On Anisotropic Geometric Diffusion in 3D Image Processing and Image Sequence Analysis

Abstract

A morphological multiscale method in 3D image and 3D image sequenceprocessing is discussed which identifies edges on level sets andthe motion of features in time. Based on these indicator evaluationthe image data is processed applying nonlinear diffusion and thetheory of geometric evolution problems. The aim is to smooth levelsets of a 3D image while preserving geometric features such as edgesand corners on the level sets and to simultaneously respect the motionand acceleration of object in time. An anisotropic curvature evolutionis considered in space. Whereas, in case of an image sequence a weakcoupling of these separate curvature evolutions problems is incorporatedin the time direction of the image sequence. The time of the actualevolution problem serves as the multiscale parameter. The spatialdiffusion tensor depends on a regularized shape operator of the evolvinglevel sets and the evolution speed is weighted according to an approximationof the apparent acceleration of objects. As one suitable regularizationtool local L^2--projection onto polynomials is considered. A spatialfinite element discretization on hexahedral meshes, a semi-implicit,regularized backward Euler discretization in time, and an explicitcoupling of subsequent images in case of image sequences are thebuilding blocks of the algorithm. Different applications underlinethe efficiency of the presented image processing tool.