The study of anatomical morphology is of great importance to medical imaging, with applications varying from clinical diagnosis to computer-aided surgery. To this end, automated tools are required for accurate extraction of the anatomical boundaries from the image data and detailed interpretation of morphological information. This thesis introduces a novel approach to shape-based analysis of medical images based on Inter- Landmark Descriptors (ILDs). Unlike point coordinates that describe absolute position, these shape variables represent relative configuration of landmarks in the shape. The proposed work is motivated by the inherent difficulties of methods based on landmark coordinates in challenging applications. Through explicit invariance to pose parameters and decomposition of the global shape constraints, this work permits anatomical shape analysis that is resistant to image inhomogeneities and geometrical inconsistencies. Several algorithms are presented to tackle specific image segmentation and analysis problems, including automatic initialisation, optimal feature point search, outlier handling and dynamic abnormality localisation. Detailed validation results are provided based on various cardiovascular magnetic resonance datasets, showing increased robustness and accuracy.