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3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations

Published online by Cambridge University Press:  28 May 2015

Arjan Kuijper ,
Andreas Schwarzkopf ,
Thomas Kalbe ,
Chandrajit Bajaj ,
Stefan Roth  and
Michael Goesele
Arjan Kuijper*
Affiliation:
Fraunhofer IGD, 64283 Darmstadt, Germany Department of Computer Science, TU Darmstadt, D-64289 Darmstadt, Germany
Andreas Schwarzkopf
Affiliation:
Department of Computer Science, TU Darmstadt, D-64289 Darmstadt, Germany
Thomas Kalbe
Affiliation:
Department of Computer Science, TU Darmstadt, D-64289 Darmstadt, Germany
Chandrajit Bajaj
Affiliation:
ICES-CVC, University of Texas at Austin, Austin, Texas 78712, USA
Stefan Roth
Affiliation:
Department of Computer Science, TU Darmstadt, D-64289 Darmstadt, Germany
Michael Goesele
Affiliation:
Department of Computer Science, TU Darmstadt, D-64289 Darmstadt, Germany
*
Corresponding author.Email: arjan.kuijper@gris.informatik.tu-darmstadt.de
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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 ℝ3. 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

68U10Image processingenhancementanisotropic diffusiontensors3D filtering
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 72 - 94
Copyright
Copyright © Global Science Press Limited 2013

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