How do i generate a rotation matrix iteratively.
조회 수: 1 (최근 30일)
이전 댓글 표시
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.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/237861/image.png)
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:
![Snip20190911_1.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/237873/Snip20190911_1.png)
댓글 수: 0
채택된 답변
Walter Roberson
2019년 9월 11일
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.
댓글 수: 3
Walter Roberson
2019년 9월 11일
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.
Walter Roberson
2019년 9월 11일
I would suggest that Bruno's answer is probably better for your purposes.
추가 답변 (1개)
Bruno Luong
2019년 9월 11일
편집: Bruno Luong
2019년 9월 11일
You can use this implementation by Matt J using the Horn's method. It do for you the scaling and translation as well.
댓글 수: 0
참고 항목
카테고리
Help Center 및 File Exchange에서 MATLAB Support Package for USB Webcams에 대해 자세히 알아보기
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!