Technological innovations in medical imaging is revolutionizing the field of medicine by expanding from simple visualization and inspection of human anatomical struc- tures to surgical planning and simulation, intra-operative image guided surgery, ra- diotherapy planning, and for tracking the progress of disease in patients. The problem of automatic diagnoses of disease by identifying diagnostically significant information about imaged anatomical structures through medical imaging modalities has been studied by many researchers with numerous novel contributions. However, extracting clinically useful information from medical images, in automatic and robust manner through efficient and accurate algorithms for computer-based medical image analysis, is still an open and challenging area of current research. Modeling shapes for digital image processing and analysis in the context of human visual system is an area extensively explored by researchers for biomedical, industrial, and remote sensing applications. Statistical models of shape and appearance built from labeled set of training samples proved to be powerful tools for interpreting medical images. The emerging information-rich medical imaging modalities and sub- sequent higher structural complexity in imagined image has increased computational demand and need of more robust algorithms for image analysis. In this thesis, we develop a shape modeling system for sphere shape image objects using wavelets. In our shape modeling approach, we develop and integrate various simple algorithms to formulate 2D and 3D hexagonal approximation models corre- sponding to 3D sphere shape structure. We demonstrate applications of our developed algorithms to image segmentation and tracking, left ventricle shape modeling, iden- tification of end diastole (maximum filling) and end systole (maximum contraction) phases in normal cardiac cycle, and computation of left ventricle ejection fraction. Developing of fairly simple models for sphere like image objects (structures) in critical applications such as in medical image analysis is a crucial and difficult task. Our proposed regular hexagonal approximation model is insensitive to variations in size, translation, and rotation. These features are desirable in pattern recognition and machine learning applications. The results have shown the prominence of our developed algorithms over previous approaches with less computational requirements.