by their respective national boundaries. In such a context, the process of map generalisation entails selecting objects from that detailed database, and representing them in various simplified forms appropriate to the level of detail required, and according to some purpose (or theme). By way of example, Figure 1 shows a series of maps at different scales, of Lanvollon in France. The goal remains the creation of automated map generalisation techniques that would enable the derivation of such maps from a single detailed database. This vision is driven by a variety of motivations: data redundancy (maintaining a single detailed database rather than a set of separate scale specific databases - Oosterom, 1995); storage efficiency (recording the fine detail of a feature in as few points as possible); exploratory data analysis (MacEachren and Kraak 1997) (being able to dynamically zoom in and explore the data, and to support hypermapping); integration (combining data from disparate databases of varying levels of detail); and paper map production (for traditional series mapping). Figure 1: 1: : : (Copyright of the IGN). Given the strong association of map generalisation with traditional cartography it is worth stressing its broader relevance to spatial analysis and ideas inherent in visualisation methodologies. Though discussion will focus on the cartographic, we are in essence dealing with the generalisation of spatial databases (Muller 1991; Smaalen 2003). In this context we can view the fine scale, detailed database as the first abstraction of space often called the Primary Model or Digital Landscape Model (DLM) (Grunreich 1985). As a prerequisite the DLM requires the definition of a schema that will support the explicit storage, analysis and characterisation of all the geographic phenomenon we wish to record. A series of secondary models can be derived from this primary model via the process of model generalisation. These abstractions are free from cartographic representational information, and could be used to support spatial analysis at various levels of detail. Both primary and secondary models can be used as a basis for - 2 -

3 creating cartographic products (Digital Cartographic Models) via the process of cartographic generalisation. Figure 2 summarises the relationships between these models and the generalisation processes. Primary Model Digital Landscape Model (DLM) model generalisation Secondary Models DLM cartographic generalisation Cartographic Model Digital Cartographic Model (DCMs) Figure 2: Generalisation as a sequence of modelling operations (after Grunreich 1985). Model generalisation may involve reduction of data volume, for example via the selection, classification or grouping of phenomenon, or the simplification of phenomenon such as network structures. This may be required as a prerequisite to spatial analysis, the integration of different datasets, or for computational efficiency. It is certainly an integral step in the derivation of multi scaled cartographic products. Though it has important ramifications for cartographic generalisation, model generalisation does not itself seek to resolve issues of graphic depiction such as clarity or emphasis in depiction. Cartographic generalisation describes the process by which phenomena are rendered, dealing with the challenges of appropriate symbolisation, and the placement of text within the limited space of the medium (whether on paper or the small screen of a mobile device). The symbology used to represent a geographic feature must be of a size discernible to the naked eye. At reduced scale, less space is available on the map to place the symbols. At coarser scales, the symbols become increasingly larger than the feature they represent. It therefore becomes necessary to omit symbology associated with certain features, to group features, to characterise them in a simpler way, or to choose alternate forms of symbology in response to this competition for space (Mark 1990). Figure 3 nicely illustrates this idea, showing The Tower of London and its surroundings at 1:10, 000, 1:25,000, and 1:50, 000 scale. At the finest level of detail we can discern individual walls, courtyards, pavements, trees and the buildings are individually named. We can make many inferences drawing on our understanding and experiences of geographic space, such as the function of buildings, and the components of the various fortifications. At a coarser scale we see - 3 -

4 less detail, in exchange for more of the context. For example we discern its strategic importance along the bank of the river Thames, and text is used in a different way to label various features. At the coarse scale of 1:50,000 we see how competition for space has presented further challenges for the cartographer. The thick red symbology used to represent the roads has encroached upon surrounding features, which have had to be slightly displaced or made smaller in order to avoid overlapping and causing confusion among the represented features. We can also discern more of a thematic edge to this representation, with the Tower highlighted as a tourist attraction. Overall then, we can discern the processes of model and cartographic generalisation at work in the creation of such map designs. Figure 3: Model and Cartographic generalisation acting in unison to reveal different qualities about The Tower of London (Copyright OS). 1.3 Conceptual Models of Generalisation Initial research in automated cartography began in the 1960s (Coppock and Rhind 1991) and sought to replace the manual scribing tools and techniques used by the human cartographer, with their automated equivalent. Paper based maps were digitised to create inherently cartographic, vector based databases in essence the map became a set of points, lines, areas and text to which feature codes were attached in order to control the symbolisation process. But research soon highlighted the limits of this approach, and revealed the art and science of cartographer as a design task involving complex decision making. There was a clear need for conceptual models (such as those presented by Brassel and Weibel 1988 and McMaster and Shea 1992) as a basis for understanding the process of generalisation, and developing automated solutions. McMaster and Shea (1992) presented a comprehensive model that decomposed the generalisation process into three stages: definition of philosophical objectives (why generalise), cartometric evaluation (when to generalise) and a set of spatial and attribute transformations (how to generalise). A -4-

