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3D流体表面是困难的，因为它们的特征在空间和时间上变化很大，并且测量设备不应该侵入流体。其次，流体表面的演化受复杂的物理机制控制，需要将其纳入重建方法中。在这项研究中，PI提出了一种新的方法，从采样数据精确重建三维流体表面。该项目包括两个关键部分：流体表面获取方法和流体表面重建方法。对于数据采集，PI建议设计一个使用光场相机阵列的新型实验系统，该系统可以同时捕获流体表面的不同视图。一个已知的图案被放置在表面之下，每个摄像机观察到一个明显的随时间变化的失真图案。通过分析这些变形，可以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，该算法使相对于采样数据的误差最小化，并通过求解3D自由表面流的完整欧拉方程来找到重建的表面。本文的研究成果在流体力学、计算机图形学和视觉等领域有着广泛的应用，如验证现有的流体模型，将重构的流体表面整合到动画和电影胶片中再现真实的现象等。这个跨学科的项目将促进培养研究生数学建模，实验室实验和计算机模拟。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.