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Abstract	Image registration has been for many years the gold standard method to bring two images into correspondence. It has been used extensively in the eld of medical imaging in order to put images of dierent patients into a common overlapping spatial position. However, medical image registration is a slow, iterative optimization process, where many variables and prone to fall into the pit traps local minima. A coordinate system parameterizing the interior of organs is a powerful tool for a systematic localization of injured tissue. If the same coordinate values are assigned to specic anatomical sites, parameterizations ensure integration of data across different medical image modalities. Harmonic mappings have been used to produce parametric meshes over the surface of anatomical shapes, given their ability to set values at specic locations through boundary conditions. However, most of the existing implementations in medical imaging restrict to either anatomical surfaces, or the depth coordinate with boundary conditions is given at discrete sites of limited geometric diversity. The medial surface of the shape can be used to provide a continuous basis for the denition of a depth coordinate. However, given that dierent methods for generation of medial surfaces generate dierent manifolds, not all of them are equally suited to be the basis of radial coordinate for a parameterization. It would be desirable that the medial surface will be smooth, and robust to surface shape noise, with low number of spurious branches or surfaces. In this thesis we present methods for computation of smooth medial manifolds and apply them to the generation of for anatomical volumetric parameterization that extends current harmonic parameterizations to the interior anatomy using information provided by the volume medial surface. This reference system sets a solid base for creating anatomical models of the anatomical shapes, and allows comparing several patients in a common framework of reference.
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