Learning Shape: Optimal Models for Analysing Natural Variability

Statistical shape models have wide application in biomedical image analysis – both for image segmentation and morphometry. This thesis addresses an important issue in shape modelling, that of establishing correspondence between a set of shapes. Current methods involve either manual annotation of the data (the current ‘gold standard’) or establishing correspondences in an essentially arbitrary manner. The thesis establishes a principled framework for establishing correspondences completely automatically by treating this as part of the learning process. Ideas from information theory are used to develop an objective function that measures the utility of a model, based on the minimum description length principle. Model-building can then be posed as the problem of finding the set of correspondences that optimise the objective function. Efficientmethods are presented for manipulating correspondences via re-parameterisation and for optimising the objective function. Practical results are presented for both 2D and 3D training sets of shapes from medical images. A quantitative evaluation shows that the resulting models have better compactness, generalisation ability and specificity than those obtained using existing methods. A 3D model is used in a practical application to explore the possibility of using 3Dmagnetic resonance images to detect differences in shape between the hippocampi of schizophrenic patients and normal controls. A more significant effect is demonstrated using the newmethod than that obtained using the best previous approach.