Morphometric characterisation of the cerebral cortex can provide information about patterns of brain development and ageing and may be relevant for diagnosis and estimation of the progression of diseases such as Alzheimer's, Huntington's, and schizophrenia. Therefore, understanding and describing the differences between populations in terms of structural volume, shape and thickness is of critical importance. Methodologically, due to data quality, presence of noise, PV effects, limited resolution and pathological variability, the automated, robust and time-consistent estimation of morphometric features is still an unsolved problem. This thesis focuses on the development of tools for robust cross-sectional and longitudinal morphometric characterisation of the human cerebral cortex. It describes techniques for tissue segmentation, structural and morphometric characterisation, cross-sectional and longitudinally cortical thickness estimation from serial MRI images in both adults and neonates. Two new probabilistic brain tissue segmentation techniques are introduced in order to accurately and robustly segment the brain of elderly and neonatal subjects, even in the presence of marked pathology. Two other algorithms based on the concept of multi-atlas segmentation propagation and fusion are also introduced in order to parcelate the brain into its multiple composing structures with the highest possible segmentation accuracy. Finally, we explore the use of the Khalimsky cubic complex framework for the extraction of topologically correct thickness measurements from probabilistic segmentations without explicit parametrisation of the edge. A longitudinal extension of this method is also proposed. The work presented in this thesis has been extensively validated on elderly and neonatal data from several scanners, sequences and protocols. The proposed algorithms have also been successfully applied to breast and heart MRI, neck and colon CT and also to small animal imaging. All the algorithms presented in this thesis are available as part of the open-source package NiftySeg