Volumetric Harmonic Map
Yalin Wang, Xianfeng Gu, and Shing-Tung Yau
Communications in Information and Systems, 3(3), 2004, pp. 191-202
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.