The choice of 3D shape representation for anatomical structures determines the effectiveness with which segmentation,
visualization, deformation, and shape statistics are performed. Medial axis-based shape representations
have attracted considerable attention due to their inherent ability to encode information about the natural
geometry of parts of the anatomy. In this paper, we propose a novel approach, based on nonlinear manifold
learning, to the parameterization of medial sheets and object surfaces based on the results of skeletonization.
For each single-sheet figure in an anatomical structure, we skeletonize the figure, and classify its surface points
according to whether they lie on the upper or lower surface, based on their relationship to the skeleton points.
We then perform nonlinear dimensionality reduction on the skeleton, upper, and lower surface points, to find
the intrinsic 2D coordinate system of each. We then center a planar mesh over each of the low-dimensional
representations of the points, and map the meshes back to 3D using the mappings obtained by manifold learning.
Correspondence between mesh vertices, established in their intrinsic 2D coordinate spaces, is used in order
to compute the thickness vectors emanating from the medial sheet. We show results of our algorithm on real
brain and musculoskeletal structures extracted from MRI, as well as an artificial multi-sheet example. The main
advantages to this method are its relative simplicity and noniterative nature, and its ability to correctly compute
nonintersecting thickness vectors for a medial sheet regardless of both the amount of coincident bending and
thickness in the object, and of the incidence of local concavities and convexities in the object's surface.