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Multi-representation databases with explicitly modeled horizontal, vertical, and update relations.

Article Excerpt
Introduction

The lack of fully automatic, real-time generalization functionality has stimulated research and development of multi-representation databases (MRDB). A wide range of applications for MRDB exists in conventional map production, as well as in web cartography (Jones et al. 1996; Devogele et al. 1996; Hampe et al. 2003). These have, however, been realized in only a few cases. The aim of this paper is to present the implementation of an MRDB in a cartographic map production system. Our research and development focuses thereby on explicitly modeled relationships (see also Neun et al. 2004; Neun and Steiniger 2005). The explicit modeling supports the generalization process in two ways: by aiding in the analysis of data of one resolution and thus supporting the process of generalization, and by maintaining incremental updates.

The research and development work corresponds to the current requirements of various European national mapping agencies. Their aim is to introduce flexibility and process consolidation by putting in place a GIS-based cartographic production line in conjunction with MRDB containing linked features at different resolutions. A typical map example is shown in Figure 1. The figure depicts a resolution change between three different resolutions. The modeling discussed here is intended to cover any range of resolution change.

The explicitly modeled relationships are divided into three different types: horizontal, vertical, and update relationships. Horizontal relationships describe the relations between features in one resolution (level of detail, LOD). Examples are partitions, neighborhood and topology, semantic, structure, and patterns (Duchene 2004; Steiniger and Weibel 2007). Vertical relationships connect features that represent the same real-world entities. These relations between features of different resolutions are created during a generalization process or by matching operations. The update relationships describe temporal changes of features that may be derived from an updating process or from matching of data sets with different time states. For each of these types of relationships we present existing approaches for their creation and analyze their dependencies.

The connections between the three types of relationships are explained briefly: Horizontal relations support the automated generalization process. The result of this process is stored in different resolutions, connected by a vertical relation. This relation is required for automated incremental updating triggered by updates; it is modeled through an update relation between different temporal states. The update relation enables spatio-temporal analyses as well. The choice of the terms "horizontal" and "vertical" refers to a stack of data layers of different resolutions (Neun and Steiniger 2005; Steiniger and Weibel 2007). Horizontal relations affect only a single layer (or resolution), while the vertical relation extends across the stack of (resolution) layers. The terms are not meant in a geometrical (three-dimensional) sense.

[FIGURE 1 OMITTED]

The main result of our work is the integration of the three types of relationships in one common model within a MRDB. The similarities and differences between horizontal, vertical, and update relations are examined. An approach for explicit representation of these relationships is proposed. The result is an enriched MRDB. The advantages of this enriched MRDB are enhanced support of the generalization process, improved possibilities of data analysis through resolution and time, and consistent management of geographic and cartographic data. The relationships can also be used within the context of generalization services.

Theory and Definitions of Horizontal, Vertical, and Update Relations

Relations are a concept widely used in a variety of fields. They are all based on the mathematical concept of relation where a relation is defined as a set of tuples with a fixed length, with each tuple being built from given sets. Formally a relation R is a subset of the Cartesian product of a couple of sets [A.sub.1], ... [A.sub.n], thus R [subset not equal to] [A.sub.1] x ... x [A.sub.n]. The number n is called the order or arity of the relation. In many cases only relations of cardinality 2 are considered, expressed by "a is related to b". In a broader sense, relations of any order n with n [greater than or equal to] 1 can be considered and the relation is called n-ary relation. The usual case of n = 2 is called a binary relation, whereas the cases n = 1 and n = 3 are called unary and ternary relations, respectively. Unary relations are a special case, in the sense that a relation is simply a subset of the given set [A.sub.1].

The following sections introduce the types of relations that are important for the analysis, generalization, handling, and updating of geodata, namely horizontal relations, vertical relations, and update relations. Subsequently, combinations of these types will be examined and the possibilities of describing relations of relations will be discussed.

Horizontal Relations

Horizontal relations characterize map features of one specific resolution or level of detail (LOD) on a defined time stamp. Examples are partonomic relations, neighborhood relations, structural relations or patterns, semantic relations, and hierarchical relations. The order of the horizontal relations can be between 1 ... n, depending on the number of features which are characterized through the relation. A special case is a horizontal relation of order one. An example of this case is the modeling of partitions through horizontal relations, such that a single feature creates one partition. Another unary horizontal relation of a semantic nature, modeled practically in every GIS, is the assignment of a feature to a specific class, for example Mainstreet to the class "road."

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Very common is the modeling of binary relations applied to groups of features. For example a building alignment is modeled as a meso object (Ruas 2000; Ruas and Holzapfel 2003; Li et al. 2004). The relations between the individual building features and the alignment of a meso object are binary part-of-relations. Our definitions deviate from this explicit introduction of groups, or meso objects, and reduce the...

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