EPnL: 一种高效且精确的PnL问题求解算法

王平; 何卫隆; 张爱华; 姚鹏鹏; 徐贵力

doi:10.16383/j.aas.c200927

EPnL: 一种高效且精确的PnL问题求解算法

doi: 10.16383/j.aas.c200927

1.
兰州理工大学电气工程与信息工程学院兰州 730050 中国
2.
香港理工大学纺织与制衣学系香港 999077 中国
3.
南京航空航天大学自动化学院南京 211106 中国

基金项目: 国家自然科学基金(62001198, 62073161, 61866021), 流程工业综合自动化国家重点实验室开放基金 (PAL-N201808), 甘肃省国际合作科技计划(18YF1WA068), 甘肃省青年科技基金(20JR10RA-186)资助

详细信息

作者简介:
王平：兰州理工大学电气工程与信息工程学院讲师. 2019年获南京航空航天大学博士学位. 主要研究方向为计算机视觉, 机器学习和信号处理. 本文通信作者. E-mail: pingwangsky@163.com

何卫隆：兰州理工大学电气工程与信息工程学院硕士研究生. 主要研究方向为机器视觉和视觉测量. E-mail: heweilongd@163.com

张爱华：兰州理工大学电气工程与信息工程学院教授. 2005年获西安交通大学博士学位. 主要研究方向为检测技术和模式识别与智能系统. E-mail: zhangaihua@lut.edu.cn

姚鹏鹏：中国香港理工大学纺织与制衣学系博士研究生. 主要研究方向为多光谱颜色测量, 相机矫正和图像检索. E-mail: p.p.yao@connect.polyu.hk

徐贵力：南京航空航天大学自动化学院教授. 2002年获江苏大学博士学位. 主要研究方向为光电检测, 计算机视觉和智能系统. E-mail: guilixu2002@163.com

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出版历程
- 收稿日期: 2020-11-09
- 录用日期: 2021-03-05
- 网络出版日期: 2021-05-12
- 刊出日期: 2022-10-14

EPnL: An Efficient and Accurate Algorithm to the PnL Problem

1.
College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2.
Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong 999077, China
3.
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Funds: Supported by National Natural Science Foundation of China (62001198, 62073161, 61866021), State Key Laboratory of Synthetical Automation for Process Industries (PAL-N201808), International Cooperation Science and Technology Program of Gansu Province (18YF1WA068), and Gansu Province Science Foundation for Youths (20JR10RA186)

More Information

Author Bio:
WANG Ping　Lecturer at the College of Electrical and Information Engineering, Lanzhou University of Technology. He received his Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 2019. His research interest covers computer vision, machine learning and signal processing. Corresponding author of this paper

HE Wei-Long　Master student at the College of Electrical and Information Engineering, Lanzhou University of Technology. His research interest covers machine vision and vision measurement

ZHANG Ai-Hua　Professor at the College of Electrical and Information Engineering, Lanzhou University of Technology. She received her Ph.D. degree from Xi＇an Jiaotong University in 2005. Her research interest covers detection technology, pattern recognition and intelligent system

YAO Peng-Peng　Ph.D. candidate at the Institute of Textile and Clothing, Hong Kong Polytechnic University, China. His research interest covers multi-spectral color measurement, camera calibration and image retrieval

XU Gui-Li　Professor at the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. He received his Ph.D. degree from Jiangsu University in 2002. His research interest covers photoelectric detection, computer vision and intelligent system

摘要

摘要: 现有Perspective-n-line (PnL)问题求解算法无法在获得高求解精度的同时保证高求解效率. 为解决这个缺点, 提出了同时兼具求解效率和求解精度算法EPnL. 该方法首先将PnL问题转换为求二次曲面方程组交点的问题, 然后利用单位四元数中变量不同时为零的特性, 分类参数化PnL问题中的旋转矩阵. 最后, 为克服常规优化方法可靠性和效率较低的问题, 同时兼具求解效率和求解精度算法利用二次曲面方程组自身的结构信息, 采用低次项参数化高次项的方式将二次曲面方程组的求解问题转换为单变量多项式的求解问题. 实验表明, 相比于现有算法, 该算法在具有高求解精度的同时也兼具有高求解效率.
- 计算机视觉 /
- PnL问题 /
- 位姿估计 /
- 视觉导航
Abstract: The existing algorithms for solving the perspective-n-line (PnL) problem cannot achieve high accuracy as well as maintain high computational efficiency. To solve this disadvantage, the EPnL algorithm is proposed. The EPnL firstly transfers the PnL problem into the problem of finding the intersection of quadratic surface equations, and then uses a classification parametrization, which is derived from the fact that variables are not simultaneously zero in the unit-quaternion, to parameterize the rotation matrix in the PnL problem. At last, to overcome the problem of low reliability and low efficiency of conventional optimization methods, the EPnL uses the structure information of the system of quadratic surface equations, and transfers the problem of finding the intersection of quadratic surface equations into the solving problem of univariate polynomials using the strategy that the higher order terms are parameterized by the lower order terms in the system of quadratic surface equations. Experimental results show that the proposed algorithm has high accuracy as well as high efficiency compared with existing algorithms.
- Computer vision /
- PnL problem /
- pose estimation /
- vision-based navigation
注释:

