Diffusion curves with diffusion coefficients
- 141 Downloads
Diffusion curves can be used to generate vector graphics images with smooth variation by solving Poisson equations. However, using the classical diffusion curve model, it is difficult to ensure that the generated diffusion image satisfies desired constraints. In this paper, we develop a model for producing a diffusion image by solving a diffusion equation with diffusion coefficients, in which color layers and coefficient layers are introduced to facilitate the generation of the diffusion image. Doing so allows us to impose various constraints on the diffusion image, such as diffusion strength, diffusion direction, diffusion points, etc., in a unified computational framework. Various examples are presented in this paper to illustrate the capabilities of our model.
Keywordsdiffusion curves diffusion coefficients color layers coefficient layers vector graphics
This paper was supported by the National Natural Science Foundation of China (No. 61379072), the National Key R&D Program of China (No. 2016YFB1001501), and the Fundamental Research Funds for the Central Universities (No. 2017XZZX009-03).
- Sun, J.; Liang, L.; Wen, F.; Shum, H.-Y. Image vectorization using optimized gradient meshes. ACM Transactions on Graphics Vol. 26, No. 3, Article No. 11, 2007.Google Scholar
- Lai, Y.-K.; Hu, S.-M.; Martin, R. R. Automatic and topology-preserving gradient mesh generation for image vectorization. ACM Transactions on Graphics Vol. 28, No. 3, Article No. 85, 2009.Google Scholar
- Xia, T.; Liao, B.; Yu, Y. Patch-based image vectorization with automatic curvilinear feature alignment. ACM Transactions on Graphics Vol. 28, No. 5, Article No. 115, 2009.Google Scholar
- Sun, T.; Thamjaroenporn, P.; Zheng, C. Fast multipole representation of diffusion curves and points. ACM Transactions on Graphics Vol. 33, No. 4, Article No. 53, 2014.Google Scholar
- Finch, M.; Snyder, J.; Hoppe, H. Freeform vector graphics with controlled thin-plate splines. ACM Transactions on Graphics Vol. 30, No. 6, Article No. 166, 2011.Google Scholar
- Takayama, K.; Sorkine, O.; Nealen, A.; Igarashi, T. Volumetric modeling with diffusion surfaces. ACM Transactions on Graphics Vol. 29, No. 6, Article No. 180, 2010.Google Scholar
- Jeschke, S.; Cline, D.; Wonka, P. A GPU Laplacian solver for diffusion curves and Poisson image editing. ACM Transactions on Graphics Vol. 28, No. 5, Article No. 116, 2009.Google Scholar
- Jeschke, S.; Cline, D.; Wonka, P. Rendering surface details with diffusion curves. ACM Transactions on Graphics Vol. 28, No. 5, Article No. 117, 2009.Google Scholar
- Boyé, S.; Barla, P.; Guennebaud, G. A vectorial solver for free-form vector gradients. ACM Transactions on Graphics Vol. 31, No. 6, Article No. 173, 2012.Google Scholar
- Sun, X.; Xie, G.; Dong, Y.; Lin, S.; Xu, W.; Wang W.; Tong, X.; Guo, B. Diffusion curve textures for resolution independent texture mapping. ACM Transactions on Graphics Vol. 31, No. 4, Article No. 74, 2012.Google Scholar
- Ilbery, P.; Kendall, L.; Concolato, C.; McCosker, M. Biharmonic diffusion curve images from boundary elements. ACM Transactions on Graphics Vol. 32, No. 6, Article No. 219, 2013.Google Scholar
- Zhang, R.-J.; Ma, W. An efficient scheme for curve and surface construction based on a set of interpolatory basis functions. ACM Transactions on Graphics Vol. 30, No. 2, Article No. 10, 2011.Google Scholar
Open Access The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Other papers from this open access journal are available free of charge from http://www.springer.com/journal/41095. To submit a manuscript, please go to https://www.editorialmanager.com/cvmj.