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基于观测概率有效下界估计的二维激光雷达和摄像机标定方法

彭梦 万琴 陈白帆 邬书跃

彭梦, 万琴, 陈白帆, 邬书跃. 基于观测概率有效下界估计的二维激光雷达和摄像机标定方法[J]. 电子与信息学报, 2022, 44(7): 2478-2487. doi: 10.11999/JEIT210800
引用本文: 彭梦, 万琴, 陈白帆, 邬书跃. 基于观测概率有效下界估计的二维激光雷达和摄像机标定方法[J]. 电子与信息学报, 2022, 44(7): 2478-2487. doi: 10.11999/JEIT210800
PENG Meng, WAN Qin, CHEN Baifan, WU Shuyue. A Calibration Method of 2D Lidar and a Camera Based on Effective Lower Bound Estimation of Observation Probability[J]. Journal of Electronics & Information Technology, 2022, 44(7): 2478-2487. doi: 10.11999/JEIT210800
Citation: PENG Meng, WAN Qin, CHEN Baifan, WU Shuyue. A Calibration Method of 2D Lidar and a Camera Based on Effective Lower Bound Estimation of Observation Probability[J]. Journal of Electronics & Information Technology, 2022, 44(7): 2478-2487. doi: 10.11999/JEIT210800

基于观测概率有效下界估计的二维激光雷达和摄像机标定方法

doi: 10.11999/JEIT210800
基金项目: 国家自然科学基金(62173134, 62006075),湖南省自然科学基金(2021JJ10002, 2020JJ4246),湖南省教育厅资助科研项目(18B386, 18A356),湖南省大学生创新创业训练计划(S201911342021)
详细信息
    作者简介:

    彭梦:男,1978年生,博士,讲师,研究方向为多传感器融合

    万琴:女,1980年生,博士,教授,研究方向为机器视觉、机器人多目标定位跟踪

    陈白帆:女,1979年生,博士,副教授,研究方向为移动机器人环境感知与定位

    邬书跃:男,1963年生,博士,教授,研究方向为数字信号处理

    通讯作者:

    彭梦 pengmeng@hnie.edu.cn

  • 中图分类号: TN958.98; TN911.7

A Calibration Method of 2D Lidar and a Camera Based on Effective Lower Bound Estimation of Observation Probability

Funds: The National Natural Science Foundation of China (62173134, 62006075), The Natural Science Foundation of Hunan Province (2021JJ10002, 2020JJ4246), The Hunan Education Department Funded Research Project (18B386, 18A356), The Innovation and Entrepreneurship Training Program for College Students in Hunan Province (S201911342021)
  • 摘要: 针对2D激光雷达和摄像机最小解标定方法的多解问题,该文提出一种基于观测概率有效下界估计的标定方法。首先,提出一种最小解集合的分级聚类方法,将每类最优解替换原来的解集合,从而减少解集合样本个数。然后,提出一种基于激光误差的联合观测概率度量,对解集合元素的优劣进行度量。最后,利用聚类结果和观测概率度量结果,该文提出基于观测概率有效下界估计的有效解选取策略,将优化初始值从最优解转化为有效解候选集合,提高了标定结果的准确性。仿真实验结果表明,在真解命中率性能上相比于Francisco方法,该文方法在不同棋盘格个数情况下提升真解命中率16%~20%,在不同噪声水平下提升真解命中率6%~20%,有效提高真解比例。
  • 图  1  2维激光雷达坐标系和摄像机坐标系转换关系

