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matlabtransformationmatrix-multiplicationaffinetransform

Get 2d Affine transformation from 2 pair of points Matlab

I have matrix with 5 points in homogeneous coordinates x1(x1; y1; z1).. x4(x4; y4; z4). I know that after applying Affine transformation to this matrix x1 moved to x1_prime, x2 - to x2_prime. How can I find the transformation matrix?

I tried 

X = [x1 x2];
X_prime = [x1_prime x2_prime];
T = X_prime/X;

But this does not work. After I apply T on my 4 points I get 1 segment.

enter image description here

I tried fitgeotrans() in Matlab, but I suppose I have used it incorrect. Could you please help me to find Affine transformation matrix in Matlab?

Thanks

Solution

  • With 2 points it is impossible to find Affine transformation matrix 

     [a b c;
  d e f; 
  g h i].

    We need 3 points for it. Only then for each line of matrix we will have 3 unknowns and 3 equations. With 2 points we can find 

    [a b;
 d e]

    part of matrix, then add 0 0 1's and we will get Affine transformation

       [a b 0;
    d e 0;
    0 0 1]