Abstract
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.
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References
Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)
Lindeberg, T.: Scale-Space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers, Dordrecht (1994)
Weickert, J.: A review of nonlinear diffusion filtering. In: ter Haar Romeny, B.M., Florack, L.M.J., Viergever, M.A. (eds.) Scale-Space 1997. LNCS, vol. 1252, pp. 1–28. Springer, Heidelberg (1997)
Lindeberg, T.: Generalized Gaussian scale-space axiomatics comprising linear scale-space, affine scale-space and spatio-temporal scale-space. Journal of Mathematical Imaging and Vision, 1–46 (2010)
Kuijper, A.: Geometrical PDEs based on second order derivatives of gauge coordinates in image processing. Image and Vision Computing 27(8), 1023–1034 (2009)
Weickert, J.: Coherence enhancing diffusion filtering. International Journal of Computer Vision 31, 111–127 (1999)
Tasdizen, T., Whitaker, R., Burchard, P., Osher, S.: Geometric surface smoothing via anisotropic diffusion of normals. In: Proc. VIS 2002, pp. 125–132 (2002)
Bajaj, C.L., Xu, G.: Adaptive surfaces fairing by geometric diffusion. In: Symp. CAGD, pp. 731–737 (2001)
Bajaj, C.L., Xu, G.: Anisotropic diffusion of surfaces and functions on surfaces. ACM Trans. Graph. 22(1), 4–32 (2003)
Lipnikov, K., Shashkov, M., Svyatskiy, D., Vassilevski, Y.: Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. Journal of Computational Physics 227(1), 492–512 (2007)
Agelas, L., Masson, R.: Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes. Comptes Rendus Mathematique 346(17-18), 1007–1012 (2008)
Zhang, X., Chen, W., Qian, L., Ye, H.: Affine invariant non-linear anisotropic diffusion smoothing strategy for vector-valued images. Imaging Science Journal 58(3), 119–124 (2010)
Hadwiger, M., Sigg, C., Scharsach, H., Bühler, K., Gross, M.H.: Real-time ray-casting and advanced shading of discrete isosurfaces. Comp. Graph. Forum 24(3), 303–312 (2005)
Tabik, S., Garzon, E., Garcia, I., Fernandez, J.: Implementation of anisotropic nonlinear diffusion for filtering 3D images in structural biology on SMP clusters. In: Proc. Int. Conf. Parallel Computing: Current & Future Issues of High-End Computing, ParCo., vol. 33, pp. 727–734 (2005)
Interactive 3D seismic fault detection on the graphics hardware. In: Proc. Volume Graphics (2006)
Zhao, Y.: Lattice Boltzman based PDE solver on the GPU. The Visual Computer 24(5), 323–333 (2008)
Beyer, J., Langer, C., Fritz, L., Hadwiger, M., Wolfsberger, S., Bühler, K.: Interactive diffusion-based smoothing and segmentation of volumetric datasets on graphics hardware. Methods Inf. Med. 46(3), 270–274
Bajaj, C.L., Wu, Q., Xu, G.: Level set based volumetric anisotropic diffusion for 3D image denoising. ICES TR03-10, UTexas, Austin USA (2003)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Analysis and Machine Intelligence 12, 629–639 (1990)
Weickert, J.: Anisotropic Diffusion in Image Processing. B.G. Teubne, Stuttgart (1998)
Kindlmann, G., Whitaker, R., Tasdizen, T., Mller, T.: Curvature-based transfer functions for direct volume rendering: Methods and applications. In: Proc. IEEE Vis., pp. 513–520 (2003)
Sigg, C.: Representation and Rendering of Implicit Surfaces. PhD thesis, ETH Zurich (2006)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proc. IEEE Int. Conf. on Computer Vision 1998, pp. 839–846 (1998)
Durand, F., Dorsey, J.: Fast bilateral filtering for the display of high-dynamic-range images. ACM Trans. Graph. 21(3), 257–266 (2002)
Paris, S., Kornprobst, P., Tumblin, J., Durand, F.: A gentle introduction to bilateral filtering and its applications. In: SIGGRAPH Course (2007)
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Schwarzkopf, A., Kalbe, T., Bajaj, C., Kuijper, A., Goesele, M. (2012). Volumetric Nonlinear Anisotropic Diffusion on GPUs. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_6
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DOI: https://doi.org/10.1007/978-3-642-24785-9_6
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