3D Harmonic Mapping and Tetrahedral Meshing of Brain Imaging Data

We developed two techniques to address 3D volume parameterization and deformation mapping problems that arise in medical imaging [1]. The first algorithm finds a harmonic map from a 3-manifold to a 3D solid sphere and the second is a novel sphere carving algorithm which calculates the simplicial decomposition of a complex 3D image volume while preserving its surface topology. In this paper, we apply these two techniques to brain mapping problems. We use a tetrahedral finite element mesh (FEM) to reconstruct the brain volume from a sequence of magnetic resonance images (MRI). A heat flow method is used to solve the volumetric harmonic mapping problem. Experimental results on both synthetic and brain volume data are reported. We suggest that 3D harmonic mapping of brain volumes to a solid sphere may provide a canonical coordinate system for feature identification and segmentation, as well as anatomical normalization and nonlinear image registration.