The task of automatically segmenting 3-D surfaces representing object boundaries is important in quantitative analysis of volumetric images, which plays a vital role in numerous biomedical applications. For the diagnosis and management of disease, segmentation of images of organs and tissues is a crucial step for the quantification of medical images. Segmentation finds the boundaries or, limited to the 3-D case, the surfaces, that separate regions, tissues or areas of an image, and it is essential that these boundaries approximate the true boundary, typically by human experts, as closely as possible. Recently, graph-based methods with a global optimization property have been studied and used for various applications. Sepecifically, the state-of-the-art graph search (optimal surface segmentation) method has been successfully used for various such biomedical applications. Despite their widespread use for image segmentation, real world medical image segmentation problems often pose difficult challenges, wherein graph based segmentation methods in its purest form may not be able to perform the segmentation task successfully. This doctoral work has a twofold objective. 1)To identify medical image segmentation problems which are difficult to solve using existing graph based method and develop novel methods by employing graph search as a building block to improve segmentation accuracy and efficiency. 2) To develop a novel multiple surface segmentation strategy using deep learning which is more computationally efficient and generic than the exisiting graph based methods, while eliminating the need for human expert intervention as required in the current surface segmentation methods. This developed method is possibly the first of its kind where the method does not require and human expert designed operations. To accomplish the objectives of this thesis work, a comprehensive framework of graph based and deep learning methods is proposed to achieve the goal by successfully fulfilling the follwoing three aims. First, an efficient, automated and accurate graph based method is developed to segment surfaces which have steep change in surface profiles and abrupt distance changes between two adjacent surfaces. The developed method is applied and validated on intra-retinal layer segmentation of Spectral Domain Optical Coherence Tomograph (SD-OCT) images of eye with Glaucoma, Age Related Macular Degneration and Pigment Epithelium Detachment. Second, a globally optimal graph based method is developed to attain subvoxel and super resolution accuracy for multiple surface segmentation problem while imposing convex constraints. The developed method was applied to layer segmentation of SD-OCT images of normal eye and vessel walls in Intravascular Ultrasound (IVUS) images. Third, a deep learning based multiple surface segmentation is developed which is more generic, computaionally effieient and eliminates the requirement of human expert interventions (like transformation designs, feature extrraction, parameter tuning, constraint modelling etc.) required by existing surface segmentation methods in varying capacities. The developed method was applied to SD-OCT images of normal and diseased eyes, to validate the superior segmentaion performance, computation efficieny and the generic nature of the framework, compared to the state-of-the-art graph search method.