IEEE Trans Pattern Anal Mach Intell. 2012 Jan;34(1):51-65. doi: 10.1109/TPAMI.2011.105. Epub 2011 May 19.
While the study of geometry has mainly concentrated on single viewpoint (SVP) cameras, there is growing attention to more general non-SVP systems. Here, we study an important class of systems that inherently have a non-SVP: a perspective camera imaging through an interface into a medium. Such systems are ubiquitous: They are common when looking into water-based environments. The paper analyzes the common flat-interface class of systems. It characterizes the locus of the viewpoints (caustic) of this class and proves that the SVP model is invalid in it. This may explain geometrical errors encountered in prior studies. Our physics-based model is parameterized by the distance of the lens from the medium interface, besides the focal length. The physical parameters are calibrated by a simple approach that can be based on a single frame. This directly determines the system geometry. The calibration is then used to compensate for modeled system distortion. Based on this model, geometrical measurements of objects are significantly more accurate than if based on an SVP model. This is demonstrated in real-world experiments. In addition, we examine by simulation the errors expected by using the SVP model. We show that when working at a constant range, the SVP model can be a good approximation.
虽然几何的研究主要集中在单视点（SVP）相机上，但人们越来越关注更一般的非 SVP 系统。在这里，我们研究了一类重要的系统，这些系统本质上是非 SVP 的：一个透视相机通过一个界面到一个介质中成像。这种系统无处不在：当观察水基环境时，它们很常见。本文分析了常见的平面界面类系统。它描述了这个类别的视点（焦散线）的轨迹，并证明了 SVP 模型在其中是无效的。这可能解释了之前研究中遇到的几何误差。我们的物理模型除了焦距之外，还由透镜到介质界面的距离来参数化。物理参数可以通过一种简单的方法进行校准，这种方法可以基于单个帧。这直接确定了系统的几何形状。然后，校准用于补偿模型系统的失真。基于这个模型，对物体的几何测量比基于 SVP 模型更准确。这在实际实验中得到了证明。此外，我们通过模拟检查了使用 SVP 模型的预期误差。我们表明，在恒定距离下，SVP 模型可以是一个很好的近似。
