Enriching the spatial reasoning system RCC8

Abstract

One of the necessary basic concepts for the spatial data analysis in GIS is to determine the spatial relations between arbitrary geographical objects. In a two-dimensional space (IR 2 ), most existing topological models can distinguish the eight topological relations between two spatial regions A and B. These eight relations are written in the traditional form of the spatial reasoning system RCC8: DC, EC, EQ, PO, TPP, TPPi, NTPP and NTPPi. Because of the complexity of topological relations between geographic regions, it is difficult for these models to describe in detail the topological relations by defining the separation number of lines and points that characterize these relations, and which is very important to enrich the spatial relations of system RCC8. To overcome the insufficiency in existing models, the extension of the Intersection and Difference (ID) model has the ability to describe in detail the topological relations of system RCC8. In our study, we focus our work on the four relations EC, PO, TPP and TPPi which can be described by the boundary-boundary intersection operator ∂A∩∂B. The main contributions are these four detailed relations which are written and described in the general form EC mL, nP, kR , PO mL, nP, jRI, kR , TPP mLT, nPT, kR and TPPi mLT, nPT, kR . Then, we develop definitions for the generalization of these detailed relations. Finally, examples are provided to illustrate the generalization of these new detailed spatial relations.

Modeling topological relations between fuzzy spatiotemporal regions over time

“…The well known 4-Intersection approach described in [16], [19], as well as the 9-Intersection approach as discussed in [20], and the Intersection and Difference (ID) model studied in [2], [3], [13], are proposed to formalize topological relations between simple and crisp regions.…”

“…In [2], [3], [13], the topological complexity is considered as number of non-empty value in the topological relation model. It is hereof natural to define the topological complexity denoted by C T according to our topological relation model as follow: It is observed intuitively from the above list that the lowest topological complexity of the topological relations is the ones in the first group and the highest topological complexity of the topological relations is the ones in the eighth group.…”

Modeling Topological Relations between Uncertain Spatial Regions in Geo-spatial Databases: Uncertain Intersection and Difference Topological Model

“…Then the topological distance between these two relations (UID 5 and UID 127 ) can be computed by (5) as follows:…”

“…Then the topological distance is given by: Then the topological distance between these two relations (UID 63 and UID 136 ) can be computed by (5) as follows: Then the topological distance between these two relations (UID 84 and UID 103 ) can be computed by ( 5) as follows: In the properties from (1) to ( 6) of the topological distance, the notations UID k , UID m and UID n represent three topological relations obtained by the UID model, respectively. Compared to the definition of distance in metric space, it is easily observed that the topological distance is very similar to Manhattan distance.…”

“…1 represents the closure, interior and boundary of a closed disk as crisp spatial regions as in [1][2][3][4] [5] [6]. Eight topological relations of the system (Region Connection Calculus) RCC8 (DC, EC, PO, TPP, NTPP, TPPi, NTPPi, and EQ) have been identified between two simple regions by using these models in [1] [2] [3] [4] [5] [6]. Geographical phenomena in GIS with uncertain boundaries can be modelled by Regions with Broad Boundaries (BBRs) as in [8].…”