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

在计算机图形渲染、外观获取和成像中，涉及到高维（4D-8D）信号的采样、重建和集成的广泛问题。例如，实时渲染光滑材料和复杂的灯光效果（如焦散）可能需要预先计算场景对不同光线和观看方向的响应，这通常是一个6D数据集。同样，基于图像的面部细节、汽车油漆或釉面木材的外观获取需要我们从不同的光线和观看方向拍摄图像。即使是脱机渲染视觉效果，比如快速行驶的汽车的动态模糊，或者景深，也需要跨越时间和镜头光圈进行高维采样。同样的问题在计算成像应用中也很常见，比如光场相机。虽然pi和其他人在后续分析和紧凑表示方面取得了重大进展，但最初的完整数据集几乎总是必须通过蛮力获取或计算，这是非常昂贵的，需要数小时到数天的计算和获取时间，并且对内存使用和存储也是一个挑战。pi在这个项目中的目标是在获得或模拟完整数据集之前，对这些信号进行更稀疏的采样和重建，从而做出根本性的贡献。关键思想是利用通常位于低频、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。这使得新的剪切（非轴对齐）滤波器和稀疏采样成为可能。pi将建立在这些初步结果的基础上，开发一个统一的框架，用于计算机图形学中视觉外观的频率分析和稀疏数据重建。为此，他们将首先奠定理论基础，包括一种新的蒙特卡洛积分频率分析和光场的5D时空分析。然后，他们将为各种问题领域开发高效实用的算法，包括用于重照明的光传输矩阵的稀疏重建，用于离线阴影渲染的剪切采样和去噪，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。更广泛的影响：从理论角度来看，该项目将发展光传输、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方面，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各样的问题，并将导致整个渲染和成像应用领域的变革性进步。pi将利用现有的与工业界的合作，将新技术转化为实际生产使用。一个新的科普博客将利用公众对数码摄影进步的兴奋来介绍新颖的技术概念，并通过诸如加州大学伯克利分校高中生计算机科学教育日等活动，使K-12学生和公众能够接触到。这项工作产生的新算法和数据集将提供给研究界；此外，成像算法将以开源格式发布，用于消费者数码相机和手机相机。

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.