On the closed-form solution of the rotation matrix arising in computer vision problems

Details On the closed-form solution of the rotation matrix arising in computer vision problems On the closed-form solution of the rotation matrix arising in computer vision problems

2009-04-09

arxiv.org/abs/0904.1613v1

Computer Science

Computer Vision and Pattern Recognition

Scientific paper

We show the closed-form solution to the maximization of trace(A'R), where A is given and R is unknown rotation matrix. This problem occurs in many computer vision tasks involving optimal rotation matrix estimation. The solution has been continuously reinvented in different fields as part of specific problems. We summarize the historical evolution of the problem and present the general proof of the solution. We contribute to the proof by considering the degenerate cases of A and discuss the uniqueness of R.

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