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11,576
Spherical Topological Relations
, 2005
"... Analysis of global geographic phenomena requires nonplanar models. In the past, models for topological relations have focused either on a twodimensional or a threedimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the twodimensional plan ..."
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Cited by 152 (22 self)
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Analysis of global geographic phenomena requires nonplanar models. In the past, models for topological relations have focused either on a twodimensional or a threedimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the two
Topological Relations Between Regions With Holes
 Int. Journal of Geographical Information Systems
, 1994
"... The 4intersection, a model for the representation of topological relations between 2dimensional objects with connected boundaries and connected interiors, is extended to cover topological relations between 2dimensional objects with arbitrary holes, called regions with holes. Each region with hole ..."
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Cited by 89 (6 self)
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The 4intersection, a model for the representation of topological relations between 2dimensional objects with connected boundaries and connected interiors, is extended to cover topological relations between 2dimensional objects with arbitrary holes, called regions with holes. Each region
An Ordering of Convex Topological Relations
"... Abstract. Klippel has recently identified topological relativity as an important question for geographic information theory. One way of assessing at the importance of topology in spatial reasoning and in spatial theory is to analyze commonplace terms from natural language relative to conceptual neig ..."
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Cited by 2 (2 self)
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Abstract. Klippel has recently identified topological relativity as an important question for geographic information theory. One way of assessing at the importance of topology in spatial reasoning and in spatial theory is to analyze commonplace terms from natural language relative to conceptual
Determining Consistency of Topological Relations
 Constraints
, 1998
"... . This paper examines the problem of testing consistency of sets of topological relations which are instances of the RCC8 relation set (Randell, Cui and Cohn 1992). Representations of these relations as constraints within a number of logical frameworks are considered. It is shown that, if the argum ..."
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Cited by 12 (2 self)
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. This paper examines the problem of testing consistency of sets of topological relations which are instances of the RCC8 relation set (Randell, Cui and Cohn 1992). Representations of these relations as constraints within a number of logical frameworks are considered. It is shown that
Topological Relational Quantales
"... Abstract We introduce and present results about a class of quantales, the topological relational quantales, that can be associated with tuples (X,R) such that X is a topological space and R is a lowersemicontinuous equivalence relation on X (see Definition 1 below). Our motivating case studies and ..."
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Abstract We introduce and present results about a class of quantales, the topological relational quantales, that can be associated with tuples (X,R) such that X is a topological space and R is a lowersemicontinuous equivalence relation on X (see Definition 1 below). Our motivating case studies
Uncertainty Of Topological Relations In GIS
 In ISPRS Commission III Symposium
, 1994
"... : We present a concept for representing uncertain topological relations and their derivation from uncertain sets, useful for spatial and temporal reasoning in GIS. The concept is based on the notion of a stochastic boundary of a geometric set and on tests performed to decide the validity of relation ..."
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Cited by 1 (0 self)
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: We present a concept for representing uncertain topological relations and their derivation from uncertain sets, useful for spatial and temporal reasoning in GIS. The concept is based on the notion of a stochastic boundary of a geometric set and on tests performed to decide the validity
Distances for Uncertain Topological Relations
"... Considering uncertainty of spatial data in any GIS analysis is a theme of actual research, but far from practicability. One prerequisite is the availability of descriptions concerning uncertainty (metadata), and another is the attachment of uncertainty to spatial analysis. In our contribution we pr ..."
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propose a method to determine the topological relation between two positional uncertain regions. The decision is based on morphological distances along a skeleton through uncertain intersection sets. These measures are equivalent to the known representation by intersection sets, but yield additionally
MODAL LOGICS OF TOPOLOGICAL RELATIONS
 ACCEPTED FOR PUBLICATION IN LOGICAL METHODS IN COMPUTER SCIENCE
, 2006
"... Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we int ..."
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Cited by 24 (6 self)
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introduce a family of modal logics equipped with eight modal operators that are interpreted by the EgenhoferFranzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns
Defined Topological Relations in Description Logics
 Proceedings of the International Workshop on Description Logics, DL'97
, 1997
"... : In this paper we extend the language ALC(D) by a new operator which allows one to define roles on behalf of properties of objects which are given by a concrete domain. This operator can be used to define topological relations. We show that the extension results in an undecidable language and ask f ..."
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Cited by 16 (8 self)
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: In this paper we extend the language ALC(D) by a new operator which allows one to define roles on behalf of properties of objects which are given by a concrete domain. This operator can be used to define topological relations. We show that the extension results in an undecidable language and ask
A Growing Neural Gas Network Learns Topologies
 Advances in Neural Information Processing Systems 7
, 1995
"... An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this m ..."
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Cited by 401 (5 self)
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An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994
Results 1  10
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11,576