关于PnP问题多解的分布与解的稳定性的讨论  

A Note on the Roots Distribution and Stability of the PnP Problem

作　　者：孙凤梅[1] 王波[2] 

机构地区：[1]北方工业大学理学院,北京100144 [2]中国科学院自动化研究所,北京100190

出　　处：《自动化学报》2010年第9期1213-1219,共7页Acta Automatica Sinica

基　　金：国家自然科学基金(60673104;60973005)资助~~

摘　　要：PnP(Perspectire-n-Point)问题是一种基于单幅图像的定位方法,由于不需要建立图像点之间的对应关系,所以,在机器人定位等应用中得到了广泛的应用.多解性和解的稳定性是PnP问题的两个重要问题,直接关系到具体视觉问题的成败.那么,PnP问题的多解是如何分布的呢?多解一定意味着解是不稳定的吗?这些问题文献中几乎没有任何报道.本文以P3P问题为研究对象,对这些问题进行了一些探讨,研究结果对揭示PnP问题解的分布规律以及解的稳定性问题具有一定的参考价值.The PnP problem is a widely used method in pose determination since it is a single-view based approach and does not need any image point correspondences,a difficult task itselfin computer vision.The multiplicity and stability of solutions in the PnP problem are two important issues,they somehow directly determine the sucess or failure of a real application.Then questions arise：What is the distribution of the multiple solutions？ Does the exsistence of multple solutions necessarily mean that the solutions are not stable？ There are no related reports on such issues in the literature to our knowledge.In this work,these two issues are investigated in terms of P3P problem,and the obtained results could provide some insight for the problem of the multiplicity and stability of the PnP problem,and could be of reference to the people in the field.

关 键 词：PNP问题 多解分布 解的稳定性 解的唯一性 物体定位 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]