相机姿态估计：如何解释旋转和平移矩阵？ [英] Camera pose estimation: How do I interpret rotation and translation matrices?

问题描述

假设我有两个图像之间的良好对应，并尝试恢复它们之间的相机运动。
我可以使用OpenCV 3的新设施，像这样：

  Mat E = findEssentialMat（imgpts1，imgpts2， focal，principalPoint，RANSAC，0.999，1，mask）; 
 
 int inliers = recoverPose（E，imgpts1，imgpts2，R，t，focal，principalPoint，mask）; 
 
 Mat mtxR，mtxQ; 
 Mat Qx，Qy，Qz; 
 Vec3d angles = RQDecomp3x3（R，mtxR，mtxQ，Qx，Qy，Qz）; 
 
 cout<< Translation：< t.t（）<< endl; 
 cout<< 欧拉角[x y z]以度表示：< angle.t（）<< endl; 
  

现在，我无法围绕 R 和 t 实际上意味着。是否需要将坐标从摄像机空间1映射到摄像机空间2，如 p_2 = R * p_1 + t ？

考虑这个例子，用ground-truth手动标记为对应

我得到的输出是：

 翻译：[-0.9661243151855488，-0.04921320381132761，0.253341406362796] 
欧拉角度[xyz]，以度为单位：[9.780449804801876，46.49315494782735，15.66510133665445] 
  

我尝试匹配这个和我在图片中看到的一样， c> [ - 0.96，-0.04,0.25] 告诉我，我已经移动到右边，坐标沿着负x轴移动，但它也会告诉我，更远，因为坐标已经沿着正z轴移动。

我还围绕y轴旋转摄像机（向左，我认为这是围绕负y轴的逆时针旋转，因为在OpenCV ，y轴向下，不是吗？）

问题：我的解释是否正确，如果没有，什么是正确的 c> p2 = R * p1 + t

/ code>确实有效。可以通过使用 cv :: triangulatePoints（）和 cv :: convertPointsFromHomogeneous 来验证这一点（相对于相机1），然后应用上述等式。用相机2的相机矩阵乘法产生 p2 图像坐标。

Assume I have good correspondences between two images and attempt to recover the camera motion between them. I can use OpenCV 3's new facilities for this, like this:

 Mat E = findEssentialMat(imgpts1, imgpts2, focal, principalPoint, RANSAC, 0.999, 1, mask);

 int inliers = recoverPose(E, imgpts1, imgpts2, R, t, focal, principalPoint, mask);

 Mat mtxR, mtxQ;
 Mat Qx, Qy, Qz;
 Vec3d angles = RQDecomp3x3(R, mtxR, mtxQ, Qx, Qy, Qz);

 cout << "Translation: " << t.t() << endl;
 cout << "Euler angles [x y z] in degrees: " << angles.t() << endl;

Now, I have trouble wrapping my head around what R and t actually mean. Are they the transform needed to map coordinates from camera space 1 to camera space two, as in p_2 = R * p_1 + t?

Consider this example, with ground-truth manually labeled correspondences

The output I get is this:

Translation: [-0.9661243151855488, -0.04921320381132761, 0.253341406362796]
Euler angles [x y z] in degrees: [9.780449804801876, 46.49315494782735, 15.66510133665445]

I try to match this to what I see in the image and come up with the interpretation, that [-0.96,-0.04,0.25] tells me, I have moved to the right, as the coordinates have moved along the negative x-Axis, but it would also tell me, I have moved further away, as the coordinates have moved along the positive z-Axis.

I have also rotated the camera around the y-Axis (to the left, which I think would be a counter-clockwise rotation around the negative y-Axis because in OpenCV, the y-Axis points downwards, does it not?)

Question: Is my interpretation correct and if no, what is the correct one?

解决方案

It turns out my interpretation is correct, the relation p2 = R * p1 + t does indeed hold. One can verify this by using cv::triangulatePoints() and cv::convertPointsFromHomogeneous to obtain 3D coordinates from corresponding points (relative to camera 1) and then applying the above equation. Multiplication with camera 2's camera matrix then yields the p2 image coordinates.

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