Numerical stability of fast computation algorithms of Zernike moments

Papakostas, GA; Boutalis, YS; Papaodysseus, CN; Fragoulis, DK

dc.contributor.author	Papakostas, GA	en
dc.contributor.author	Boutalis, YS	en
dc.contributor.author	Papaodysseus, CN	en
dc.contributor.author	Fragoulis, DK	en
dc.date.accessioned	2014-03-01T01:28:54Z
dc.date.available	2014-03-01T01:28:54Z
dc.date.issued	2008	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19021
dc.subject	Finite precision error	en
dc.subject	Numerical stability	en
dc.subject	Recursive algorithm	en
dc.subject	Zernike moments	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Algorithms	en
dc.subject.other	Numerical methods	en
dc.subject.other	Robustness (control systems)	en
dc.subject.other	Finite precision error	en
dc.subject.other	Recursive algorithm	en
dc.subject.other	Zernike moments	en
dc.subject.other	Computational complexity	en
dc.title	Numerical stability of fast computation algorithms of Zernike moments	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2007.04.110	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2007.04.110	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	A detailed, comparative study of the numerical stability of the recursive algorithms, widely used to calculate the Zernike moments of an image, is presented in this paper. While many papers, introducing fast algorithms for the computation of Zernike moments have been presented in the literature, there is not any work studying the numerical behaviour of these methods. These algorithms have been in the past compared to each other only according to their computational complexity, without been given the appropriate attention, as far as their numerical stability is concerned, being the most significant part of the algorithms' reliability. The present contribution attempts to fill this gap in the literature, since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity, but most of all by its numerical robustness. This paper exhaustively compares some well known recursive algorithms for the computation of Zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state. The experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance. (C) 2007 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2007.04.110	en
dc.identifier.isi	ISI:000253009100030	en
dc.identifier.volume	195	en
dc.identifier.issue	1	en
dc.identifier.spage	326	en
dc.identifier.epage	345	en