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Bilateral Recovering of Sharp Edges on Feature-Insensitive Sampled Meshes
July/August 2006 (vol. 12 no. 4)
pp. 629-639

Abstract—A variety of computer graphics applications sample surfaces of 3D shapes in a regular grid without making the sampling rate adaptive to the surface curvature or sharp features. Triangular meshes that interpolate or approximate these samples usually exhibit relatively big error around the insensitive sampled sharp features. This paper presents a robust general approach conducting bilateral filters to recover sharp edges on such insensitive sampled triangular meshes. Motivated by the impressive results of bilateral filtering for mesh smoothing and denoising, we adopt it to govern the sharpening of triangular meshes. After recognizing the regions that embed sharp features, we recover the sharpness geometry through bilateral filtering, followed by iteratively modifying the given mesh's connectivity to form singlewide sharp edges that can be easily detected by their dihedral angles. We show that the proposed method can robustly reconstruct sharp edges on feature-insensitive sampled meshes.

[1] V. Adzhiev, E. Kartasheva, T. Kunii, A. Pasko, and B. Schmitt, “Cellular-Functional Modeling of Heterogeneous Objects,” Proc. Seventh ACM Symp. Solid Modeling and Applications, pp. 192-203, 2002.
[2] M. Attene, B. Falcidino, M. Spagnuolo, and J. Rossignac, “Sharpen&Bend: Recovering Curved Edges in Triangle Meshes Produced By Feature-Insensitive Sampling,” IEEE Trans. Visualization and Computer Graphics, vol. 11, no. 2, pp. 181-192, Mar.-Apr. 2005.
[3] C.L. Bajaj and G. Xu, “Anisotropic Diffusion of Surfaces and Functions on Surfaces,” ACM Trans. Graphics, vol. 22, no. 1, pp. 4-32, 2003.
[4] A. Biswas, V. Shapiro, and I. Tsukanov, “Heterogeneous Material Modeling with Distance Fields,” Computer-Aided Geometric Design, vol. 21, pp. 215-242, 2004.
[5] J. Bloomenthal, “An Implicit Surface Polygonizer,” Graphics Gems IV, pp. 324-349, 1994.
[6] M. Botsch and L.P. Kobbelt, “A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes,” Proc. Vision Modeling and Visualization Conf. 2001, pp. 283-290, 2001.
[7] P. Cignoni, C. Rocchini, and R. Scopigno, “Metro: Measuring Error on Simplified Surfaces,” Computer Graphics Forum, vol. 17, no. 2, pp. 167-174, June 1998.
[8] A.U. Clarenz, U. Diewald, and M. Rumpf, “Anisotropic Geometric Diffusion in Surface Processing,” Proc. IEEE Visualization Conf., pp. 397-405, 2000.
[9] D. Cohen-Or, D. Levin, and A. Solomovici, “Three-Dimensional Distance Field Metamorphosis,” ACM Trans. Graphics, vol. 17, no. 2, pp. 116-141, Apr. 1998.
[10] M. Desbrun, M. Meyer, P. Schröder, and A.H. Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow,” Proc. SIGGRAPH '99 Conf., pp. 317-324, 1999.
[11] M. Desbrun, M. Meyer, P. Schröder, and A.H. Barr, “Anisotropic Feature-Preserving Denoising of Height Fields and Bivariate Data,” Graphics Interface, pp. 145-152, 2000.
[12] S. Fleishman, I. Drori, and D. Cohen-Or, “Bilateral Mesh Denoising,” ACM Trans. Graphics, vol. 22, no. 3, pp. 950-953, 2003.
[13] S. Frisken, R. Perry, A. Rockwood, and R. Jones, “Adaptively Sampled Distance Field: A General Representation of Shapes for Computer Graphics,” Proc. ACM SIGGRAPH 2000 Conf., pp. 249-254, 2000.
[14] S. Gumhold, X. Wang, and R. McLeod, “Feature Extraction from Point Clouds,” Proc. 10th Int'l Conf. Meshing Roundtable, pp. 293-305, 2001.
[15] T. He, L. Hong, A. Kaufman, A. Varshney, and S. Wang, “Voxel Based Object Simplification,” Proc. IEEE Visualization Conf., pp. 296-303, 1995.
[16] K. Hildebrandt and K. Polthier, “Anisotropic Filtering of Nonlinear Surface Features,” Computer Graphics Forum, vol. 23, no. 3, 2004.
[17] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh Optimization,” Proc. SIGGRAPH Conf., pp. 19-26, 1993.
[18] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh Optimization,” Technical Report, Extended_ TR_UW_CSE_1993-01-01, http://www.research.microsoft.comhhoppe, 1993.
[19] A. Hubeli and M. Gross, “Multiresolution Feature Extraction for Unstructured Meshes,” Proc. IEEE Visualization Conf., pp. 16-25, 2001.
[20] T.R. Jones, F. Durand, and M. Desbrun, “Noniterative, Feature-Preserving Mesh Smoothing,” ACM Trans. Graphics, vol. 22, no. 3, pp. 943-949, 2003.
[21] T. Ju, “Robust Repair of Polygonal Models,” ACM Trans. Graphics, vol. 23, no. 3, pp. 888-895, Aug. 2004.
