c++ - 从基本矩阵中提取平移和旋转

Question

我正在尝试从计算的基本矩阵中检索平移和旋转 vector 。我确实使用 OpenCV，一般方法来自维基百科。我的代码是这样的:

//Compute Essential Matrix
Mat A = cameraMatrix(); //Computed using chessboard
Mat F = fundamentalMatrix(); //Computed using matching keypoints
Mat E = A.t() * F * A;

//Perfrom SVD on E
SVD decomp = SVD(E);

//U
Mat U = decomp.u;

//S
Mat S(3, 3, CV_64F, Scalar(0));
S.at<double>(0, 0) = decomp.w.at<double>(0, 0);
S.at<double>(1, 1) = decomp.w.at<double>(0, 1);
S.at<double>(2, 2) = decomp.w.at<double>(0, 2);

//V
Mat V = decomp.vt; //Needs to be decomp.vt.t(); (transpose once more)

//W
Mat W(3, 3, CV_64F, Scalar(0));
W.at<double>(0, 1) = -1;
W.at<double>(1, 0) = 1;
W.at<double>(2, 2) = 1;

cout << "computed rotation: " << endl;
cout << U * W.t() * V.t() << endl;
cout << "real rotation:" << endl;
Mat rot;
Rodrigues(images[1].rvec - images[0].rvec, rot); //Difference between known rotations
cout << rot << endl;

最后，我尝试将估计的旋转与我使用每个图像中的棋盘计算的旋转进行比较(我计划在没有棋盘的情况下获取外部参数)。例如我得到这个:

computed rotation:
[0.8543027125286542, -0.382437675069228, 0.352006107978011;
  0.3969758209413922, 0.9172325022900715, 0.03308676972148356;
  0.3355250705298953, -0.1114717965690797, -0.9354127247453767]

real rotation:
[0.9998572365450219, 0.01122579241510944, 0.01262886032882241;
  -0.0114034800333517, 0.9998357441946927, 0.01408706050863871;
  -0.01246864754818991, -0.01422906234781374, 0.9998210172891051]

很明显，似乎有问题，我只是想不通它可能是什么。

编辑:这是我使用未转置 vt 得到的结果(显然来自另一个场景):

computed rotation: 
[0.8720599858028177, -0.1867080200550876, 0.4523842353671251;
 0.141182538980452, 0.9810442195058469, 0.1327393312518831;
-0.4685924368239661, -0.05188790438313154, 0.8818893204535954]
real rotation
[0.8670861432556456, -0.427294988334106, 0.2560871201732064;
 0.4024551137989086, 0.9038194629873437, 0.1453969040329854;
-0.2935838918455123, -0.02300806966752995, 0.9556563855167906]

这是我计算出来的相机矩阵，误差非常低(大约 0.17...)。

[1699.001342509651, 0, 834.2587265398068;
  0, 1696.645251354618, 607.1292618175946;
  0, 0, 1]

这是我在尝试重新投影立方体时得到的结果...摄像机 0，立方体是轴对齐的，旋转和平移是 (0, 0, 0)。 image http://imageshack.us/a/img802/5292/bildschirmfoto20130110u.png

和另一个，第一张图像中的点的epilines。 image http://imageshack.us/a/img546/189/bildschirmfoto20130110uy.png

Answer 1

请看一下这个链接:

DIKU-3DCV2/Handouts/Lecture16.pdf .

alternative link

请参阅第 2 页。R 有两种可能性。第一种是 UWVT，第二种是 UWTVT。你用的是第二个。尝试第一个。