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判定P3P问题正解数目的充要条件
引用本文:苏成,徐迎庆,李华,刘慎权,李冬果.判定P3P问题正解数目的充要条件[J].计算机学报,1998,21(12):1084-1095.
作者姓名:苏成  徐迎庆  李华  刘慎权  李冬果
作者单位:1. 中国科学院计算技术研究所CAD开放实验室,北京,100080
2. 首都医科大学,北京,100054
基金项目:国家自然科学基金!69673020,69573034,国家重点科技项目基金!96-920-02-04
摘    要:本文研究用于摄像机定位的三点透视问题(P3P),长期以来由于缺少判定非线性方程组根数目的充要的方法,P3P问题的多解现象使其应用一直受到限制。本文采用新提法对P3P问题分类,采用新的化简方法,充分利用多项式根的数目估计实现了对非线性的P3P方程组根的数目估计,并完整地分析了P3P问题种种多解现象的充要条件。我们的定理能够解释前人已发现的现象。把结合从前人“对P3P问题1-4解的不确定集合作出了一种

关 键 词:计算机视觉  机器视觉  计算机动画  三点透视问题
修稿时间:1997年7月8日

NECESSARY AND SUFFICIENT CONDITION OF POSITIVE ROOT NUMBER OF PERSPECTIVE-THREE-POINT PROBLEM
SU Cheng,XU Ying-Qing,LI Hua,LIU Shen-Quan,LI Dong-guo.NECESSARY AND SUFFICIENT CONDITION OF POSITIVE ROOT NUMBER OF PERSPECTIVE-THREE-POINT PROBLEM[J].Chinese Journal of Computers,1998,21(12):1084-1095.
Authors:SU Cheng  XU Ying-Qing  LI Hua  LIU Shen-Quan  LI Dong-guo
Abstract:This paper gives some new useful theorems about the perspective-three-point problem(P3P), which is an open problem in Camera Calibration for its multi-solution phenomenon. Some new mathematical methods, new classifications and new adjudicate conditions have been applied to analyze the every aspect of P3P problem. A powerful improved conclusion has been drawn to "determine the root numbers, if and only if", which is used to be "a systematic analysis of the geometric configurations with ambiguity sets of 1-4 solutions". And the distribution of the roots in 3D is also concerned. This will lead to a widely applicable prospect of the composer of animation images and video films and other fields.
Keywords:Computer vision  machine vision  computer animation  location determination problem (LDP)  perspective-three-point problem (P3P)
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