“Mesh denoising via L0 minimization” by He and Schaefer

  • ©Lei He and Scott Schaefer




    Mesh denoising via L0 minimization

Session/Category Title: Points




    We present an algorithm for denoising triangulated models based on L0 minimization. Our method maximizes the flat regions of the model and gradually removes noise while preserving sharp features. As part of this process, we build a discrete differential operator for arbitrary triangle meshes that is robust with respect to degenerate triangulations. We compare our method versus other anisotropic denoising algorithms and demonstrate that our method is more robust and produces good results even in the presence of high noise.


    1. Bajaj, C. L., and Xu, G. 2003. Anisotropic diffusion of surfaces and functions on surfaces. ACM Trans. Graph. 22, 1, 4–32. Google ScholarDigital Library
    2. Candes, E., Romberg, J., and Tao, T. 2006. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 52, 2, 489–509. Google ScholarDigital Library
    3. Clarenz, U., Diewald, U., and Rumpf, M. 2000. Anisotropic geometric diffusion in surface processing. VIS, 397–405. Google ScholarDigital Library
    4. Desbrun, M., Meyer, M., Schröder, P., and Barr, A. H. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. SIGGRAPH, 317–324. Google ScholarDigital Library
    5. Desbrun, M., Meyer, M., Schröder, P., and Barr, A. H. 2000. Anisotropic feature-preserving denoising of height fields and bivariate data. Graphics Interface, 145–152.Google Scholar
    6. Donoho, D. 2006. Compressed sensing. IEEE Transactions on Information Theory 52, 4, 1289–1306. Google ScholarDigital Library
    7. Dziuk, G. 1990. An algorithm for evolutionary surfaces. Numerische Mathematik 58, 1, 603–611.Google ScholarDigital Library
    8. El Ouafdi, A. F., Ziou, D., and Krim, H. 2008. A smart stochastic approach for manifolds smoothing. In Proceedings of the Symposium on Geometry Processing, 1357–1364. Google ScholarDigital Library
    9. Fan, H., Yu, Y., and Peng, Q. 2010. Robust feature-preserving mesh denoising based on consistent subneighborhoods. IEEE Trans. Vis. Comp. Graph. 16, 2, 312–324. Google ScholarDigital Library
    10. Fleishman, S., Drori, I., and Cohen-Or, D. 2003. Bilateral mesh denoising. SIGGRAPH, 950–953. Google ScholarDigital Library
    11. Floater, M., Hormann, K., and Kos, G. 2006. A general construction of barycentric coordinates over convex polygons. Advances in Comp. Math 24, 311–331.Google ScholarCross Ref
    12. Hildebrandt, K., and Polthier, K. 2004. Anisotropic filtering of non-linear surface features. Computer Graphis Forum 23, 3, 391–400.Google ScholarCross Ref
    13. Jones, T. R., Durand, F., and Desbrun, M. 2003. Non-iterative, feature-preserving mesh smoothing. SIGGRAPH, 943–949. Google ScholarDigital Library
    14. Kazhdan, M., Solomon, J., and Ben-Chen, M. 2012. Can mean-curvature flow be modified to be non-singular? Computer Graphics Forum 31, 5, 1745–1754. Google ScholarDigital Library
    15. Kim, B., and Rossignac, J. 2005. Geofilter: Geometric selection of mesh filter parameters. Computer Graphis Forum 24, 3, 295–302.Google ScholarCross Ref
    16. Lee, K.-W., and Wang, W.-P. 2005. Feature-preserving mesh denoising via bilateral normal filtering. In Proceedings of Computer Aided Design and Computer Graphics, 275–280. Google ScholarDigital Library
    17. Levoy, M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller, D., Pereira, L., Ginzton, M., Anderson, S., Davis, J., Ginsberg, J., Shade, J., and Fulk, D. 2000. The digital michelangelo project: 3d scanning of large statues. SIGGRAPH, 131–144. Google ScholarDigital Library
