计算没有点对应的基本矩阵？ [英] Compute fundamental matrix without point correspondences?
问题描述
我想验证我对基本矩阵的理解是否正确，以及是否可以在不使用任何对应点对的情况下计算F.
I would like to verify that my understanding of the fundamental matrix is correct and if it's possible to compute F without using any corresponding point pairs.
基本矩阵是计算为 F = inv（transpose（Mr））* R * S * inv（M1）其中Mr和Ml是右和左固有照相机矩阵，矩阵，其将右坐标系统引向左边的坐标系，并且S是斜对称矩阵。
The fundamental matrix is calculated as F = inv(transpose(Mr))*R*S*inv(Ml) where Mr and Ml are the right and left intrinsic camera matrices, R is the rotation matrix that brings the right coordinate system to the left one, and S is the skew symmetric matrix
S = 0 -T[3] T[2] where T is the translation vector of the right coordinate system
T[3] 0 -T[1] from the left.
-T[2] T[1] 0
我知道基本矩阵用8点算法计算，但我没有任何点对应。然而，我的两个相机都是校准的，所以我有所有的内在和外在的参数。从上面的基本矩阵的定义，可以用这些参数单独计算F，正确的？
I understand that the fundamental matrix can be computed with the 8-point algorithm, but I do not have any point correspondences. However, both of my cameras are calibrated, so I have all intrinsic and extrinsic parameters. From the definition of the fundamental matrix above, it is possible to compute F with these parameters alone, right?
（我遇到的问题是，基本矩阵看起来错了， ）
(The problem I experience is that the fundamental matrix seems wrong when calculated from its definition. At the moment, I would just like to know if my understanding above is correct.)
推荐答案
如果你具有每个相机相对于公共坐标系的旋转和平移，然后可以计算相机之间的旋转和平移，然后使用所引用的公式来计算基本矩阵。
If you have the rotation and translation of each of the cameras relative to a common coordinate system, then you can compute the rotation and translation between the cameras, and then use the formula you have cited to compute the fundamental matrix.
更好的方法是将两台摄像机一起校准为单个立体声系统。计算机视觉系统工具箱的最新版本（2014a）允许您这样做。请参见此示例。
A better way to go would be to calibrate both cameras together as a single stereo system. The latest release (2014a) of the Computer Vision System Toolbox lets you do that. See this example.
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