Topological information are the most important kind of qualitative spatial information. Current formalisms for the topological aspect of space focus on relations between regions or properties of regions. This work provides a qualitative model for representing the topological internal structure of complex regions, which could be of multiple pieces and or have holes and islands to any finite level. We propose a layered graph model for representing the internal structure of complex plane regions, where each node represents the closure of a connected component of the interior or the exterior of a complex region. The model provides a complete representation in the sense that the (global) nine-intersections between the interiors, the boundaries, and the exteriors of two complex regions can be determined by the (local) RCC8 topological relations between the associated simple regions. Moreover, this graph model has an inherent hierarchy which could be exploited for map generalization.
In this section, we give a detailed comparison of our work with related works. Section 6.1 compares related works on various kinds of complex regions. The tree model of @cite_13 is closely related to our link graph model. Section 6.2 then compares our model with the tree model. We show in Section 6.3 how our graph model can be used to produce representations of bounded regions at multiple levels of detail.
@cite_13
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This study aims to model an appropriate set of 2-dimensional spatial objects (i.e. areas) embedded in R2 with the usual metric and topology. The set of objects to be modelled is an extension of the set of 2-dimensional objects which can be represented within the vector-based data model. The model aims to capture explicitly some important topological properties of the spatial objects, e.g. connectedness and region inclusion. The construction discussed in this paper is capable of representing a large class of areal objects, including objects with holes which have islands (to any finite level). It has the virtue of being canonical, in the sense that any appropriate areal object has a unique representation in this model. The paper describes the model by specifying the areal objects under consideration and providing their representation. It also defines a set of operations and discusses algorithms for their implementation.