Discrete pulse transform of images and applications

dc.contributor.advisorAnguelov, Roumenen
dc.contributor.emailinger@up.ac.zaen
dc.contributor.postgraduateFabris-Rotelli, Inger Nicoletteen
dc.date.accessioned2013-09-06T17:04:54Z
dc.date.available2013-05-17en
dc.date.available2013-09-06T17:04:54Z
dc.date.created2013-04-17en
dc.date.issued2013-05-17en
dc.date.submitted2013-05-02en
dc.descriptionThesis (PhD)--University of Pretoria, 2013.en
dc.description.abstractThe LULU operators Ln and Un operate on neighbourhoods of size n. The Discrete Pulse Transform (DPT) of images is obtained via recursive peeling of so-called local maximum and minimum sets with the LULU operators as n increases from 1 to the maximum number of elements in the array. The DPT provides a new nonlinear decomposition of a multidimensional array. This thesis investigates the theoretical and practical soundness of the decomposition for image analysis. Properties for the theoretical justification of the DPT are provided as consistency of the decomposition (a pseudo-linear property), and its setting as a nonlinear scale-space, namely the LULU scalespace. A formal axiomatic theory for scale-space operators and scale-spaces is also presented. The practical soundness of the DPT is investigated in image sharpening, best approximation of an image, noise removal in signals and images, feature point detection with ideas to extending work to object tracking in videos, and image segmentation. LULU theory on multidimensional arrays and the DPT is now at a point where concrete signal, image and video analysis algorithms can be developed for a wide variety of applications.en
dc.description.availabilityunrestricteden
dc.description.departmentMathematics and Applied Mathematicsen
dc.identifier.citationFabris-Rotelli, IN 2012, Discrete pulse transform of images and applications, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/24290 >en
dc.identifier.otherD13/4/518/agen
dc.identifier.upetdurlhttp://upetd.up.ac.za/thesis/available/etd-05022013-114134/en
dc.identifier.urihttp://hdl.handle.net/2263/24290
dc.language.isoen
dc.publisherUniversity of Pretoriaen_ZA
dc.rights© 2012 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.en
dc.subjectTransform of images and applicationsen
dc.subjectNonlinear decompositionen
dc.subjectMultidimensional arrayen
dc.subjectUCTDen_US
dc.titleDiscrete pulse transform of images and applicationsen
dc.typeThesisen

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