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Discrete pulse transform of images and applications
Thesis (PhD)--University of Pretoria, 2013.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613703628652544 |
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| access_status_str | Open Access |
| author2 | Anguelov, Roumen |
| author_browse | Anguelov, Roumen |
| author_facet | Anguelov, Roumen |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Thesis (PhD)--University of Pretoria, 2013. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/24290 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:40:22.099Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/24290 Discrete pulse transform of images and applications Anguelov, Roumen inger@up.ac.za Fabris-Rotelli, Inger Nicolette Transform of images and applications Nonlinear decomposition Multidimensional array UCTD Thesis (PhD)--University of Pretoria, 2013. The 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. Mathematics and Applied Mathematics unrestricted 2013-09-06T17:04:54Z 2013-05-17 2013-09-06T17:04:54Z 2013-04-17 2013-05-17 2013-05-02 Thesis Fabris-Rotelli, IN 2012, Discrete pulse transform of images and applications, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/24290 > D13/4/518/ag http://hdl.handle.net/2263/24290 http://upetd.up.ac.za/thesis/available/etd-05022013-114134/ © 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. application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf application/pdf University of Pretoria |
| spellingShingle | Transform of images and applications Nonlinear decomposition Multidimensional array UCTD Discrete pulse transform of images and applications |
| title | Discrete pulse transform of images and applications |
| title_full | Discrete pulse transform of images and applications |
| title_fullStr | Discrete pulse transform of images and applications |
| title_full_unstemmed | Discrete pulse transform of images and applications |
| title_short | Discrete pulse transform of images and applications |
| title_sort | discrete pulse transform of images and applications |
| topic | Transform of images and applications Nonlinear decomposition Multidimensional array UCTD |
| url | http://hdl.handle.net/2263/24290 http://upetd.up.ac.za/thesis/available/etd-05022013-114134/ |