Imaging through refractive media is challenged by the alteration of light trajectory from their linear path, thus incurring severe distortions. These distortions are depth-dependent, non-linear, and, more importantly, alter the standard single viewpoint geometry into an axial form. Though modeling such imaging systems has been studied in the past, an in-depth analysis of their two-view geometry is still lacking. We demonstrate in this paper that the value of such form is not limited to the estimation of the relative motion as it allows to calibrate the system independent of any scene knowledge. Therefore, we relieve the establishment of external reference frames and estimate the system parameters through the course of the mission and on-the-fly. In our development, we identify relations among the parameters that allow us to separate them into two orthogonal groups. Using these relations we calibrate the system and solve the pose components. Only a minimal set of five corresponding points is needed for that purpose. We also show that while existing solutions constrain subsets of the parameters or apply hardware installations, our model requires no additional information, still estimating all parameters simultaneously and directly. In the paper, the formulation of two common imaging setups are developed, the first is of a single camera acquiring data through motion, and the other is of a stereo-rig, where the relative pose is fixed but where the system model is more involved. Numerical and experimental results demonstrate that the proposed calibration model exhibits stability to the presence of high levels of noise and achieves high levels of accuracy. Furthermore, we demonstrate how our modeling improves the accuracy by an order of magnitude or more compared to the state-of-the-art.

通过折射介质成像受到光轨迹从其线性路径改变的挑战，从而导致严重失真。这些扭曲是与深度相关的、非线性的，更重要的是，将标准的单视点几何改变为轴向形式。尽管过去曾研究过对此类成像系统进行建模，但仍缺乏对其双视图几何结构的深入分析。我们在本文中证明，这种形式的值不限于相对运动的估计，因为它允许独立于任何场景知识来校准系统。因此，我们减轻了外部参考系的建立，并通过任务过程和即时估计系统参数。在我们的发展中，我们确定参数之间的关系，使我们能够将它们分成两个正交组。使用这些关系，我们校准系统并解决姿势分量。为此只需要最少的五个对应点集。我们还表明，虽然现有解决方案约束参数的子集或应用硬件安装，但我们的模型不需要额外的信息，仍然同时直接估计所有参数。在本文中，开发了两种常见成像设置的公式，第一种是单相机通过运动获取数据，另一种是立体装置，其中相对姿势是固定的，但系统模型更多地涉及. 数值和实验结果表明，所提出的校准模型对高水平噪声的存在表现出稳定性，并实现了高水平的准确性。此外，我们展示了我们的建模与最先进技术相比如何将准确性提高一个数量级或更多。