Anisotropic geometric diffusion in image and image-sequence processing Anisotrope geometrische Diffusion in der Verarbeitung von Bildern und Bildsequenzen
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.
Advisor:Prof. Dr. Martin Rumpf; Prof. Dr. Reiner Schätzle
Source Type:Master's Thesis
Keywords:mathematik universitaet duisburg essen
Date of Publication:07/02/2003