In this paper implicit representations of deformable models for medical image enhancement and segmentation are considered. The advantage of implicit models over classical explicit models is that their topology can be naturally adapted to objects in the scene. A geodesic formulation of implicit deformable models is especially attractive since it has the energy minimizing properties of classical models. The aim of this paper is twofold. First, a modification to the customary geodesic deformable model approach is introduced by considering all the level sets in the image as energy minimizing contours. This approach is used to segment multiple objects simultaneously and for enhancing and segmenting cardiac computed tomography (CT) and magnetic resonance images. Second, the approach is used to effectively compare implicit and explicit models for specific tasks. This shows the complementary character of implicit models since in case of poor contrast boundaries or gaps in boundaries, e.g. due to partial volume effects, noise, or motion artifacts, they do not perform well, since the approach is completely data-driven.