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

Abstract

Topological relations have played important roles in spatial query, analysis and reasoning in Geographic Information Systems (GIS) and geospatial databases. The topological relations between crisp, uncertain and fuzzy spatial regions based upon the 9-intersections model have been identified. The research issue of topological relations, particularly, between spatial regions with uncertainties, has gained a lot of attention during the past two decades. However, the formal representation and calculation of the topological relations between uncertain regions is still an open issue and needs to be further developed. The paper provides a theoretical framework for modeling topological relations between uncertain spatial regions based upon a new uncertain topological model called the Uncertain Intersection and Difference (UID) Model. In order to derive all topological relations between two spatial regions with uncertainties, the spatial object of type Region (A) is decomposed in four components: the Interior, the Interior's Boundary, the Object's Boundary, and the Exterior's Boundary of A. By use of this definition of spatial region with uncertainties, new 4*4-Intersection and Uncertain Intersection and Difference (UID) models are proposed as a qualitative model for the identification of all topological relations between two spatial regions with uncertainties. These two new models are compared with other models studied in the literature. 152 binary topological relations can be identified by these two models. Then, the topological complexity and distance of the 152 relations will be study in details by using the UID model. Based upon this study of topological complexity and distance, a conceptual neighborhood graph for the 152 relations can be obtained. Examples are provided to illustrate the utility of these two models presented in this paper with results which can be applied for modeling GIS, geospatial databases and satellite image processing.

Modeling topological relations between fuzzy spatiotemporal regions over time

“…The first three properties in our topological relation model are similar to the ones in [4]. We mainly talk about the last property.…”

“…From the study about the topological distance, several properties of it are investigated as in [4]. Those properties are applicable for our topological relation model and topological distance where 1≤ x, y, z ≤ 92: • The values of topological distance may change from 0 to 7: 0 ≤ TD (M x , M y ) ≤ 7.…”

A 25-Intersection Model for Representing Topological Relations between Simple Spatial Objects in 3-D Space

“…The interior, the edge, and the exterior of the body are 3-D, 2-D, and 3-D, respectively. However, a line in 3-D space has an empty interior [9,11]. Similarly, a point in 3-D space has an empty interior, and a region in 3-D space also has an empty interior.…”

“…In 2008, Yohei Kurata proposed a 9+-intersection model (9+IM) for expressing the topological relations between two complex objects with multiple holes by considering the relations between the subparts of the three topological parts of objects A and B [10]. The uncertain intersection and difference model was proposed to express topological relations between uncertain spatial regions [11]. The 27-intersection model (27IM) was proposed taking both the dimension of intersections and the number of separations into account [12].…”

Classification of topological relations between spatial objects in two‐dimensional space within the dimensionally extended 9‐intersection model

“…The formalization of topological relations among spatial objects (such as interval‐based temporal logic—Allen, ; Masunaga, , point‐set topology—Chen, Li, Li, & Gold, ; Egenhofer & Franzosa, ; Egenhofer, Sharma, & Mark, , and region connection calculus (RCC)—Cohn, Bennett, Gooday, & Gotts, ; Cohn, Randell, & Cui, ; Gotts, Gooday, & Cohn, ; Jonsson & Drakengren, ; Randell & Cohn, ; Randell, Cui, & Cohn, ) has gained increasing attention in the last few decades. Research on formalizing topological relations based on point‐set topology has been conducted, and the 4‐intersection model (4IM) (Egenhofer & Franzosa, ), the 9‐intersection model (9IM) (Egenhofer & Herring, ), the Voronoi‐based 9‐intersection model (Chen, Li, Li, & Gold, ), the dimensionally extended 9‐intersection model (DE‐9IM) (Clementini, Felice, & Oosterom, ; Open GIS Consortium, ), the intersection and difference model (Deng, Cheng, Chen, & Li, ), the extended model expressed as 4 × 4 matrices (Liu & Shi, ), the 9+‐intersection model (Kurata, ), the uncertain intersection and difference model (Alboody, Sedes, & Inglada, ), the double straight line 4‐intersection model (Leng, Yang, & Chen, ), and the 27‐intersection model (Shen, Zhou, & Chen, ) have all been proposed. The intersection models and the extended models based on these have been widely studied.…”