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A Multiscale Fairing Method for Textured Surfaces

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Book cover Visualization and Mathematics III

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Summary

Based on image processsing methodology and the theory of geometric evolution problems a novel multiscale method on textured surfaces is presented. The aim is fairing of parametric noisy surfaces coated by a noisy texture. Simultaneously features in the texture and on the surface are enhanced. Considering an appropriate coupling of the two fairing processes one can take advantage of the frequently present strong correlations between edge features in the texture and on the surface edges.

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References

  1. M. Desbrun, M. Meyer, P. Schroeder, and A. Barr, “Implicit fairing of irregular meshes using diffusion and curvature flow,” in Computer Graphics (SIGGRAPH ‘89 Proceedings), 1999, pp. 317–324.

    Google Scholar 

  2. L. Kobbelt, “Discrete fairing,” in Proceedings of the 7th IMA Conference on the Mathematics of Surfaces 1997, pp. 101–131.

    Google Scholar 

  3. L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel, “Interactive multi-resolution modeling on arbitrary meshes,” in Computer Graphics (SIGGRAPH ‘88 Proceedings), 1998, pp. 105–114.

    Google Scholar 

  4. G. Taubin, “A signal processing approach to fair surface design,” in Computer Graphics (SIGGRAPH ‘85 Proceedings) 1995, pp. 351–358.

    Google Scholar 

  5. B. Curless and M. Levoy, “A volumetric method for building complex models from range images,” in Computer Graphics (SIGGRAPH ‘86 Proceedings), 1996, pp. 303–312.

    Google Scholar 

  6. W.E. Lorensen and H.E. Cline, “Marching cubes: A high resolution 3d surface construction algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163–169, 1987.

    Article  Google Scholar 

  7. M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston- Basel-Berlin, 1993.

    Google Scholar 

  8. I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.

    Google Scholar 

  9. I. Guskov, W. Sweldens, and P. Schroeder, “Multiresolution signal processing for meshes,” in Computer Graphics (SIGGRAPH ‘89 Proceedings), 1999.

    Google Scholar 

  10. U. Dierkes, S. Hildebrandt, A. Küster, and O. Wohlrab, Minimal Surfaces, Grundlehren der Mathematischen Wissenschaften. 295. Berlin: Springer- Verlag, 1992.

    Google Scholar 

  11. G. Dziuk, “An algorithm for evolutionary surfaces,” Numer. Math., vol. 58, pp. 603–611, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Perona and J. Malik, “Scale space and edge detection using anisotropic diffusion,” in IEEE Computer Society Workshop on Computer Vision, 1987.

    Google Scholar 

  13. F. Catté, P. L. Lions, J. M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal., vol. 29, pp. 182–193, 1992.

    Google Scholar 

  14. J. Weickert, “Foundations and applications of nonlinear anisotropic diffusion filtering,” Z. Angew. Math. Mech., vol. 76, pp. 283–286, 1996.

    MATH  Google Scholar 

  15. U. Diewald, U. Clarenz, and M. Rumpf, “Nonlinear anisotropic diffusion in surface processing,” in Proceedings of IEEE Visualization 2000, 2000, pp. 397 405.

    Google Scholar 

  16. T. Preußer and M. Rumpf, “A level set method for anisotropic geometric diffusion in 3D image processing,” To appear in SIAM J. Appl., 2002.

    Google Scholar 

  17. R. Kimmel, “Intrinsic scale space for images on surfaces: The geodesic curvature flow,” Graphical Models and Image Processing, vol. 59 (5), pp. 365–372, 1997.

    Article  Google Scholar 

  18. J. Weickert, “Coherence-enhancing diffusion of colour images,” Image and Vision Computing, vol. 17, pp. 201–212, 1999.

    Article  Google Scholar 

  19. J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Addison-Wesley, 1990.

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Clarenz, U., Diewald, U., Rumpf, M. (2003). A Multiscale Fairing Method for Textured Surfaces. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics III. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05105-4_13

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  • DOI: https://doi.org/10.1007/978-3-662-05105-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05682-6

  • Online ISBN: 978-3-662-05105-4

  • eBook Packages: Springer Book Archive

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