Abstract
This paper describes a stable and robust finite element solver for physically-based texture synthesis over arbitrary manifold surfaces. Our approach solves the reaction-diffusion equation coupled with an anisotropic diffusion equation over surfaces, using a Galerkin based finite element method (FEM). This method avoids distortions and discontinuities often caused by traditional texture mapping techniques, especially for arbitrary manifold surfaces. Several varieties of textures are obtained by selecting different values of control parameters in the governing differential equations, and furthermore enhanced quality textures are generated by fairing out noise in input surface meshes.
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References
Bajaj, C., Xu, G.: Anisotropic Diffusion of Subdivision Surfaces and Functions on Surfaces. ACM Transactions on Graphics 22(1), 4–32 (2003)
Grinspun, E., Krysl, P., Schroder, P.: CHARMS: a simple framework for adaptive simulation. ACM SIGGRAPH, 281–290 (2002)
Futterling, S., Klein, R., Strasser, W., Weber, H.: Automated Finite Element of Human Mandible with Dental Implants. In: The Sixth International Conference in Central Europe on Computer Graphics and Visualization (1998)
Witkin, A., Kass, M.: Reaction-Diffusion Texture. ACM SIGGRAPH, 299–308 (1991)
Turk, G.: Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion. ACM SIGGRAPH, 289–298 (1991)
Wei L., Levoy M.: Texture Synthesis Over Arbitrary Manifold Surfaces. ACM SIGGRAPH, 355–360 (2001)
Turk, G.: Texture Synthesis on Surfaces. ACM SIGGRAPH, 347–354 (2001)
Loop, C.: Smooth Subdivision Surfaces Based on Triangles. Master thesis. Technical Report, Department of Mathematics, University of Utah (1978)
Stam, J.: Evaluation Of Loop Subdivision Surfaces. ACM SIGGRAPH (1998)
Balmelli, L., Taubin, G., Bernardini, F.: Space-Optimized Texture Maps. Proceedings of Eurographics 21(3) (2002)
Ferrant, M., Warfield, S., Guttmann, C., Mulkern, R., Jolesz, F., Kikinis, R.: 3D Image Matching Using a Finite Element Based Elastic Deformation Model. In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, pp. 202–209. Springer, Heidelberg (1999)
Heeger, D.J., Begen, J.R.: Pyramid-based Texture Analysis/Synthesis. ACM SIGGRAPH, 229–238 (1995)
De Bonet, J.S.: Multiresolution Sampling Procedure for Analysis and Synthesis of Texture Images. ACM SIGGRAPH, 361–368 (1997)
Wei, L.-Y., Levy, B.: Fast Texture Synthesis using Three-Structured Vector Quantization. ACM SIGGRAPH, 479–488 (2000)
Kwatra, V., Essa, I., Bobick, A., Kwatra, N.: Texture Optimization for Example-based Synthesis. ACM SIGGRAPH, 795–802 (2005)
Lefebvre, S., Hoppe, H.: Appearance-space Texture Synthesis. ACM SIGGRAPH, 541–548 (2006)
Qin, X., Yang, Y.-H.: Aura 3D Textures. IEEE Transactions on Visualization and Computer Graphics 13(2), 379–389 (2007)
Kopf, J., Fu, C.-W., Cohen-Or, D., Deussen, O., Lischinski, D., Wong, T.-T.: Solid Texture Synthesis from 2D Exemplars. ACM SIGGRAPH 26(3) (2007)
Levy, B., Mallet, J.-L.: Non-distorted Texture Mapping for Sheared Triangluated Meshes. ACM SIGGRAPH, 343–352 (1998)
Soler, C., Cani, M.: Angelidis A.: Hierarchical Pattern Mapping. ACM SIGGRAPH, 673–680 (2002)
Wu, X., Downes, M., Goktekin, T., Tendick, F.: Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes. In: Proceedings of Eurographics, vol. 20(3) (2001)
Weickert, J.: Anisotropic Diffusion in Image Processing. B. G. Teubner Stuttagart (1998)
Tomasi, C., Manduchi, R.: Bilateral Filtering for Gray and Color Images. IEEE Computer Vision, 839–846 (1998)
Clarenz, U., Diewald, U., Rumpf, M.: Nonlinear anisotropic diffusion in surface processing. IEEE Visualization Conference, 397–405 (2000)
Lin, A.L., Hagberg, A., Ardelea, A., Bertram, M., Swinney, H.L., Meron, E.: Four-Phase patterns in forced oscillatory systems. Phys. Rev. E. 62, 3790–3798 (2000)
Xu, G., Zhang, Q.: Construction of Geometric Partial Differential Equations in Computational Geometry. Mathematica Numerica Sinica 28(4), 337–356 (2006)
Tong, X., Zhang, J., Liu, L., Wang, X., Guo, B., Shum, H.-Y.: Synthesis of Bidirectional Texture Functions on Arbitrary Surfaces. ACM SIGGRAPH, 665–672 (2002)
Zhang, J., Zhou, K., Velho, L., Guo, B., Shum, H.-Y.: Synthesis of Progressively-Variant Textures on Arbitrary Surfaces. ACM SIGGRAPH, 295–302 (2003)
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Bajaj, C., Zhang, Y., Xu, G. (2008). Physically-Based Surface Texture Synthesis Using a Coupled Finite Element System. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_26
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DOI: https://doi.org/10.1007/978-3-540-79246-8_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79245-1
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