Tensor Field Visualization with PDE’s and Application to DT-MRI Fiber Visualization

We propose a PDE-based method to create textured representations of dense tensor-valued fields, for visualization purposes. Within the framework of anisotropic diffusion PDE’s, we focus on the general trace-based expressions (that we previously investigated in [39]) that are particularly well adapted to control the local smoothing performed by the regularization processes. Using this formalism, we propose then a new PDE which uses the spectral informations of a tensor field T : Ω → Pn to a create texture view of T, starting from an image of pure noise. We show moreover how our method can be practically applied, using a precise numerical scheme based on local filtering considerations. The equation is then considered to deal specifically with DT-MRI datasets (Diffusion Tensor-MRI), offering an alternative solution to parametric methods for the visualization of fibers bundles in the biological tissues. Application results are finally proposed with the visualization of fibers within the white matter of the brain.