    18. Lipman, Y., Cohen-Or, D., Levin, D., and Tal-Ezer, H. 2007. Parameterization-free projection for geometry reconstruction. ACM Trans. Graph. 26, 3, 22:1–22:5. Google ScholarDigital Library
    19. Liu, X., Bao, H., Shum, H.-Y., and Peng, Q. 2002. A novel volume constrained smoothing method for meshes. Graphical Models 64, 169–182. Google ScholarDigital Library
    20. Mallet, J.-L. 1989. Discrete smooth interpolation. ACM Trans. Graph. 8, 2, 121–144. Google ScholarDigital Library
    21. Nealen, A., Igarashi, T., Sorkine, O., and Alexa, M. 2006. Laplacian mesh optimization. GRAPHITE, 381–389. Google ScholarDigital Library
    22. Pinkall, U., Juni, S. D., and Polthier, K. 1993. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2, 15–36.Google ScholarCross Ref
    23. Schaefer, S., Ju, T., and Warren, J. 2007. A unified, integral construction for coordinates over closed curves. Computer Aided Geometric Design 24, 8-9, 481–493. Google ScholarDigital Library
    24. Shen, Y., and Barner, K. E. 2004. Fuzzy vector median-based surface smoothing. IEEE Trans. Vis. Comp. Graph. 10, 3, 252–265. Google ScholarDigital Library
    25. Sivan Toledo, D. C., and Rotkin, V. 2001. Taucs: A library of sparse linear solvers.Google Scholar
    26. Su, Z., Wang, H., and Cao, J. 2009. Mesh denoising based on differential coordinates. Shape Modeling International, 1–6.Google Scholar
    27. Sun, X., Rosin, P. L., Martin, R. R., and Langbein, F. C. 2007. Fast and effective feature-preserving mesh denoising. IEEE Trans. Vis. Comp. Graph., 925–938. Google ScholarDigital Library
    28. Sun, X., Rosin, P. L., Martin, R. R., and Langbein, F. C. 2008. Random walks for feature-preserving mesh denoising. Computer Aided Geometric Design 25, 7, 437–456. Google ScholarDigital Library
    29. Tasdizen, T., Whitaker, R., Burchard, P., and Osher, S. 2002. Geometric surface smoothing via anisotropic diffusion of normals. VIS, 125–132. Google ScholarDigital Library
    30. Taubin, G. 1995. A signal processing approach to fair surface design. SIGGRAPH, 351–358. Google ScholarDigital Library
    31. Taubin, G. 2001. Linear anisotropic mesh filtering. IBM Research Report RC22213(W0110-051).Google Scholar
    32. Tomasi, C., and Manduchi, R. 1998. Bilateral filtering for gray and color images. In Proceedings of the Sixth International Conference on Computer Vision, 839–846. Google ScholarDigital Library
    33. Tschumperlé, D. 2006. Fast anisotropic smoothing of multivalued images using curvature-preserving pde’s. Int. J. Comput. Vision 68, 1, 65–82. Google ScholarDigital Library
    34. Vollmer, J., Mencl, R., and Mller, H. 1999. Improved laplacian smoothing of noisy surface meshes. Computer Graphics Forum 18, 3, 131–138.Google ScholarCross Ref
    35. Wang, C. C. L. 2006. Bilateral recovering of sharp edges on feature-insensitive sampled meshes. IEEE Trans. Vis. Comp. Graph. 12, 4, 629–639. Google ScholarDigital Library
    36. Xu, L., Lu, C., Xu, Y., and Jia, J. 2011. Image smoothing via l0 gradient minimization. ACM Trans. Graph. 30, 6, 174:1–174:12. Google ScholarDigital Library
    37. Yagou, H., Ohtake, Y., and Belyaev, A. 2002. Mesh smoothing via mean and median filtering applied to face normals. GMP, 124–131. Google ScholarDigital Library
    38. Yagou, H., Ohtake, Y., and Belyaev, A. G. 2003. Mesh denoising via iterative alpha-trimming and nonlinear diffusion of normals with automatic thresholding. Computer Graphics International Conference, 28–33.Google Scholar
    39. Zheng, Y., Fu, H., Au, O. K.-C., and Tai, C.-L. 2011. Bilateral normal filtering for mesh denoising. IEEE Trans. Vis. Comp. Graph. 17, 10, 1521–1530. Google ScholarDigital Library

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