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Computation With Imprecise Geospatial Data
, 1998
"... Imprecision in spatial data arises from the granularity or resolution at which observations of phenomena are made, and from the limitations imposed by computational representations, processing and presentational media. Precision is an important component of spatial data quality, and a key to appropr ..."
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Cited by 33 (6 self)
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Imprecision in spatial data arises from the granularity or resolution at which observations of phenomena are made, and from the limitations imposed by computational representations, processing and presentational media. Precision is an important component of spatial data quality, and a key to appropriate integration of collections of data sets. Previous work of the author provides a theoretical foundation for imprecision of spatial data resulting from finite granularities, and gives the beginnings of an approach to reasoning with such data using methods similar to rough set theory. This paper develops the theory further, and extends the work to a model that includes both spatial and semantic components. Notions such as observation, schema, frame of discernment and vagueness are examined and formalised. Keywords: GIS, imprecision, vagueness, resolution, spatial reasoning, data quality, uncertainty. Computers, Environment and Urban Systems 2 1. INTRODUCTION We now live in a world of ...
A Formal Model of the Process of Wayfinding in Built Environments
 In C. Freksa & D.M. Mark (Eds.), Spatial
, 1999
"... . Previous recent research on human wayfinding has focused primarily on mental representations rather than processes of wayfinding. This paper presents a formal model of some aspects of the process of wayfinding, where appropriate elements of human perception and cognition are formally realized ..."
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Cited by 21 (3 self)
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. Previous recent research on human wayfinding has focused primarily on mental representations rather than processes of wayfinding. This paper presents a formal model of some aspects of the process of wayfinding, where appropriate elements of human perception and cognition are formally realized using image schemata and affordances. The goaldriven reasoning chain that leads to action begins with incomplete and imprecise knowledge derived from imperfect observations of space. Actions result in further observations, derived knowledge and, recursively, further actions, until the goal is achieved or the wayfinder gives up. This paper gives a formalization of this process, using a modal extension to classical propositional logic to represent incomplete knowledge. Both knowledge and action are represented through a wayfinding graph. A special case of wayfinding in a building, that is finding one's way through an airport, is used to demonstrate the formal model. Keywords. Wayfind...
Stratified Map Spaces: A Formal Basis for Multiresolution Spatial Databases
 SDH'98 Proceedings 8th International Symposium on Spatial Data Handling, pages 180189. International Geographical
, 1998
"... Precision is a key component of spatial data quality and in this era of globally distributed spatial data it is essential to be able to integrate multiple distributed data sets with heterogeneous levels of precision. Imprecision arises through limitations on semantic and geometric resolution of data ..."
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Cited by 21 (8 self)
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Precision is a key component of spatial data quality and in this era of globally distributed spatial data it is essential to be able to integrate multiple distributed data sets with heterogeneous levels of precision. Imprecision arises through limitations on semantic and geometric resolution of data representations. Generalization, and in particular modeloriented generalization, is an important process in this context, because it enables translation between different levels of precision. This paper provides a formal approach to multiresolution in spatial data handling. It begins by motivating the work and pointing to some of the background research, and then introduces the basic concepts underlying the approach, focusing on the new concept of a stratified map space. The approach is quite general, and to show its application, the paper uses it to provide a formal foundation for generalization and vague regions. Keywords: resolution, generalization, vagueness, theory 1. Introduction W...
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 18 (5 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...
A Design of Topological Predicates for Complex Crisp and Fuzzy Regions
 Int. Conf. on Conceptual Modeling
, 2001
"... For a long time topological predicates between spatial objects have been a main area of research on spatial data handling, reasoning, and query languages. But these predicates still suffer from two main restrictions: first, they are only applicable to simplified abstractions of spatial objects l ..."
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Cited by 16 (8 self)
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For a long time topological predicates between spatial objects have been a main area of research on spatial data handling, reasoning, and query languages. But these predicates still suffer from two main restrictions: first, they are only applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions, as they occur in systems like current geographical information systems and spatial database systems. Since these abstractions are usually not sufficient to cope with the complexity of geographic reality, their generalization is needed which especially has influence on the nature and definition of their topological relationships. This paper gives a formal definition of complex crisp regions, which may consist of several components and which may have holes, and it especially shows how topological predicates can be defined on them. Second, topological predicates so far only operate on crisp but not on fuzzy spatial objects which occur frequently in geographical reality. Based on complex crisp regions, this paper gives a definition of their fuzzy counterparts and shows how topological predicates can be defined on them. 1
A Formal Approach to Imperfection in Geographic Information
 Computers, Environment and Urban Systems
, 2001
"... Traditional computational models of geographic phenomena offer no room for imperfection. Underlying this tradition is the simplifying assumption that reality is certain, crisp, unambiguous, independent of context, and capable of quantitative representation. This paper reports on initial work which e ..."
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Cited by 15 (3 self)
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Traditional computational models of geographic phenomena offer no room for imperfection. Underlying this tradition is the simplifying assumption that reality is certain, crisp, unambiguous, independent of context, and capable of quantitative representation. This paper reports on initial work which explicitly recognises that most geographic information is intrinsically imperfect. Based on an ontology of imperfection the paper explores a formal model of imperfect geographic information using multivalued logic. The development of Java software able to assist with a geodemographic retail site assessment application is used to illustrate the utility of a formal approach.
Capturing Fuzziness and Uncertainty of Spatiotemporal Objects
 In ADBIS
, 2001
"... For the majority of spatiotemporal applications, we assume that the modeled world is precise and bound. This simplification seems unnecessary crude for many environments handling spatial and temporal extents, such as navigational applications. In this work, we explore fuzziness and uncertainty, ..."
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Cited by 13 (2 self)
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For the majority of spatiotemporal applications, we assume that the modeled world is precise and bound. This simplification seems unnecessary crude for many environments handling spatial and temporal extents, such as navigational applications. In this work, we explore fuzziness and uncertainty, which we subsume under the term indeterminacy, in the spatiotemporal context.
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...
Stratified Rough Sets And Vagueness
 Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. International Conference COSITâ€™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
FINITE RESOLUTION CRISP AND FUZZY SPATIAL OBJECTS
"... Uncertainty management for geometric data is currently an important problem in spatial databases, image databases, and GIS. Spatial objects do not always have homogeneous interiors and sharply defined boundaries but frequently their interiors and boundaries are partially or totally indeterminate and ..."
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Cited by 7 (3 self)
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Uncertainty management for geometric data is currently an important problem in spatial databases, image databases, and GIS. Spatial objects do not always have homogeneous interiors and sharply defined boundaries but frequently their interiors and boundaries are partially or totally indeterminate and vague. For an important kind of spatial vagueness called fuzziness this paper provides a conceptual model of fuzzy spatial objects that also incorporates fuzzy geometric union, intersection, and difference operations as well as fuzzy topological predicates. In particular, this model is not based on Euclidean space and on an infiniteprecision arithmetic which lead to lacking numerical robustness and to topological inconsistency; it rests on a finite, discrete geometric domain called grid partition which takes into account finiteprecision number systems available in computers. Last but not least this paper shall also be a contribution to achieve a uniform treatment of vector and raster data.