• Acta Photonica Sinica
  • Vol. 50, Issue 7, 285 (2021)
Linmei ZHU1, Xiucheng DONG1, Zhengyu ZHANG2, Fan ZHANG1, Haibin WANG1, and Lei REN1
Author Affiliations
  • 1School of Electrical and Electronic Information, Xihua University, Chengdu60039, China
  • 2High Speed Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang, Sichuan61000, China
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    DOI: 10.3788/gzxb20215007.0715001 Cite this Article
    Linmei ZHU, Xiucheng DONG, Zhengyu ZHANG, Fan ZHANG, Haibin WANG, Lei REN. Camera Pose Estimation Algorithm for Singular Configuration of Target Points[J]. Acta Photonica Sinica, 2021, 50(7): 285 Copy Citation Text show less

    Abstract

    Aiming at improving the accuracy and stability of the pose estimation when the target points located in the planar, quasi-planar and quasi-linear case. In this study, we propose an iterative solution for singular configuration of target points. The main idea of the algorithm is to select two farthest points as the basic reference points, and divide n points into n-2 three-point sets. Then, the auxiliary points are constructed according to the geometric relationship of the three-point set, aiming to increase the geometric constraints of the perspective similar triangle algorithm, and obtain a more accurate initial value. Finally, the simplified EPnP algorithm is combined with Gaussian Newton algorithm for optimization. Experiments conducted on synthetic data and real images show that when the number of planar target points n=4, the average image re-projection error of this algorithm is 0.003 mm, compared with the orthogonal iterative algorithm, EPnP algorithm and IEPnP algorithm, which is 0.062 mm, 0.324 mm and 2.238 mm respectively, this algorithm effectively improves the accuracy and stability of the pose estimation of the target point in singular configuration.
    λuv1=fu0u00fvv0001XcYcZc=AXcYcZc(1)

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    XcYcZc=R TXwYwZw(2)

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    d2=l2+ sd3=l3+t(3)

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    A1s2-t2+A2=0(4)

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    A3s+A4t+A5st+A6s2+A7=0(5)

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    fs=B4s4+B3s3+B2s2+B1s1+B0=0(6)

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    t=-A3s+A6s2+A7/A4+A5s(7)

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    t=±A1s2+A2(8)

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    f1s=a1s4+b1s3+c1s2+d1s1+e1=0f2s=a2s4+b2s3+c2s2+d2s1+e2=0fn-2s=an-2s4+bn-2s3+cn-2s2+dn-2s1+en-2=0(9)

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    λ=P1wP2wp1'p2'=D1s2+sin2γ1(10)

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    d1cosp1'pi'=d2cosp2'pi'(11)

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    x1xi+y1yi+z1zi=x2xi+y2yi+z2zi(12)

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    x=13x1+x2+xiy=13y1+y2+yiz=13z1+z2+zi(13)

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    d2+d12-2dd1cosp'p1'=p'p1'2d2+d22-2dd2cosp'p2'=p'p2'2(14)

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    d=p'p2'2-p'p1'2+d22-d122d2cosp'p2'-d1cosp'p1'(15)

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    F1=xx2+yy2+zz2-xx1+yy1+zz1x2+y2+z2(16)

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    F1=x22+y22+z22-x12+y12+z123x2+y2+z2(17)

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    x=12x1+xiy=12y1+yiz=12z1+zi(18)

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    F2=xx2+yy2+zz2-xx1+yy1+zz1x2+y2+z2(19)

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    F2=x1x2+y1y2+z1z2-x12+y12+z123x2+y2+z2(20)

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    di2+d22-2did2cospi'p2'=pi'p2'2di2+d2-2didcospi'p'=pi'p'2(21)

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    Pic=λdivi(22)

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    Piw=j=14αijcjw ,  j=14αij=1(23)

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    Pic=j=14αijcjc(24)

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    X=i=14βiVi(25)

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    β=VTV-1VTX(26)

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    β=argminβi,j=1,i<j4cic-cjc2 - ciw-cjw2(27)

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    eR=2arccos0.51+trRRtrueTeT=Ttrue-T/Ttrue(28)

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    error=i=1nui'-ui2+vi'-vi2/n(29)

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    Linmei ZHU, Xiucheng DONG, Zhengyu ZHANG, Fan ZHANG, Haibin WANG, Lei REN. Camera Pose Estimation Algorithm for Singular Configuration of Target Points[J]. Acta Photonica Sinica, 2021, 50(7): 285
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