Volumetric Segmentation of Medical

The segmentation of structure from images is an inherently di cult problem in computer vision and a bottleneck to its widespread application, e.g., in medical imaging. This paper presents an approach for integrating local evidence such as regional homogeneity and edge response to form global structure for gure-ground segmentation. This approach is motivated by a shock-based morphogenetic language where the growth of four types of shocks results in a complete description of shape. Speci cally, objects are randomly hypothesized in the form of fourth-order shocks (seeds) which then grow, merge, split, shrink and in general deform under physically motivated \forces", but slow down and come to a halt near di erential structures. Two major issues arise in the segmentation of 3D images using this approach. First, it is shown that the segmentation of 3D images by 3D bubbles is superior to a slice-byslice segmentation by 2D bubbles or by \21 2D bubbles" which are inherently 2D but use 3D information for their deformation. Speci cally, the advantages lie in an intrinsic treatment of the underlying geometry and accuracy of reconstruction. Second, gaps and weak edges which frequently present a signi cant problem for 2D and 3D segmentation, are regularized by curvature-dependent curve and surface deformations which constitute di usion processes. The 3D bubbles evolving in the 3D reaction-di usion space are a powerful tool in the segmentation of medical and other images, as illustrated for several realistic examples.