CGV: Small: Collaborative Research: Sparse Reconstruction and Frequency Analysis for Computer Graphics Rendering and Imaging

计算机图形绘制、外观获取和成像中的广泛问题涉及高维(4D-8D)信号的采样、重建和积分。例如，实时渲染有光泽的材质和焦散等复杂的照明效果，可能需要预先计算场景对不同光线和观察方向的响应，这通常是一个6D数据集。同样，基于图像的面部细节、车漆或上釉木材的外观获取要求我们从不同的光线和视角方向获取图像。即使是像快速行驶的汽车的运动模糊或景深这样的视觉效果的离线渲染，也需要跨越时间和镜头光圈的高维采样。同样的问题在计算成像应用中也很常见，例如光场相机。虽然PI和其他人在随后的分析和对其中一些问题的紧凑表示方面取得了重大进展，但初始的完整数据集几乎总是必须通过暴力来获取或计算，这是一种令人望而却步的昂贵的计算和获取时间，并且对内存使用和存储构成挑战。该项目的PI的目标是做出基本贡献，在获取或模拟完整的数据集之前，实现这些信号的显著稀疏采样和重建。其关键思想是利用通常位于较低频率、稀疏或低维空间中的数据结构。他们最近在运动模糊的傅里叶分析上的合作表明，动态场景的频谱在时空域中被剪切成一个狭窄的楔形。这实现了新颖的剪切(非轴对齐)过滤器和稀疏采样。投资促进局将在这些初步结果的基础上，为计算机图形学中视觉外观的频率分析和稀疏数据重建制定一个统一的框架。为此，他们将首先奠定理论基础，包括蒙特卡罗积分的新频率分析和光场的5D时空分析。然后，他们将为各种问题领域开发有效的实用算法，包括用于重新照明的光传输矩阵的稀疏重建，用于离线阴影绘制的剪切采样和去噪，用于外观获取的时间相干压缩采样，以及用于计算摄影和成像的新方法。广泛影响：从理论角度来看，该项目将开发光传输和外观和成像数据集的基本信号处理分析，这将为进一步的工作奠定基础，不仅在计算机图形学，而且在信号处理、计算机视觉和图像分析方面。项目成果将适用于各种问题，并将在渲染和成像应用程序的范围内带来变革性的进步。PIS将利用与业界的现有合作，将新技术转化为实际生产用途。将通过一个新的科普博客，利用公众对数字摄影进步的兴奋来介绍新的技术概念，以及加州大学伯克利分校的高中生计算机科学教育日等活动，实现对K-12学生和公众的推广。这项工作产生的新算法和数据集将向研究界提供；此外，成像算法将以开源格式发布，以便与消费类数码相机和手机相机一起使用。

A broad range of problems in computer graphics rendering, appearance acquisition, and imaging, involve sampling, reconstruction, and integration of high-dimensional (4D-8D) signals. Real-time rendering of glossy materials and intricate lighting effects like caustics, for example, can require pre-computing the response of the scene to different light and viewing directions, which is often a 6D dataset. Similarly, image-based appearance acquisition of facial details, car paint, or glazed wood requires us to take images from different light and view directions. Even offline rendering of visual effects like motion blur from a fast-moving car, or depth of field, involves high-dimensional sampling across time and lens aperture. The same problems are also common in computational imaging applications such as light field cameras. While the PIs and others have made significant progress in subsequent analysis and compact representation for some of these problems, the initial full dataset must almost always still be acquired or computed by brute force which is prohibitively expensive, taking hours to days of computation and acquisition time, as well as being a challenge for memory usage and storage.The PIs' goal in this project is to make fundamental contributions that enable dramatically sparser sampling and reconstruction of these signals, before the full dataset is acquired or simulated. The key idea is to exploit the structure of the data that often lies in lower-frequency, sparse, or low-dimensional spaces. Their recent collaboration on a Fourier analysis of motion blur has shown that the frequency spectrum of dynamic scenes is sheared into a narrow wedge in the space-time domain. This enables novel sheared (not axis-aligned) filters and a sparse sampling. The PIs will build upon these preliminary results to develop a unified framework for frequency analysis and sparse data reconstruction of visual appearance in computer graphics. To these ends, they will first lay the theoretical foundations, including a novel frequency analysis of Monte Carlo integration and 5D space-time analysis of light fields. They will then develop efficient practical algorithms for a variety of problem domains, including sparse reconstruction of light transport matrices for relighting, sheared sampling and denoising for offline shadow rendering, time-coherent compressive sampling for appearance acquisition, and new approaches to computational photography and imaging.Broader Impacts: From a theoretical perspective, this project will develop a fundamental signal-processing analysis of light transport and appearance and imaging datasets, which will provide the foundation for further work not just in computer graphics but in signal-processing, computer vision, and image analysis as well. Project outcomes will apply to diverse sets of problems and will lead to transformative advances across the spectrum of rendering and imaging applications. The PIs will leverage existing collaborations with industry to transition the new technologies to practical production use. Outreach to K-12 students and the public will be enabled by a new science popularization blog that will leverage the public's excitement for advances in digital photography to introduce novel technical concepts, as well as by events such as the Computer Science Education Day for high school students at UC-Berkeley. The new algorithms and datasets resulting from this work will be made available to the research community; moreover, imaging algorithms will be released in open-source format to work with consumer digital and cell-phone cameras.