Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 72–94
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.mssvm04
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 72–94
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Image processing enhancement anisotropic diffusion tensors 3D filtering.