On Consistency Checking of Spatial Relationships in Content-based Image Database Systems

Abstract

In this paper we investigate the consistency problem for spatial relationships in content-based image database systems. We use the mathematically simple matrix representation approach to present an efficient (i.e., polynomial-time) algorithm for consistency checking of spatial relationships in an image.

It is shown that, there exists an efficient algorithm to detect whether, given a set $SR$ of absolute spatial relationships, the maximal set of $SR$ under $\cal R$ contains one pair of contradictory spatial relationships. The time required by it is at most a constant multiple of the time to compute the transitive reduction of a graph or to compute the transitive closure of a graph or to perform Boolean matrix multiplication, and thus is always bounded by time complexity $O(n^{3})$ (and space complexity $O(n^{2})$), where $n $ is the number of all involved objects. As a corollary, this detection algorithm can completely answer whether a given set of three-dimensional absolute spatial relationships is consistent.