To support diagnosis and therapy, it is a fundamental aim of medical image processing to describe morphological characteristics of pathological structures or image objects in general. Different authors propose quantitative methods of description like bounding boxes[l], fourier descriptors[2] or contour moments [3]. Unfortunately, these methods either don't supply a complete, respectively precise description of the object or only operate on two-dimensional images.

Among the range of application are systems to classify lung nodules [4] or to help the diagnosis of brain tumors [5]. In this paper we present a method to analyze the morphology or shape of any three-dimensional object in order to describe it mathematically well-defined. We show how the description can be used to perform statistical operations on morphologies. The method presented in this paper was developed to assist the planning of craniofacial surgery. We analyze the shape of a given set of skull CT-data and use the mathematical description to statistically calculate the average shape of the skulls.