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Nonlinear diffusion filtering of images using the topological gradient approach to edges detection

  • In this thesis, the problem of nonlinear diffusion filtering of gray-scale images is theoretically and numerically investigated. In the first part of the thesis, we derive the topological asymptotic expansion of the Mumford-Shah like functional. We show that the dominant term of this expansion can be regarded as a criterion to edges detection in an image. In the numerical part, we propose the finite volume discretization for the Catté et al. and the Weickert diffusion filter models. The proposed discretization is based on the integro-interpolation method introduced by Samarskii. The numerical schemes are derived for the case of uniform and nonuniform cell-centered grids of the computational domain \(\Omega \subset \mathbb{R}^2\). In order to generate a nonuniform grid, the adaptive coarsening technique is proposed.

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Author:Monika Muszkieta
URN (permanent link):urn:nbn:de:hbz:386-kluedo-21730
Advisor:Helmut Neunzert
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2007/08/30
Date of the Publication (Server):2008/03/17
Tag:image analysis; nonlinear diffusion filtering; topological asymptotic expansion
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J20 Variational methods for second-order elliptic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Mxx Basic methods / 80M35 Asymptotic analysis
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011