%0 Journal Article
%T A General Sufficient Condition of Four Positive Solutions of the P3P Problem
%A Cai-Xia Zhang
%A Zhan-Yi Hu
%A <br>Cai-Xia
%A Zhang
%A and
%A Zhan-Yi
%A Hu
%J 计算机科学技术学报
%D 2005
%I 
%X In this paper, it is proved that, given 3 control points A, B and C, if the camera's optical center O lies on one of the three planes perpendicular to the plane ABC and going through one of the three altitudes of the triangle ABC, and additionally its projection on the plane ABC is within the circumscribed circle of the triangle, that is, O is within the so-called "danger cylinder", then the corresponding P3P problem {O, (ABC)} must have 4 positive solutions. This result is purely geometrical, and more instructive. It can bring some new insight into a better understanding of multiple-solution problem in the PnP problem, and could be used as some theoretical guide to arrange control points in real applications.
%K P3P (Perspective-3-Point) problem
%K danger cylinder
%K multiple solutions<br>计算机图象
%K P3P问题
%K 多重解
%K 空间控制
%K 线性传输
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=F57FEF5FAEE544283F43708D560ABF1B&aid=B51B6ECE859220566A33A00F813F546E&yid=2DD7160C83D0ACED&vid=A04140E723CB732E&iid=B31275AF3241DB2D&sid=BC60A9A1D91963F5&eid=043C7D0F3F6AC1B3&journal_id=1000-9000&journal_name=计算机科学技术学报&referenced_num=1&reference_num=14