Issue No. 07 - July (2012 vol. 34)

ISSN: 0162-8828

pp: 1444-1450

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPAMI.2012.41

Chi Xu , Huazhong University of Science & Technology, Wuhan

Ming Xie , Nanyang Technological University, Singapore

Shiqi Li , Huazhong University of Science & Technology, Wuhan

ABSTRACT

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).

INDEX TERMS

Perspective-n-point problem, camera pose estimation, augmented reality.

CITATION

Chi Xu, Ming Xie, Shiqi Li, "A Robust O(n) Solution to the Perspective-n-Point Problem",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 34, no. , pp. 1444-1450, July 2012, doi:10.1109/TPAMI.2012.41