    图  2  局部最优观测概率分布示意图,其中${\hat p_{{\rm{opt}}}}$为观测概率有效下界

    图  3  3种方法的真解命中率对比分析

    图  4  不同棋盘格个数输入下3种方法的误差均值

    图  5  不同棋盘格数目情况下3种方法标定误差值的分布

    图  6  不同激光噪声方差情况下3种方法的误差均值

    图  7  不同激光噪声方差情况下3种方法标定误差值的分布

    图  8  激光点在图像上的投影结果

    图  9  真实实验中旋转矩阵分布和平移向量分布示意图

    表  1  本文所提标定算法伪代码

     输入: 基于$ N $个棋盘格${{\boldsymbol{\varPi}} _i}$和对应的共面直线${\boldsymbol{L}}_i^{\rm{l}}$。
     输出: 旋转矩阵${\boldsymbol{R}}$和平移向量$ t $。
     (1) 构造一个集合${\boldsymbol{K} } = \left\{ {\left. { {k_1},{k_2}, \cdots ,{k_d} } \right\} } \right.\;\left( {d = C_N^3} \right)$,其中$ {k_i} \in {Z^3} $表示从$\left\{ {\left. {1,2, \cdots ,N} \right\} } \right.$的$ N $个数中选取3个数的一种可能组合,${\boldsymbol{K}}$表示所有
      的可能组合。
     (2) 设置解集合${\boldsymbol{D}} = \phi$, ${\boldsymbol{S}} = \phi$。
     (3) For t =1,2,···, d do
     (4) 选择和$ {k_t} $的各元素对应的3个棋盘格${{\boldsymbol{\varPi}} _{ {k_{t,1} } } }$, ${{\boldsymbol{\varPi}} _{ {k_{t,2} } } }$和${{\boldsymbol{\varPi}} _{ {k_{t,3} } } }$以及对应的共面直线${\boldsymbol{L} }_{ {k_{t,1} } }^{\text{l} }$, ${\boldsymbol{L}}_{ {k_{t,2} } }^l$和${\boldsymbol{L}}_{ {k_{t,3} } }^l$,使用文献[5]的算法计算一组最
      小解$\left( {{\boldsymbol{R}}_t^{(m)},{\boldsymbol{t}}_t^{(m)} } \right)$, $ m \lt 8 $。
     (5) 将当前这组解合并到解集合${\boldsymbol{D}} = {\boldsymbol{D}} \cup \left( {{\boldsymbol{R}}_t^{(m)},{\boldsymbol{t}}_t^{(m)} } \right)$。
     (6) End for
     (7) 利用式(3)和式(4)作为类之间的距离度量,对解集合${\boldsymbol{D}}$进行分级聚类,聚类结果为$ \left\{ {{C_i}} \right\}_{i = 1}^k $。
     (8) 根据式(8)—式(11)计算基于激光误差的联合观测概率$ {\pi _j} $。
     (9) 根据聚类结果$ \left\{ {{C_i}} \right\}_{i = i}^k $和联合观测概率$ {\pi _j} $,利用式(12)获取每类中局部最优观测概率的解$\left\{ {\left( { { {\tilde {\boldsymbol{R}}}_i},{ {\tilde {\boldsymbol{t}}}_i} } \right)} \right\}_{i = i}^k$,其对应的观测概率为
      $ \left\{ {{p_i}} \right\}_{i = i}^k $。
     (10) 根据式(13)计算观测概率有效下界${\hat p_{{\rm{opt}}} }$,将${p_i} \gt {\hat p_{{\rm{opt}}} }$的局部最优解$\left( { { {\tilde {\boldsymbol{R}}}_i},{ {\tilde {\boldsymbol{t}}}_i} } \right)$加入到有效解候选集合$ S $,将$ S $作为标定参数优化的初始值。
    下载: 导出CSV

    表  2  本文方法的有效解个数以及运算时间的比较

    棋盘格的个数
    345678
    本文方法的有效解个数均值(个)2.12.32.42.62.72.7
    本文方法的运算时间(s)1.3511.7252.4372.6503.8964.682
    Francisco方法的运算时间(s)0.2100.3510.5310.7201.2411.631
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-09
  • 修回日期:  2022-04-01
  • 网络出版日期:  2022-04-14
  • 刊出日期:  2022-07-25

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