Volumetric Harmonic Map

Abstract

We develop two different techniques to study volume mapping problem in Computer Graphics and Medical Imaging fields. The first one is to find a harmonic map from a 3 manifold to a {3D} solid sphere and the second is a sphere carving algorithm which calculates the simplicial decomposition of volume adapted to surfaces. We derive the {3D} harmonic energy equation and it can be easily extended to higher dimensions. We use a textrehedral mesh to represent the volume data. We demonstrate our method on various solid {3D} models. We suggest that {3D} harmonic mapping of volume can provide a canonical coordinate system for feature identification and registration for computer animation and medical imaging.