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<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> While MR-only treatment planning has shown promise, there are still several well-known challenges that are currently limiting widespread clinical implementation. Firstly, MR images are affected by both patient-induced and system-level geometric distortions that can significantly degrade treatment planning accuracy. In addition, the availability of comprehensive distortion analysis software is currently limited. Also while many groups have been working toward a synthetic CT solution, further study is needed on the implementation of synCTs as the reference datasets for linac-based image-guided radiation therapy (IGRT) to help determine their robustness in an MR-only workflow. </p><p> To determine candidate materials for phantom and software development, 1.0 T MR and CT images were acquired of twelve urethane foam samples of various densities and strengths. Samples were precision machined to accommodate 6 mm diameter paintballs used as landmarks. Final material candidates were selected by balancing strength, machinability, weight, and cost. Bore sizes and minimum aperture width resulting from couch position were tabulated from the literature. Bore geometry and couch position were simulated using MATLAB to generate machine-specific models to optimize the phantom build. Previously developed software for distortion characterization was modified for several magnet geometries, compared against previously published 1.0 T results, and integrated into the 3DSlicer application platform. </p><p> To evaluate the performance of synthetic CTs in an image guided workflow, magnetic resonance simulation and CT simulation images were acquired of an anthropomorphic skull phantom and 12 patient brain cancer cases. SynCTs were generated using fluid attenuation inversion recovery, ultrashort echo time, and Dixon data sets through a voxel-based weighted summation of 5 tissue classifications. The DRRs were generated from the phantom synCT, and geometric fidelity was assessed relative to CT-generated DRRs through bounding box and landmark analysis. An offline retrospective analysis was conducted to register cone beam CTs to synCTs and CTs using automated rigid registration in the treatment planning system. Planar MV and KV images were rigidly registered to synCT and CT DRRs using an in-house script. Planar and volumetric registration reproducibility was assessed and margin differences were characterized by the van Herk formalism. </p><p> Over the sampled FOV, non-negligible residual gradient distortions existed as close as 9.5 cm from isocenter, with a maximum distortion of 7.4mm as close as 23 cm from isocenter. Over 6 months, average gradient distortions were -0.07&plusmn;1.10 mm and 0.10&plusmn;1.10 mm in the x and y-directions for the transverse plane, 0.03&plusmn;0.64 and -0.09&plusmn;0.70 mm in the sagittal plane, and 0.4&plusmn;1.16 and 0.04&plusmn;0.40 mm in the coronal plane. After implementing 3D correction maps, distortions were reduced to &lt; 1 pixel width (1mm) for all voxels up to 25 cm from magnet isocenter. </p><p> Bounding box and landmark analysis of phantom synCT DRRs were within 1 mm of CT DRRs. Absolute planar registration shift differences ranged from 0.0 to 0.7 mm for phantom DRRs on all treatment platforms and from 0.0 to 0.4 mm for volumetric registrations. For patient planar registrations, the mean shift differences were 0.4&plusmn;0.5 mm, 0.0&plusmn;0.5 mm, and 0.1&plusmn;0.3 mm for the superior-inferior (S-I), left-right (L-R), and anterior-posterior (A-P) axes, respectively. The mean shift differences in volumetric registrations were 0.6&plusmn;0.4 mm (range, 0.2 to 1.6 mm), 0.2&plusmn;0.4 mm, and 0.2&plusmn;0.3 mm for the S-I, L-R, and A-P axes, respectively. The CT-SIM and synCT derived margins were &lt;0.3mm different. </p><p> This work has characterized the inaccuracies related to GNL distortion for a previously uncharacterized MR-SIM system at large FOVs, and established that while distortions are still non-negligible after current vendor corrections are applied, simple post-processing methods can be used to further reduce these distortions to less than 1mm for the entire field of view. Additionally, it was important to not only establish effective corrections, but to establish the previously uncharacterized temporal stability of these corrections. This work also developed methods to improve the accessibility of these distortion characterizations and corrections. We first tested the application of a more readily available 2D phantom as a surrogate for 3D distortion characterization by stepping the table with an integrated batch script file. Later we developed and constructed a large modular distortion phantom using easily obtainable materials, and showed and constructed a large modular distortion phantom using easily obtainable materials, and used it to characterize the distortion on several widely available MR systems. To accompany this phantom, open source software was also developed for easy characterization of system-dependent distortions. Finally, while the dosimetric equivalence of synCT with CT has been well established, it was necessary to characterize any differences that may exist between synCT and CT in an IGRT setting. This work has helped to establish the geometric equivalence of these two modalities, with some caveats that have been discussed at length. (Abstract shortened by ProQuest.) </p>