Volumetric segmentation of medical images by three-dimensional bubbles

The segmentation of structure from 3D images is an inherently difficult problem and a bottleneck to the widespread use of computer vision in such applications as medical imaging. Local low-level voxel-based features must somehow be integrated to obtain global object-based descriptions. Deformable models in the form of snakes, balloons, level sets, and bubbles have been proposed for this task. In this paper, we extend the reaction-diffusion segmentation bubble technique to three dimensions. In generalizing this approach to 3D, two separate issues arise. First, should segmentations be achieved by treating images as a series of disjoint 2D slides, as 2D slices with interslice interactions, or intrinsically as a 3D image? We will show that the existence of saps of information in low-level features guides us to make maximal use of continuity in all directions, thus advocating an intrinsic 3D approach. The treatment of bubbles in 3D, however, requires the generalization of the reaction-diffusion space. While the reaction process is trivially extended, the generalization of diffusion is not straightforward. We utilize a particular mean-Gauss curvature deformation to serve as the regularizing diffusion process. The resulting 3D reaction-diffusion bubbles are intrinsic, can deal with a variety of gaps, and place captured surfaces in a hierarchy of scale. The process is illustrated on MRI images of the ventricle cavity and the vascular structure in MRA images