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In geographic information retrieval and spatial data mining, similarity is used to resolve shape matching and clustering. Many approaches have been developed to calculate similarity between simple geometric shapes. However, complex spatial objects are common in spatial database systems, spatial query languages and Geographic Information Science (GIS) applications. With holed polygons, many similarity measurement approaches are restricted to address the relationships between holes or between the holes and the entire complex geometric shape. A successful method should remove the restrictions due to these complex relations and retain invariant during geometric translation (rotation, moving and scaling). To overcome these deficiencies, we utilize position graphs to describe the distribution of holes in complex geometric shapes by storing invariants, such as angles and distances. In addition, Fourier descriptors and the position graph-based method are used to measure the similarity between holed polygons. Experiments show that the proposed method takes into account the relationships in an entire complex geometric shape. It can effectively calculate the similarity of holed polygons, even if they contain different numbers of holes.
Xu et al. (Thu,) studied this question.