author = {Mikula, K. and Preu{\ss}er, T. and Rumpf, M. and Sgallari, F.},
  title = {On Anisotropic Geometric Diffusion in 3{D} Image Processing and Image
	Sequence Analysis},
  booktitle = {Trends in Nonlinear Analysis},
  year = {2001},
  editor = {Markus Kirkilionis and Susanne Kr\"omker and Rolf Rannacher and Friedrich
  abstract = {A morphological multiscale method in 3D image and 3D image sequence
	processing is discussed which identifies edges on level sets and
	the motion of features in time. Based on these indicator evaluation
	the image data is processed applying nonlinear diffusion and the
	theory of geometric evolution problems. The aim is to smooth level
	sets of a 3D image while preserving geometric features such as edges
	and corners on the level sets and to simultaneously respect the motion
	and acceleration of object in time. An anisotropic curvature evolution
	is considered in space. Whereas, in case of an image sequence a weak
	coupling of these separate curvature evolutions problems is incorporated
	in the time direction of the image sequence. The time of the actual
	evolution problem serves as the multiscale parameter. The spatial
	diffusion tensor depends on a regularized shape operator of the evolving
	level sets and the evolution speed is weighted according to an approximation
	of the apparent acceleration of objects. As one suitable regularization
	tool local $L^2$--projection onto polynomials is considered. A spatial
	finite element discretization on hexahedral meshes, a semi-implicit,
	regularized backward Euler discretization in time, and an explicit
	coupling of subsequent images in case of image sequences are the
	building blocks of the algorithm. Different applications underline
	the efficiency of the presented image processing tool.},
  pdf = { 1}