Complex multi-holed-region entity scenes (i.e., sets of random region with holes) are common in spatial database systems, spatial query languages, and the Geographic Information System (GIS). A multi-holed-region (region with an arbitrary number of holes) is an abstraction of the real world that primarily represents geographic objects that have more than one interior boundary, such as areas that contain several lakes or lakes that contain islands. When the similarity of the two complex holed-region entity scenes is measured, the number of regions in the scenes and the number of holes in the regions are usually different between the two scenes, which complicates the matching relationships of holed-regions and holes. The aim of this research is to develop several holed-region similarity metrics and propose a hierarchical model to measure comprehensively the similarity between two complex holed-region entity scenes. The procedure first divides a complex entity scene into three layers: a complex scene, a micro-spatial-scene, and a simple entity (hole). The relationships between the adjacent layers are considered to be sets of relationships, and each level of similarity measurements is nested with the adjacent one. Next, entity matching is performed from top to bottom, while the similarity results are calculated from local to global. In addition, we utilize position graphs to describe the distribution of the holed-regions and subsequently describe the directions between the holes using a feature matrix. A case study that uses the Great Lakes in North America in 1986 and 2015 as experimental data illustrates the entire similarity measurement process between two complex holed-region entity scenes. The experimental results show that the hierarchical model accounts for the relationships of the different layers in the entire complex holed-region entity scene. The model can effectively calculate the similarity of complex holed-region entity scenes, even if the two scenes comprise different regions and have different holes in each region.
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