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

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.