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Chunlin Wu, Jiansong Deng, Falai Chen, "Diffusion Equations over Arbitrary Triangulated Surfaces for Filtering and Texture Applications," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 3, pp. 666679, May/June, 2008.  
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@article{ 10.1109/TVCG.2008.10, author = {Chunlin Wu and Jiansong Deng and Falai Chen}, title = {Diffusion Equations over Arbitrary Triangulated Surfaces for Filtering and Texture Applications}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {14}, number = {3}, issn = {10772626}, year = {2008}, pages = {666679}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.10}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Diffusion Equations over Arbitrary Triangulated Surfaces for Filtering and Texture Applications IS  3 SN  10772626 SP666 EP679 EPD  666679 A1  Chunlin Wu, A1  Jiansong Deng, A1  Falai Chen, PY  2008 KW  Computer Graphics KW  Partial Differential Equations KW  Image Processing and Computer Vision VL  14 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] “Compatible Spatial Discretizations” The IMA Volumes in Mathematics and Its Applications, vol. 142, D.N. Arnold, P.B. Bochev, R.B.Lehoucq, R.A. Nicolaides, and M. Shashkov, eds., Springer, 2006.
[2] O.K.C. Au, C.L. Tai, L.G. Liu, and H.B. Fu, “Dual Laplacian Editing for Meshes,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 3, pp. 386395, May/June 2006.
[3] J.F. Aujol, G. Aubert, L.B. Feraud, and A. Chambolle, “Image Decomposition into a Bounded Variation Component and an Oscillating Component,” J. Math. Imaging and Vision, vol. 22, no. 1, pp. 7188, 2005.
[4] J.F. Aujol, G. Gilboa, T.F. Chan, and S. Osher, “StructureTexture Image DecompositionModeling, Algorithms, and Parameter Selection,” Int'l J. Computer Vision, vol. 67, no. 1, pp. 111136, 2006.
[5] C.L. Bajaj and G. Xu, “Anisotropic Diffusion of Surfaces andFunctions on Surfaces,” ACM Trans. Graphics, vol. 22, no. 1, pp. 432, 2003.
[6] C.A.Z. Barcelos and M.A. Batista, “Image Inpainting and Denoisingby Nonlinear Partial Differential Equations,” Proc. 16th Brazilian Symp. Computer Graphics and Image Processing (SIBGRAPI '03), pp. 287293, 2003.
[7] C.A.Z. Barcelos, M.A. Batista, A.M. Martins, and A.C. Nogueira, “LevelLines Continuation Based Digital Inpainting,” Proc. 17thBrazilian Symp. Computer Graphics and Image Processing (SIBGRAPI'04), pp. 5057, 2004.
[8] T. Barth and M. Ohlberger, “Finite Volume Methods: Foundation and Analysis,” Encyclopedia of Computational Mechanics. John Wiley & Sons, 2004.
[9] M. Bertalmio, A.L. Bertozzi, and G. Sapiro, “NavierStokes, Fluid Dynamics, and Image and Video Inpainting,” Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '01), pp. 355362, 2001.
[10] M. Bertalmio, L.T. Cheng, S. Osher, and G. Sapiro, “Variational Problems and Partial Differential Equations on Implicit Surfaces,” J. Computational Physics, vol. 174, no. 2, pp. 759780, 2001.
[11] M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, “Image Inpainting,” Proc. ACM SIGGRAPH '00, pp. 417424, 2000.
[12] A. Bossavit, “Generalized Finite Differences in Computational Electromagnetics,” Progress in Electromagnetics Research, vol. 32, pp. 4564, 2001.
[13] A. Bossavit, Computational Electromagnetism. Academic Press, 2004.
[14] V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic Active Contours,” Int'l J. Computer Vision, vol. 22, pp. 6179, 1997.
[15] E. Catmull and J. Clark, “Recursively Generated BSpline Surfaces on Arbitrary Topological Meshes,” ComputerAided Design, vol. 10, no. 6, pp. 350355, 1978.
[16] T.F. Chan, S.H. Kang, and J. Shen, “Total Variation Denoising andEnhancement of Color Images Based on the CB and HSVColor Models,” J. Visual Comm. and Image Representation, vol. 12, pp. 422435, 2001.
