A robust O(n) solution to the perspective-n-point problem
We propose a noniterative solution for the Perspective-n-Point (PnP) 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 p...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/85423 http://hdl.handle.net/10220/13516 |
| _version_ | 1811679657202810880 |
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| author | Li, Shiqi. Xu, Chi. Xie, Ming. |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Li, Shiqi. Xu, Chi. Xie, Ming. |
| author_sort | Li, Shiqi. |
| collection | NTU |
| description | We propose a noniterative solution for the Perspective-n-Point (PnP) 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 PnP solution that can achieve more accurate results than the iterative algorithms when no redundant reference points can be used (n≤ 5). Third, large-size point sets can be handled efficiently because its computational complexity is O(n). |
| first_indexed | 2024-10-01T03:12:38Z |
| format | Journal Article |
| id | ntu-10356/85423 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:12:38Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/854232020-03-07T13:19:24Z A robust O(n) solution to the perspective-n-point problem Li, Shiqi. Xu, Chi. Xie, Ming. School of Mechanical and Aerospace Engineering DRNTU::Engineering::Computer science and engineering::Computing methodologies::Pattern recognition We propose a noniterative solution for the Perspective-n-Point (PnP) 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 PnP solution that can achieve more accurate results than the iterative algorithms when no redundant reference points can be used (n≤ 5). Third, large-size point sets can be handled efficiently because its computational complexity is O(n). 2013-09-18T03:18:43Z 2019-12-06T16:03:30Z 2013-09-18T03:18:43Z 2019-12-06T16:03:30Z 2012 2012 Journal Article Li, S., Xu, C., & Xie, M. (2012). A robust O(n) solution to the perspective-n-point problem. IEEE transactions on pattern analysis and machine intelligence, 34(7), 1444-1450. 0162-8828 https://hdl.handle.net/10356/85423 http://hdl.handle.net/10220/13516 10.1109/TPAMI.2012.41 en IEEE transactions on pattern analysis and machine intelligence © 2012 IEEE |
| spellingShingle | DRNTU::Engineering::Computer science and engineering::Computing methodologies::Pattern recognition Li, Shiqi. Xu, Chi. Xie, Ming. A robust O(n) solution to the perspective-n-point problem |
| title | A robust O(n) solution to the perspective-n-point problem |
| title_full | A robust O(n) solution to the perspective-n-point problem |
| title_fullStr | A robust O(n) solution to the perspective-n-point problem |
| title_full_unstemmed | A robust O(n) solution to the perspective-n-point problem |
| title_short | A robust O(n) solution to the perspective-n-point problem |
| title_sort | robust o n solution to the perspective n point problem |
| topic | DRNTU::Engineering::Computer science and engineering::Computing methodologies::Pattern recognition |
| url | https://hdl.handle.net/10356/85423 http://hdl.handle.net/10220/13516 |
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