Extract Translation and Rotation from Fundamental Matrix
Please take a look at this link:
http://isit.u-clermont1.fr/~ab/Classes/DIKU-3DCV2/Handouts/Lecture16.pdf.
Refer to Page 2. There are two possibilities for R. The first is UWVT and the second is UWTVT. You used the second. Try the first.
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Teris over 3 years
I am trying to retrieve translation and rotation vectors from a computed fundamental Matrix. I do use OpenCV and the general approach is from wikipedia. My Code is like this:
//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;
At the end I try to compare the estimated rotation to the one I computed using the chessboard which is in every Image (I plan to get the extrinsic parameters without the chessboard). For example I get this:
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]
So clearly there seems to be a problem, I just can't figure out what it could be.
EDIT: Here are the results I got with the untransposed vt(obviously from another scene):
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]
Here is my computed camera matrix, the error was pretty low(about 0.17...).
[1699.001342509651, 0, 834.2587265398068; 0, 1696.645251354618, 607.1292618175946; 0, 0, 1]
Here are the results I get when trying to reproject a cube... Camera 0, the cube is axis-aligned, rotation and translation are (0, 0, 0). image http://imageshack.us/a/img802/5292/bildschirmfoto20130110u.png
and the other one, with the epilines of the points in the first image. image http://imageshack.us/a/img546/189/bildschirmfoto20130110uy.png