An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem

Qida Yu; Guili Xu; Jiachen Shi

doi:10.1007/978-3-030-68793-9_4

An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem

Qida Yu, Guili Xu, Jiachen Shi

Nanjing University of Aeronautics and Astronautics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In this work, we propose an efficient and simple method for solving the perspective-three-point (P3P) problem. This algorithm leans substantially on linear algebra, in which the rotation matrix and translation vector are parameterized as linear combinations of known vectors with particular coefficients. We also show how to avoid degeneracy when performing this algorithm. Moreover, we present an approach to roughly remove invalid solutions based on the orthogonal property of the rotation matrix. The proposed method is simple to implement and easy to understand, with improved results demonstrating that it is competitive with the leading methods in accuracy, but with reduced computational requirements.

Original language	English
Title of host publication	Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings
Editors	Alberto Del Bimbo, Rita Cucchiara, Stan Sclaroff, Giovanni Maria Farinella, Tao Mei, Marco Bertini, Hugo Jair Escalante, Roberto Vezzani
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	46-59
Number of pages	14
ISBN (Print)	9783030687922
DOIs	https://doi.org/10.1007/978-3-030-68793-9_4
State	Published - 2021
Externally published	Yes
Event	25th International Conference on Pattern Recognition Workshops, ICPR 2020 - Milan, Italy Duration: 10 Jan 2021 → 11 Jan 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12668 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th International Conference on Pattern Recognition Workshops, ICPR 2020
Country/Territory	Italy
City	Milan
Period	10/01/21 → 11/01/21

Keywords

Computer vision
Linear algebra
Perspective-three-point (p3p)

Access to Document

10.1007/978-3-030-68793-9_4

Cite this

Yu, Q., Xu, G., & Shi, J. (2021). An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem. In A. Del Bimbo, R. Cucchiara, S. Sclaroff, G. M. Farinella, T. Mei, M. Bertini, H. J. Escalante, & R. Vezzani (Eds.), Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings (pp. 46-59). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12668 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-68793-9_4

Yu, Qida ; Xu, Guili ; Shi, Jiachen. / An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem. Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings. editor / Alberto Del Bimbo ; Rita Cucchiara ; Stan Sclaroff ; Giovanni Maria Farinella ; Tao Mei ; Marco Bertini ; Hugo Jair Escalante ; Roberto Vezzani. Springer Science and Business Media Deutschland GmbH, 2021. pp. 46-59 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem",

abstract = "In this work, we propose an efficient and simple method for solving the perspective-three-point (P3P) problem. This algorithm leans substantially on linear algebra, in which the rotation matrix and translation vector are parameterized as linear combinations of known vectors with particular coefficients. We also show how to avoid degeneracy when performing this algorithm. Moreover, we present an approach to roughly remove invalid solutions based on the orthogonal property of the rotation matrix. The proposed method is simple to implement and easy to understand, with improved results demonstrating that it is competitive with the leading methods in accuracy, but with reduced computational requirements.",

keywords = "Computer vision, Linear algebra, Perspective-three-point (p3p)",

author = "Qida Yu and Guili Xu and Jiachen Shi",

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doi = "10.1007/978-3-030-68793-9_4",

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editor = "{Del Bimbo}, Alberto and Rita Cucchiara and Stan Sclaroff and Farinella, {Giovanni Maria} and Tao Mei and Marco Bertini and Escalante, {Hugo Jair} and Roberto Vezzani",

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Yu, Q, Xu, G & Shi, J 2021, An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem. in A Del Bimbo, R Cucchiara, S Sclaroff, GM Farinella, T Mei, M Bertini, HJ Escalante & R Vezzani (eds), Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12668 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 46-59, 25th International Conference on Pattern Recognition Workshops, ICPR 2020, Milan, Italy, 10/01/21. https://doi.org/10.1007/978-3-030-68793-9_4

An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem. / Yu, Qida; Xu, Guili; Shi, Jiachen.
Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings. ed. / Alberto Del Bimbo; Rita Cucchiara; Stan Sclaroff; Giovanni Maria Farinella; Tao Mei; Marco Bertini; Hugo Jair Escalante; Roberto Vezzani. Springer Science and Business Media Deutschland GmbH, 2021. p. 46-59 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12668 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this work, we propose an efficient and simple method for solving the perspective-three-point (P3P) problem. This algorithm leans substantially on linear algebra, in which the rotation matrix and translation vector are parameterized as linear combinations of known vectors with particular coefficients. We also show how to avoid degeneracy when performing this algorithm. Moreover, we present an approach to roughly remove invalid solutions based on the orthogonal property of the rotation matrix. The proposed method is simple to implement and easy to understand, with improved results demonstrating that it is competitive with the leading methods in accuracy, but with reduced computational requirements.

AB - In this work, we propose an efficient and simple method for solving the perspective-three-point (P3P) problem. This algorithm leans substantially on linear algebra, in which the rotation matrix and translation vector are parameterized as linear combinations of known vectors with particular coefficients. We also show how to avoid degeneracy when performing this algorithm. Moreover, we present an approach to roughly remove invalid solutions based on the orthogonal property of the rotation matrix. The proposed method is simple to implement and easy to understand, with improved results demonstrating that it is competitive with the leading methods in accuracy, but with reduced computational requirements.

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Yu Q, Xu G, Shi J. An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem. In Del Bimbo A, Cucchiara R, Sclaroff S, Farinella GM, Mei T, Bertini M, Escalante HJ, Vezzani R, editors, Pattern Recognition. ICPR International Workshops and Challenges, 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 46-59. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-68793-9_4

An Efficient and Reasonably Simple Solution to the Perspective-Three-Point Problem

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Keywords

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