[1] 
T. Preusser.
Anisotropic geometric diffusion in image and imagesequence
processing.
Dissertation, University Duisburg, 2003. [ bib  .pdf 1 ] In this thesis nonlinear anisotropic geometric diffusion methods for the processing of static images and imagesequences are discussed. The models depend only on the morphology of the underlying data, and thus they are invariant under monotone transformations of the gray values. The evolution, which depends on the principal curvatures and the principal directions of curvature of levelsets, is capable of preserving important features of codimension 2, i.e. corners and edges of the levelsets. For the processing of imagesequences an anisotropic behavior in direction of the apparent motion of the levelsets is prescribed. 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 semiimplicit timediscretization together with finite elements on regular quadrilateral and hexahedral grids. Furthermore for the processing of imagesequences an operator splitting scheme is derived, which enables to solve this high dimensional problem with moderate effort.
