Cardiovascular disease is the primary cause of death in many developed countries. To reduce morbidity, quantitative analysis of global and local cardiac function is valuable for understanding normal and abnormal physiology and patient diagnosis. Recent advances in cardiac imaging offer a non-invasive means to capture 4-D (3-D+t) dynamics of the heart. However, as cardiac data becomes increasingly available in 4-D, it is challenging to analyze the mass amount of data. This dissertation focuses on two important and related topics of cardiac image analysis, namely cardiac image segmentation and deformation analysis. First, we develop a coupled deformable model which simultaneously segments the endocardium and epicardium of the left ventricle. This coupled deformable model takes into account the incompressibility property of the myocardium during a cardiac cycle, and takes this property as a vital constraint in myocardial segmentation. We formulate the segmentation problem in a probabilistic framework, which simultaneously evolves the endocardial and epicardial surfaces, each driven by its regional intensity distribution while maintaining the coupling between the endocardial and epicardial surfaces in order to preserve the myocardial volume. Second, we develop a subject-specific dynamical model (SSDM) which simultaneously takes into account cardiac dynamics and inter-subject variability. It is distinct from previous models in the sense that it is both subject-specific and dynamic, while the existing models are either static models or generic dynamical models. In addition, we develop a dynamic prediction algorithm that can progressively identify the specific motion patterns of an input sequence based on the shapes observed in past frames. This SSDM is incorporated into the segmentation process in a recursive Bayesian framework, which segments each frame based on intensity information of the current frame, as well as the prediction from past frames. Third, we develop a joint segmentation and deformation analysis framework, which combines the SSDM developed in the second part with the shape-based tracking algorithm previously developed at Yale Image Processing and Analysis Group (IPAG). In particular, we use the segmentation results as a guide in selecting feature points with reliable geometric properties. The extract feature points are then fed into the Generalized Robust Point Matching (G-RPM) approach with boundary element method (BEM) strategy to estimate physically plausible displacements within the myocardium. The estimated dense displacements are then used to compute strain map of the left ventricular myocardium.