Efficiently computing and deriving topological relation matrices between complex regions with broad boundaries

The extended 9-intersection matrix is used to formalize topological relations between uncertain regions while it is designed to satisfy the requirements at a concept level, and to deal with the complex regions with broad boundaries (CBBRs) as a whole without considering their hierarchical structures. In contrast to simple regions with broad boundaries, CBBRs have complex hierarchical structures. Therefore, it is necessary to take into account the complex hierarchical structure and to represent the topological relations between all regions in CBBRs as a relation matrix, rather than using the extended 9-intersection matrix to determine topological relations. In this study, a tree model is first used to represent the intrinsic configuration of CBBRs hierarchically. Then, the reasoning tables are presented for deriving topological relations between child, parent and sibling regions from the relations between two given regions in CBBRs. Finally, based on the reasoning, efficient methods are proposed to compute and derive the topological relation matrix. The proposed methods can be incorporated into spatial databases to facilitate geometric-oriented applications.