Principles of Geographical Information Systems
Peter A. Burrough AND Rachael A. McDonnell
OXFORD UNIVERSITY PRESS
1998
Data Models and Axioms
TWO
Data Models and Axioms: Formal Abstractions of Reality
When someone views an environment they simplify the inherent complexity of it by abstracting key features to create a 'model' of the area. This cognitive exercise is influenced by the cultural norms of the observer and the purpose of the study. This chapter examines the various model development stages that take place in the process of producing geographical data that may be used by others in a graphical or digital form. It is important to examine these theoretical ideas as all the data we use in a GIS will have been schematized using these geographical data models. The two extremes in approach perceive space either as being occupied by a series of entities which are described by their properties and mapped using a co- ordinate system, or as a continuous field of variation with no distinct boundaries. Formalized geographical data models are used to characterize these conceptual ideas so that they may be broken down into units which may be recorded and mapped. The principal approaches use either a series of points, lines, and polygons, or tessellated units to describe the various features in a landscape. The adoption of a particular model influences the type of data that may be used to describe the phenomena and the spatial analysis that may be undertaken. The fundamental procedures and axioms for handling and modifying spatial data are explained. Practical examples of the choice and use of various data models in frequently encountered applications are given.
Imagine that you are talking on the telephone to someone and they ask you to describe the view from your window. How would you depict the variations you see? It is likely that you would break down the landscape into units such as a building, road, field, valley, or hill and use geographical referencing in terms of 'beside', 'to the left of', or 'in front of' to describe the features. You have in fact developed a conceptual model of the Spatial data models and data structures.
The creation of analogue and digital spatial data sets involves seven levels of model development and abstraction (cf. Peuquet 1984a, Rhind and Green 1988, Worboys 1995) : (a) A view of reality (conceptual model) (b) Human conceptualization leading to an analogue abstraction (analogue model) (c) A formalization of the analogue abstraction without any conventions or restrictions on implementation (spatia data model) (d) A representation of the data model that reflects how the data are recorded in the computer (database model) (e) A file structure, which is the particular representation of the data structure in the computer memory (physical computational model). (f) Accepted axioms and rules for handling the data (data manipulation model) (g) Accepted rules and procedures for displaying and presenting spatial data to people (graphical model
landscape. Your interpretation of the features you have observed and the ones you have decided to ignore will be influenced by your experience, your cultural background, and that of the person to whom you are describing the scene. When information needs to be exchanged over a larger domain it becomes necessary to formalize the models used to describe an area to ensure that data are interpreted without ambiguity and communicated effectively. This chapter will describe the main data models used for describing geographical phenomena (see Couclelis 1992, Frank et al. 1992; Frank and Campari 1993; Egenhofer and Herring 1995; and Burrough and Frank 1996 for more detailed discussion). It gives an essential background to the following chapters of this book, because we do not store real world phenomena in the computer but only representations based on these formalized models. The major steps involved in proceeding from human observation of the world, either directly or with the assistance of tools like aerial photographs, remotely sensed images, or statistically located samples, to an analogue or digital representation are outlined in Box 2.1 and illustrated in Figure 2.1. The most important first step is that people observe the world and perceive phenomena that are fixed or change in space and time. Their perception will influence all subsequent analysis; success or failure with GIS does not depend in the first instance on technology but more on the appropriateness or otherwise of the conceptual models of space and spatial interactions
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