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 Apr15 asked System of linear equation with limited solution space Mar27 awarded Commentator Mar27 comment Transforming matrix-equation to overdetermined minimum problem If you are interested: docs.opencv.org/trunk/modules/calib3d/doc/… Mar27 comment Transforming matrix-equation to overdetermined minimum problem In addition to this solution I actually found a library to do the work for me. In opencv is a function called solvePNP(Ransac), which does everything I need, BUT until now I wasn't able to tweak the parameters so that I get a working solution. This speaks for the problem lying elsewhere. There are definetly some very wrong values in my pool, a few correct values and the major part is nearly correct. The ransac part of the function should kick out the wrong values, but what it currently does is kicking out many values and keeping 3 of (50-200) and 1 of them is wrong. ^^ Mar27 comment Transforming matrix-equation to overdetermined minimum problem I actually used SVD to solve the problem. I just took the last column of the matrix as a solution. And as mentioned before, the resulting transformation matrix works for the points near the features. Thanks for the hint with the SVD. I'll work on it and see what informations I can gather. Furthormore you are right. I have a rank 12 matrix. Mar26 comment Transforming matrix-equation to overdetermined minimum problem Well, i tried this solution. Works pretty well for computed UV Points, but doesn't work for me with real XYZ - UV Pairs. The resulting camera transformation is correct for points near the points in the calculation, but does not work at all for any point. I get a determinant of 0.0001 or sth.(and with multiplying i get wrong positions (tx), which is very wrong. I haven't figured out how to improve the results yet. Mar18 comment Transforming matrix-equation to overdetermined minimum problem About the QR factorization. I learned about that before, but can't remember that much. The only thing I remember was sth like: $R^{-1}b = b_{1}:b_{2}$ and $Qb_{1} = x$ isnt that always zero, if b is zero? I can't get the non zero solution with my knowledge. ^^ Mar18 comment Transforming matrix-equation to overdetermined minimum problem You are pretty fast. ^^ So I used the property of det(R)=1 for any rotation matrix. I scale it by the factor the current det offers me. Works pretty well so far. I hope I can see this solution in action tomorrow. Should be possible, if i find a proper library to do the SVD algorithm... Mar18 accepted Transforming matrix-equation to overdetermined minimum problem Mar18 comment Transforming matrix-equation to overdetermined minimum problem Sooo, i'm pretty sure that i'm right. There are 12 variables, so the matrix needs to have rank 12 to have only one solution. I finally got some non zero values from this equation using SVD. The good thing: rank 11 leaves only a unsolved factor, which i have to apply to get the correct values for Rt. If i can't figure out how to get a rank 12 koefficientmatrix, i PROBABLY can figure this factor out by applying some rotationmatrix properties. And again. Thanks to you, you were huge help. I'm actually looking forward to go to work tomorrow. ^^ Mar17 comment Transforming matrix-equation to overdetermined minimum problem Well, I tried this equation in matlab. Code: pastebin.com/iGwkru4S I'm not a Matlab genius, but I tried solving it according to this: mathworks.de/de/help/matlab/math/… The message I get is that the matrix has a rank of 11. I dont really know why. I'll continue to figure it out, but maybe you are able to get me there faster. – Mar17 awarded Scholar Mar16 comment Transforming matrix-equation to overdetermined minimum problem Can't edit anymore: Thanks man, can't I transform your last 2 equations to this: $\begin{pmatrix} fX & fY & fZ & f & 0 & 0 & 0 & 0 & (px-U)X & (px-U)Y & (px-U)Z & (px-U) \\ 0 & 0 & 0 & 0 & fX & fY & fZ & f & (py-V)X & (py-V)Y & (py-V)Z & (py-V) \\ \end{pmatrix} \begin{pmatrix} r_{1} \\ r_{2} \\ r_{3} \\ t_{1} \\ r_{4} \\ r_{5} \\ r_{6} \\ t_{2} \\ r_{7} \\ r_{8} \\ r_{9} \\ t_{3} \end{pmatrix} = 0$ I should be able to solve this with a QR-Decomposition or another method. Did you mean this formulation does not fit on the site? Then I'm sorry. ^^ Mar16 awarded Student Mar15 comment Transforming matrix-equation to overdetermined minimum problem Come on guys. There needs to be a solution for this. This is the very last piece in the assemblyline to complete my application... Mar15 revised Transforming matrix-equation to overdetermined minimum problem edited body Mar15 revised Transforming matrix-equation to overdetermined minimum problem deleted 15 characters in body Mar15 awarded Editor Mar15 revised Transforming matrix-equation to overdetermined minimum problem deleted 15 characters in body Mar15 asked Transforming matrix-equation to overdetermined minimum problem