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Volume 6, Issue 1
3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations

Arjan Kuijper, Andreas Schwarzkopf, Thomas Kalbe, Chandrajit Bajaj, Stefan Roth & Michael Goesele

DOI: 10.4208/nmtma.2013.mssvm04

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 72-94.

Published online: 2013-06

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  • 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.

  • Keywords

Image processing, enhancement, anisotropic diffusion, tensors, 3D filtering.

  • AMS Subject Headings

68U10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-72, author = {Arjan Kuijper, Andreas Schwarzkopf, Thomas Kalbe, Chandrajit Bajaj, Stefan Roth and Michael Goesele}, title = {3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm04}, url = {http://global-sci.org/intro/article_detail/nmtma/5895.html} }
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 -

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.

Arjan Kuijper, Andreas Schwarzkopf, Thomas Kalbe, Chandrajit Bajaj, Stefan Roth and Michael Goesele. (2013). 3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 72-94. doi:10.4208/nmtma.2013.mssvm04
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