P3P问题多解现象的普遍性  

Generality of the multi-solution phenomenon in the P3P problem

作　　者：王波[1] 胡浩[1,2] 张彩霞[1,3] 许华荣[1,4] Bo WANG Hao HU Caixia ZHANG Huarong XU(Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China School of Information Science and Engineering, Shandong University, Jinan 250100, China Science College, North China University of Technology, Beijing 100144, China School of Computer Information Engineering, Xiamen University of Technology, Xiamen 361024, China)

机构地区：[1]中国科学院自动化研究所,北京100190 [2]山东大学信息科学与工程学院,济南250100 [3]北方工业大学理学院,北京100144 [4]厦门理工学院计算机与信息工程学院,厦门361024

出　　处：《中国科学：信息科学》2017年第4期482-491,共10页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:61273290;61403373;61503004)资助项目

摘　　要：P3P问题是一种重要的基于单幅图像的物体定位方法,而多解性是P3P问题研究的一个重要方向.本文从几何观点出发,证明当摄像机光心与3个控制点之间的距离相对比较大时,对应的P3P问题一般不可能存在唯一解,即一般至少存在两个解可以同时满足P3P问题的所有三个约束条件.本文的另一个贡献是将P3P问题中"空间三个南瓜面的相交问题"通过"南瓜面与控制点平面交线之间的相交性"进行判断,给出了一种研究P3P问题多解现象的新思路和途径.本文工作可望为P3P问题的研究和应用人员提供一些参考价值.The P3P problem is a significant single-view-based pose estimation method,and its multi-solution phenomenon has been the focus of investigation since its inception.In this work,we demonstrate from a geometrical point of view that when the distance from the camera＇s optical center to the three control points is relatively large,the corresponding P3P problem cannot have a unique solution in general;alternatively,or it should have at least two solutions satisfying the three original constraints.A further contribution of this study is the finding that the intersection of the three 3D pumpkin surfaces in the P3P problem can be generally deduced from the intersection of the three 2D intersecting curves of the three pumpkin surfaces with the control point plane,which provides a new way to investigate the multi-solution phenomenon.Our results may be significant for both P3P theorists and practitioners.

关 键 词：P3P问题 多解现象 南瓜面 视觉定位 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]