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Calculating the transform matrix

  1. Oct 30, 2013 #1
    I have 2 sets of known 3x1 vectors A = [ x y 1 ] and B =[ x' y' 1 ] which represent points on two coordinates calculated by some MATLAB algorithm. I was wondering what I could do to find the 2x3 transform matrix that turns the x y set into the x' y' set.

    [x'] [ ] [x]
    [y']=[?] [y]
    [1] [1]

    B = QA

    Q = 2x3 unknown transform matrix

    What I've tried:
    multiplying both sides by A-1, and im left with A-1*B which is just a 1x1 scalar value. I've tried multiplying the variables out and I'm left with 2 equations and 6 unknowns. I also have many different values of xy & x'y' pairs given by the matlab algorithm but I dont see how that could help me. Any help is appreciated.
     
  2. jcsd
  3. Oct 31, 2013 #2

    Erland

    User Avatar
    Science Advisor

    The system QA has two equations and six unknowns, the elements of Q. We can solve the system for these unknowns, which gives a solution with four parameters.
     
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