RI: Small: Collaborative Research: Stochastic Sampling for Rendering, Imaging, and Modeling

随机采样是大多数计算机图形应用中的基本组件，包括渲染、成像、建模和模拟。例如，在渲染中，随机采样对于高效求解复杂积分至关重要;在纹理合成中，它是生成视觉上令人愉悦的图案的关键;在几何处理中，它用于表征重要的几何特征。虽然以前的工作主要集中在平面样本的蓝噪声谱，很少有研究更一般类型的随机采样。本研究旨在推进一般随机抽样的最新技术，提供新的理论见解，计算方法和实际应用。该成果不仅有利于计算机图形学和视觉，也有利于许多依赖随机抽样技术的其他学科。在分析方面，研究引入了新的技术，基于空间统计，量化随机样本的分布特性。在合成方面，该研究提出了计算效率高的方法来生成具有所需分布特性的高质量样本。现代GPU被用来实现并行计算。这些技术反过来又能实现新的应用。在渲染中，该项目回答了一些基本问题，例如抗锯齿和半色调的最佳采样模式。在计算摄影中，该项目引入了新的场景相关编码模式，允许相机系统在一个镜头中捕捉更多的细节（空间，时间和光谱）。在几何处理方面，本计画提出了新的技术来产生曲面上的样本，以重新划分网格，定义形状特征，以及执行形状匹配。

Stochastic sampling is a fundamental component in most computer graphics applications, including rendering, imaging, modeling, and simulation. For example, in rendering, stochastic sampling is crucial to efficiently solving complex integrals; in texture synthesis, it is the key to generate visually pleasing patterns; in geometry processing, it is used to characterize important geometry features. While much previous work has focused on planar samples with blue noise spectrum, little research has studied more general types of stochastic sampling. This research aims to advance the state of the art in general stochastic sampling, providing new theoretical insights, computational methods, and practical applications. The outcome benefits not only computer graphics and vision, but many other disciplines that rely on stochastic sampling techniques.This project studies new methods for analyzing and synthesizing stochastic samples. On the analysis side, the research introduces new techniques, based on spatial statistics, to quantify the distribution properties of stochastic samples. On the synthesis side, the research presents computationally efficient methods to generate high-quality samples with desired distribution properties. Modern GPUs are employed to achieve parallel computation. These techniques in turn enable new applications. In rendering, the project answers fundamental questions such as the optimal sample patterns for anti-aliasing and half-toning. In computational photography, the project introduces novel scene-dependent coded patterns that allow a camera system to capture more details (spatially, temporally, and spectrally) in a single shot. In geometry processing, the project presents new technique to generate samples on surfaces, for remeshing, defining shape features, and performing shape matching.