A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be...A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gr?bner 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.展开更多
In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt's zero ...In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation 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. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given.展开更多
基金supported by the National Nature Science Foundation of China under Grant Nos.11371356 and 61121062
文摘A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gr?bner 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.
基金the National Natural Science Foundation of China under an outstanding youth grant (No. 69725002) and by the NKBRSF of China (N
文摘In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation 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. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given.
