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Variational Blue Noise Sampling
Oct. 2012 (vol. 18 no. 10)
pp. 1784-1796
Zhonggui Chen, Xiamen University, Xiamen
Zhan Yuan, The University of Hong Kong, Hong Kong
Yi-King Choi, The University of Hong Kong, Hong Kong
Ligang Liu, University of Science and Technology of China, Hefei
Wenping Wang, The University of Hong Kong, Hong Kong
Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces.

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Index Terms:
Noise measurement,Density functional theory,Optimization,Computer graphics,quasi-Newton method.,Point sampling,blue noise,centroidal Voronoi tessellation,capacity-constrained
Zhonggui Chen, Zhan Yuan, Yi-King Choi, Ligang Liu, Wenping Wang, "Variational Blue Noise Sampling," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 10, pp. 1784-1796, Oct. 2012, doi:10.1109/TVCG.2012.94
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