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

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