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 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 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.

[1]  H. Ye,et al.  Affine invariant non-linear anisotropic diffusion smoothing strategy for vector-valued images , 2010 .

[2]  Arjan Kuijper,et al.  Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing , 2009, Image Vis. Comput..

[3]  Tony Lindeberg,et al.  Generalized Gaussian Scale-Space Axiomatics Comprising Linear Scale-Space, Affine Scale-Space and Spatio-Temporal Scale-Space , 2011, Journal of Mathematical Imaging and Vision.

[4]  Siham Tabik,et al.  Implementation of Anisotropic Nonlinear Diffusion for Filtering 3D Images in Structural Biology on SMP Clusters , 2006 .

[5]  Roland Masson,et al.  Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes , 2008 .

[6]  Ross T. Whitaker,et al.  Curvature-based transfer functions for direct volume rendering: methods and applications , 2003, IEEE Visualization, 2003. VIS 2003..

[7]  Joachim Weickert,et al.  A Review of Nonlinear Diffusion Filtering , 1997, Scale-Space.

[8]  Ye Zhao,et al.  Lattice Boltzmann based PDE solver on the GPU , 2008, The Visual Computer.

[9]  Inmaculada García,et al.  Filtering 3D images in Structural Biology with Anisotropic Nonlinear Diffusion on SMP Clusters , 2005, PARCO.

[10]  Markus Hadwiger,et al.  Real‐Time Ray‐Casting and Advanced Shading of Discrete Isosurfaces , 2005, Comput. Graph. Forum.

[11]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[13]  Christian Sigg,et al.  Representation and rendering of implicit surfaces , 2006 .

[14]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.

[15]  Daniel Cohen-Or,et al.  Volume graphics , 1993, Computer.

[16]  J. Koenderink.  The structure of images , 2004, Biological Cybernetics.

[17]  Inmaculada García,et al.  Multiprocessing of anisotropic nonlinear diffusion for filtering 3D images , 2006, 14th Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP'06).

[18]  Johanna Beyer,et al.  Interactive Diffusion-based Smoothing and Segmentation of Volumetric Datasets on Graphics Hardware , 2007, Methods of Information in Medicine.

[19]  Joachim Weickert,et al.  Coherence-Enhancing Diffusion Filtering , 1999, International Journal of Computer Vision.

[20]  Ross T. Whitaker,et al.  Geometric surface smoothing via anisotropic diffusion of normals , 2002, IEEE Visualization, 2002. VIS 2002..

[21]  Ross T. Whitaker,et al.  Interactive 3D seismic fault detection on the Graphics Hardware , 2006, VG@SIGGRAPH.

[22]  Daniil Svyatskiy,et al.  Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes , 2007, J. Comput. Phys..

[23]  Chandrajit L. Bajaj,et al.  Anisotropic diffusion of surfaces and functions on surfaces , 2003, TOGS.

[24]  Alexei A. Efros,et al.  Fast bilateral filtering for the display of high-dynamic-range images , 2002 .

[25]  C. Bajaj,et al.  Adaptive surfaces fairing by geometric diffusion , 2004 .

[26]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .