Atrial fibrillation (AF) is the most common cardiac arrhythmia, characterized by chaotic electrical activation and unsynchronized contraction of the atria. This epidemic and its life-threatening complications and fast progression call for diagnosis and effective treatment as early as possible. Catheter ablation, an invasive procedure that establishes lesions to block the trigger points of AF and creates a barrier to the propagation of the arrhythmia, is an effective treatment for patients refractory to anti-arrhythmic drugs. However, the success rate of the first-time ablation may range from 30% to 75%, such that multiple ablation procedures may be recommended, and atrial mechanical function may be adversely affected.With evolving imaging and digital technologies, the objective of the study is to understand the underlying physiology of AF better and to provide tools to assist clinical decision-making. We analyze the correlations between recurrent arrhythmia and patient characteristics before ablation, including the left atrial shape extracted from computed tomography images. Non-invasive extraction of the anatomical structures of the heart is a crucial prerequisite. We first developed semi-automatic methods to segment the left atrium and the left atrial wall from images. Next, we achieved good segmentation results with a neural network model. Then, we studied markers of shape related to both global and local remodeling, and the quantification of adipose tissue, deploying diffeomorphometry and statistical analysis tools. Finally, we extended the work to the statistical analysis of temporal deformation. We proposed a symmetric reformulation of the pole ladder, which improves the numerical consistency and stability.