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Spatial data types
"... Data types are a well known concept in computer science (for example, in programming languages or in database systems). A data type defines a set of homogeneous values and the allowable operations on those values. An example is a type integer representing the set of 32bit integers and including ope ..."
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Cited by 45 (18 self)
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Data types are a well known concept in computer science (for example, in programming languages or in database systems). A data type defines a set of homogeneous values and the allowable operations on those values. An example is a type integer representing the set of 32bit integers and including operations such as addition, subtraction, and multiplication that can be performed on integers. Spatial data types or geometric data types provide a fundamental abstraction for modeling the geometric structure of objects in space as well as their relationships, properties, and operations. They are of particular interest in spatial databases [5, 8, 13] and Geographical Information Systems [14]. One speaks of spatial objects as values of spatial data types. Examples are twodimensional data types for points (for example, representing the locations of lighthouses in the U.S.), lines (for example, describing the ramifications of the Nile Delta), regions (for example, depicting airpolluted zones), spatial networks (for example, representing the routes of the Metro in New York), and spatial partitions (for example, describing the 50 states of the U.S. and their exclusively given topological relationships of adjacency or disjointedness) as well as threedimensional data types for surfaces (for example, modeling the shape of landscapes) or volumes (for example, representing urban areas). Operations on spatial data types include spatial operations like the geometric intersection, union, and difference of spatial objects, numerical operations like the length of a line or the area of a region, topological relationships checking the relative position of spatial objects to each other
Uncertainty Management for Spatial Data in Databases: Fuzzy Spatial Data Types
 6th Int. Symp. on Advances in Spatial Databases, LNCS 1651
, 1999
"... . In many geographical applications there is a need to model spatial phenomena not simply by sharply bounded objects but rather through vague concepts due to indeterminate boundaries. Spatial database systems and geographical information systems are currently not able to deal with this kind of data. ..."
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Cited by 38 (16 self)
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. In many geographical applications there is a need to model spatial phenomena not simply by sharply bounded objects but rather through vague concepts due to indeterminate boundaries. Spatial database systems and geographical information systems are currently not able to deal with this kind of data. In order to support these applications, for an important kind of vagueness called fuzziness, we propose an abstract, conceptual model of socalled fuzzy spatial data types (i.e., a fuzzy spatial algebra) introducing fuzzy points, fuzzy lines, and fuzzy regions. This paper ? focuses on defining their structure and semantics. The formal framework is based on fuzzy set theory and fuzzy topology. 1 Introduction Representing, storing, quering, and manipulating spatial information is important for many nonstandard database applications. Specialized systems like geographical information systems (GIS) and spatial database systems to a certain extent provide the needed technology to su...
Generalizing Graphs using Amalgamation and Selection
 Advances in Spatial Databases. 6th International Symposium, SSD'99, volume 1651 of Lecture Notes in Computer Science
, 1999
"... . This work is a contribution to the developing literature on multiresolution data models. It considers operations for modeloriented generalization in the case where the underlying data is structured as a graph. The paper presents a new approach in that a distinction is made between generalization ..."
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Cited by 20 (6 self)
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. This work is a contribution to the developing literature on multiresolution data models. It considers operations for modeloriented generalization in the case where the underlying data is structured as a graph. The paper presents a new approach in that a distinction is made between generalizations that amalgamate data objects and those that select data objects. We show that these two types of generalization are conceptually distinct, and provide a formal framework in which both can be understood. Generalizations that are combinations of amalgamation and selection are termed simplifications, and the paper provides a formal framework in which simplifications can be computed (for example, as compositions of other simplifications). A detailed case study is presented to illustrate the techniques developed, and directions for further work are discussed. 1 Introduction Specialist spatial information systems (SIS) play an increasingly important role within the Information Tech...
Granulation for Graphs
 Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. International Conference COSIT'99, volume 1661 of Lecture Notes in Computer Science
, 1999
"... . In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure ..."
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Cited by 10 (6 self)
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. In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the granulation of graphs is an important topic. The importance of graphs arises from their widespread use in modelling networks, and also from the use of dual graphs of spatial partitions. This paper demonstrates that there are several quite different kinds of granulation for graphs. Four kinds are described in detail, and situations where some of these may arise in spatial information systems are indicated. One particular kind of granulation leads to a new formulation of the boundarysensitive approach to qualitative location developed by Bittner and Stell. Vague graphs and their connection with granulation are also discusse...
The Honeycomb Model of SpatioTemporal Partitions
 In Int. Workshop on SpatioTemporal Database Management, LNCS 1678
, 1999
"... . We define a formal model of spatiotemporal partitions which can be used to model temporally changing maps. We investigate new applications and generalizations of operations that are wellknown for static spatial maps. We then define a small set of operations on spatiotemporal partitions that are ..."
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Cited by 9 (4 self)
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. We define a formal model of spatiotemporal partitions which can be used to model temporally changing maps. We investigate new applications and generalizations of operations that are wellknown for static spatial maps. We then define a small set of operations on spatiotemporal partitions that are powerful enough to express all these tasks and more. Spatiotemporal partitions combine the general notion of temporal objects and the powerful spatial partition abstraction into a new, highly expressive spatiotemporal data modeling tool. 1 Introduction The subject of this paper is the temporal evolution of maps. The metaphor of a map has turned out to be a fundamental and ubiquitous spatial concept in many spatiallyoriented disciplines like geography and cartography as well as in computerassisted systems like geographical informations systems (GIS), spatial database systems, and image database systems, but also simply for human's spatial orientation in everyday life. A map is a widely ...
Stratified Rough Sets And Vagueness
 Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. International Conference COSIT’03
, 2003
"... The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in modeloriented generalization, also called semantic generalization, is the notion of an equivalence relation. Given an equivalence re ..."
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Cited by 8 (1 self)
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The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in modeloriented generalization, also called semantic generalization, is the notion of an equivalence relation. Given an equivalence relation on a set, the techniques of rough set theory can be applied to give generalized descriptions of subsets of the original set. The notion of equivalence relation, or partition, has recently been significantly extended by the introduction of the notion of a granular partition. A granular partition provides what may be thought of as a hierarchical family of partial equivalence relations. In this paper we show how the mechanisms for making rough descriptions with respect to an equivalence relation can be extended to give rough descriptions with respect to a granular partition. In order to do this, we also show how some of the theory of granular partitions can be reformulated; this clarifies the connections between equivalence relations and granular partitions. With the help of this correspondence we then can show how the notion of hierarchical systems of partial equivalence classes relates to partitions of partial sets, i.e., partitions of sets in which not all members are known. This gives us new insight into the relationships between roughness and vagueness. 1
Spatial Partition Graphs: A Graph Theoretic Model of Maps
"... Abstract. The notion of a map is a fundamental metaphor in spatial disciplines. However, there currently exist no adequate data models for maps that define a precise spatial data type for map geometries for use in spatial systems. In this paper, we consider a subclass of map geometries known as spat ..."
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Abstract. The notion of a map is a fundamental metaphor in spatial disciplines. However, there currently exist no adequate data models for maps that define a precise spatial data type for map geometries for use in spatial systems. In this paper, we consider a subclass of map geometries known as spatial partitions that are able to model maps containing region features. However, spatial partitions are defined using concepts such as infinite point sets that cannot be directly represented in computers. We define a graph theoretic model of spatial partitions, called spatial partition graphs, based on discrete concepts that can be directly implemented in spatial systems. 1