1) ¹ https://sites.google.com/view/ping-wang-homepage

2) ² http://www.robots.ox.ac.uk/~vgg/

HTML全文

图 1 PnL问题

Fig. 1 PnL problem

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图 2 当直线数目变化时旋转和平移误差的均值和中值

Fig. 2 The mean and median of rotation and translation errors when the number of lines varies

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图 3 当噪声等级变化时旋转和平移误差的均值和中值

Fig. 3 The mean and median of rotation and translation errors when the noise level varies

下载: 全尺寸图片幻灯片

图 4 最小情况下(n = 3)旋转和平移误差的均值和中值

Fig. 4 The mean and median of rotation and translation errors in the minimal case (n = 3)

下载: 全尺寸图片幻灯片

图 5 对比算法的计算效率

Fig. 5 The computational efficiency of compared the methods

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图 6 VGG数据集中的图片

Fig. 6 Images from the VGG dataset

下载: 全尺寸图片幻灯片

表 1 解的个数对比

Table 1 Comparison of the number of solutions

文献 [9]	文献 [12]	文献 [13]	文献 [14]	本文方法
15	27	15	60	14

下载: 导出CSV

表 2 各算法在VGG数据集上的旋转和平移误差均值

Table 2 The mean of rotation and translation errors for each method on the VGG dataset

数据集名称		Model-House	Corridor	Merton-College- Ⅰ	Merton-College- Ⅱ	Merton-College-Ⅲ	University-Library	Wadham-College
图像数量		10	11	3	3	3	3	5
AlgLS	$\Delta \theta [ \circ ]$	0.4220	0.1983	3.6200	55.8037	3.7495	1.8838	60.0517
AlgLS	$\Delta T[m]$	0.0384	0.0888	1.1504	14.1879	1.3683	0.9519	9.8801
DLT-Lines	$\Delta \theta [ \circ ]$	0.8651	0.1104	0.0869	0.2117	0.1751	0.1736	0.1343
DLT-Lines	$\Delta T[m]$	0.0834	0.0415	0.0274	0.1224	0.0625	0.0751	0.0809
LPnL-Bar-LS	$\Delta \theta [ \circ ]$	0.4135	0.1178	0.0241	0.0261	0.0652	0.3642	0.1526
LPnL-Bar-LS	$\Delta T[m]$	0.0403	0.0440	0.0099	0.0149	0.0233	0.1632	0.0909
RPnL	$\Delta \theta [ \circ ]$	0.5521	0.3652	1.0870	0.3249	1.7528	2.9731	0.4200
RPnL	$\Delta T[m]$	0.0631	0.1150	0.3215	0.1660	0.9121	1.5613	0.1909
ASPnL	$\Delta \theta [ \circ ]$	0.2265	0.0911	0.1141	0.1515	1.5584	3.6662	0.4227
ASPnL	$\Delta T[m]$	0.0162	0.0298	0.0314	0.0600	0.5571	1.6683	0.1955
SRPnL	$\Delta \theta [ \circ ]$	0.2258	158.952	0.4381	0.1151	36.4034	4.1848	0.0880
SRPnL	$\Delta T[m]$	0.0160	17.557	0.1064	0.0495	3.9398	2.0632	0.0407
EPnL	$\Delta \theta [ \circ ]$	0.2265	0.0969	0.0306	0.0170	0.0504	0.0871	0.0808
EPnL	$\Delta T[m]$	0.0162	0.0252	0.0097	0.0123	0.0147	0.0343	0.0375

下载: 导出CSV

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