根据内参数在射影空间中的无穷远平面
假设相机已校准，因此存在多个视图中的视图 i 的公制投影矩阵 M_i(3x4)。同样，每个视图的相机矩阵 K_i(3x3) 是可用的。我们可以计算射影空间中无穷远平面的位置吗？
Suppose cameras are calibrated therefore Metric projection matrices M_i(3x4) are there for view i from multiple views. As well, K_i(3x3) the camera matrix of each view is available. Can we calculate the location of plane at infinity in projective space?
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当然，无穷远平面始终是 w = 0 的平面。如果应用仿射变换，它保持固定。仅当您使用单应性时它才会发生变化。
Sure, the plane at infinity is always the plane where w = 0. If you are applying affine transformations, it remains fixed. It only shifts if you use a homography.
是的，理论上是可能的。在实际的投影 3D 世界中，无穷远平面始终保持固定。然而，移动摄像机在每个视图上的成像方式不同，在这些情况下，我们说无穷远平面并不处于其规范位置。与其认为相机移动了，不如认为整个3D投影空间移动了更方便！因此，我们发明了 3D 单应性来“指责”这种变化。从数学上讲，3D 单应性标签沿着投影矩阵的左侧：
x = (P*H)*X
因此，回答这个问题：虽然很棘手，但只要您有足够多的场景重建视图，您就可以恢复它。这是一个称为自动校准的过程，它本质上涉及一个方程（有多种形式），但不幸的是，它给出了非线性方程。我建议您查看以下内容：
http://nguyendangbinh.org/Proceedings/CVPR /1999/DATA/03_34.PDF
我相信它包含迭代计算平面的最新方法无穷大。
Yes, it is theoretically possible. The plane at infinity always remains fixed in terms of the actual projective 3D world. However, it is imaged differently by a moving camera upon each view and in these cases we say that the plane at infinity is not at its canonical position. Instead of thinking that the camera moved, it is more convenient to think that the entire 3D projective space has moved! Thus, we invent a 3D homography to "blame" for this change. Mathematically, the 3D homography tags along the left side of the projection matrix:
x = (P*H)*X
So, to answer the question: Although tricky, yes you may recover it, given that you have sufficiently enough reconstructed views of the scene. This is a process called auto calibration and it essentially involves one equation (that comes in many flavors) but unfortunately, gives non-linear equations. I suggest you look at the following:
http://nguyendangbinh.org/Proceedings/CVPR/1999/DATA/03_34.PDF
I believe it contains the most up-to-date method to iteratively compute the plane at infinity.