Diffusion curve textures for resolution independent texture mapping

Abstract

We introduce a vector representation called diffusion curve textures for mapping diffusion curve images (DCI) onto arbitrary surfaces. In contrast to the original implicit representation of DCIs [Orzan et al. 2008], where determining a single texture value requires iterative computation of the entire DCI via the Poisson equation, diffusion curve textures provide an explicit representation from which the texture value at any point can be solved directly, while preserving the compactness and resolution independence of diffusion curves. This is achieved through a formulation of the DCI diffusion process in terms of Green's functions. This formulation furthermore allows the texture value of any rectangular region (e.g. pixel area) to be solved in closed form, which facilitates anti-aliasing. We develop a GPU algorithm that renders anti-aliased diffusion curve textures in real time, and demonstrate the effectiveness of this method through high quality renderings with detailed control curves and color variations.

References

1. Bayin, Ş. 2006. Mathematical methods in science and engineering. Wiley-Interscience.
2. Bezerra, H., Eisemann, E., DeCarlo, D., and Thollot, J. 2010. Diffusion constraints for vector graphics. In Proceedings of the 8th International Symposium on Non-Photorealistic Animation and Rendering, ACM, New York, NY, USA, NPAR '10, 35--42.
3. Bolz, J., Farmer, I., Grinspun, E., and Schröoder, P. 2003. Sparse matrix solvers on the gpu: conjugate gradients and multigrid. ACM Trans. Graph. 22 (July), 917--924.
4. Bowers, J. C., Leahey, J., and Wang, R. 2011. A Ray Tracing Approach to Diffusion Curves. Computer Graphics Forum 30, 4, 1345--1352.
5. D'Eon, E., and Irving, G. 2011. A quantized-diffusion model for rendering translucent materials. ACM Trans. Graph. 30 (Aug.), 56:1--56:14.
6. Elder, J., and Goldberg, R. 2001. Image editing in the contour domain. Pattern Analysis and Machine Intelligence, IEEE Transactions on 23, 3 (mar), 291--296.
7. Farbman, Z., Fattal, R., and Lischinski, D. 2011. Convolution pyramids. ACM Trans. Graph. 30 (Dec.), 175:1--175:8.
8. Finch, M., Snyder, J., and Hoppe, H. 2011. Freeform vector graphics with controlled thin-plate splines. ACM Trans. Graph. 30 (Dec.), 166:1--166:10.
9. Jeschke, S., Cline, D., and Wonka, P. 2009. A gpu laplacian solver for diffusion curves and poisson image editing. In ACM SIGGRAPH Asia 2009 papers, ACM, New York, NY, USA, SIGGRAPH Asia '09, 116:1--116:8.
10. Jeschke, S., Cline, D., and Wonka, P. 2009. Rendering surface details with diffusion curves. ACM Trans. Graph. 28 (December), 117:1--117:8.
11. Kazhdan, M., and Hoppe, H. 2008. Streaming multigrid for gradient-domain operations on large images. ACM Trans. Graph. 27 (August), 21:1--21:10.
12. Lai, Y.-K., Hu, S.-M., and Martin, R. R. 2009. Automatic and topology-preserving gradient mesh generation for image vectorization. ACM Trans. Graph. 28 (July), 85:1--85:8.
13. Lecot, G., and Levy, B. 2006. Ardeco: Automatic region detection and conversion. In Eurographics Symposium on Rendering.
14. Lipman, Y., Levin, D., and Cohen-Or, D. 2008. Green coordinates. In ACM SIGGRAPH 2008 papers, ACM, New York, NY, USA, SIGGRAPH '08, 78:1--78:10.
15. Nehab, D., and Hoppe, H. 2008. Random-access rendering of general vector graphics. ACM Trans. Graph. 27 (December), 135:1--135:10.
16. NVIDIA, 2011. CUDA programming guide 4.0, May. http://developer.nvidia.com/object/cuda.html.
17. Orzan, A., Bousseau, A., Winnemöller, H., Barla, P., Thollot, J., and Salesin, D. 2008. Diffusion curves: a vector representation for smooth-shaded images. In ACM SIGGRAPH 2008 papers, ACM, New York, NY, USA, SIGGRAPH '08, 92:1--92:8.
18. Pang, W., Qin, J., Cohen, M., Heng, P., and Choi, K. 2011. Fast rendering of diffusion curves with triangles. Computer Graphics and Applications, IEEE PP, 99, 1.
19. Qin, Z., McCool, M. D., and Kaplan, C. S. 2006. Real-time texture-mapped vector glyphs. In Proceedings of the 2006 symposium on Interactive 3D graphics and games, ACM, New York, NY, USA, I3D '06, 125--132.
20. Qin, Z., McCool, M. D., and Kaplan, C. 2008. Precise vector textures for real-time 3d rendering. In Proceedings of the 2008 symposium on Interactive 3D graphics and games, ACM, New York, NY, USA, I3D '08, 199--206.
21. Ramanarayanan, G., Bala, K., and Walter, B. 2004. Feature-Based Textures. Eurographics Symposium on Rendering.
22. Sen, P., Cammarano, M., and Hanrahan, P. 2003. Shadow Silhouette Maps. ACM Transactions on Graphics (TOG) (Proceedings of SIGGRAPH 2003) 22, 3, 521--526.
23. Sen, P. 2004. Silhouette maps for improved texture magnification. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware, ACM, New York, NY, USA, HWWS '04, 65--73.
24. Sun, J., Liang, L., Wen, F., and Shum, H.-Y. 2007. Image vectorization using optimized gradient meshes. ACM Trans. Graph. 26 (July).
25. Takayama, K., Sorkine, O., Nealen, A., and Igarashi, T. 2010. Volumetric modeling with diffusion surfaces. ACM Trans. Graph. 29 (December), 180:1--180:8.
26. Tarini, M., and Cignoni, P. 2005. Pinchmaps: textures with customizable discontinuities. Computer Graphics Forum 24, 3, 557--568.
27. Tumblin, J., and Choudhury, P. 2004. Bixels: Picture samples with sharp embedded boundaries. In Rendering Techniques, 255--264.
28. Wang, L., Zhou, K., Yu, Y., and Guo, B. 2010. Vector solid textures. ACM Trans. Graph. 29 (July), 86:1--86:8.
29. Wang, L., Yu, Y., Zhou, K., and Guo, B. 2011. Multiscale vector volumes. ACM Trans. Graph. 30 (Dec.), 167:1--167:8.
30. Xia, T., Liao, B., and Yu, Y. 2009. Patch-based image vectorization with automatic curvilinear feature alignment. ACM Trans. Graph. 28 (December), 115:1--115:10.

Index Terms

• Computing methodologies

  • Computer graphics

    • Image manipulation

      • Texturing