A novel method that allows the development of surface point-based three-dimensional statistical shape models is presented. The method can be applied to shapes of arbitrary topology. Given a set of medical objects, a statistical shape model can be obtained by Principal Component Analysis. This technique requires that a set of complex shaped objects is represented as a set of vectors that on the one hand uniquely determine the shapes of the objects and on the other hand are suitable for a statistical analysis. The correspondence between the vector components and the respective shape features has to be the same in order for all shape parameter vectors to be considered. We present a novel approach to the correspondence problem for complex three-dimensional objects. The underlying idea is to develop a template shape and to fit this template to all objects to be analyzed The method is successfully applied to obtain a statistical shape model for the lumbar vertebrae. The obtained shape model is well suited to support image segmentation tasks.