  We are concerned with the estimation of the exterior surface and interior
summaries of tube-shaped anatomical structures. This interest is motivated by
two distinct scientific goals, one dealing with the distribution of HIV
microbicide in the colon and the other with measuring degradation in
white-matter tracts in the brain. Our problem is posed as the estimation of the
support of a distribution in three dimensions from a sample from that
distribution, possibly measured with error. We propose a novel tube-fitting
algorithm to construct such estimators. Further, we conduct a simulation study
to aid in the choice of a key parameter of the algorithm, and we test our
algorithm with validation study tailored to the motivating data sets. Finally,
we apply the tube-fitting algorithm to a colon image produced by single photon
emission computed tomography (SPECT) and to a white-matter tract image produced
using diffusion tensor imaging (DTI).
