A coordinate system parameterizing the interior of organs is/na powerful tool for a systematic localization of injured tissue. If the same/ncoordinate values are assigned to speci c anatomical sites, parameterizations/nensure integration of data across di erent medical image modalities./nHarmonic mappings have been used to produce parametric meshes over/nthe surface of anatomical shapes, given their /nexibility to set values at/nspeci c locations through boundary conditions. However, most of the existing/nimplementations in medical imaging restrict to either anatomical/nsurfaces, or the depth coordinate with boundary conditions is given at/nsites of limited geometric diversity. In this paper we present a method for/nanatomical volumetric parameterization that extends current harmonic/nparameterizations to the interior anatomy using information provided by/nthe volume medial surface. We have applied the methodology to de ne/na common reference system for the liver shape and functional anatomy./nThis reference system sets a solid base for creating anatomical models of/nthe patient's liver, and allows comparing livers from several patients in/na common framework of reference.

This research has been funded by the Catalan project 2009-TEM-00007, Spanish/nprojects TIN2009-13618, TIN2012-3311, and the European Union FP7 grant agreement/nno. HEAR-EU 304857