{
  "id": "0904.1613",
  "version": "v1",
  "published": "2009-04-09T22:15:25.000Z",
  "updated": "2009-04-09T22:15:25.000Z",
  "title": "On the closed-form solution of the rotation matrix arising in computer vision problems",
  "authors": [
    "Andriy Myronenko",
    "Xubo Song"
  ],
  "categories": [
    "cs.CV"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-09T22:15:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "computer vision problems",
      "closed-form solution",
      "rotation matrix arising",
      "optimal rotation matrix estimation",
      "computer vision tasks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1613M"
    }
  }
}