English

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

Computer Vision and Pattern Recognition 2009-04-13 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0904.1613,
  title  = {On the closed-form solution of the rotation matrix arising in computer vision problems},
  author = {Andriy Myronenko and Xubo Song},
  journal= {arXiv preprint arXiv:0904.1613},
  year   = {2009}
}
R2 v1 2026-06-21T12:50:00.951Z