基于机器视觉的最大似然位姿估计算法
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摘要
针对现有位姿估计算法对采样数据不做任何的统计假设,缺少评判标准等问题,从信号的概率密度函数出发,推导了基于机器视觉的最大似然位姿估计的一般形式,并证明利用单幅图像时,在各向同性高斯噪声情况下传统迭代算法与最大似然估计等效。推导了位姿估计的克拉美-罗界,给出了位姿估计的方差下限。根据仿真结果可以看出,利用10张图像时,最大似然算法在噪声功率大于5dB的情况下,性能明显优于传统迭代算法,证明适当增加图像数可有效提高估计性能。
The existing pose estimation algorithms do not make any statistical assumptions on the sampled data,and lack the evaluation criteria.Aiming at this problem,based on the probability density function of the signal,we derived the general form of maximum likelihood pose estimation based on machine vision was and proved that the traditional iterative algorithm is equivalent to the maximum likelihood estimation using single imag ein the case of isotropic Gaussian noise.What's more,we derived the Cramér-Rao bound of pose estimation,which could be regarded as the variance low bound of any unbiased estimations.By the analysis of the simulation,the maximum likelihood method is much better than the traditional iterative method by using 10 pictures when noise power is greater than 5 dB,it proves that the performance of pose estimation can be improved by increasing the number of images.
The existing pose estimation algorithms do not make any statistical assumptions on the sampled data,and lack the evaluation criteria.Aiming at this problem,based on the probability density function of the signal,we derived the general form of maximum likelihood pose estimation based on machine vision was and proved that the traditional iterative algorithm is equivalent to the maximum likelihood estimation using single imag ein the case of isotropic Gaussian noise.What's more,we derived the Cramér-Rao bound of pose estimation,which could be regarded as the variance low bound of any unbiased estimations.By the analysis of the simulation,the maximum likelihood method is much better than the traditional iterative method by using 10 pictures when noise power is greater than 5 dB,it proves that the performance of pose estimation can be improved by increasing the number of images.
引文
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[2]CAMPA G,MAMMARELLA M,NAPOLITANOM R,et al.A comparison of pose estimation algorithms for machine vision based aerial refueling for UAV[C].US:IEEE,2006.
[3]WANG Qiyue,WANG Zhongyu.Position and pose measurement of spacecraft based on monocular vision[J].Journal of Applied Optics,2017,38(2):250-255.汪启跃,王中宇.基于单目视觉的航天器位姿测量[J].应用光学,2017,38(2):250-255.
[4]LI S Q,XU C,XIE M.A robust O(n)solution to the perspective-n-point problem[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2012,34(7):1444-1450.
[5]LEPETIT V,MORENO-NOGUER F,FUA P.EPnP:an accurate O(n)solution to the PnP problem[J].International Journal of Computer Vision,2009,81(2):155-166.
[6]HMAM H,KIM J.Optimal non-iterative pose estimation via convex relaxation[J].Image and Vision Computing,2010,28(11):1515-1523.
[7]LOWE D G.Three-dimensional object recognition from single two-dimensional images[J].Artificial Intelligence,1987,31(3):355-395.
[8]CHEN Peng.Monocular based camera pose estimation[D].Beijing:University of Science and Technology Beijing,2015.陈鹏.基于单目视觉的像机位姿估计技术[D].北京:北京科技大学,2015.
[9]LU C P,HAGER G D,MJOLSNESS E.Fast and globally convergent pose estimation from video images[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(6):610-622.
[10]LI Xin,LONG Gucan,LIU Jinbo,et al.Accelerative orthogonal iteration algorithm for camera pose estimation[J].Acta Optica Sinica,2015,35(1):258-265.李鑫,龙古灿,刘进博,等.相机位姿估计的加速正交迭代算法[J].光学学报,2015,35(1):258-265.
[11]SCHWEIGHOFER G,PINZ A.Robust pose estimation from a planar target[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(12):2024-2030.
[12]LUO Pengfei,ZHANG Wenming,LIU Zhong,et al.Fundamentals of statistical signal processing[M].Beijing:Publishing House of Electronics Industry,2014:155-202.罗鹏飞,张文明,刘忠,等.统计信号处理基础[M].北京:电子工业出版社,2014:155-202.
[13]STOICA P,NEHORIA A.Mode,maximum likelihood,and Cramér-Rao bound:conditional and unconditional results[R].New Haven:Center for Systems Science Yale University,1989.
[14]FRIEDLANDER B,PORAT B.The exact CramerRao bound for Gaussian autoregressive processes[J].IEEE Transactions on Aerospace and Electronic Systems,1989,25(1):3-7.
[15]VAN TREES H L.Detection,estimation,and modulation theory,Part VI[M].New York:Wiley Interscience,2001:689-785.