Volumetric Nonlinear Anisotropic Diffusion on GPUs

We present an efficient implementation of volumetric nonlinear anisotropic image diffusion on modern programmable graphics processing units (GPUs). We avoid the computational bottleneck of a time consuming eigenvalue decomposition in R. Instead, we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining two tangent space eigenvectors. We derive closed formulas to achieve this resulting in efficient GPU code. We show that our most complex volumetric nonlinear anisotropic diffusion gains a speed up of more than 600 compared to a CPU solution.