Image segmentation is one of the most critical tasks in the fields of image processing and computer vision. It is a preliminary step to several image processing schemes and its robustness and accuracy immediately impact the rest of the scheme. Applicability of image segmentation algorithms varies broadly from tracking in computer games to tumor monitoring and tissue classification in clinics. Over the last couple of decades, formulating the image segmentation as a curve evolution problem has been the state-of-the-art. Research groups have been competing in presenting efficient formulation, robust optimization and fast numerical implementation to solve the curve evolution problem. From another perspective, graph cuts have been gaining popularity over the last decade and its applicability in image processing and computer vision fields is vastly increasing. Recent studies are in favor of combining the benefits of variational formulations of deformable models and the graph cuts optimization tools. In this dissertation, we present a graph cut based framework for front propagation with application to 2D/3D image segmentation. As a starting point, we will introduce a Graph Cut Based Active Contour (GCBAC) model that serves as a unified framework that combines the advantages of both level sets and graph cuts. Mainly, a discrete formulation of the active contour without edges model introduced by Chan and Vese will be presented. We will prove that the discrete formulation of the energy function is graph representable and can be minimized using the min-cut/max-flow algorithm. The major advantages of our model over that of Chan and Vese are: (1) A global minimum will be obtained because graph cuts are used in the optimization step and hence, our segmentation approach is not sensitive to initialization. (2) The polynomial time complexity of the min-cut/max-flow algorithm makes our algorithm much faster than the level sets approaches. Meanwhile, all the advantages associated with the level sets formulation such as robustness to noise, topology changes and ill-defined edges are preserved. The basic formulation will be presented for 2D scalar images. The GCBAC will be the core of this dissertation upon which extensions will be presented to establish the scalability of the model. Extensions of the model to segment vector valued images such as RGB images and volumetric data such as brain MRI scans will be provided. The dissertation will also present a multiphase image segmentation approach based on GCBAC. Further challenges such as intensities inhomogeneities and shared intensity distributions among different objects will be discussed and resolved in the course of this dissertation. The dissertation will include pictorial results, as well as, quantitative assessments that illustrate the performance of the proposed models.