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A Robust O(n) Solution to the Perspective-n-Point Problem

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3 Author(s)
Shiqi Li ; Sch. of Mech. Sci. & Eng., Huazhong Univ. of Sci. & Technol., Wuhan, China ; Chi Xu ; Ming Xie

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 (nle 5). Third, large-size point sets can be handled efficiently because its computational complexity is O(n).

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:34 ,  Issue: 7 )