[17] T.F. Chan, S. Osher, and J. Shen, “The Digital TV Filter and Nonlinear Denoising,” IEEE Trans. Image Processing, vol. 10, no. 2, pp. 231241, 2001.
[18] T.F. Chan and F. Park, “Data Dependent Multiscale Total Variation Based Image Decomposition and Contrast Preserving Denoising,” Technical Report UCLA CAM Report 0415, UCLACAM, 2004.
[19] T.F. Chan and J. Shen, “Mathematical Models for Local NontextureInpaintings,” SIAM J. Applied Math., vol. 62, no. 3, pp. 10191043, 2001.
[20] T.F. Chan, J. Shen, and L. Vese, “Variational PDE Models in Image Processing,” Notice of Am. Math. Soc., vol. 50, pp. 1426, 2003.
[21] T.F. Chan and L.A. Vese, “An Active Contour Model without Edges,” Lecture Notes in Computer Science, vol. 1682, pp. 141151, Springer, 1999.
[22] M. Desbrun, A.N. Hirani, M. Leok, and J.E. Marsden, Discrete Exterior Calculus, http://arxiv.org/abs/math.DG0508341, 2005.
[23] M. Desbrun, M. Meyer, P. Schröder, and A.H. Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow,” Proc. ACM SIGGRAPH, 1999.
[24] Q. Du and L.L. Ju, “Finite Volume Methods on Spheres and Spherical Centroidal Voronoi Meshes,” SIAM J. Numerical Analysis, vol. 43, no. 4, pp. 16731692, 2005.
[25] S. Elcott, Y. Tong, E. Kanso, P. Schröder, and M. Desbrun, “Stable, CirculationPreserving, Simplicial Fluids,” ACM Trans. Graphics, vol. 26, no. 1, 2007.
[26] P.M. Gandoin and O. Devillers, “Progressive Lossless Compression of Arbitrary Simplicial Complexes,” ACM Trans. Graphics, vol. 21, no. 3, pp. 372379, 2002.
[27] G. Gilboa, N. Sochen, and Y.Y. Zeevi, “A ForwardandBackward Diffusion Process for Adaptive Image Enhancement and Denoising,” IEEE Trans. Image Processing, vol. 11, no. 7, pp. 689703, 2002.
[28] A.N. Hirani, “Discrete Exterior Calculus,” PhD dissertation, California Inst. Tech nology, 2003.
[29] A. Hummel, “Representations Based on ZeroCrossings in ScaleSpace,” Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '86), pp. 204209, 1986.
[30] R. Kimmel, “Intrinsic Scale Space for Images on Surfaces: The Geodesic Curvature Flow,” Graphical Models and Image Processing, vol. 59, no. 5, pp. 365372, 1997.
[31] J. Koenderink, “The Structure of Images,” Biological Cybernetics, vol. 50, pp. 363370, 1984.
[32] G. Lin and P.Y. Yu, “An Improved Vertex Caching Scheme for 3DMesh Rendering,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 4, pp. 640648, July/Aug. 2006.
[33] M. Meyer, M. Desbrun, P. Schröder, and A. Barr, “Discrete DifferentialGeometry Operator for Triangulated 2Manifolds,” Visualization and Math. III, H.C. Hege and K. Polthier, eds., Springer, 2002.
[34] S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer, 2002.
[35] S. Osher, A. Sole, and L. Vese, “Image Decomposition and Restoration Using Total Variation Minimization and the $H^{1}$ Norm,” Multiscale Modeling and Simulation, vol. 1, pp. 349370, 2003.
[36] P. Perona and J. Malik, “ScaleSpace and Edge Detection Using Anisotropic Diffusion,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629639, July 1990.
[37] W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, second ed. Cambrige Univ. Press, 1992.
[38] E. Radmoser, O. Scherzer, and J. Weickert, “ScaleSpace Properties of Regularization Methods,” Lecture Notes in Computer Science, vol. 1682, pp. 211222, Springer, 1999.
[39] J.R. Rommelse, H.X. Lin, and T.F. Chan, “A Robust Level Set Algorithm for Image Segmentation and Its Parallel Implementation,” Technical Report UCLA CAM Report 0305, UCLA CAM, 2003.
