相机校准的失真参数

Question

我正在开发校准算法，对失真参数有些怀疑。我的疑问在于如何解释此信息。我知道失真有两种类型：

1）径向

x'' = x'(1+k1*r^2+k2*r^4+k3r^6)
y'' = y'(1+k1*r^2+k2*r^4+k3r^6)

2）Tangencial

x'' = 2*p1x'*y' + p2(r^2 + 2x'^2)
x'' = 2*p2x'*y' + p1(r^2 + 2y'^2)

第一个问题：

Here which is the distorted/undistorted coordinate x'' or x'?

第二个问题：

In which coordinates are given this coordinates meters, pixels, adimensional)?

第三个问题：

 When this distorions are applied after/before intrinsec camera matrix (focus and optic center)?

四个问题：

  Why some developments interpret this info in a different way? For example:

  - OpenCv. Applies the distortion before camera matrix.
  - Learning OpenCV. Considers x'' are undistorted and x' distorted.
  - MATLAB. Applies distortion after intrinsec camera matrix.

我让您here总结所有评论的方法。对我来说，这是一团糟。有人可以帮助我吗？