Multiple index structures for efficient retrieval of 2D objects

Many applications require the storage and management of large databases of 2D objects. One of the important functionalities required by all of these applications is the capability to find objects in a database that match a given object. We concentrate on whole matching queries, in which a query object is compared with a set of objects to find the ones that are either exactly identical or similar to the query object. There are two obstacles for efficient execution of whole-match queries. First, the general problem of comparing two 2D objects under rotation, scaling and translation invariance is known to be computationally expensive. Second, the size of the databases are growing, and hence a query should be answered without accessing all the objects in the database. To address both obstacles, we identify a set of six features that could be extracted from the objects' minimum bounding circle (MBC). These are: the radius of the MBC, the coordinates of the center of MBC, the set of touch-points on the MBC, the touch-points angle sequence, the vertex angle sequence and the start-point of the angle sequence. The features are unique per object and can be utilized for both efficiently indexing the objects and expediting the comparison between two objects. We focus on three variations of match queries: an exact shape match, an exact match with rotation, scaling or translation, and similarity shape retrieval.