A Feature-Preserving and Volume-Constrained Flow for Fairing Irregular Meshes

  • Chunxia Xiao
  • Shu Liu
  • Qunsheng Peng
  • A. R. Forrest
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4035)


In this paper, we introduce a novel approach to denoise meshes taking the balanced flow equation as the theoretical foundation.The underlying model consists of an anisotropic diffusion term and a forcing term. The balance between these two terms is made in a selective way allowing prominent surface features and other details of the meshes to be treated in different ways. The forcing term keeps smoothed surface close to the initial surface.Thus the volume is preserved, and most important, the shape distortion is prevented. Applying a dynamic balance technique, the equation converges to the solution quickly meanwhile generating a more faithful approximation to the original noisy mesh. Our smoothing method maintains simplicity in implementation and numerical results show its high performance.


Force Term Original Surface Anisotropic Mesh IEEE Visualization Mesh Smoothing 
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  1. 1.
    Jones, T.R., Durand, F., Desbrun, M.: Non-iterative, feature-preserving mesh smoothing. In: Proc. of ACM SIGGRAPH (2003)Google Scholar
  2. 2.
    Fleishman, S., Drori, I., Cohen-Or, D.: Bilateral mesh denoising. In: Proc. of ACM SIGGRAPH, pp. 950–953 (2003)Google Scholar
  3. 3.
    Taubin, G.: A signal processing approach to fair surface design. In: Proc. SIGGRAPH, pp. 351–358 (1995)Google Scholar
  4. 4.
    Desbrun, M., Meyer, M., Schroer, P., Barr, A.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proc. SIGGRAPH, pp. 317–324 (1999)Google Scholar
  5. 5.
    Desbrun, M., Meyer, M., Schroer, P., Barr, A.: Anisotropic feature-preserving denoising of height fields and bivariate data. In: Graphics Interface, pp. 145–152 (2000)Google Scholar
  6. 6.
    Meyer, M., Desbrun, M., Schroder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III, pp. 35–57 (2003)Google Scholar
  7. 7.
    Clarenz, U., Diewald, U., Rumpf, M.: Anisotropic geometric diffusion in surface processing. In: Proc. IEEE Visualization, pp. 397–405 (2000)Google Scholar
  8. 8.
    Bajaj, C., Xu, G.: Anisotropic diffusion on surfaces and functions on surfaces. ACM Transactions on Graphics 22, 4–32 (2003)CrossRefGoogle Scholar
  9. 9.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: ICCV, pp. 839–846 (1998)Google Scholar
  10. 10.
    Peng, J., Strela, V., Zorin, D.: A simple algorithm for surface denoising. In: Proc. IEEE Visualization (2001)Google Scholar
  11. 11.
    Black, M., Sapiro, G., Marimont, D., Heeger, D.: Robust anisotropic diffusion. IEEE Trans. Image Processing 7(3), 421–432 (1998)CrossRefGoogle Scholar
  12. 12.
    Ohtake, Y., Belyaev, A., Bogaevski, I.: Mesh regularization and adaptive smoothing. Computer Aided Design 33(11), 789–800 (2001)CrossRefGoogle Scholar
  13. 13.
    Perona, P., Malik, J.: Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)CrossRefGoogle Scholar
  14. 14.
    Taubin, G.: Linear anisotropic mesh filtering, IBM Research Report RC2213 (2001)Google Scholar
  15. 15.
    Tasdizen, T., Whitaker, R., Burchard, P., Osher, S.: Geometric surface smoothing via anisotropic diffusion of normals. In: Proc. of IEEE Visualization, pp. 125–132 (2002)Google Scholar
  16. 16.
    Hildebrandt, K., Polthier, K.: Anisotropic Filtering of Non-Linear Surface Features. Computer Graphics Forum (Eurographics 2004) 23(3), 391–400 (2004)CrossRefGoogle Scholar
  17. 17.
    Liu, X., Bao, H., Shum, H.-Y., Peng, Q.: A novel volume constrained smoothing method for meshes. Graphical Models 64, 169–182 (2002)MATHCrossRefGoogle Scholar
  18. 18.
    Vollmer, J., Mencl, R., Muller, H.: Improved Laplacian smoothing of noisy surface meshes. In: Proc. of Eurographics, pp. 131–138 (1999)Google Scholar
  19. 19.
    Guskov, I., Sweldens, W., Schroder, P.: Multiresolution signal processing for meshes. In: Proceedings of SIGGRAPH, pp. 325–334 (1999)Google Scholar
  20. 20.
    Caz, B., Boaventura, M., Silva, E.: A well-balanced flow equation for noise removal and edge detection. IEEE Trans. on Image Processing 14, 751–763 (2003)Google Scholar
  21. 21.
    Nordstrom, K.N.: Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection. Image Vis. Comput. 8(3), 18–327 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Chunxia Xiao
    • 1
  • Shu Liu
    • 1
  • Qunsheng Peng
    • 1
  • A. R. Forrest
    • 2
  1. 1.State Key Lab of CAD&CGZhejiang UniversityZhejiangP.R. China
  2. 2.School of Computing SciencesUniversity of East AngliaNorwichEngland

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