Complete solution classification for the perspective-three-point problem
Abstract
We use two approaches to solve the perspective-three-point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. We also give a complete solution classification for the P3P equation system, i.e., we give explicit criteria for the P3P problem to have one, two, three, and four solutions. Combining the analytical solutions with the criteria, we provide an algorithm, CASSC, which may be used to find complete and robust numerical solutions to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions.
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Previous satellite pose estimation approaches represent a satellite as a set of 2D keypoints and then estimate the satellite pose using PnP algorithms.
“Meanwhile, previous satellite pose estimation approaches [12], [15] represent a satellite as a set of 2D keypoints, and then estimate the satellite pose using the perspective-n-point (PnP) algorithms [27].”
From Bridging the Domain Gap in Satellite Pose Estimation: A Self-Training Approach Based on Geometrical Constraints (2024) · cites this paper as [27]
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- Authors
- Gao, X.-S., Hou, X.-R., Tang, J., & Cheng, H.-F.
- Affiliations
- Chinese Academy of Sciences (CN)
- Pennsylvania State University (US)
- ORCID
- Xiao-Shan Gao
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2003-08
- Volume
- 25
- Issue
- 8
- Pages
- 930-943
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2097649661
- Cited by
- 976
- References
- 24
- Citations by year
- 2026: 51 · 2025: 81 · 2024: 78 · 2023: 101 · 2022: 83 · 2021: 90 · 2020: 90 · 2019: 93 · 2018: 62 · 2017: 38 · 2016: 26 · 2015: 32 · 2014: 27 · 2013: 21 · 2012: 12
- FWCI
- 6.89
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Pattern Analysis and Machine Intelligence (publishedVersion)
- Funders
- National Natural Science Foundation of China
- Chinese Academy of Sciences
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Vision and Imaging
- Physical Sciences › Engineering › Control and Systems Engineering › Robotic Mechanisms and Dynamics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
- Keywords
- classification of solutions, triangular decomposition, algebraic geometry, camera pose estimation, real solutions
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