<p> Image segmentation entails the partitioning of an image domain, usually two or three dimensions, so that each partition or segment has some meaning that is relevant to the application at hand. Accurate image segmentation is a crucial challenge in many disciplines, including medicine, computer vision, and geology. In some applications, heterogeneous pixel intensities; noisy, ill-defined, or diffusive boundaries; and irregular shapes with high variability can make it challenging to meet accuracy requirements. Various segmentation approaches tackle such challenges by casting the segmentation problem as an energy-minimization problem, and solving it using efficient optimization algorithms. These approaches are broadly classified as either region-based or edge (surface)-based depending on the features on which they operate. </p><p> The focus of this dissertation is on the development of a surface-based energy model, the design of efficient formulations of optimization frameworks to incorporate such energy, and the solution of the energy-minimization problem using graph cuts. This dissertation utilizes a set of four papers whose motivation is the efficient extraction of the left atrium wall from the late gadolinium enhancement magnetic resonance imaging (LGE-MRI) image volume. This dissertation utilizes these energy formulations for other applications, including contact lens segmentation in the optical coherence tomography (OCT) data and the extraction of geologic features in seismic data. </p><p> Chapters 2 through 5 (papers 1 through 4) explore building a surface-based image segmentation model by progressively adding components to improve its accuracy and robustness. The first paper defines a parametric search space and its discrete formulation in the form of a multilayer three-dimensional mesh model within which the segmentation takes place. It includes a generative intensity model, and we optimize using a graph formulation of the <i> surface net</i> problem. The second paper proposes a Bayesian framework with a Markov random field (MRF) prior that gives rise to another class of surface nets, which provides better segmentation with smooth boundaries. The third paper presents a maximum a posteriori (MAP)-based surface estimation framework that relies on a generative image model by incorporating global shape priors, in addition to the MRF, within the Bayesian formulation. Thus, the resulting surface not only depends on the learned model of shapes,but also accommodates the test data irregularities through smooth deviations from these priors. Further, the paper proposes a new shape parameter estimation scheme, in closed form, for segmentation as a part of the optimization process. Finally, the fourth paper (under review at the time of this document) presents an extensive analysis of the MAP framework and presents improved mesh generation and generative intensity models. It also performs a thorough analysis of the segmentation results that demonstrates the effectiveness of the proposed method qualitatively, quantitatively, and clinically. </p><p> Chapter 6, consisting of unpublished work, demonstrates the application of an MRF-based Bayesian framework to segment coupled surfaces of contact lenses in optical coherence tomography images. This chapter also shows an application related to the extraction of geological structures in seismic volumes. Due to the large sizes of seismic volume datasets, we also present fast, approximate surface-based energy minimization strategies that achieve better speed-ups and memory consumption.</p>

<p> Eye exam can be as efficacious as physical one in determining health concerns. Retina screening can be the very first clue to detecting a variety of hidden health issues including pre-diabetes and diabetes. Through the process of clinical diagnosis and prognosis; ophthalmologists rely heavily on the binary segmented version of retina fundus image; where the accuracy of segmented vessels, optic disc and abnormal lesions extremely affects the diagnosis accuracy which in turn affect the subsequent clinical treatment steps. This thesis proposes an automated retinal fundus image segmentation system composed of three segmentation subsystems follow same core segmentation algorithm. Despite of broad difference in features and characteristics; retinal vessels, optic disc and exudate lesions are extracted by each subsystem without the need for texture analysis or synthesis. For sake of compact diagnosis and complete clinical insight, our proposed system can detect these anatomical structures in one session with high accuracy even in pathological retina images. </p><p> The proposed system uses a robust hybrid segmentation algorithm combines adaptive fuzzy thresholding and mathematical morphology. The proposed system is validated using four benchmark datasets: DRIVE and STARE (vessels), DRISHTI-GS (optic disc), and DIARETDB1 (exudates lesions). Competitive segmentation performance is achieved, outperforming a variety of up-to-date systems and demonstrating the capacity to deal with other heterogenous anatomical structures. </p><p>