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，把结论从前人“对P3P问题1—4解的不确定集合作出了一种几何解释”的水平提高到建立了简明的“判定正解数目的充要条件的定理”，并讨论了多解的分布规律．
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.
出处
《计算机学报》
EI
CSCD
北大核心
1998年第12期1084-1095,共12页
Chinese Journal of Computers
基金
国家自然科学基金!69673020
69573034
国家重点科技项目基金!96-920-02-04
关键词
计算机视觉
机器视觉
计算机动画
三点透视问题
Computer vision, machine vision, computer animation, location determination problem (LDP), perspective-three-point problem (P3P)
