Dynamic refraction stereo

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