In this paper, we provide a framework for extracting tubular structures from medical imagery. The general methodology will be applied to modeling and extracting the cingulum bundle (CB) from diffusion-weighted imagery (DW-MRI) of the brain. The CB is a tube-like structure in the brain that is of major importance to clinicians since it may be helpful in diagnosing schizophrenia. This structure consists of a collection of fibers in the brain that have locally similar diffusion patterns, but vary globally. Standard region-based segmentation techniques adapted to DW-MRI are not suitable for this application because the diffusion pattern of the CB cannot be described by a few simple global statistics. Typical active surface models extended to DW-MRI allow for arbitrary deformations that give rise to unlikely shapes, which do not respect the tubular geometry of the CB. In this work, we explicitly model the CB as a tube-like surface and construct a general class of energies defined on tube-like surfaces. Modeling the CB as a tube-like surface is a natural shape prior. Since a tube is characterized by a center-line and a radius function, the method is reduced to a curve evolution that is computationally much less costly than an arbitrary surface evolution. Our tubular model of the CB also has the advantage that computing shape statistics and functions defined on the CB are much simplified.
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