MSPA-MCS: 3D Fluid Surface Reconstruction Using A Multi-Camera System

时变三维流体表面的建模和重建是一个具有挑战性的问题。首先，精确测量三维流体表面是困难的，因为它们的特征在空间和时间上可能会有很大的变化，而且测量装置不应该侵入流体。其次，流体表面的演变是由复杂的物理机制控制的，需要将其纳入重建方法中。在这项研究中，pi提出了一种从采样数据精确重建三维流体表面的新方法。该项目由流体表面采集法和流体表面构建法两个关键部分组成。对于数据采集，pi建议设计一种新的实验系统，该系统使用光场相机阵列，可以同时捕获流体表面的不同视图。在表面下放置一个已知的图案，每个相机观察到一个独特的随时间变化的扭曲图案。然后可以通过分析这些扭曲来测量采样的流体表面。对于表面重建，pi建议开发一种迭代优化算法，该算法通过求解三维自由表面流动的完整欧拉方程来最小化相对于采样数据的误差，并找到重建的表面。用一种有效的数值方法计算了这些方程的解。本研究成果在流体力学以及计算机图形学和视觉领域有许多应用，例如对现有流体模型的验证以及将重建的流体表面集成到动画和电影片段中以再现现实现象。这个跨学科的项目将促进研究生在数学建模、实验室实验和计算机模拟方面的训练。pi还将为对这些主题感兴趣的本科生和研究生开发课程和研讨会。

Modeling and reconstructing time-varying 3D fluid surfaces is achallenging problem. First, accurately measuring 3D fluid surfaces isdifficult because their features can be highly varying in space and time,and the measuring device should not be intrusive to the fluid. Second, theevolution of fluid surfaces is governed by complex physical mechanismsthat need to be incorporated into the reconstruction methods. In thisresearch, the PIs propose a novel approach for accurately reconstructing3D fluid surfaces from sampled data. This project consists of two keycomponents: a fluid surface acquisition method and a fluid surfacereconstruction method. For data acquisition, the PIs propose to design anovel experimental system using a light field camera array that cansimultaneously capture different views of a fluid surface. A known patternis placed beneath the surface and each camera observes a distincttime-varying distortion pattern. A sampled fluid surface can then bemeasured by analyzing these distortions. For surface reconstruction, thePIs propose to develop an iterative optimization algorithm which minimizesthe error relative to the sampled data and finds the reconstructed surfaceby solving the full Euler equations for 3D free-surface flows. Solutionsof these equations are computed by using an efficient numerical method.The results of this research have many applications in Fluid Mechanics aswell as in Computer Graphics and Vision, such as the validation ofexisting fluid models and the integration of reconstructed fluid surfacesinto animations and film footage to reproduce realistic phenomena. Thisinterdisciplinary project will promote the training of graduate studentson mathematical modeling, laboratory experiments, and computersimulations. The PIs will also develop courses and seminars for bothundergraduate and graduate students interested in these topics.