P3P问题的解与本质二次曲线对交点之间的关系  

Relationship between P3P Solutions and the Intersecting Points of Intrinsic Quadratic Pair

作　　者：王波[1] 胡立华[1,2] 张彩霞[1,3] 许华荣[4] Wang Bo;Hu Lihua;Zhang Caixia;Xu Huarong(Integrated Information System Research Center, Institute of Automation, Chinese Academy of Sciences, Beijing 100190;School of Computer Science & Technology, Taiyuan University of Science & Technology, Taiyuan 030024;Science College, North China University of Technology, Beijing 100144;Department of Computer Science & Technology, Xiamen Institute of Technology, Xiamen 361024)

机构地区：[1]中国科学院自动化研究所综合信息系统研究中心,北京100190 [2]太原科技大学计算机科学与技术学院,太原030024 [3]北方工业大学理学院,北京100144 [4]厦门理工学院计算机科学与技术系,厦门361024

出　　处：《计算机辅助设计与图形学学报》2017年第6期1022-1027,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61273290;61403373;61503004;61402316);太原科技大学博士启动基金(20162009)

摘　　要：P3P问题是一种重要的基于单幅图像的视觉定位方法,其多解性研究一直是重要的研究方向.针对P3P问题解个数的判定问题,提出一种基于本质二次曲线交点的解个数的判定方法.P3P问题的解与由其基本约束方程导出的2条本质二次曲线在第一象限内的交点存在一一对应关系,通过判断这2条二次曲线在第一象限内交点的个数,可以直观地判定P3P问题的解的个数.最后就共边解、共点解、二重解等特殊解对应的本质二次曲线交点的几何分布性质进行了讨论.The P3P problem is an important single-view based pose-estimation method,and its multi-solutionphenomenon has been a focus of investigation since its very inception.A new approach is proposed to determinethe number of P3P solutions based on the intersecting points of the intrinsic quadratic pair,which isderived from the3original constraint equations in the P3P problem.Our results show that solutions of theP3P problem have a one-to-one relationship with the intersecting points of the intrinsic quadratic pair in thefirst quadrant.Hence by locating the intersecting points,the solutions of the P3P problem can be uniquelydetermined.In addition,we also analyze the corresponding geometric configurations of the intersectingpoints for some special P3P solutions,such as the side-sharing pair of solutions,the point-sharing pair ofsolutions,and the double solution.

关 键 词：P3P问题 多解性 本质二次曲线对 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]