P3P问题的多解现象的概率研究(英文)  

A Probabilistic Study on the Multiple Solutions of the P3P Problem

作　　者：张彩霞[1] 胡占义[1] 

机构地区：[1]中国科学院自动化研究所模式识别国家重点实验室

出　　处：《软件学报》2007年第9期2100-2104,共5页Journal of Software

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos.60375006,60475009(国家自然科学基金);the Research Foundation of North China University of Technology(北方工业大学校科研基金)

摘　　要：一般情况下,P3P问题可能出现1,2,3或4个解.但是,若3个控制点和摄像机光心这4点共圆,则会出现无穷多组解.利用"蒙特卡洛"方法模拟出P3P问题分别出现1,2,3,4个解的概率为0.9993,0.0007,0.0000,0.0000.结果论证了如下的事实,即在大多数情况下,P3P问题有唯一解.Under some special conditions, the P3P problem can have 1, 2, 3 and 4 solutions, and if the 3 control points and the optical center lie on a circle, the problem is indeterminate. In this paper, by the Monte Carlo approach of up to 1 million samples, it is shown that the probabilities of the P3P problem with one solution, two solutions, three solutions, and four solutions are respectively 0.9993, 0.0007, 0.0000, 0.0000. The result confirms the well-known fact that in the most cases, the P3P has a unique solution.

关 键 词：P3P问题 多解现象 蒙特卡洛方法 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]