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Elements of a Fuzzy Geometry for Visual Space

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Book cover Shape in Picture

Part of the book series: NATO ASI Series ((NATO ASI F,volume 126))

Abstract

This study introduces the notions of fuzzy location and fuzzy proximity to capture the imprecision associated with judgements of absolute and relative visual position. These notions are used to establish the elements of a fuzzy geometry for visual space, including the fuzzy betweenness of points, the fuzzy orientation of a pair of points, and the fuzzy collinearity of three or more points. Fuzzy orientation and fuzzy collinearity are, in turn, used to define the fuzzy straightness of a curve and the fuzzy tangency of two curves.

We are grateful to V.A. Kovalevsky for helpful comment, and to P. Fletcher and S.R. Pratt for critical review of the manuscript. This work was supported by the Consiglio Nazionale delle Ricerche and ESPRIT Basic Research Action No. 6448 (VIVA).

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica Sperimentale, Università di Torino, via Giuria 1, 10125, Torino, Italy

    Mario Ferraro

  2. Department of Communication and Neuroscience, Keele University, Staffordshire, ST5 5BG, UK

    David H. Foster

Authors
  1. Mario Ferraro
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  2. David H. Foster
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Editor information

Editors and Affiliations

  1. Centre for Mathematics and Computer Science (CWI), Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Ying-Lie O  & Henk J. A. M. Heijmans  & 

  2. Institute for Human Factors (TNO-IZF), Netherlands Organization for Applied Scientific Research, Kampweg 5, 3769 DE, Soesterberg, The Netherlands

    Alexander Toet

  3. Department of Communication and Neuroscience, University of Keele, ST5 5BG, Keele, Staffordshire, UK

    David Foster

  4. Department of Electrical and Computer Engineering, Rutgers University, 08855-0909, Piscataway, NJ, USA

    Peter Meer

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© 1994 Springer-Verlag Berlin Heidelberg

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Ferraro, M., Foster, D.H. (1994). Elements of a Fuzzy Geometry for Visual Space. In: O, YL., Toet, A., Foster, D., Heijmans, H.J.A.M., Meer, P. (eds) Shape in Picture. NATO ASI Series, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03039-4_21

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  • DOI: https://doi.org/10.1007/978-3-662-03039-4_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08188-0

  • Online ISBN: 978-3-662-03039-4

  • eBook Packages: Springer Book Archive

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