TY - JOUR
T1 - 3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations
AU - Arjan Kuijper, Andreas Schwarzkopf, Thomas Kalbe, Chandrajit Bajaj, Stefan Roth & Michael Goesele
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 72
EP - 94
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.mssvm04
UR - https://global-sci.org/intro/article_detail/nmtma/5895.html
KW - Image processing, enhancement, anisotropic diffusion, tensors, 3D filtering.
AB - <p style="text-align: justify;">We present an efficient implementation of volumetric anisotropic image diffusion filters on
modern programmable graphics processing units (GPUs), where the mathematics behind volumetric diffusion is effectively reduced to the diffusion in 2D images.
We hereby avoid the computational bottleneck of a time consuming eigenvalue decomposition in $\mathbb{R}^3$.
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 and prevent the GPU code from branching.
We show that our most complex volumetric anisotropic diffusion filters gain a speed up of more than 600 compared to a CPU solution.</p>