This portfolio thesis addresses several topics in the field of 3D medical image analysis. Automated methods are used to identify structures and points of interest within the body to aid the radiologist. The automated algorithms presented here incorporate many classical machine learning and imaging techniques, such as image registration, image filtering, supervised classification, unsupervised clustering, morphology and probabilistic modelling. All algorithms are validated against manually collected ground truth. Chapter two presents a novel algorithm for automatically detecting named anatomical landmarks within a CT scan, using a linear registration based atlas framework. The novel scans may contain a wide variety of anatomical regions from throughout the body. Registration is typically posed as a numerical optimisation problem. For this problem the associated search space is shown to be non-convex and so standard registration approaches fail. Specialised numerical optimisation schemes are developed to solve this problem with an emphasis placed on simplicity. A semi-automated algorithm for finding the centrelines of coronary arterial trees in CT angiography scans given a seed point is presented in chapter three. This is a modified classical region growing algorithm whereby the topology and geometry of the tree are discovered as the region grows. The challenges presented by the presence of large organs and other extraneous material in the vicinity of the coronary trees is mitigated by the use of an efficient modified 3D top-hat transform. Chapter four compares the accuracy of three unsupervised clustering algorithms when applied to automated tissue classification within the brain on 3D multi-spectral MR images. Chapter five presents a generalised supervised probabilistic framework for the segmentation of structures/tissues in medical images called a spatially varying classifier (SVC). This algorithm leverages off non-rigid registration techniques and is shown to be a generalisation of atlas based techniques and supervised intensity based classification. This is achieved by constructing a multivariate Gaussian classifier for each voxel in a reference scan. The SVC is applied in the context of tissue classification in multi-spectral MR images in chapter six, by simultaneously extracting the brain and classifying the tissues types within it. A specially designed pre-processing pipeline is presented which involves inter-sequence registration, spatial normalisation and intensity normalisation. The SVC is then applied to the problem of multi-compartment heart segmentation in CT angiography data with minimal modification. The accuracy of this method is shown to be comparable to other state of the art methods in the field.