Projekt: DFG Project: 2D / 3D Image processing
Forscher: Wietzke L. , Fleischmann O.This research project deals with the geometrical and structural description of multidimensional signals. These signals are not limited to but focus on image signals in two and three dimensions. Multidimensional signals can be described by geometrical properties arising from certain group operations acting on the signal. These geometrical properties are for example orientation, apex angle, or curvature. Further, depending on the signal model, the signals allow a structural description. The most prominent example is the local phase of sinusoidal signals. We focus on the estimation of geometrical and structural parameters of these signals with emphasis on techniques which allow a direct exact calculation of the parameters without using any optimization algorithms. To obtain a deeper geometrical knowledge of the signal geometry we identify the parameters with points of certain signal manifolds such that transformations acting on these signal manifolds encode the transformations acting on the signal. Occasionally we model these manifolds with the help of certain geometrical algebras which provide natural descriptions of the signals.