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

IEEE Transactions on Pattern Analysis and Machine Intelligence
Shiqi Li Ming Xie

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).

References

Nov 24, 2004·Archives of Disease in Childhood·L McGlone
Aug 26, 2006·IEEE Transactions on Pattern Analysis and Machine Intelligence·Vincent Lepetit, Pascal Fua
Nov 17, 2006·IEEE Transactions on Pattern Analysis and Machine Intelligence·Gerald Schweighofer, Axel Pinz

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Citations

Mar 26, 2013·International Journal of Computer Assisted Radiology and Surgery·Michael MüllerLena Maier-Hein
Jun 22, 2014·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Haoyin ZhouWeining Lu
Jun 23, 2016·IEEE Transactions on Pattern Analysis and Machine Intelligence·Chi XuReinhard Koch
May 9, 2019·Computational Intelligence and Neuroscience·Francisco Gomez-DonosoMiguel Cazorla
Mar 7, 2021·Sensors·Honglin YuanRemco C Veltkamp
Jun 12, 2021·International Journal of Occupational Safety and Ergonomics : JOSE·Ramtin NazerianEhsan Shakeri

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