Heart failure is a major challenge for which it is essential to significantly improve patient assessment and follow-up. While imaging is essential, the heterogeneity of abnormalities in cardiac structure and function complicates the analyses. It is crucial to go beyond the imaging measurements done in clinical routine, which are highly inadequate for characterizing the complexity of the disease. Recent advances in imaging and machine learning allow extracting fine physiological biomarkers from images. The other major challenge of computational analyses is the integration of such a deluge of data at a population scale, which poses a number of challenges. It requires considering descriptors of cardiac shape and function more complex than scalar measurements. These descriptors may be high-dimensional data, to be mapped to a reference (an "atlas") before any comparison. Their analysis should preserve their mathematical and physiological properties (using non-linear learning methods). Finally, multi-parametric analysis of these data is difficult and computationally expensive, due to their heterogeneous types and complexity/dimensionality. I have developed recognized expertise on the key techniques for such population-scale analyses (statistical atlases and representation learning, in cardiac imaging). This document offers a summary of the major contributions I have been able to propose in response to these issues, bringing together the work published with my collaborators and the staff I have supervised since my thesis, and particularly since I joined the CREATIS laboratory as MCU in 2016. It also provides an overview of my professional career in terms of research, teaching, and scientific supervision. Finally, it presents the main current projects I’m involved in and the perspectives that these may bring, particularly from the point of view of transferring methodological developments to the scale of large clinical studies.