5 complimentary view that reflects the potential of more complete solutions to automated generalisation is one in which a variety of candidate solutions are considered (synthesis), based on cartometric and topological analysis (analysis). This is followed by an evaluation phase that selects the most appropriate candidate based on both fine scale and holistic evaluation techniques (Figure 4). Analysis Measuring many properties (metric, topological and non spatial) both within and among classes of features. Synthesis Creation of a variety of solutions using a combination of model and cartographic generalisation techniques. Candidate solutions in response to analysis phase, constrained by rules governing design. Evaluation Selection of optimal solution according to intended map use and task, reflecting analysis at both the fine and broad scale. Figure 4: Generalisation in the context of automated solutions Multi Scale Databases Aligned closely to the topic of map generalisation is the idea of multiple representation, in which various cartographic representations of a single object are stored for viewing or analysis at various levels of abstraction (Kidner and Jones 1994; Devogele et al. 1997; Goodchild and Yang 1992; Kilpelainen and Sajakoski 1995). A specific advantage being that their forms can be pre-cast and immediately presented to the user (thus avoiding the time cost associated with creating solutions on the fly ). Though the DLM (Figure 2) remains unchanged, a series of multiple representations can be derived at any time, only needing to be recast when the central database is updated to reflect changes in the real world. There are complicating issues in the management of the database, in particular ensuring the seamless joining together of multiple representation after an update cycle. Ideas of multiple representation mirror the idea of a single detailed database, from which other databases are derived using map generalisation techniques. 1.4 Generalisation Methods and Algorithms For any given conceptual framework, it is necessary to precisely define the methods by which we can analyse, synthesise and evaluate solutions. Early research focused on reverse engineering the design process, observing the human cartographer at work, and via a process of stepwise refinement, identify the discrete methods used by the cartographer. In some instances the cartographer would omit selected features, or whole classes of features. Some features were merged and enlarged and if space allowed, and where symbology overlapped, features were marginally displaced in order to distinguish more easily between features. These and other methods can be divided into two types of transformation: spatial and attribute transformation. The ten spatial transformation methods are: amalgamate, aggregate, collapse, displace, eliminate, enhance, merge, refine, simplify, and smooth. The two transformation methods are: classify and symbolise (Weibel and Dutton 1999). Smaalen (2003) argues that in essence map features fall into one of three metaclasses (Molenaar 1998). Classes that contain network like objects, such as railways, rivers and roads; classes of relatively small, often rigid, island objects typically buildings, and a third class of mostly natural area objects often forming exhaustive - 5 -

