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，实时渲染光泽材质和复杂的灯光效果（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。 类似地，基于图像的面部细节、汽车油漆或上釉木材的外观采集要求我们从不同的光线和视图方向拍摄图像。 即使是离线渲染的视觉效果，如运动模糊从快速移动的汽车，或景深，涉及高维采样跨时间和透镜光圈。 同样的问题在诸如光场相机的计算成像应用中也是常见的。 虽然PI和其他人在这些问题中的一些问题的后续分析和紧凑表示方面取得了重大进展，但初始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，以及内存使用和存储的挑战。PI在这个项目中的目标是做出基本的贡献，使显着稀疏采样，在采集或模拟完整数据集之前，这些信号的重建。 其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立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。 这使得能够实现新颖的剪切（非轴对齐）滤波器和稀疏采样。 PI将建立在这些初步结果的基础上，开发一个统一的框架，用于频率分析和稀疏数据重建计算机图形学中的视觉外观。 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高效的实用算法，包括用于重新照明的光传输矩阵的稀疏重建、用于离线阴影渲染的剪切采样和去噪、用于外观采集的时间相干压缩采样，以及计算摄影和成像的新方法。从理论的角度来看，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，这不仅为计算机图形学的进一步工作提供了基础，也为信号处理、计算机视觉和图像分析提供了基础。 项目成果将适用于各种各样的问题，并将在渲染和成像应用领域带来变革性的进步。 PI将利用与行业的现有合作，将新技术过渡到实际生产使用。 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，以及加州大学伯克利分校高中生计算机科学教育日等活动，为K-12学生和公众提供宣传。 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，以与消费者数码相机和手机相机配合使用。

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.