The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution a...The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.展开更多
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...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.展开更多
In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt's zero ...In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given.展开更多
In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with...In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and,thus, the imaging rays may not pass through a common point.Such generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective technique.Using the Wu-Ritt＇s zero decomposition method,the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem.展开更多
2维激光雷达和摄像机的最小解标定方法存在精度较差、解缺失等不足,为此,提出了一种新的可靠最小解标定方法。首先,利用透视相似三角形(perspective similar triangle,PST)算法求解3个棋盘格构建的P3P(perspective three points,P3P)问...2维激光雷达和摄像机的最小解标定方法存在精度较差、解缺失等不足,为此,提出了一种新的可靠最小解标定方法。首先,利用透视相似三角形(perspective similar triangle,PST)算法求解3个棋盘格构建的P3P(perspective three points,P3P)问题,并通过多项式极值点获取缺失的解,提高了算法对噪声的抗干扰能力。其次,提出基于两类激光点约束的误差度量模型来评估多解的误差程度,从而更准确地从标定结果的多解中选取最优解。实验结果表明,该文算法相比于文献中的FRANCISCO算法和HU算法,能明显提高有效解概率和标定精度;在不同噪声水平下,该文算法的有效解概率提高了5%—20%和5%—13%,旋转矩阵精度提高了46%—63%和41%—47%,平移向量精度提高了170—430mm和120—170mm,性能提高明显。展开更多
基金Supported by"973"Program(2002CB312104)National Natural Science Foundation of P.R.China(60375006)the Research Foundation of North China Unversity of Technology University
文摘The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60375006,60475009(国家自然科学基金)the Research Foundation of North China University of Technology(北方工业大学校科研基金)
基金the National Natural Science Foundation of China under an outstanding youth grant (No. 69725002) and by the NKBRSF of China (N
文摘In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given.
基金This project was partially supported by Shuxue Tianyuan Foundation(No.10526031).
文摘In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and,thus, the imaging rays may not pass through a common point.Such generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective technique.Using the Wu-Ritt＇s zero decomposition method,the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem.
文摘2维激光雷达和摄像机的最小解标定方法存在精度较差、解缺失等不足,为此,提出了一种新的可靠最小解标定方法。首先,利用透视相似三角形(perspective similar triangle,PST)算法求解3个棋盘格构建的P3P(perspective three points,P3P)问题,并通过多项式极值点获取缺失的解,提高了算法对噪声的抗干扰能力。其次,提出基于两类激光点约束的误差度量模型来评估多解的误差程度,从而更准确地从标定结果的多解中选取最优解。实验结果表明,该文算法相比于文献中的FRANCISCO算法和HU算法,能明显提高有效解概率和标定精度;在不同噪声水平下,该文算法的有效解概率提高了5%—20%和5%—13%,旋转矩阵精度提高了46%—63%和41%—47%,平移向量精度提高了170—430mm和120—170mm,性能提高明显。
