Hierarchical topological relations model of fuzzy raster regions

The modeling of topological relations between spatial regions is a primary topic in spatial reasoning, geographic information systems (GIS) and spatial databases. In many geographical applications spatial regions do not always have homogeneous interiors and sharply defined boundaries, but frequently their interiors and boundaries are fuzzy. Recently, representing fuzzy spatial regions and modeling the topological relations between them plays an increasingly important theory and application role. Based on the characteristics of fuzzy regions in raster data model and the requirement of topological relations analysis in applications, a hierarchical topological relations model is proposed. The model can determine the topological relation between fuzzy raster regions on multiple levels with the values of three predicate. When predicates are evaluated within two values, it can deal with crisp raster regions as a specific case and there are 5 possible cases of topological relations. When predicates are evaluated within three values, there are 27 possible cases. There are 51 possible cases when predicates are evaluated within six values. In practical applications, the model can analyze topological relations of fuzzy raster regions according to the existing facts and the requirement. The model is wieldy in practical applications and achieves satisfactory results.