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A New Approach to Incorporate Uncertainty in Terrain Modeling

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Geographic Information Science (GIScience 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2478))

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Abstract

A method for incorporating uncertainty in terrain modelling by expressing elevations as fuzzy numbers is proposed. Given a finite set of fuzzy elevations representative of the topographic surface in a certain region, we develop methods to construct surfaces that incorporate the uncertainty. The smoothness and continuity conditions of the surface generating method are maintained. Using this approach, we generalize some classic interpolators and compare them qualitatively. Extensions to wider classes of interpolators follow naturally from our approach. A numerical example is presented to illustrate this idea.

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Author information

Authors and Affiliations

  1. Secção de Engenharia Geográfica, Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001 - 454, Coimbra, Portugal

    Jorge Santos

  2. Mathematics Department, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO, 80217-3364, USA

    Weldon A. Lodwick

  3. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Arnold Neumaier

Authors
  1. Jorge Santos
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  2. Weldon A. Lodwick
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  3. Arnold Neumaier
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Editor information

Editors and Affiliations

  1. Department of Spatial Information Science and Engineering, National Center for Geographic Information and Analysis, Orono, ME, 04469-5711, USA

    Max J. Egenhofer

  2. Department of Computer Science, University of Maine, Orono, ME, 04469-5711, USA

    Max J. Egenhofer

  3. National Center for Geographic Information and Analysis Department of Geography, University at Buffalo, 105 Wilkeson Quad., Box 610023, Buffalo, NY, 14261-0023, USA

    David M. Mark

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© 2002 Springer-Verlag Berlin Heidelberg

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Santos, J., Lodwick, W.A., Neumaier, A. (2002). A New Approach to Incorporate Uncertainty in Terrain Modeling. In: Egenhofer, M.J., Mark, D.M. (eds) Geographic Information Science. GIScience 2002. Lecture Notes in Computer Science, vol 2478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45799-2_20

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  • DOI: https://doi.org/10.1007/3-540-45799-2_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44253-0

  • Online ISBN: 978-3-540-45799-2

  • eBook Packages: Springer Book Archive

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