How do i generate a rotation matrix iteratively.
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I have two matrices containing coordinates:
example1 = [1 3;
4 5;
2 3;
6 17];
example2 = [1 4;
6 2;
8 9;
10 11];
and I'm implementing the RANSAC algorithm to remove outlier coordinates. To do that, I will need to include a factor of whether a not one coordinate in example1 is either a rotation, scaling or translation which result in the coordinate in example2. (1 3 -> 1 4, 4 5 -> 6 2 etc..) Hence, I will need to have a rotation matrix, scaling and translation matrix to be built iteratively within the RANSAC algorithm.
For now, I'll just keep it simple by just using a rotation matrix.
How do i generate a rotation matrix [cos θ -sin θ; sin θ cos θ] if i do not have anything else other than the two coordinate matrices above?
Edit: sorry for the confusion but the goal is to "estimate" the transformation matrix in every N iteration. The following shows:
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Walter Roberson
2019-9-11
example1 = [1 3;
4 5;
2 3;
6 17];
example2 = [1 4;
6 2;
8 9;
10 11];
syms theta
RM = [cos(theta) -sin(theta); sin(theta) cos(theta)];
residue = simplify( sum(sum((example2 - (RM * example1.').').^2)) );
best_theta = vpasolve(diff(residue,theta));
It is also possible to code it as a numeric minimization of residue over a bounded range, without using the symbolic toolbox.
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Walter Roberson
2019-9-11
Your original goal was restricted to rotation matrix, and my code finds the rotation matrix that produces the least squared error of rotation between the given sets of coordinates.
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Bruno Luong
2019-9-11
编辑:Bruno Luong
2019-9-11
You can use this implementation by Matt J using the Horn's method. It do for you the scaling and translation as well.
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