6 tessellations of space, for example land parcels, lakes, forested regions, and farms. Each class has different behaviours, and can be characterised in different ways. One can therefore envisage a matrix of these metaclasses against generalisation methods. Each cell in the matrix containing a number of algorithms for modelling transformations of that particular metaclass for varying levels of detail, and for a range of themes. A huge amount of research has been devoted to populating such a matrix developing methods that can be applied to various classes of objects. By way of illustration, Dutton (1999) and other have worked on methods for generalising linear features (Buttenfield 1985; Plazanet et al. 1998); finite element analysis and other techniques have been used to model displacement among features (Hojholt 2000; Burghardt and Meier 1997). Considerable effort has been devoted to methods for generalising buildings (Jiang and Claramunt 2004; Regnauld 2001), whilst other research has focused on how space exhaustive tessellations of space can be generalised - for example as is found in geological mapping (Bader and Weibel 1997; Downs and Mackaness 2002). Others have researched the problem of attenuating network structures (Mackaness and Mackechnie 1999; Richardson and Thomson 1996) whilst others have proposed solutions to the problem of text placement (Christensen et al 1995). These methods have been framed in a variety of strategic contexts. For example Molenaar (1998) stratifies these methods under four headings that reflect a need to model both individual and structural characteristics of the map. Importantly he discusses the idea of functional generalisation a generalisation technique used to group close proximity, non-similar objects in order to create meaningful composites (Smaalen 2003). Figure 1 presents a nice example of this whereby the various objects comprising the town of Lanvollon represented at 1: scale, have been grouped and replaced by a single point symbol at the 1: scale. Functional generalisation is particularly appropriate in the case of significant scale change Analysis A strong recurrent theme in all the research into generalisation algorithms has been the need for techniques that make explicit the metric and topological qualities that exist within and between classes of features. Effective characterisation of geographic space requires us to make explicit the trends and patterns among and between phenomenon, to examine densities and neighbourhoods, and to model connectivity and network properties, as well as the tessellation of space. Thus the field draws heavily on spatial analysis techniques such as graph theory (Hartsfield and Ringel 1990), Voronoi techniques (Peng et al 1995; Christophe and Ruas 2002) and skeletonisation techniques (Costa 2000). The identification of pattern draws on regression techniques, and automated feature recognition techniques (Priestnall et al 2003). These supporting structures (Jones and Ware 1998; Jones et al. 95) are used to enrich the database and enable the modelling of topological transitions (Molenaar 1998) Synthesis and Evaluation Research has also tried to model the process by which a combination of methods is used to synthesise various solutions. For example a group of Islands may be merged, and enlarged in order to remain visible to the naked eye at smaller scale. The process of enlargement may require marginal displacement to distinguish between the Islands. Different results emerge according to the sequence in which the methods are applied, and the degree to which they are applied (Mackaness 1996). The evaluation of candidate solutions must be graded against a set of criteria, - 6 -

7 themselves defined by the map task. For example, a map intended for tourists may accommodate greater generalisation of the characteristic form than a map intended for sea navigation. In Figure 5 the two generalised forms (hand drawn) are shown at the same scale as the original (in order to compare), prior to being reduced in size to 30% of the original. Figure 5: The choice, sequence and degree of application of various methods enable synthesis of different solutions, but which one is correct? Even in the very simple example of Figure 5, with a restricted set of considerations, it is easy to imagine a very large set of permutations. But it is possible to define evaluation criteria. For example shape and area metrics can be used to measure alignments (Christophe and Ruas 2002) or the degree of distortion from the original (Whang and Muller 1998; Cheung and Shi 2004). Topological modelling in surfaces and networks can be used to model neighbourhood changes among a group of objects. Density and distribution measures can be used to determine trends in the frequency of occurrence or the degree of isolation of a feature. Distance metrics can be used to assess the perceptibility of an object (is it too small to be represented at the intended scale), and the degree of crowding among objects. Evaluation also includes assessment of non-spatial attributes. For example is it a rare geological unit relative to the surrounding region (Downs and Mackaness 2002), or a special point of interest in the landscape? Techniques have also been developed to measure the content of map, and to evaluate levels of content as a function of change in scale (Topfer and Pillewizer 1966; Dutton 1999). Many of the cartometric techniques used to analyse the properties of a map as part of the synthesis of candidate solutions can also be used in this process of evaluation. In effect, each and every one of these techniques makes explicit some property within or between classes of objects. But a map in its generalised form reflects a compromise among a competing set of characteristics. There is very little in the map that remains invariant over changes in scale. Indeed generalisation is all about changing the characteristics of a map in order to reveal different patterns and relationships among the phenomenon being mapped. Often the preservation of one characteristic can only be achieved by compromising another. Thus among a group of - 7 -

