The segmentation of structure from three-dimensional images is an inherently difficult problem in computer vision and a bottleneck to its widespread application, \EG, in medical imaging. In analogy to the two-dimensional figure-ground segmentation, local evidence such as edges, must be integrated to form global structure. Previously, we presented an approach to the two-dimensional figure-ground segmentation problem. In this approach, objects are randomly hypothesized in the form of small bubbles which then grow, merge, split, shrink and in general deform under physically motivated ``forces'', but slow down and come to a halt near differential structures. In this paper, we address the three dimensional problem and examine three approaches. First, three-dimensional images can be treated as set of two-dimensional images along some axis. This approach has three drawbacks: ($i$) large gaps in two-dimensional slices can often prevent successful segmentation; ($ii$) the solutions may differ if cross sectional slices are taken along a different axis; ($iii$) the accuracy reconstruction of the final surface from segmented slices can be improve d. Second, the gap problem is sometimes avoided if two-dimensional bubbles are guided by three-dimensional edge information. This, ``2$\frac{1}{2}$D bubble'' approach resolves the gap problem due to diffusion of inter-slice edge information. Unfortunately, this solution is limited to large but shallow gaps and even then at the cost of blurring corners and other discontinuities. Finally, we propose three-dimensional segmentation bubbles evolving in the reaction-diffusion space. The reaction process in three-dimensions is trivially extended, but the generalization of diffusion is not straightforward. We utilize a particular Mean-Gauss curvature deformation to serve as the diffusion process. The three-dimensional reaction-diffusion bubbles are intrinsic, can deal with a variety of gaps, capture surfaces accurately, and place captured surfaces in a hierarchy of scale. The process is illustrated on MRI images of the ventricle cavity and the vascular structure present in MRA images. The results depict detailed stable segmentation of these medical images. We expect that an automated volumetric segmentation of medical data will tremendously aid the timely presentation of three-dimensional therapeutic data sets.