CHS: Small: Higher-Order Monte Carlo Samples for Computer Graphics Rendering

随着计算机图形渲染变得更加逼真，它对我们的经济、安全和日常生活越来越重要：从诊断疾病到自动驾驶汽车，再到设计、可视化和制造产品。这些应用领域是由渲染算法推动的，该算法模拟光源如何发射光子，然后在进入相机(或我们的眼睛)形成虚拟图像之前，这些光子在场景中四处散射。不幸的是，与自然相比，即使是最快的计算机也能模拟的光子数量如此之少，以至于渲染高质量的图像仍然是一项极其耗时的工作。这个项目将开发新的方式来表达数值光传输模拟，这些模拟不限于直接模拟自然，从而推广计算机图形学中使用的广泛的渲染算法，以便它们可以更有效地操作。项目成果将从根本上改变蒙特卡罗集成的定义，并提供一套新的工具来设计、实施和分析此类算法，从而改变该领域，对上述和许多其他应用程序具有深远而广泛的影响。一个综合的教育和推广计划将利用无处不在的对光的熟悉向来自不同教育和社会经济背景的学生传授原本抽象的数学和物理概念。准确和高效的光传输模拟一直是计算机图形学的核心问题，它仍然具有挑战性，因为目前流行的蒙特卡罗(MC)算法通过随机点采样从光到传感器的路径来直接模拟自然。虽然直观，但这些算法太慢了，因为每个样本对答案的贡献很小，所以需要很多样本，但在可预见的未来，即使是最快的计算机也不能指望与自然的计算速度竞争。本项目将通过以下方式解决这一挑战：建立MC集成的通用理论，通过利用线(1D)、平面(2D)和更高阶(ND)等高阶样本，实现比自然更有效地模拟光线的新渲染算法；通过开发必要的工具来分析和优化一般MC集成中的此类样本；并将这些优势应用于逆光传输问题。项目成果将在依赖计算机图形渲染的所有应用领域以及依赖MC集成和一般基于物理的光传输的其他领域产生深远影响。该奖项反映了NSF的法定使命，并已通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

As computer graphics rendering becomes more realistic, it is increasingly critical to our economy, safety, and daily lives: from diagnosing illnesses, to self-driving cars, and to designing, visualizing and manufacturing products. These application domains are fueled by rendering algorithms which simulate how light sources emit photons that then scatter around in a scene before making their way into a camera (or our eyes) to form a virtual image. Unfortunately, the number of such photons that even the fastest computers are able to simulate is so tiny in comparison to nature that rendering high-quality images remains an incredibly time-consuming enterprise. This project will develop new ways of expressing numerical light transport simulations which are not restricted to operate in direct analogy to nature, thereby generalizing a broad range of rendering algorithms used in computer graphics so they can operate more efficiently. Project outcomes will transform the field by fundamentally changing the definition of Monte Carlo integration, and by providing a suite of new tools to design, implement, and analyze such algorithms, with far-reaching and broad impact on applications such as those mentioned above and many others. An integrated educational and outreach program will leverage ubiquitous familiarity with light to teach otherwise abstract mathematical and physical concepts to students from diverse educational and socio-economic backgrounds.Accurate and efficient light transport simulation has always been a central problem of computer graphics, and it continues to be challenging because the currently prevailing Monte Carlo (MC) algorithms operate in direct analogy to nature by randomly point-sampling paths from the light to the sensor. While intuitive, these algorithms are too slow because each sample contributes little to the answer so that many samples are required, but even the fastest computers cannot hope to compete with the computational speed of nature in the foreseeable future. This project will address that challenge by: establishing a generalized theory of MC integration enabling new rendering algorithms that simulate light more efficiently than nature by leveraging higher-order samples such as lines (1D), planes (2D), and beyond (nD); by developing the necessary tools to analyze and optimally leverage such samples in general MC integration; and by applying these benefits to inverse light transport problems. Project outcomes will have far-reaching impact in all application domains relying on computer graphics rendering, as well as in other fields that rely on MC integration and physically based light transport in general.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.