Volumetric Harmonic Brain Mapping

Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, and Shing-Tung Yau


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.

Figures (click on each for a larger version):

Image of Volumetric Harmonic Brain Mapping
Image of Volumetric Harmonic Brain Mapping

Related Publications

  • Y. Wang, X. Gu, T. F. Chan, P. M. Thompson and S.-T. Yau “ Volumetric Harmonic Brain Mapping“, IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Apr. 2004, pp. 1275-1278
  • Y. Wang, X. Gu and S.-T. Yau, “ Volumetric Harmonic Map“, Communications in Information and Systems, 3(3), 2004, pp. 191-202