IEEE Trans Pattern Anal Mach Intell. 2011 Aug;33(8):1518-31. doi: 10.1109/TPAMI.2011.24. Epub 2011 Feb 4.
In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarily-shaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requirements are 1) knowledge of a function that maps each point on the two image planes to a known 3D point that refracts to it, and 2) light is refracted only once. We apply this result to the problem of reconstructing the time-varying surface of a liquid from patterns placed below it. To do this, we introduce a novel "stereo matching" criterion called refractive disparity, appropriate for refractive scenes, and develop an optimization-based algorithm for individually reconstructing the position and normal of each point projecting to a pixel in the input views. Results on reconstructing a variety of complex, deforming liquid surfaces suggest that our technique can yield detailed reconstructions that capture the dynamic behavior of free-flowing liquids.
在本文中，我们考虑了重建位于未知任意形状折射表面上的点的 3D 位置和表面法线的问题。我们证明，即使折射率未知，通常情况下两个视点就足以解决这个问题。关键要求是 1）了解将两个图像平面上的每个点映射到折射到该点的已知 3D 点的函数，以及 2）光线仅折射一次。我们将这一结果应用于从其下方放置的图案重建液体的时变表面的问题。为此，我们引入了一种新的“立体匹配”准则，称为折射视差，适用于折射场景，并开发了一种基于优化的算法，用于单独重建投射到输入视图中像素的每个点的位置和法线。在重建各种复杂、变形的液体表面的结果表明，我们的技术可以产生详细的重建，捕捉自由流动液体的动态行为。
