Abstract
Topological relations have played important roles in spatial query, analysis and reasoning. In a two-dimensional space (IR2), most existing topological models can distinguish the eight basic topological relations between two spatial regions. Due to the arbitrariness and complexity of topological relations between spatial regions, it is difficult for these models to describe the order property of transformations among the topological relations, which is important for detailed analysis of spatial relations. In order to overcome the insufficiency in existing models, a multi-level modeling approach is employed to describe all the necessary details of region–region relations based upon topological invariants. In this approach, a set of hierarchically topological invariants is defined based upon the boundary–boundary intersection set (BBIS) of two involved regions. These topological invariants are classified into three levels based upon spatial set concept proposed, which include content, dimension and separation number at the set level, the element type at the element level, and the sequence at the integrated level. Corresponding to these hierarchical invariants, multi-level formal models of topological relations between spatial regions are built. A practical example is provided to illustrate the use of the approach presented in this paper.
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This work was supported by the RGC of Hong Kong (Project PolyU 5228/06E) and the National Science Foundation of China under grant numbers 40501053 and 40571127.
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Deng, M., Cheng, T., Chen, X. et al. Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants. Geoinformatica 11, 239–267 (2007). https://doi.org/10.1007/s10707-006-0004-x
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DOI: https://doi.org/10.1007/s10707-006-0004-x