[22] T. Ju, F. Losasso, S. Schaefer, and J. Warren, “Dual Contouring of Hermite Data,” ACM Trans. Graphics, vol. 21, no. 3, pp. 339-346, July 2002.
[23] L.P. Kobbelt, M. Botsch, U. Schwanecke, and H.-P. Seidel, “Feature Sensitive Surface Extraction from Volume Data,” Proc. SIGGRAPH Conf., pp. 57-66, 2001.
[24] L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel, “Interactive Multiresolution Modeling on Arbitrary Meshes,” Proc. SIGGRAPH Conf., pp. 105-114, 1998.
[25] J. Lawrence and T. Funkhouser, “A Painting Interface for Interactive Surface Deformations,” Proc. Pacific Graphics Conf., 2003.
[26] T. Lewiner, H. Lopes, A.W. Vieira, and G. Tavares, “Efficient Implementation of Marching Cubes' Cases with Topological Guarantees,” J. Graphics Tools, vol. 8, pp. 1-15, 2003.
[27] W. Lorensen and H. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics, vol. 21, pp. 163-169, 1987.
[28] L. Markosian, J.M. Cohen, T. Crulli, and J. Hughes, “Skin: A Constructive Approach to Modeling Free-Form Shapes,” Proc. SIGGRAPH Conf., pp. 393-400, 1999.
[29] M. Meyer, M. Desbrun, P. Schroder, and A.H. Barr, “Discrete Differential-Geometry Operators for Triangulated 2-Manifolds,” Proc. Visualization and Math. Conf, 2002.
[30] A. Miropolsky and A. Fischer, “Reconstruction with 3D Geometry Bilateral Filtering,” Proc. ACM Symp. Solid Modeling and Applications, pp. 225-229, 2004.
[31] G.M. Nielson and B. Hamann, “The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes,” Proc. IEEE Visualization Conf., pp. 83-91, 1991.
[32] F.S. Nooruddin and G. Turk, “Simplification and Repair of Polygonal Models Using Volumetric Techniques,” IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 2, pp. 191-205, Apr.-June 2003.
[33] Y. Ohtake and A. Belyaev, “Dual-Prime Mesh Optimization for Polygonized Implicit Surfaces with Sharp Features,” Proc. ACM Solid Modeling Symp., pp. 171-178, 2003.
[34] Y. Ohtake, A. Belyaev, and I. Bogaevski, “Mesh Regularization and Adaptive Smoothing,” Computer-Aided Design, vol. 33, pp. 789-800, 2001.
[35] Y. Ohtake, A. Belyaev, and A. Pasko, “Dynamic Mesh Optimization for Polygonized Implicit Surfaces with Sharp Features,” The Visual Computer, vol. 19, pp. 115-126, 2003.
[36] K. van Overveld and B. Wyvill, “Shrinkwrap: An Efficient Adaptive Algorithm for Triangulating an Iso-Surface,” The Visual Computer, vol. 20, no. 6, pp. 362-379, 2004.
[37] S.M. Smith and J.M. Brady, “SUSAN— A New Approach to Low Level Image Processing,” Int'l J. Computer Vision, vol. 23, no. 1, pp. 45-78, May 1997.
[38] V. Surazhsky and C. Gotsman, “Explicit Surface Remeshing,” Proc. 2003 Eurographics/ACM SIGGRAPH Symp. Geometry, pp. 20-30, 2003.
[39] T. Tasdizen, R. Whitaker, P. Burchard, and S. Osher, “Geometric Surface Smoothing via Anisotropic Diffusion of Normals,” Proc. Conf. Visualization Conf., pp. 125-132, 2002.
[40] G. Taubin, “A Signal Processing Approach to Fair Surface Design,” Proc. SIGGRAPH Conf., pp. 351-358, 1995.
[41] J.F. Thompson, B.K. Soni, and N.P. Weatherill, Handbook of Grid Generation. Fla.: CRC Press, 1999.
[42] C. Tomasi and R. Manduchi, “Bilateral Filtering for Gray and Color Images,” Proc. Sixth Int'l Conf. Computer Vision, pp. 839-846, 1998.
[43] G. Varadhan, S. Krishnan, Y.J. Kim, and D. Manocha, “Feature-Sensitive Subdivision and Isosurface Reconstruction,” Proc. IEEE Visualization Conf., pp. 99-106, 2003.
[44] J. Vorsatz, C. Rössl, L.P. Kobbelt, and H.-P. Seidel, “Feature Sensitive Remeshing,” Computer Graphics Forum, vol. 20, no. 3, pp. 393-402, 2001.
[45] M.Y. Wang and X. Wang, “A Level-Set Based Variational Method for Design and Optimization of Heterogeneous Objects,” Computer-Aided Design, vol. 37, pp. 321-337, 2004.
[46] K. Watanabe and A. Belyaev, “Detection of Salient Curvature Features on Polygonal Surfaces,” Computer Graphics Forum, vol. 20, no. 3, pp. 385-392, 2001.
[47] W. Welch and A. Witkin, “Free-Form Shape Design Using Triangulated Surfaces,” Proc. SIGGRAPH Conf., pp. 247-256, 1994.
[48] http://www.mpi-sb.mpg.de/~ohtakesoftware /, 2006.

Index Terms:
Boundary representations, geometric algorithms, languages, systems.
Citation:
Charlie C.L. Wang, "Bilateral Recovering of Sharp Edges on Feature-Insensitive Sampled Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 629-639, July-Aug. 2006, doi:10.1109/TVCG.2006.60
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