Michael Worboys

A Unified Model for Spatial and Temporal Information

Many applications of spatial information systems require not just spatial data handling but a unified approach to space and time. This paper begins by motivating this requirement with some examples, continues by identifying some of the key issues in this area and then discusses a unified generic model for information which is referenced to two spatial dimensions and two temporal dimensions (database and event times)

Imprecision in Finite Resolution Spatial Data

An important component of spatial data quality is the imprecision resulting from the resolution at which data are represented. Current research on topics such as spatial data integration and generalization needs to be well-founded on a theory of multi-resolution. This paper provides a formal framework for treating the notion of resolution and multi-resolution in geographic spaces. It goes further to develop an approach to reasoning with imprecision about spatial entities and relationships resulting from finite resolution representations. The approach is similar to aspects of rough and fuzzy set theories. The paper concludes by providing the beginnings of a geometry of vague spatial entities and relationships.

Object-oriented approaches to geo-referenced information

Abstract This paper surveys the current state of the object-oriented paradigm as it applies to the handling of geo-referenced information. The model of any computerized system is multi-layered, with a high-level system-independent conceptual model of the application domain supported by increasingly system-oriented models beneath. The author argues that object-oriented approaches can be taken at each of these layers. The major constructs of object-orientation are discussed from this layered viewpoint and in the context of geo-information handling.

A formal approach to imperfection in geographic information

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 multi-valued 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.

A Formal Model of the Process of Wayfinding in Built Environments

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 goal-driven 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 ones way through an airport, is used to demonstrate the formal model.

Computation with imprecise geospatial data

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.

Integration of Imperfect Spatial Information

The theme of this paper is integration of information arising from observations of spatial entities and relationships. The assumption is that observations are imperfect; in particular, that they are imprecise and inaccurate. Each observation is made in a context that among other things provides a level of resolution. So, a treatment of integration of observations of this type must take account of multiresolution spatial data models. After an introduction, the paper discusses an ontology of imperfection, focusing on imprecision and inaccuracy. The paper goes on to consider logics that are appropriate for integration of information arising from imperfect observations. Two case studies, showing some of the facets of this treatment are developed in greater detail. The first case study considers integration of imperfect (inaccurate and imprecise) observations of a single spatial region. The second case study develops the theory of regions with broad boundary to address the issue of integrating imprecise observations of spatial relationships. ( 2001 Academic Press

A generic model for planar geographical objects

Abstract The lack of a coherent theory underpinning geographical databases is a serious obstacle to research efforts in this field. This article attempts to construct part of such a theory, namely the formalization of the underlying object mode for geographical data whose spatial references are embedded in the plane. Questions of approximation and error analysis, while exposed and briefly discussed here, do not form a major part of the discussion. This work extends earlier work by giving a detailed construction of the classes and operations for spatial objects embedded in the plane. It goes on to provide an explicit link between this object model and its representation in computationally meaningful terms using classes of simplicial complexes and operations acting upon these classes.

The Algebraic Structure of Sets of Regions

The provision of ontologies for spatial entities is an important topic in spatial information theory. Heyting algebras, co-Heyting algebras, and bi-Heyting algebras are structures having considerable potential for the theoretical basis of these ontologies. This paper gives an introduction to these Heyting structures, and provides evidence of their importance as algebraic theories of sets of regions. The main evidence is a proof that elements of certain Heyting algebras provide models of the Region-Connection Calculus developed by Cohn et al. By using the mathematically well known techniques of “pointless topology”, it is straight-forward to conduct this proof without any need to assume that regions consist of sets of points. Further evidence is provided by a new qualitative theory of regions with indeterminate boundaries. This theory uses modal operators which are related to the algebraic operations present in a bi-Heyting algebra.

Generalizing Graphs Using Amalgamation and Selection

This work is a contribution to the developing literature on multi-resolution data models. It considers operations for model-oriented 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.