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Proceedings Paper

Interactions between number theory and image analysis
Author(s): Reinhard Klette; Jovisa Zunic
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Paper Abstract

The conceptual design of many procedures used in image analysis starts with models which assume as an input sets in Euclidean space which we regard as real objects. However, the application finally requires that the Euclidean (real) objects have to be modelled by digital sets, i.e. they are approximated by their corresponding digitizations. Also 'continuous' operations (for example integrations or differentiations) are replaced by 'discrete' counterparts (for example summations or differences) by assuming that such a replacement has only a minor impact on the accuracy or efficiency of the implemented procedure. This paper discusses applications of results in number theory with respect to error estimations, accuracy evaluations, correctness proofs etc. for image analysis procedures. Knowledge about digitization errors or approximation errors may help to suggest ways how they can be kept under required limits. Until now have been only minor impacts of image analysis on developments in number theory, by defining new problems, or by specifying ways how existing results may be discussed in the context of image analysis. There might be a more fruitful exchange between both disciplines in the future.

Paper Details

Date Published: 23 October 2000
PDF: 12 pages
Proc. SPIE 4117, Vision Geometry IX, (23 October 2000); doi: 10.1117/12.404823
Show Author Affiliations
Reinhard Klette, Univ. of Auckland (New Zealand)
Jovisa Zunic, Univ. of Novi Sad (United Kingdom)


Published in SPIE Proceedings Vol. 4117:
Vision Geometry IX
Longin Jan Latecki; David M. Mount; Angela Y. Wu, Editor(s)

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