On the probability of the number of solutiong for the P4P problem

被引：14

作者：

Gao, Xiao-Shan ^{[1
]}

Tang, Jianliang

机构：

[1] Acad Sinica, Inst Syst Sci, Key Lab Math Mechanizat, Beijing 100080, Peoples R China

[2] Shenzhen Univ, Coll Sci, Shenzhen 518060, Peoples R China

来源：

JOURNAL OF MATHEMATICAL IMAGING AND VISION | 2006年 / 25卷 / 01期

基金：

美国国家科学基金会;

关键词：

camera calibration; pose determination; perspective four point problem; P4P; probability; number of solutions;

D O I：

10.1007/s10851-006-5149-6

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper studies the multi-solution phenomenon for the perspective four point (P4P) problem from geometric and algebraic aspects. We give a pure geometric proof that the P4P problem could have up to five solutions. We also give a clear picture on how these five solutions could be realized. We prove that with probability one, the P4P problem has a unique solution which can be represented by a set of rational functions in the parameters. The simulant experiments show that to solve the P4P problem with the rational functions is stable and accurate.

引用

页码：79 / 86

页数：8

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