Minimally invasive technique (MIS) revolutionized the field of surgery for its shorter hospitalization time, lower complication rates, and ultimately reduced morbidity and mortality. However, one of the critical challenges that prevent it from reaching the full potentials is the restricted visualization from the traditional monocular camera systems at the presence of tissue deformations. This dissertation aims to design a new approach which can provide the surgeons with real time 3D visualization of complete organ deformations during the MIS operation. This new approach even allows the surgeon to see through the wall of an organ rather than just looking at its surface. The proposed design consists of two stages. The first training stage identified the deformation subspaces from a training data set in the transformed spherical harmonic domain, such that each surface can be sparsely represented in the structured dictionary with low dimensionality. This novel idea is based on our experimental discovery that the spherical harmonic coefficients of any organ surface lie in specific low dimensional subspaces. The second reconstruction stage reconstructs the complete deformations in realtime using surface samples obtained with an optical device from a limited field of view while applying the structured dictionary. The sparse surface representation algorithm is also applied to ultrasound image enhancement and efficient surgical simulation. The former is achieved by fusing ultrasound samples 5 with optical data under proper weighting strategies. The high speed of surgical simulation is obtained by decreasing the computational cost based on the high compactness of the surface representation algorithm. In order to verify the proposed approaches, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques. Then ex-vivo experiments are conducted on freshly excised porcine kidneys utilizing a 3D MRI machine, a 3D optical device and an ultrasound machine to further test the feasibility under practical settings. / text