Department of Computer Science, Xiamen University, Xiamen, Fujian 361005, China.
IEEE Trans Vis Comput Graph. 2012 Oct;18(10):1784-96. doi: 10.1109/TVCG.2012.94.
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.
蓝噪声点采样是计算机图形学的核心算法之一。在本文中，我们提出了一种新的、通用的变分框架，用于生成具有高质量蓝噪声特性的点分布，同时精确地适应给定的密度函数。与以前基于容量约束 Voronoi 细分的离散设置的方法不同，我们将蓝噪声采样生成作为具有连续设置的变分问题。基于对能量函数梯度的精确评估，开发了一种高效的优化方法，其性能明显优于以前基于优化的方法。我们的框架可以轻松扩展到流形表面和多类采样的蓝噪声点样本生成。优化公式还允许我们自然地处理动态域，例如可变形表面，并生成具有时间一致性的蓝噪声采样。我们呈现了实验结果来验证我们的变分框架的有效性。最后，我们展示了所提出方法的各种应用，包括非真实感图像点状化、彩色点状化以及可变形表面上的蓝噪声采样。
