In this diploma thesis a skeleton-based matching technique for 2D shapes is introduced. First, current approaches for the matching of shapes will be presented. The basics of skeleton-based matchings will be introduced. In the context of this thesis, a skeleton-based matching approach was implemented as presented in the original paper. This implementation is evaluated by performing a similarity search in three shape databases. Strengths and limitations of the approach are pointed out. In addition, the introduced algorithm will be examined with respect to extending it towards matching of 3D objects. In particular, the approach is applied to medical data sets: Pre- and postoperative CT images of the abdominal aorta of one patient will be compared. Problems and approaches for matching of 3D objects in general and blood vessels in particular will be presented.