The thymus, an organ responsible for the development, selection, and maintenance of the peripheral T-cell population, is an important regulator of the immune system. Despite its physiological significance, it has received little attention in the medical image analysis literature. In practice, the anatomical location and variable shape of this gland pose challenges both in the image acquisition and analysis processes. We present an automated method for segmenting the thymus from water and fat parametric MR images that permits further analysis of volumetrics and tissue characterization. We compute fat ratio and water ratio parametric images and introduce the use of a stochastic edge detector that is embedded in a geometric variational segmentation model. Validation experiments of the proposed algorithm against manual delineations of the thymus indicate the applicability of our approach.