The Development of Phenomenological Generalization Within an Object-oriented Paradigm.

Author:Ormsby, Daniel
 
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Introduction

In the authors' opinion, there is a pressing need to change the conceptual approach to cartographic generalization. Although there is a growing interest in methods for detecting and resolving conflicts, much of the recent generalization literature has focused on very specific techniques. Some typical examples are: how best to generalize a line (Plazanet et al. 1995; Buttenfield 1991); how to most effectively design a data structure that allows features to be merged or conflicts detected (Bundy et al. 1995; Ruas and Plazanet 1996); how best to displace features from one another (Mackaness 1994); or how to simplify groups of buildings (Hangouet 1996). Whilst the development of such techniques is fundamental to producing automated solutions, what appears to be lacking is a broader philosophy that encompasses an approach in which cartographic generalization can be collectively and comprehensively achieved.

Our research attempts to illustrate how a philosophy that centers around the concept of phenomena could be implemented. Although this illustration shall be achieved through the design of a methodology for generalizing area features, the primary aims are to demonstrate the importance of a phenomenological approach which can be equally applied to any type of cartographic feature in combination with a mix of generalization techniques.

A Phenomenological Approach

The proposed phenomenological approach centers on one simple concept, namely, that there is never a single correct solution to the generalization of a feature, or group of features, but a number of feasible alternatives. For example, Bertin (1967) illustrates that a group of lakes may be generalized to the same target scale yet with considerably different results depending on whether the final map is for an atlas, road map, or air chart. The assertion is made in this paper that the feasible alternatives depend on the phenomena involved. In this context, phenomena are considered in two ways:

  1. Type of object. For example, lakes, islands, buildings, and forest patches are all different phenomena of area features. Each is further decomposable. For example schools, shops, and hospitals can all be regarded as different phenomena of building objects.

  2. Type of map or map task and associated scale. Tourist maps, road atlases, topographic maps, hydrographic and pilotage charts, represent the same features differently, and can thus be regarded as different cartographic phenomena.

Examples of how required solutions vary according to object type and map task are found in Mark (1991) and Richardson and Muller (1991) respectively.

The many-to-many relationship between the different objects and different map types give rise to a large number of permutations of alternative solutions. For example, given the four object classes (lakes, islands, buildings, and forest patches) and five map types (tourist maps, road atlases, topographic maps, hydrographic, and pilotage charts) given above there are potentially 20 different solutions required as output from a generic algorithm for area features, even if only a single scale change is considered. The fundamental challenge, therefore, is to design generic algorithms that are powerful and flexible enough to provide varying solutions, depending on the object and cartographic phenomena, and are able to apply those algorithms to a variety of phenomena types simultaneously. This paper attempts to illustrate that this can be achieved in a convenient manner by implementing functionality at the object level (e.g., objects simplify their own geometries), so that the algorithm that calls on the object to simplify itself remains broadly applicable to any type of object.

The Nature of Object Phenomena

The phenomena of objects are determined by geometry, semantic meaning, and inter-object relationships in both spatial and semantic contexts. For example in Figure 1, if only geometry is considered, the rectangular form implies some sort of anthropogenic feature that could be a building, tennis court, or car park. When semantic information is included, namely that it is a building, the object is given some degree of importance. Finally, when inter-object relationships are added, such as remoteness from a town which indicates a possible rural context, the user may surmise that the object is a farm or a cottage. The critical issue for successful generalization is to include all three notions, so that the characteristics that define the phenomena are communicated to the user even after the scale change.

Figure 1. Components defining the phenomena of an object.

Contextual vs. Phenomenological Approaches to Map Generalization

Automated generalization in its broadest sense is concerned with maintaining the meaningful communication of a real-world phenomenon during transitions from one scale or theme to another. The approach to this has so far been to apply a set of geometric operations (such as selection, amalgamation, typification, and displacement) to a set of lines, points, and areas. However, as has long been understood, different thematic results can be achieved by varying the choice, sequence, and degree of application of the operations (Ruas and Plazanet 1996). Experiments in automated generalization have highlighted the need to consider the context in which these operators are applied. For example, excessive application of line simplification (leading to changes in topology and self intersection) has highlighted the need for contextual generalization, whilst also identifying the need for better modeling of the behavior of operators (Edwardes and Mackaness 1998; Weibel 1996).

Even more important, however, is the observation that these geometric operations are driven by the desire to convey meaning. It is critically important, therefore, that geometric generalization is driven by the semantics of the phenomenon being mapped. Map semantics are conveyed through the geometry of the object itself, the representation of its attributes, and its thematic and spatial interrelationships with other objects. The phenomenological approach extends beyond the conventional views on contextual generalization in that it makes explicit the contribution made by these three components.

Example: Area Patch Generalization

The phenomenological approach has been used in this paper to consider a highly successful generalization algorithm from a new perspective. An algorithm for "area patch generalization"--a term coined by Bertin (1967) to refer to the generalization of area features which all bear the same semantic meaning but vary in size, shape, and distribution--was developed by Muller and Wang (1992). On the sole basis of geometric statistics / measures (area and compactness indices) and various user parameters, the algorithm "chooses" and applies an operation to each individual feature--either expansion, contraction, or elimination. Once completed, merging, displacement, or random reselection are applied to resolve conflicts and maintain global visual balance. The overall aim, as indicated in Figure 2, is to preserve the relative size, shapes, patterns, and density during a scale transition.

Figure 2. The objectives of area patch generalization--automating A to B (after Bertin 1967). When B is enlarged back to the original size (C), the generalization that has been applied is evident.

By reconsidering the algorithm from a phenomenological perspective, it is clear that geometry alone is not a sufficient criteria for determining the operation applied to a feature. Without a consideration of its semantic meaning, a small but highly important feature may be eliminated solely on account of size. Ignoring the inter-object relationships may result in the loss of meaningful structures (such as archipelagos) which are conveyed by collections of objects. Muller and Wang (1992) recognize such limitations, however the phenomenological approach makes explicit the need to consider the internal geometry, the semantics, and the inter-object relationships in the design of the algorithm.

Methodology

The application of a phenomenological approach to area patch generalization is expected to result in an algorithm that can vary solutions according to object type and map task. While it is the synergy of an object's geometry, semantics, and relationships with other objects that is fundamental in this approach, each of these phenomena is examined separately for reasons of methodological clarity.

Geometry

A key contribution that the Muller and Wang (1992) algorithm made to automated generalization was its ability to to apply such geometric operations as elimination, expansion, and contraction to individual objects. However, where the technique may be criticized is that the application of generic operations, such as buffering for the purposes of expansion, fails to take into account the intrinsic meaning that the characteristics of the phenomenon's geometry conveys to the map user. For example, if Muller and Wang's algorithm were applied to a selection of anthropogenic features, the buffering technique would not preserve the right-angled form typical of such objects, and a critical part of the phenomena's meaning would be lost in the generalization process (Figure 3).

Figure 3. A buffered anthropogenic feature.

Such limitations significantly reduce the generic use of the algorithm as they restrict its application solely to phenomena that are appropriate to buffering techniques--namely natural features such as lakes. Thus Muller and Wang's (1992)...

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