On Completeness of Reasoning about Planar Spatial Relationships in Pictorial Retrieval Systems

Abstract

In this paper we consider the completeness problem of reasoning about planar spatial relationships in pictorial retrieval systems. We define a large class of two-dimensional scenes, the extended pseudo-symbolic pictures. The existing rule system R is proved to be complete for (extended) pseudo-symbolic pictures. We also introduce a new iconic indexing, the (extended) pseudo- 2D string representation, for them. The (extended) pseudo-2D string has the good properties of the 2D string. It is unambiguous, like the augmented 2D string, and has a compact form suitable for image retrieval. We then present efficient algorithms to determine whether a given planar picture is (extended) pseudo-symbolic or not, and if it is, these algorithms also return its (extended) pseudo-2D string representation. Picture retrieval by (extended) pseudo-2D strings is also discussed.