Authors: Klette, Reinhard
Žunić, Joviša 
Title: Interactions between number theory and image analysis
Journal: Proceedings of SPIE - The International Society for Optical Engineering
Volume: 4117
First page: 210
Last page: 221
Conference: Vision Geometry IX; San Diego, CA, USA; 30 July 2000 through 31 July 2000
Issue Date: 1-Dec-2000
ISSN: 0277-786X
DOI: 10.1117/12.404823
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 an 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.
Publisher: SPIE

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