Refraction is a common physical phenomenon and has long been researched in computer vision. Objects imaged through a refractive object appear distorted in the image as a function of the shape of the interface between the media. This hinders many computer vision applications, but can be utilized for obtaining the geometry of the refractive interface. Previous approaches for refractive surface recovery largely relied on various priors or additional information like multiple images of the analyzed surface. In contrast, we claim that a simple energy function based on Snell's law enables the reconstruction of an arbitrary refractive surface geometry using just a single image and known background texture and geometry. In the case of a single point, Snell's law has two degrees of freedom, therefore to estimate a surface depth, we need additional information. We show that solving for an entire surface at once introduces implicit parameter-free spatial regularization and yields convincing results when an intelligent initial guess is provided. We demonstrate our approach through simulations and real-world experiments, where the reconstruction shows encouraging results in the single-frame monocular setting.

翻译：折射是一种常见的物理现象，并在计算机视觉领域长期被研究。通过折射物体成像时，图像中的物体会因介质界面的形状而出现畸变。这阻碍了许多计算机视觉应用，但也可用于获取折射界面的几何形状。先前折射表面重建的方法主要依赖各种先验信息或附加数据，例如分析表面的多幅图像。相比之下，我们提出，基于斯涅尔定律的简单能量函数，仅需单张图像以及已知的背景纹理和几何结构，即可重建任意折射表面的几何形状。在单点情况下，斯涅尔定律具有两个自由度，因此估计表面深度需要额外信息。我们证明，一次性求解整个表面引入了隐式的无参数空间正则化，并在提供智能初始猜测时获得令人信服的结果。我们通过仿真和真实世界实验展示了该方法，在单帧单目设置下，重建结果表现出令人鼓舞的效果。