Direct Glyph-based Visualization of Diffusion MR Data Using Deformed Spheres

Abstract

For visualization of medical diffusion data one typically computes a tensor field from a set of diffusion volume images scanned with different gradient directions. The resulting diffusion tensor field is visualized using glyph- or tracking-based approaches. The derivation of the tensor, in general, involves a loss in information, as the n > 6 diffusion values for the n gradient directions are reduced to six diverse entries of the symmetric 3 × 3 tensor matrix. We propose a direct diffusion visualization approach that does not operate on the diffusion tensor. Instead, we assemble the gradient vectors on a unit sphere and deform the sphere by the measured diffusion values in the respective gradient directions. We compute a continuous deformation model from the few discrete directions by applying several processing steps. First, we compute a triangulation of the spherical domain using a convex hull algorithm. The triangulation leads to neighborhood information for the position vectors of the discrete directions. Using a parameterization over the sphere we perform a Powell-Sabin interpolation, where the surface gradients are computed using least-squares fitting. The resulting triangular mesh is subdivided using a few Loop subdivision steps. The rendering of this subdivided triangular mesh directly leads to a glyph-based visualization of the directional diffusion measured in the respective voxel. In a natural and intuitive fashion, our deformed sphere visualization can exhibit additional, possibly valuable information in comparison to the classical tensor glyph visualization.