This work approaches the problems of image segmentation and image registration against the background of biomedical applications. The first part of the dissertation is devoted to the development of a novel approach for the computation of binary edge maps. In contrast to existing methods, the edges obtained are truly binary, i.e., no thresholding has to be performed. A rigorous mathematical analysis covering both the continuum as well as a discrete finite element setting is carried out. An extensive investigation of practical results obtained by the proposed approach is presented and its performance compared to existing segmentation techniques is discussed. The second part of the thesis focuses on image registration. Based on previously developed techniques a registration strategy for edge maps based on successive deblurring is presented. Theoretical findings are summarized and a practical implementation is discussed. Finally the proposed segmentation approach is embedded in the introduced registration framework. It is shown that a combination of the developed strategies is indeed capable of successfully registering image sequences that pose to be challenging for classical intensity based registration techniques.