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Shape in Picture pp 127–146Cite as

Can Categorical Shape Theory Handle Grey-level Images?

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

Abstract

Categorical shape theory can be considered as a formal model of a recognition process, but can it handle grey-level images? In this paper, some of the available pure mathematics, mostly from topology and category theory, that may be useful in this context are considered and the feasibility of such a model is discussed both from the machine-implementation viewpoint and a biological one.

The author would like to thank Gavin Wraith for providing an explanation of Lawvere’s ideas on metric spaces and Andrée Charles Ehresmann for discussions of her ideas on the modelling of brain functions.

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Authors and Affiliations

  1. School of Mathematics, University of Wales at Bangor, Dean Street, Bangor, Gwynedd, LL57 lUT, UK

    Timothy Porter

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  1. Timothy Porter
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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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Porter, T. (1994). Can Categorical Shape Theory Handle Grey-level Images?. 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_10

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  • DOI: https://doi.org/10.1007/978-3-662-03039-4_10

  • 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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