This thesis presents image-based methods for the analysis of cardiac motion to enable group-wise statistics, automatic diagnosis and longitudinal study. This is achieved by combining advanced medical image processing with machine learning methods and statistical modelling. The first axis of this work is to define an automatic method for the segmentation of the myocardium. We develop a very-fast registration method based on convolutional neural networks that is trained to learn inter-subject heart registration. Then, we embed this registration method into a multi-atlas segmentation pipeline. The second axis of this work is focused on the improvement of cardiac motion tracking methods in order to define relevant low-dimensional representations. Two different methods are developed, one relying on Barycentric Subspaces built on ref- erences frames of the sequence, and another based on a reduced order representation of the motion from polyaffine transformations. Finally, in the last axis, we apply the previously defined representation to the problem of diagnosis and longitudinal analysis. We show that these representations encode relevant features allowing the diagnosis of infarcted patients and Tetralogy of Fallot versus controls and the analysis of the evolution through time of the cardiac motion of patients with either cardiomyopathies or obesity. These three axes form an end to end framework for the study of cardiac motion starting from the acquisition of the medical images to their automatic analysis. Such a framework could be used for diagonis and therapy planning in order to improve the clinical decision making with a more personalised computer-aided medicine.