Statistical Analysis of Medical Shapes and Directional Data

Abstract

The use of statistical shape analysis in medical settings has increased during the last decades. This thesis presents contributions to three major topics of statistical shape analysis with application to medical problems. These topics are: the modeling of the shape by a geometrical model, the study of rotational shape deformations and the comparison of shapes between populations. Paper I presents a semiautomatic method for the prostate segmentation in radiotherapy treatment planning. To facilitate the manual delineation of the prostate in medical images, an intuitive approach is developed for 3D modeling of the prostate by slice-wise best fitting ellipses in each image. The focus is to estimate a mean shape from a set of training data and to register the estimate by the definition of a few control points in a new patient. The obtained results are fairly accurate and suggest possible time saving effects. Paper II studies rotational deformations of objects. The rotational deformations such as twisting or bending have been observed as the major variations in some medical applications, where the features of the deformed 3D objects are directional data. Models and estimators are proposed for one or the composition of two simple deformations based on the directional features. The proposed method uses a generalized small circle fitting on the unit sphere. Two analyses of 3D object data are presented: one using skeletal representations in medical image analysis as well as one from biomechanical gait analysis of the knee joint. Paper III investigates shape mean differences between two populations using a hypothesis test. Several aspects of a sensitive hypothesis test are elaborated which support accurate statistics of populations. A novel permutation test is developed for data whose representations include both Euclidean and non-Euclidean elements. By supporting non-Euclidean components, the proposed hypothesis test is novel in the study of morphological shape differences. Both global and local analyses showed statistically significant differences between first episode schizophrenics and controls and demonstrated the sensitivity of the method.