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Nonlinear Diffusion in Graphics Hardware

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Data Visualization 2001

Part of the book series: Eurographics ((EUROGRAPH))

Abstract

Multiscale methods have proved to be successful tools in image denoising, edge enhancement and shape recovery. They are based on the numerical solution of a nonlinear diffusion problem where a noisy or damaged image which has to be smoothed or restorated is considered as initial data. Here a novel approach is presented which will soon be capable to ensure real time performance of these methods. It is based on an implementation of a corresponding finite element scheme in texture hardware of modern graphics engines. The method regards vectors as textures and represents linear algebra operations as texture processing operations. Thus, the resulting performance can profit from the superior bandwidth and the build in parallelism of the graphics hardware. Here the concept of this approach is introduced and perspectives are outlined picking up the basic Perona Malik model on 2D images.

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References

  1. L. Alvarez, F. Guichard, P. L. Lions, and J. M. Morel. Axioms and fundamental equations of image processing. Arch. Ration. Mech. Anal, 123(3):199–257, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal, 29(1):182–193, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  3. T.J. Cullip and U. Neumann. Accelerating volume reconstruction with 3d texture hardware. Technical Report TR93-027, University of North Carolina, Chapel Hill N.C., 1993.

    Google Scholar 

  4. U. Diewald, T. Preußer, and M. Rumpf. Anisotropic diffusion in vector field visualization on euclidean domains and surfaces. Trans. Vis. and Comp. Graphics, 6(2):139–149, 2000.

    Article  Google Scholar 

  5. M. Hopf and T. Ertl. Accelerating 3d convolution using graphics hardware. In Visualization’ 99, pages 471–474, 1999.

    Google Scholar 

  6. M. Hopf and T. Ertl. Hardware accelerated wavelet transformations. In Symposium on Visualization VisSym’ 00, 2000.

    Google Scholar 

  7. B. Kawohl and N. Kutev. Maximum and comparison principle for one-dimensional anisotropic diffusion. Math. Ann., 311(1):107–123, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  8. OpenGL Architectural Review Board (ARB), http://www.opengl.org/. OpenGL: graphics application programming interface (API), 1992.

  9. P. Perona and J. Malik. Scale space and edge detection using anisotropic diffusion. In IEEE Computer Society Workshop on Computer Vision, 1987.

    Google Scholar 

  10. J. A. Sethian. Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999.

    Google Scholar 

  11. V. Thomee. Galerkin-Finite Element Methods for Parabolic Problems. Springer, 1984.

    Google Scholar 

  12. J. Weickert. Anisotropic diffusion in image processing. Teubner, 1998.

    Google Scholar 

  13. R. Westermann and T. Ertl. Efficiently using graphics hardware in volume rendering applications. Computer Graphics (SIGGRAPH’ 98), 32(4):169–179, 1998.

    Google Scholar 

  14. O. Wilson, A. van Gelder, and J. Wilhelms. Direct volume rendering via 3d textures. Technical Report UCSC CRL 94-19, University of California, Santa Cruz, 1994.

    Google Scholar 

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© 2001 Springer-Verlag Wien

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Rumpf, M., Strzodka, R. (2001). Nonlinear Diffusion in Graphics Hardware. In: Ebert, D.S., Favre, J.M., Peikert, R. (eds) Data Visualization 2001. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6215-6_9

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  • DOI: https://doi.org/10.1007/978-3-7091-6215-6_9

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83674-3

  • Online ISBN: 978-3-7091-6215-6

  • eBook Packages: Springer Book Archive

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