8 buildings do we give emphasis to the odd one out because it is significantly larger than the rest, or preserve the characteristic orientation shared among the group of buildings and the adjoining road? We know that the topology among a set of objects changes if we remove, aggregate or functionally combine objects. But how do we ensure that the new topology is a valid one? And where we wish to combine data from different sources and scales, how do we validate the quality of any given solution? There is no shortage of techniques for measuring the properties of an object, but the challenge of defining tolerances and collectively prioritising those characteristics (linked to intended use) remains a significant impediment to development of systems that are more autonomous in their operation. 1.5 A Rule Based Approach More challenging than the development of generalisation methods, has been the formalisation of the procedural knowledge required to trigger the use of such methods. At any instant in the design phase, there may exist a range of alternate candidate solutions, whose creation and choice is based on rules of thumb (heuristics), to a goal state that is somewhat hazy and hard to define (Starr and Zeleny 1977). Various attempts have therefore been made to use a rule based approach to automated map generalisation (Richardson and Muller 1991; Heisser et al 1995; Keller 1995), in which sequences of conditions and actions are matched in order to control the overall process. For example a small remote building in a rural context has a significance much greater than its counterpart in a cityscape and is therefore treated differently. A solution might be to enlarge the symbology in order that the building remains discernible to the naked eye, according to those conditions: IF a building.context = rural AND building.neighbourhood = isolated AND building.size = small THEN building.generalisation = enlarge. We can formalise both the <condition> and < action> part of such rules from observation of how features are symbolised on paper maps at various scales. We observe how particular solutions operate over a band of scales (akin to the idea of an operational scale - Phillips 1997) and that beyond a certain threshold, a change in the level of generalisation is invoked. Figure 6a illustrates the various representational forms of a cathedral and Figure 6b shows the scale bands over which those representations might operate. These threshold points are determined by: 1) a feature s geometry and size, 2) its non spatial attributes, 3) its distribution and association with other features, 4) its immediate proximity to other features, and 5) the resolution of the device on which the information is being displayed or printed (Glover and Mackaness 1999). (a) a b c d (b) a b c d 1:1250 1:10,000 1:25,000 1:50,

9 Figure 6: a) Transformations with decreasing map scale; b) Corresponding scale bands for a topographic map (Glover and Mackaness 1999). Its treatment also depends on the feature s importance in relation to the intended theme. For example castles and visitor attractions in a tourist map will be given greater emphasis from those buildings deemed more general. Figure 7 is based on observations made from paper maps over a range of scales, and shows how key (or special buildings) and general buildings are typically represented. Scale 1:1250 1:10,000 1:25,000 1:50,000 1:250,000 (a) (b) (c) (d) key building CASTLE Castle general buildings Figure 7. Examples drawn from paper maps of building generalisation at various scales. Again from observation, we can identify the generalisation methods that can be applied at the fine scale, to derive these various solutions - that their forms are simplified, or grouped, or collapsed and replaced with an iconic form. For example derivation of the castle representational form at 1: scale can be formed by placing a minimum bounding rectangle (MBR) around the group of castle buildings (so deriving its convex hull), and substituting this form for the group of individual buildings. One can envisage a similar process applied to each metaclass, and for each scale band transition point (similar to the one illustrated in Figure 6). In this manner we can define a decision tree that incorporates the various generalisation methods used, according to: the building type, its association with adjacent features, and the operational scales of the various representational forms. Figure 8 is the decision tree for key buildings intended for use in urban environments

10 Scale band 1 Get source dataset geometry Scale band 2 Building area < 150? YES NO ELIMINATE SIMPLIFY ENLARGE Scale band 3 radius search - single building? YES NO CONVEX HULL get building centre PROPORTIONAL MBR get icon symbol SIMPLIFY overlaps road? NO YES get convex hull centre REGROUP Get centre of each subgroup get icon symbol convex hulls of subgroups get icon symbol H H Scale band 4 radius search - single building? YES get building centre get icon symbol NO get convex hull or convex hulls of subgroups get convex hull centre(s) get icon symbol Figure 8. Decision tree for key buildings. These and other decision trees were collectively implemented in a GIS system that was able to derive different thematic maps from a single detailed source (Glover and Mackaness 1999). The results (Figure 9) were compared with their manual equivalent, as basis for identifying future work

