Solving the perspective-three-point problem using comprehensive Gröbner systems

Solving the perspective-three-point problem using comprehensive Gröbner systems

A complete solution classification of the perspective-three-point (P3P) problem is given by using the Gröbner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gröbner system. Combining with properties o...

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Veröffentlicht in:Journal of systems science and complexity 2016-10, Vol.29 (5), p.1446-1471
Hauptverfasser: Zhou, Jie, Wang, Dingkang
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Sprache:eng
Schlagworte:
Complex Systems
Control
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Sequences
Solution space
Statistics
Systems Theory
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description A complete solution classification of the perspective-three-point (P3P) problem is given by using the Gröbner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gröbner system. Combining with properties of the generalized discriminant sequences, the authors give the explicit conditions to determine the number of distinct real positive solutions of the P3P problem. Several examples are provided to illustrate the effectiveness of the proposed conditions.
doi_str_mv 10.1007/s11424-015-4310-y
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subjects Complex Systems
Control
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Sequences
Solution space
Statistics
Systems Theory
title Solving the perspective-three-point problem using comprehensive Gröbner systems
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