[40] L. Rudin, S. Osher, and E. Fatemi, “Nonlinear Total Variation Based Noise Removal Algorithms,” Physica D, vol. 60, pp. 259268, 1992.
[41] J. Shen, “Inpainting and the Fundamental Problem of Image Processing,” SIAM News, vol. 36, no. 5, 2003.
[42] L. Shi and Y. Yu, “Inviscid and Incompressible Fluid Simulation on Triangle Meshes,” J. Computer Animation and Virtual Worlds, vol. 15, pp. 173181, 2004.
[43] O. Sorkine, D. CohenOr, R. Goldenthal, and D. Lischinski, “Bounded Distortion Piecewise Mesh Parameterization,” Proc. IEEE Conf. Visualization (VIS '02), pp. 355362, 2002.
[44] A. Spira and R. Kimmel, “Enhancing Images Painted on Manifolds,” Lecture Notes in Computer Science, vol. 3459, pp. 492502, Springer, 2005.
[45] A. Spira and R. Kimmel, “Segmentation of Images Painted on Parametric Manifolds,” Proc. European Signal Processing Conf. (EUSIPCO '05), Sept. 2005.
[46] J. Stam, “Flows on Surfaces of Arbitrary Topology,” ACM Trans. Graphics, vol. 22, no. 3, pp. 724731, 2003.
[47] G. Taubin and J. Rossignac, “Geometric Compression throughTopological Surgery,” ACM Trans. Graphics, vol. 17, no. 2, pp. 84115, 1998.
[48] A. Turing, “The Chemical Basis of Morphogenesis,” Philosophical Trans. Royal Soc. B, vol. 237, pp. 3772, 1952.
[49] G. Turk, “Generating Textures on Arbitrary Surfaces Using ReactionDiffusion,” Computer Graphics, vol. 25, no. 4, pp. 289298, 1991.
[50] L.A. Vese and T.F. Chan, “A Multiphase Level Set Framework for Image Segmentation Using the MumfordShah Model,” Int'l J.Computer Vision, vol. 50, no. 3, pp. 271293, 2002.
[51] J. Weickert and B. Benhamouda, “A Semidiscrete Nonlinear ScaleSpace Theory and Its Relation to the PeronaMalik Paradox,” Advances in Computer Vision. Springer, pp. 110, 1997.
[52] A. Witkin and M. Kass, “ReactionDiffusion Textures,” Computer Graphics (Proc. ACM SIGGRAPH '91), vol. 25, no. 4, pp. 299308, 1991.
[53] C.L. Wu, J.S. Deng, and F.L. Chen, “Fast Data Extrapolating,” J.Computational and Applied Math., vol. 206, no. 1, pp. 146157, 2007.
[54] C.L. Wu, J.S. Deng, W.M. Zhu, and F.L. Chen, “Inpainting Images on Implicit Surfaces,” Proc. 13th Pacific Conf. Computer Graphics and Applications (PG '05), pp. 142144, 2005.
[55] G. Xu, Q. Pan, and C.L. Bajaj, “Discrete Surface Modelling Using Partial Differential Equations,” Computer Aided Geometric Design, vol. 23, no. 2, pp. 125145, 2006.
[56] Y.Z. Yu, K. Zhou, D. Xu, X.H. Shi, H.J. Bao, B.N. Guo, and H.Y. Shum, “Mesh Editing with PoissonBased Gradient Field Manipulation,” Proc. ACM SIGGRAPH '04, pp. 641648, 2004.
[57] E. Zhang, K. Mischaikow, and G. Turk, “FeatureBased Surface Parameterization and Texture Mapping,” ACM Trans. Graphics, vol. 24, no. 1, pp. 127, 2005.
[58] H.K. Zhao, S. Osher, B. Merriman, and M. Kang, “Implicit and Nonparametric Shape Reconstruction from Unorganized Points Using a Variational Level Set Method,” Computer Vision and Image Understanding, vol. 80, no. 3, pp. 295319, 2000.
[59] D. Zorin and P. Schroder, “Subdivision for Modeling and Animation,” ACM SIGGRAPH '00 Course Notes, 2000.