The optic disc is the region of the retina where the optic nerve exits the back of the eye. A number of conditions can cause the optic disc to swell. Papilledema, optic disc swelling caused by raised intracranial pressure (ICP), and nonarteritic anterior ischemic optic neuropathy (NAION), swelling caused by reduced blood flow to the back of the eye, are two such conditions. Rapid, accurate diagnosis of the cause of disc swelling is important, as with papilledema the underlying cause of raised ICP could potentially be life-threatening and may require immediate intervention. The current clinical standard for diagnosing and assessing papilledema is a subjective measure based on qualitative inferences drawn from fundus images. Even with the expert training required to properly perform the assessment, measurements and results can vary significantly between clinicians. As such, the need for a rapid, accurate diagnostic tool for optic disc swelling is clear. Shape analysis of the structures of the retina has emerged as a promising quantitative tool for distinguishing between causes of optic disc swelling. Optic disc swelling can cause the retinal surfaces to distort, taking on shapes that differ from their normal arrangement. Recent work has examined how changes in the shape of one of these surfaces, Bruch's membrane (BM), varies between different types of optic disc swelling, containing clinically-relevant information. The inner limiting membrane (ILM), the most anterior retinal surface and furthest from BM, can take on shapes that are distinct from the more posterior layers when the optic disc becomes swollen. These unique shape characteristics have yet to be explored for their potential clinical utility. This thesis develops new shape models of the ILM. The ultimate goal of this work is to develop noninvasive, automated diagnostic tools for clinical use. To that end, a necessary first step in establishing clinical relevance is demonstrating the utility of retinal shape information in a machine learning classifier. Retinal layer shape information and regional volume measurements acquired from spectral-domain optical coherence tomography scans from 78 patients (39 papilledema, 39 NAION) was used to train random forest classifiers to distinguish between cases of papilledema and NAION. On average, the classifiers were able to correctly distinguish between papilledema and NAION 85.7±2.0% of the time, confirming the usefulness of retinal layer shapes for determining the cause of optic disc swelling. The results of this experiment are encouraging for future studies that will include more patients and attempt to differentiate between additional causes of optic disc edema.