Standard practice in quantitative structural neuroimaging is a segmentation into brain tissue, subcortical structures, fluid space and lesions followed by volume calculations of gross structures. On the other hand, it is evident that object characterization by size does only capture one of multiple aspects of a full structural characterization. Desirable parameters are local and global parameters like length, elongation, bending, width, complexity, bumpiness and many more. In neuroimaging research there is increasing evidence that shape analysis of brain structures provides new information which is not available by conventional volumetric measurements. This motivates development of novel morphometric analysis techniques answering clinical research questions which have been asked for a long time but which remained unanswered due to the lack of appropriate measurement tools. Challenges are the choice of biologically meaningful shape representations, robustness to noise and small perturba...