Geometric and Topological Variational Methods for Imaging and Computer Vision

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dc.contributor.advisor Hamid Krim, Committee Chair en_US
dc.contributor.advisor Griff Bilbro, Committee Member en_US
dc.contributor.advisor Gianluca Lazzi, Committee Member en_US
dc.contributor.advisor Robert White, Committee Member en_US
dc.contributor.author Ben Hamza, Abdessamad en_US
dc.date.accessioned 2010-04-02T18:51:28Z
dc.date.available 2010-04-02T18:51:28Z
dc.date.issued 2004-02-01 en_US
dc.identifier.other etd-10282003-150421 en_US
dc.identifier.uri http://www.lib.ncsu.edu/resolver/1840.16/4317
dc.description.abstract The great challenge in signal/image processing is to devise computationally efficient and optimal algorithms for estimating signals/images contaminated by noise and preserving their geometrical structure. The first problem addressed is this thesis is image denoising formulated in the calculus of variations framework. We propose robust variational models for image denoising by numerically solving partial differential equations. The core idea behind our proposed approaches is to use geometric insight in helping construct regularizing functionals and avoiding a subjective choice of a prior in maximum a posteriori estimation. Using tools from robust statistics and information theory, we show that we can extend this strategy and develop two gradient descent flows for image denoising with a demonstrated performance through illustrating experimental results. The rest of the thesis is devoted to a joint exploitation of geometry and topology of objects for as parsimonious as possible representation of objects and its subsequent application in object classification and recognition problems. Attempting to extend current approaches to image registration which have generally relied on the assumption of 2D images, we propose a novel technique for 3D object matching using a joint exploitation of geometry and topology. The key idea consists of capturing geometry along all topologically homogeneous parts of an object by way of level curves superimposed on a Reeb graph usually extracted by way of the object critical points. This resulting skeletal representation, however, is not rotationally invariant. We propose a new methodology called {em geodesic shape distribution} that lifts this limitation and which we apply to 3D object matching. The central idea is to encode a 3D shape into a 1D geodesic shape distribution. Object matching is then achieved by calculating an information-theoretic measure of dissimilarity between the resulting geodesic shape distributions in a lower dimensional space. Illustrating numerical experiments with synthetic and real data are provided to demonstrate the potential and the much improved performance of the proposed methodology in 3D object matching. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject image denoising en_US
dc.subject variational models en_US
dc.subject 3D object recognition en_US
dc.subject differential geometry and topology en_US
dc.subject geodesic distance en_US
dc.title Geometric and Topological Variational Methods for Imaging and Computer Vision en_US
dc.degree.name PhD en_US
dc.degree.level dissertation en_US
dc.degree.discipline Electrical Engineering en_US


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