I have two sets of points in 2D space, S1={a1,a2,....,an} and S2={b1,b2,....,bn}. I would like to align S2 such that min(sum(|S2i – S1i.T|^2)) from i=1 to n. where T is a 2×2 matrix for aligning the points of S1i, and S2i are the points for the target sequence.

I would like to achieve that using linear regression. Any idea how can estimate the matrix T. Matlab code could be very helpful also.

  • $\begingroup$ Apart from that, do you want matrix T to be a rotation matrix, or not necessarily? $\endgroup$ – amoeba Feb 15 '16 at 14:28
  • $\begingroup$ @amoeba since the sequences S1 and S2 take varies directions, the rotation is required to align S2 into S1 with minimum error. $\endgroup$ – Omar14 Feb 15 '16 at 14:43
  • $\begingroup$ Still not clear: do you want to constrain T to be a rotation matrix (that's a special kind of 2x2 matrix) or do you want to find the best T whatever it will be? $\endgroup$ – amoeba Feb 15 '16 at 14:45
  • 1
    $\begingroup$ @amoeba I need T whatever it (as 2x2 matrix). $\endgroup$ – Omar14 Feb 15 '16 at 14:47

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