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Issue No. 07 - July (2012 vol. 34)
ISSN: 0162-8828
pp: 1444-1450
Shiqi Li , Huazhong University of Science & Technology, Wuhan
Chi Xu , Huazhong University of Science & Technology, Wuhan
Ming Xie , Nanyang Technological University, Singapore
We propose a noniterative solution for the Perspective-n-Point ({\rm P}n{\rm P}) problem, which can robustly retrieve the optimum by solving a seventh order polynomial. The central idea consists of three steps: 1) to divide the reference points into 3-point subsets in order to achieve a series of fourth order polynomials, 2) to compute the sum of the square of the polynomials so as to form a cost function, and 3) to find the roots of the derivative of the cost function in order to determine the optimum. The advantages of the proposed method are as follows: First, it can stably deal with the planar case, ordinary 3D case, and quasi-singular case, and it is as accurate as the state-of-the-art iterative algorithms with much less computational time. Second, it is the first noniterative {\rm P}n{\rm P} solution that can achieve more accurate results than the iterative algorithms when no redundant reference points can be used (n\le 5). Third, large-size point sets can be handled efficiently because its computational complexity is O(n).
Perspective-n-point problem, camera pose estimation, augmented reality.

C. Xu, M. Xie and S. Li, "A Robust O(n) Solution to the Perspective-n-Point Problem," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 34, no. , pp. 1444-1450, 2012.
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