Tobias Preußer :Anisotropic geometric diffusion in image and image-sequence processingBetreuerIn: Prof. Dr. Martin Rumpf , Universität Duisburg-Essen, Standort Duisburg, Fakultät für Naturwissenschaften, Institut für Mathematik GutachterIn: Prof. Dr. Martin Rumpf , Universität Duisburg-Essen,
Standort Duisburg, Fakultät für Naturwissenschaften, Institut
für Mathematik
Schlüsselwörter in Englisch: level-set, curve, curvarture, evolution, surface, morphologic, parabolic PDE, finite elements, regularization |
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Klassifikation | |||||
Sachgruppe der DNB: 27 Mathematik | |||||
Abstrakt | |||||
Abstrakt in Englisch Important for the processing of noisy images is a suitable regularization of the data. Different approaches are discussed and the results of a local projection approach onto a polynomial space is compared with the convolution with kernels having compact support. For the nonlinear problems the existence of viscosity solutions is shown by using a result of Giga et. al. for the linearized problems together with a fixed point argument. The discretization of the models is done using a semi-implicit time-discretization together with finite elements on regular quadrilateral and hexahedral grids. Furthermore for the processing of image-sequences an operator splitting scheme is derived, which enables to solve this high dimensional problem with moderate effort. |
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