@INPROCEEDINGS{MiPrRuSg01,
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
Tomi},
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 = {http://numod.ins.uni-bonn.de/research/papers/public/MiPrRuSg01.pdf}
}