11 SOURCE TOPOGRAPHIC TOURIST Mu Mu Cas Mu Uni Sch Figure 9. Different products according to theme and scale derived from the same source. Such a system works quite well for relatively small changes in scale. The system is limited by its inability to generate alternate solutions to a design problem, and to automatically evaluate the correctness of the final solution. The work also highlighted the need for cartometric tools capable of analysing both local constraints (imposed by surrounding objects), and global constraints (ensuring consistency across the region including preservation of trends). What was required was a system that would enable consideration of alternate designs that took into account a shared view of of these and other design constraints. One such approach that has shown great promise in this regard has been in the use of multi agent systems. Multi Agent Systems The idea of agents came from the observation that complex processes can be modelled as a set of simple but interconnected set of task. For example the complex task of sustaining an ant colony is achieved by assigning ants (agents) to specific, defined tasks that collectively ensure the survival of the colony. Thus quite complex emergent behaviour can arise from a set of connected but simple agent tasks (Weiss 1999). Thus one definition of an agent is 'a self contained program capable of controlling its own decision making and acting, based on its perception of its environment, in pursuit of one or more objectives.' (Luck 1997, 309). Where more than one agent exists, we can

12 define what are called multi-agent systems (MAS): Multi-agent systems are ones in which several computational entities, called agents, interact with one another (Huhns and Singh 1998). In the context of map generalisation, it has been possible to model various characteristics of features and to implement an agent based approach whereby agents are assigned to manage the generalisation process across a geographic region (with a local perspective on the problem), and to communicate with other agents at a more regional scale (a global perspective) in order to ensure consistency in solution, and to ensure preservation of general trends across the map space (Duchêne 2003). This was the methodology utilised in the AGENT project, a European Union funded project, comprising a consortium of Universities, IGN (France s NMA) and commercial enterprise (Barrault et al. 2001; Lamy et al 1999). The system built on previous work undertaken among the consortium members (Ruas 1999), and was capable of analysing various properties within and between classes of objects, of synthesising alternate candidate solutions and evaluating the optimum choice against a set of design constraints. Where a solution was not forthcoming, a more radical or broadscale solution was proposed and control passed from the local perspective to a more global one. Thus there existed a hierarchical structure of mico, meso and macro agents, which, in effect, modelled both a fine scale view of design, as well as the more general view of the problem. The project commenced in 1998, and its commercial form is currently manifest in the CLARITY system from Laser Scan ( and continues to form the basis of on going research among a consortium of national mapping agencies across Europe under the MAGNET programme. Given its adoption by a number of European NMAs it is arguably the best solution to date to the challenges of autonomous map generalisation, though a number of challenges remain. The first is in the development of an interface that enables tuning of solutions that arise from complex emergent behaviour and interactions. The second is in defining the type of information that is passed among the hierarchies of agents, and how this information is utilised in the various stages of decision making. Conclusion Generalisation holds an important position in the development of a theoretical framework for handling geographic information as it deals with the structure and transformation of complex spatial notions at different levels of abstraction (Smaalen 2003, p1). As a modelling process, map generalisation is about characterising space in a way that precipitates out the broader contextual relationships that exist among geographic phenomenon. It is about making sense of things (Krippendorf 1995) and is intrinsic to geographic ways of knowing. In essence, a database is a system of relationships the process of generalisation is about abstracting and representing those patterns of relationships inherent among phenomenon viewed at different levels of detail (similar to the goals of scientific visualisation). The enduring vision is of a single detailed database from which such multiple views can be automatically derived according to a broad range of tasks. Over the years a variety of solutions have emerged in response to both a growing understanding of the complexities of automated map design, and the changing context of use arising from developments in information technology. Attempts at automation have highlighted the complexity of this task. It is certainly the case that the design of a map (irrespective of medium) is a hugely challenging task, though the paradigm shift afforded by data modelling

