by Klette, R and Zunic, J
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 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.
Reference:
Interactions between number theory and image analysis (Klette, R and Zunic, J), In Proceedings of SPIE – The International Society for Optical Engineering, Society of Photo-Optical Instrumentation Engineers, volume 4117, 2000.
Bibtex Entry:
@inproceedings{klette2000interactionsanalysis,
author = "Klette, R and Zunic, J",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",
pages = "210--221",
publisher = "Society of Photo-Optical Instrumentation Engineers",
title = "Interactions between number theory and image analysis",
volume = "4117",
year = "2000",
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 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.",
doi = "10.1117/12.404823",
issn = "0277-786X",
language = "eng",
}