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

随机抽样是大多数计算机图形学应用的基本组成部分，包括渲染、成像、建模和仿真。例如，在绘制中，随机采样是有效求解复杂积分的关键；在纹理合成中，产生视觉上令人愉悦的图案是关键；在几何处理中，它被用来描述重要的几何特征。虽然以前的许多工作都集中在具有蓝噪声谱的平面样本上，但很少有研究对更一般类型的随机抽样进行研究。本研究旨在提高一般随机抽样的技术水平，提供新的理论见解、计算方法和实际应用。这一结果不仅有利于计算机图形学和视觉，也有利于依赖随机抽样技术的许多其他学科。本项目研究分析和合成随机样本的新方法。在分析方面，研究引入了基于空间统计的新技术来量化随机样本的分布特性。在合成方面，研究提出了计算高效的方法来生成具有所需分布特性的高质量样品。采用现代图形处理器实现并行计算。这些技术反过来又支持新的应用程序。在渲染中，该项目回答了一些基本问题，如抗混叠和半色调的最佳样本模式。在计算摄影中，该项目引入了新颖的场景相关编码模式，允许相机系统在单个镜头中捕获更多细节（空间、时间和光谱）。在几何处理方面，该项目提出了在表面上生成样本的新技术，用于重新网格划分，定义形状特征和执行形状匹配。

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.