13 techniques has called into question the appropriateness of trying to mimic the human cartographer as a basis to automation. Developments in the field of generalisation continue to advance three key areas: 1) development of algorithms for model generalisation with the focus on spatial data handling and analysis; 2) methods for creating and evaluating candidate solutions for graphical visualisation and multiple representation; and 3) development of human computer interaction models that enable integration of these methodologies in both the presentation and exploration of geographic information. Research continues to reveal the subtleties of the art and science of cartography. For it to remain relevant however, it must keep abreast of the changing environments of map use and analysis (including interoperability requirements), and the broader developments in visualisation methodologies. References Bader, M., and Weibel, R., 1997, Detecting and resolving size and proximity conflicts in the generalization of polygon maps, in Ottorson, L., editor, Proceedings of the 18th ICA/ACI International Cartographic Conference: Stockholm, Sweden, ICC, p Barrault, M., Regnauld, N., Duchene, C., Haire, K., Baeijs, C., Demazeau, Y., Hardy, P., Mackaness, W., Ruas, A., and Weibel, R., 2001, Integrating multi agent, object oriented and algorithmic techniques for improved autmoated map generalisation, Proceedings of the 20th International Cartographic Conference: Beijing, China, p Burghardt, D., and Meier, S., 1997, Cartographic Displacement Using the Snakes Concept, in Foerstner, W., and Pluemer, L., editors, Semantic Modelling for the Acquistion of Topographic Information from Images and Maps, Birkhaeuser Verlag, p Brassel, K. E., and Weibel, R., 1988, A review and conceptual framework of automated map generalization: International Journal of Geographical Information Systems, v. 2, p Buttenfield, B., 1985, Treatment of the cartographic line: Cartographica, v. 22, p Cheung, C. K., and Shi, W., 2004, Estimation of the Positional Uncertainty in Line Simplification in GIS: The Cartographic Journal, v. 41, p Christensen, J., Marks, J., and Shieber, S., 1995, An Empirical Study of Algorithms for Point Feature Label Placement: ACM Transactions on Graphics, v. 14, p Christophe, S., and Ruas, A., 2002, Detecting Building Alignments for Generalisation Purposes, Advances in Spatial Data Handling, Springer, p Coppock, J. T., and Rhind, D. W., 1991, The history of GIS, in Maguire, M. F. G. a. D. W. R. D. J., editor, Geographical Information Systems: principles and applications: Essex, Longman Scientific & Technical, p Costa, L. d. F., 2000, Robust Skeletonization through Exact Euclidean Distance Transform and its Application to Neuromorphometry: Journal of real time imaging, v. 6, p

14 Devogele, T., Trevisan, J., and Ranal, L., 1996, Building a Multi Scale Database with Scale Transition Relationships, in M-J Kraak, Molenaar, M., and Fendel, E. M., editors, Advances in GIS Research II, Proceedings of the 7th International Symposium on Spatial Data Handling: Delft, London, Taylor and Francis, p Downs, T. C., and Mackaness, W. A., 2002, Automating the Generalisation of Geological Maps: The Need for an Integrated Approach: The Cartographic Journal, v. 39(2) p Duchêne, C., 2003, Automated Map Generalisation Using Communicating Agents, Proceedings of the 21st International Cartographic Conference: Durban, South Africa, p Dutton, G., 1999, Scale, Sinuosity and Point Selection in Digital Line Generalisation: Cartography and Geographic Information Systems, v. 26, p Glover, L., and Mackaness, W. A., 1999, Dynamic generalisation from single detailed database to support web based interaction, in Keller, C. P., editor, 19th International Cartographic Conference: Ottawa, ICA, p Goodchild, M. F., and Yang, S., 1992, A Hierarchical Data Structure for Global Geographic Information Systems: Computer Vision, Graphics, and Image Processing, v. 54, p Grünreich, D., 1985, Computer assisted generalisation: Papers CERCO-Cartography Course. Frankfurt am Main, Institut für Angewandte Geodasie. Hartshorne, R., 1939, The Nature of Geography: A Critical Survey of current thought in the light of the past: Lancaster, PA, Association of American Geographers. Hartsfield, N., and Ringel, G., 1990, Pearls in Graph Theory - A comprehensive Introduction: Boston, Academic Press Inc. Heisser, M., Vickus, G. And Schoppmeyer, J Rule-orientated definition of small area selection and combination steps of the generalization procedure, in Muller, J-C., Lagrange, J-P., Weibel, R. GIS and Generalization: Methodology and Practice. Taylor & Francis, London, pp Hojholt, P., 2000, Solving space conflicts in Map Generalisation: Using a Finite Element Method: Cartography and Geographic Information Science, v. 27, p Huhns, M. N., and Singh, M. P., 1998, Readings in Agents: San Francsico, Morgan Kaufmann. Jiang, B., and Claramunt, C., 2004, A structural approach to the model generalisation of an urban street network: GeoInformatica, v. 8, p Jones, C. B., and Ware, J. M., 1998, Proximity Relations with triangulated spatial models: The Computer Journal, v. 41, p Keller, S. F., 1995, Potentials and limitations of artificial intelligence techniques applied to generalization, in J.C. Muller, Lagrange, J. P., and Weibel, R., editors, GIS and Generalization: Methodology and Practice: Bristol, Taylor & Francis, p Kidner, D. B., and Jones, C. B., 1994, A deductive object oriented GIS for handling Multiple Representation, in Waugh, T. C., and Healey, R. G., editors, Advances in GIS Research (Proceedings Sixth International Symposium on Spatial Data Handling): Edinburgh, p

