Finding the best-fit affine transformation Ti,j from i to j

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Im trying to code up a function for finding the best fit affine transform between two curves i and j for checking the similarity between two curves. My main problem at the moment is getting the two curves to fit together as best as they can to make the check.

I have an approach that I want to see if it right.

  1. Run the curves curveA and curveB through a linear least-square formulation to get lines for each curve that best fits their set of points.
  2. perform an affine transformation to lineA to match it to lineB.
  3. Use the affine transformation of lineA on curveA.

Would this approach work? I'm pretty new to affine transformations and linear least-squares to be sure if this is the right approach.