Point-set topological spatial relations

Abstract

Practical needs in geographic information systems (GIS) have led to the investigation of formal and sound methods of describing spatial relations. Arter an introduction to the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in tenns of the intersections of the boundaries and interiors of two sets. By consideringemply and non-emptyas the values of'the intersections, a total of sixteen topological spatial relations is described, each of which can be realized in R 2 • This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space with an application to GIS. It is shown that these relations correspond to some of the standard set theoretical and topological spatial relations between sets such as equality, disjointness and containment in the interior. .

Data Reduction and Regression Using Principal Component Analysis in Qualitative Spatial Reasoning and Health Informatics

“…One representative approach, the Region-Connection Calculus (RCC), provides predicates for expressing and reasoning about the relationships among topological regions (arbitrarily shaped chunks of space). RCC was originally designed for 2D [1,2]; later it was extended to 3D [3]. Herein we introduce PCA to reduce 9-Intersection model to 4-intersection model in both 2D and 3D.…”

“…RCC5/RCC8 can be formalized by using first order logic [2] or by using the 9-intersection model [1]. Conceptually, for any two regions, there are three possibilities: (1) one object is outside the other; this results in the RCC5 relation DR (interiors disjoint) and RCC8 relation DC (disconnected) or EC (externally connected).…”

Spatio-temporal Evolution as Bigraph Dynamics

“…In the purely spatial case, certain basic systems of spatial relationships have been found useful; the 9-intersection model [5] has acquired the status of a standard and systems for qualitative spatial reasoning [1], including the Region-Connection Calculus, have been very widely studied and applied. The spatial relations modelled in such systems include widely accepted notions such as 'overlapping', 'inside but not touching the boundary', and 'disjoint'.…”

Modal Logics of Topological Relations

“…Regarding the relations, in the initially mentioned research areas there appears to be consensus that the eight Egenhofer-Franzosa (or RCC8) relations, which have been independently introduced in [RCC92] and [EF91], and their coarser relative RCC5 consisting of only five relations, are the most fundamental sets of relations between regions of topological spaces-both from a theoretical and a practical viewpoint, see e.g. [PSV99,Ege94,RN99,SS01,RCC92].…”