Abstract : In this thesis, we addressed the problem of comparing cardiac anatomy and function from medical images. The rst part focuses on cardiac anatomy with a statistical study of cardiac ber architecture from di usion tensor magnetic resonance imaging (DT-MRI). The second part focuses on a joint comparison of cardiac anatomy and function with the non-linear spatio-temporal registration of two sequences of 4D CT sequences of di erent patients or of the same patient at di erent times. Cardiac muscle bers are locally bound to form a plane called the laminar sheets. Moreover, the orientation of bers and laminar sheets is spatially variable in the myocardium. This complex organisation of cardiac muscle bers has an important in the electromechanical behaviour of the heart, and thus in cardiac function. We performed a study of this cardiac ber architecture from DT-MRI. To achieve it, we proposed novel computational tools for the statistical analysis of a population of di usion tensors based on the Log-Euclidean metric. The novelty of this approach lies in a statistical analysis performed directly on diffusion tensors (symmetric de nite positive matrices) by analyzing their covariance matrix giving the variability of ber and laminar sheet directions among the population. We applied this computational framework to a dataset of canine DT-MRI acquired ex vivo not only providing an average model (or atlas) of cardiac ber architecture but also revealing a consistency of ber orientation and a higher variability of laminar sheet orientations. Then, this atlas of canine hearts is compared to a human heart and a synthetic model currently used for electromechanical simulations or image analysis. The human heart had similarities in ber orientation whereas discrepancies in laminar sheet orientation. The synthetic model was too simple to describe in details to describe properly the complexity of ber architecture. The acquisition of time-series of cardiac images gives the opportunity to observe cardiac motion and thus its function in addition to its anatomy. In order to compare this cardiac function, we proposed a novel non-linear spatio-temporal registration algorithm of sequences of images. The spatio-temporal registration is decoupled into a temporal registration that aims at mapping corresponding physiological events and into a spatial registration that aims at mapping corresponding anatomical points ensuring a consistency with their respective motion. This consistency is ensured by de ning trajectory constraints linking intra-sequence transformations describing cardiac motion to inter-sequence transformations describing anatomical di erences over time. Under these trajectory constraints, the 4D spatial registration problem can be simpli ed to 3D multichannel registration problem solved using a new version of the Di eomorphic Demons called the Multichannel Di eomorphic Demons. This new registration method is applied to the inter-subject registration of 4D cardiac CT sequences for evaluation. Its comparison to other possible methods showed that it was the best compromise between accuracy, spatial and temporal regularization, and computation times. A possible clinical application of the spatiotemporal nonlinear registration is proposed by comparing cardiac anatomy and function before and after therapy by studying the remodeling strains over a cardiac cycle.