AbstractÐThis paper investigates temporal changes of topological relationships and thereby integrates two important research areas: First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial information over time. We investigate spatio-temporal predicates, which describe developments of well-known spatial topological relationships. A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary spatial predicates and sequential composition. We compare our framework with two other possible approaches: one is based on the observation that spatio-temporal objects correspond to three-dimensional spatial objects for which existing topological predicates can be exploited. The other approach is to consider possible transitions between spatial configurations. These considerations help to identify a canonical set of spatio-temporal predicates. Index TermsÐTime in geographic information, spatio-temporal data types, representation of spatio-temporal objects, changes of spatial predicates, developments of spatial objects. 1

This paper defines direction relations (e.g., north, northeast) between two-dimensional objects and shows how they can be efficiently retrieved using B-, KDB- and R- tree-based data structures. Essentially, our work studies optimisation techniques for 2D range queries that arise during the processing of direction relations. We test the efficiency of alternative indexing methods through extensive experimentation and present analytical models that estimate their performance. The analytical estimates are shown to be very close to the actual results and can be used by spatial query optimizers in order to predict the retrieval cost. In addition, we implement modifications of the existing structures that yield better performance for certain queries. We conclude the paper by discussing the most suitable method depending on the type of the range and the properties of the data. KEYWORDS: spatial databases, direction relations, indexing methods, performance analysis. 1.

Topological predicates are an important element of database systems that allow manipulation of spatial data. Based on the necessity for such systems to handle uncertainty, we introduce a general mechanism that identifies vague topological predicates. This definition forms part of a formal data model referred to as VASA (Vague Spatial Algebra), in which the data types vague regions, vague lines, and vague points are defined in terms of existing definition of crisp spatial data types. Following this trend, the mechanism presented here identifies vague topological predicates on the basis of well defined crisp topological predicates. An example implementation of the mechanism for vague regions is given.

Topological predicates, as derived from the 9-intersection model, have been widely recognized in GIS, spatial database systems, and many other geo-related disciplines. They are based on the evaluation of nine Boolean predicates checking the intersections of the boundary, interior, and exterior of a spatial object with the respective parts of another spatial object for inequality to the empty set. In this paper, we replace each Boolean predicate, which is a topological invariant, by another topological invariant. This new invariant is given as a function yielding the dimension of the respective intersection in the 9-intersection matrix, resulting in a dimension matrix. The goal of this paper is to determine the definition and semantics of all predicates that can be derived from this matrix for all combinations of spatial data types. It turns out that these dimension-based predicates are special refinements of the aforementioned topological predicates; hence, we call them dimension-refined topological predicates. We show that these predicates allow us to pose a class of more fine-grained topological queries.

Qualitative spatial reasoning is important for many spatial information systems, including GISs. It is based on the manipulation of qualitative spatial relationships and is used to infer spatial relationships which are not stored explicitly in the Geographic DataBase (GDB), to answer spatial queries given partial spatial knowledge and to maintain the consistency of the GDB. This paper compares the basic approaches developed for expressing qualitative topological, orientation and direction relationships. An extension of one of the classified approaches is then used for the representation of directional relationships (north, south, east, etc.) between objects of arbitrary shapes and for the representation of flow direction relationships (topological relationships between objects carrying flow, e.g. road segments, utility networks, etc.) as required within a GIS.

Topological predicates like overlap, inside, meet, and disjoint uniquely characterize the relative position between objects in space. They have been the subject of extensive interdisciplinary research. Spatial database systems and geographical information systems have shown a special interest in them since they enable the support of suitable query languages for spatial data retrieval and analysis. A look into the literature reveals that the research efforts so far have mainly dealt with the conceptual design of and the reasoning with these predicates while the development of efficient and robust implementation methods for them has been largely neglected. Especially the recent design of topological predicates for different combinations of complex spatial data types has resulted in a large increase of their numbers and stressed the importance of their efficient implementation. The goal of this article is to develop efficient implementation techniques of topological predicates for all combinations of the complex spatial data types point2D, line2D, and region2D within the framework of the spatial algebra SPAL2D. Our solution consists of two phases. In the exploration phase described in previous work of the authors, for a given scene of two spatial objects, all topological events are registered in so-called topological feature vectors. These vectors serve as input for the evaluation phase which is the focus of this article and which analyzes the

Qualitative spatial information plays a key role in many applications. While it is well-recognized that all but a few of these applications deal with spatial information that is affected by vagueness, relatively little work has been done on modelling this vagueness in such a way that spatial reasoning can still be performed. This paper presents a general approach to represent vague topological information (e.g., A is a part of B, A is bordering on B), using the well-known region connection calculus as a starting point. The resulting framework is applicable in a wide variety of contexts, including those where space is used in a metaphorical way. Most notably, it can be used for representing, and reasoning about, qualitative relations between regions with vague boundaries.

Abstract. Topological predicates between spatial objects have always been a main area of research on spatial data handling, reasoning, and query languages. The focus of research has definitely been on the design of and reasoning with these predicates, whereas implementation issues have been largely neglected. Besides, design efforts have been restricted to simplified abstractions of spatial objects like single points, continuous lines, and simple regions. In this paper, we present a general algorithm which is based on the well known plane-sweep paradigm and determines the topological relationship between two given complex regions. 1

Topological relationships between spatial objects such as overlap, disjoint, and inside have for a long time been a focus of research in a number of disciplines like cognitive science, robotics, linguistics, artificial intelligence, and spatial reasoning. In particular as predicates, they support the design of suitable query languages for spatial data retrieval and analysis in spatial database systems and Geographic Information Systems. While conceptual aspects of topological predicates (like their definition and reasoning with them) as well as strategies for avoiding unnecessary or repetitive predicate evaluations (like predicate migration and spatial index structures) have been emphasized, the development of correct and efficient implementation techniques for them has been rather neglected. Recently, the design of topological predicates for different combinations of complex spatial data types has led to a large increase of their numbers and accentuated the need for their efficient implementation. The goal of this article is to develop efficient implementation techniques of topological predicates for all combinations of the complex spatial data types point2D, line2D, and region2D,as