Abstract
In this paper, we present a surface-fitting based smoothing algorithm for discrete, general-purpose mesh models. The surface patch around a mesh vertex is defined in a local coordinate system and fitted with a quadratic polynomial function. An initial mesh smoothing is achieved by projecting each vertex onto the fitted surface. At each vertex of the initial mesh, the curvature is estimated and used to label the vertex as one of four types. The curvature-based vertex labeling, together with the curvature variation within a local region of a vertex, is utilized to adaptively smooth the mesh with fine features well preserved. Finally, three post-processing methods are adopted for mesh quality improvement. A number of realworld mesh models are tested to demonstrate the effectiveness and robustness of our approach.
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References
Field, D.A.: Laplacian smoothing and Delaunay triangulations. Communications in Applied Numerical Methods 4, 709–712 (1988)
Taubin, G.: A Signal Processing Approach to Fair Surface Design. In: Proceedings of SIGGRAPH 1995, pp. 351–358 (1995)
Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow. In: Proceedings of SIGGRAPH 1999, pp. 317–324 (1999)
Vollmer, J., Mencl, R., Müller, H.: Improved Laplacian smoothing of noisy surface meshes. In: Proceedings of Eurographics, pp. 131–138 (1999)
Ohtake, Y., Belyaev, A., Bogaeski, I.: Polyhedral Surface Smoothing with Simultaneous Mesh Regularization. In: Geometric Modeling and Processing, pp. 229–237 (2000)
Peng, J., Strela, V., Zorin, D.: A Simple Algorithm for Surface Denoising. In: Proceedings of IEEE Visualization 2001, pp. 107–112 (2001)
Kobbelt, L.: Discrete fairing. In: Proceedings of the 7th IMA Conference on the Mathematics of Surfaces, pp. 101–131. Springer, Cirencester (1996)
Kobbelt, L., Botsch, M., Schwanecke, U., Seidel, H.: Feature sensitive surface extraction from volume data. In: Proceedings of SIGGRAPH 2001 (2001)
Welch, W., Witkin, A.: Free-form shape design using triangulated surfaces. In: Proceedings of SIGGRAPH 1994, pp. 247–256. ACM Press, Orlando (1994)
Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Anisotropic Feature-Preserving Denoising of Height Fields and Bivariate Data. In: Graphics Interface, pp. 145–152 (2000)
Taubin, G.: Linear anisotropic mesh filtering. IBM Research Technical Report. RC2213 (2001)
Liu, X., Bao, H., Heng, P., Wong, T., Peng, Q.: Constrained fairing for meshes. Computer Graphics Forum 20(2), 115–123 (2001)
Liu, X., Bao, H., Shum, H., Peng, Q.: A novel volume constrained smoothing method for meshes. Graphical Models 64, 169–182 (2002)
Tasdizen, T., Whitaker, R., Burchard, P., Osher, S.: Geometric surface smoothing via anisotropic diffusion of normals. In: Proceedings of IEEE Visualization, pp. 125–132 (2002)
Ohtake, Y., Belyaev, A., Seidel, H.-P.: Mesh Smoothing by Adaptive and Anisotropic Gaussian Filter. In: Vision, Modeling and Visualization, pp. 203–210 (2002)
Fleishman, S., Drori, I., Cohen-Or, D.: Bilateral Mesh Denoising. ACM Trans. Gr. (2003)
Zhang, H., Fiume, E.L.: Mesh Smoothing with Shape or Feature Preservation. In: Advances in Modeling, Animation, and Rendering, pp. 167–182 (2002)
Clarenz, U., Diewald, U., Rumpf, M.: Anisotropic geometric diffusion in surface processing. In: IEEE Visualization 2000, pp. 397–405 (2000)
Bajaj, C., Xu, G.: Anisotropic Diffusion on Surfaces and Functions on Surfaces. ACM Trans. Gr. 22(1), 4–32 (2003)
Jones, T., Durand, F., Desbrun, M.: Non-iterative, feature-preserving mesh smoothing. In: Proceedings of SIGGRAPH 2003, pp. 943–949. ACM Press, San Diego (2003)
Li, Z., Ma, L., Jin, X., Zheng, Z.: A new feature-preserving mesh-smoothing algorithm. Visual Comput. 25, 139–148 (2009)
Frey, P.J.: About surface remeshing. In: Proc. in 9th IMR, New-Orleans, pp. 123–136 (2000)
Milroy, M.J., Bradley, C., Vickers, G.W.: Segmentation of a wrap-around model using an active contour. Computer Aided Designed 29(4), 299–320 (1997)
Atkinson, K.A.: An Introduction to Numerical Analysis, 2nd edn. John Wiley & Sons, New York (1989)
Besl, P.J., Jain, R.: Segmentation through Variable-Order Surface Fitting. In: IEEE PAMI 1988, vol. 10(2), pp. 167–192 (1988)
Zhou, T., Shimada, K.: An angle-based approach to two-dimensional mesh smoothing. In: Proc. in 9th IMR, New-Orleans, pp. 373–384 (2000)
Yu, Z.: A list-based method for fast generation of molecular surfaces. In: The 31st International Conference of IEEE Engineering in Medicine and Biology Society (accepted, 2009)
Yu, Z., Holst, M., Cheng, Y., McCammon, J.A.: Feature-Preserving Adaptive Mesh Generation for Molecular Shape Modeling and Simulation. Journal of Molecular Graphics and Modeling 26(8), 1370–1380 (2008)
Yu, Z., Bajaj, C.L.: Computational approaches for automatic structural analysis of large bio-molecular complexes. IEEE/ACM Transactions on Computational Biology and Bioinformatics 5(4), 568–582 (2008)
Yu, Z., Holst, M., Hayashi, T., Bajaj, C.L., Ellisman, M.H., McCammon, J.A., Hoshijima, M.: Three-dimensional geometric modeling of membrane-bound organelles in ventricular myocytes: Bridging the gap between microscopic imaging and mathematical simulation. Journal of Structural Biology 164(3), 304–313 (2008)
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Wang, J., Yu, Z. (2009). A Novel Method for Surface Mesh Smoothing: Applications in Biomedical Modeling. In: Clark, B.W. (eds) Proceedings of the 18th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04319-2_12
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DOI: https://doi.org/10.1007/978-3-642-04319-2_12
Publisher Name: Springer, Berlin, Heidelberg
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