Relation-Based Information Processing With Symbolic Spatial Indexes

to include the new fact. The goal of error correction is, given a spatial knowledge representation which is not quite accurate and a new fact which is more precise, to improve the representation. Both these problems can be treated by operators, similar to the composition operator, that take two symbolic spatial indexes as arguments (i.e., one representing the initial state and one representing the new fact) and generate one or more output indexes that describe the possible new states. Examples of update operations can be found in (Papadias and Sellis, 1994b). Route planning has been extensively studied in areas of Artificial Intelligence, such as motion planning and robot navigation (Kuipers, 1978). Papadias and Sellis (1994b) have demonstrated how symbolic spatial indexes that preserve topological information can answer queries regarding connections between cities and highways in a practical application domain. Direction information can be used in choosing a highway which is in the direction of the destination, when several choices are available. Other potential applications for symbolic spatial indexes include Image Similarity Retrieval and Spatial Pattern Matching. Similarity using spatial indexes depends on the spatial relations among distinct objects, and not on geometric properties. Lee et al., (1992) have used 2D strings, one dimensional encodings of symbolic images, in pattern matching applications. This paper describes how symbolic spatial indexes can be used in several computational tasks involving direction and topological relations in 2D space. In particular we have dealt with information retrieval, composition of spatial relations, update operations and other forms spatial information processing. Details can be found in the corresponding references. Information processing using spatial indexes, and relation-based representations in general, involves symbolic and not numerical computation and avoids the usual problems of geometric representations, like finite resolution and geometric consistency. Although relation-based systems cannot be used in all applications involving spatial knowledge (e.g., applications involving quantitative reasoning and visualisation), we believe that there is a wide scope of potential applications ranging from Qualitative The problem of composition can be defined as "if the spatial relation between X and Z, and between Z and Y is known what are the possible relations between X and Y?". Frank (1994) presented composition tables for direction relations based on the concepts of projections and angular directions. Freksa (1992) also studied composition of direction relations in 2D space and Egenhofer (1991) composition of topological relations. In this section we will show how symbolic spatial …