author = {Tobias Preusser},
  title = {Anisotropic geometric diffusion in image and image--sequence processing},
  school = {University Duisburg},
  year = {2003},
  type = {Dissertation},
  abstract = {In this thesis nonlinear anisotropic geometric diffusion methods for
	the processing of static images and image-sequences 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 level-sets, is capable
	of preserving important features of codimension 2, i.e. corners and
	edges of the level-sets. For the processing of image-sequences an
	anisotropic behavior in direction of the apparent motion of the level-sets
	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 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.},
  pdf = { 1}