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16 Phillips, J. D., 1997, Humans as geological agents and the question of scale: American Journal of Science, v. 297, p Plazanet, C., Bigolin, N. M., and Ruas, A., 1998, Experiments with Learning Techniques for Spatial Model Enrichment and Line Generalization: GeoInformatica, v. 2 (4), p Priestnall, G., Hatcher, M. J., Morton, R. D., Wallace, S. J., and Ley, R. G., 2003, A Framework for automated feature extraction and classification of linear networks: Photogrammetric Engineering and Remote Sensing. Regnauld, N., 1996, Recognition of Building Cluster for Generalization: Proceedings of the 7th International Symposium on Spatial Data Handling, p Regnauld, N., (2001), Contextual Building Typification in Automated Map Generalisation: Algorithmica. v30 Richardson, D.E. and Muller, J-C Rule selection for small-scale map generalization, in Buttenfield, B.P. and McMaster, R.B., eds. Map generalization: making rules for knowledge representation, Longman, Essex, pp. Richardson, D., and Thomson, R. C., 1996, Integrating Thematic, Geometric and Topological Information in the Generalisation of Road Networks: Cartographica, v. 33 (1), p Ruas, A., 1995, Multiple Paradigms for Automating Map Generalization: Geometry, Topology, Hierarchical Partitioning and Local Triangulation: Proceedings of Auto Carto 12, p Ruas, A., and Mackaness, W. A., 1997, Strategies for Urban Map Generalization: Proceedings of the 18th ICA/ACI International Cartographic Conference, p Ruas, A., 1999, Modèle de géneralisation de données géographiques à base de constraintes et d'autonomie, Thèse de doctorat de L'université de Marne La Vallée: Paris, Marne La Vallée. Sheppard, E., and McMaster, R. B., 2004, Scale and Geographic Inquiry: Nature Society and Method, Blackwell Publishing. Smaalen, J. W. N., van 1996, A Hierarchic Rule Model for Geographic Information Abstraction, in M-J Kraak, M. M. a. E. M. F., editor, Proceedings of the 7th International Symposium on Spatial Data Handling: Delft, p Starr, M. K. and M. Zeleny MCDM - State and Future of the Arts. InMultiple Criteria Decision Making, M. K. Starr and M. Zeleny, (ed) New York: North-Holland, pp Swyngedouw, 2004, Scaled Geographies: Nature, Place, and the Politics of Scale, in Sheppard, E., and McMaster, R. B., editors, Scale and Geographic Inquiry: Nature Society and Method, Blackwell Publishing, p Taylor, P. J., 2004, Is there a Europe of cities? World cities and the limitations of Geographical Scale Analyses., in Sheppard, E., and McMaster, B., editors, Scale and Geographic Inquiry: Nature, Society, and Method, Blackwell Publishing, p Topfer, F., and Pillewizer, W., 1966, The principles of selection: Cartographic Journal, v. 3, p Whang, Z., and Muller, J. C., 1998, Line Generalisation Based on Analysis of Shape Characteristics: Cartography and Geographic Information Systems, v. 25, p Weiss, G., 1999, Multiagent systems: A modern approach to distributed artificial intelligence, MIT Press

17 Weibel, R., and Dutton, G., 1999, Generalising Spatial Data and Dealing with Multiple Representations, in Longley, P., Goodchild, M. F., Maguire, D. J., and Rhind, D. W., editors, Geographical Information Systems: New York, John Wiley, p