The Objects Interaction Matrix for Modeling Cardinal Directions in Spatial Databases

Abstract

Besides topological relations and approximate relations, cardinal directions have turned out to be an important class of qualitative spatial relations. In spatial databases and GIS they are frequently used as selection criteria in spatial queries. But the available models of cardinal relations suffer from a number of problems like the unequal treatment of the two spatial objects as arguments of a cardinal direction relation, the use of too coarse approximations of the two spatial operand objects in terms of single representative points or minimum bounding rectangles, the lacking property of converseness of the cardinal directions computed, the partial restriction and limited applicability to simple spatial objects only, and the computation of incorrect results in some cases. This paper proposes a novel two-phase method that solves these problems and consists of a tiling phase and an interpretation phase. In the first phase, a tiling strategy first determines the zones belonging to the nine cardinal directions of each spatial object and then intersects them. The result leads to a bounded grid called objects interaction grid. For each grid cell the information about the spatial objects that intersect it is stored in an objects interaction matrix. In the second phase, an interpretation method is applied to such a matrix and determines the cardinal direction. These results are integrated into spatial queries using directional predicates.

This work was partially supported by the National Science Foundation under grant number NSF-CAREER-IIS-0347574.