A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be...A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gr?bner system. Combining with properties of the generalized discriminant sequences, the authors give the explicit conditions to determine the number of distinct real positive solutions of the P3P problem. Several examples are provided to illustrate the effectiveness of the proposed conditions.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
摄像机与激光测距仪(Camera and laser rangefinder,LRF)被广泛应用于机器人、移动道路测量车、无人驾驶等领域.其中,外参数标定是实现图像与LIDAR数据融合的第一步,也是至关重要的一步.本文提出一种新的基于最小解(Minimal solution)...摄像机与激光测距仪(Camera and laser rangefinder,LRF)被广泛应用于机器人、移动道路测量车、无人驾驶等领域.其中,外参数标定是实现图像与LIDAR数据融合的第一步,也是至关重要的一步.本文提出一种新的基于最小解(Minimal solution)外参数标定算法,即摄像机与激光仅需对标定棋盘格采集三次数据.本文首次提出虚拟三面体概念,并以之构造透视三点问题(Perspective-three-point,P3P)用以计算激光与摄像机之间的坐标转换关系.相对于文献在对偶三维空间(Dual 3D space)中构造的P3P问题,本文直接在原始三维空间中构造P3P问题,具有更直观的几何意义,更利于对P3P问题进行求解与分析.针对P3P问题多达八组解的问题,本文还首次提出一种平面物成像区域约束方法从多解中获取真解,使得最小解标定法具有更大的实用性与灵活性.实验中分别利用模拟数据与真实数据对算法进行测试.算法结果表明,在同等输入的条件下,本文算法性能超过文献中的算法.本文所提的平面物成像区域约束方法能从多解中计算出真解,大大提高了最小解算法的实用性与灵活性.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 the National Nature Science Foundation of China under Grant Nos.11371356 and 61121062
文摘A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gr?bner system. Combining with properties of the generalized discriminant sequences, the authors give the explicit conditions to determine the number of distinct real positive solutions of the P3P problem. Several examples are provided to illustrate the effectiveness of the proposed conditions.
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.
文摘摄像机与激光测距仪(Camera and laser rangefinder,LRF)被广泛应用于机器人、移动道路测量车、无人驾驶等领域.其中,外参数标定是实现图像与LIDAR数据融合的第一步,也是至关重要的一步.本文提出一种新的基于最小解(Minimal solution)外参数标定算法,即摄像机与激光仅需对标定棋盘格采集三次数据.本文首次提出虚拟三面体概念,并以之构造透视三点问题(Perspective-three-point,P3P)用以计算激光与摄像机之间的坐标转换关系.相对于文献在对偶三维空间(Dual 3D space)中构造的P3P问题,本文直接在原始三维空间中构造P3P问题,具有更直观的几何意义,更利于对P3P问题进行求解与分析.针对P3P问题多达八组解的问题,本文还首次提出一种平面物成像区域约束方法从多解中获取真解,使得最小解标定法具有更大的实用性与灵活性.实验中分别利用模拟数据与真实数据对算法进行测试.算法结果表明,在同等输入的条件下,本文算法性能超过文献中的算法.本文所提的平面物成像区域约束方法能从多解中计算出真解,大大提高了最小解算法的实用性与灵活性.
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。
