Acta Optica Sinica, Volume. 43, Issue 23, 2315002(2023)

Adaptive EKF-Based Camera Calibration Optimization Method

Xin Lai1,2, Xiao Yang2, and Qican Zhang1、*
Author Affiliations
  • 1College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, Sichuan , China
  • 2School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, Sichuan , China
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    Figures & Tables(16)
    Camera imaging model
    Flowchart of AEKF algorithm
    Virtual checkerboard targets
    Checkerboard target
    Schematic diagram of reprojection error
    Results of reprojection points for different algorithms
    Reprojection error of feature points
    Variation of reprojection error during iteration
    Reprojection error varying with noise level
    Reprojection error of calibration optimization algorithm at different Rk
    Variation of reprojection error during iteration
    Relationship between reprojection error and noise level
    Relationship between relative error of intrinsic and extrinsic parameters and noise level. Optimization of translation vector by using (a) UKF,(b) EKF, and (c) AEKF; optimization of scale factor by using (d) UKF, (e) EKF, and (f) AEKF; optimization of principal point coordinate by using (g) UKF, (h) EKF, and (i) AEKF
    • Table 1. Calibration results of simulation system

      View table

      Table 1. Calibration results of simulation system

      ParameterZhang's methodEKFAEKF
      ax /pixel1154.01211154.01661154.0136
      ay /pixel1153.91311153.91691153.9312
      u0 /pixel641.9936641.9652641.9576
      v0 /pixel367.4038367.3713367.2939
      q00.99980.70560.7058
      q10.01400.02420.0104
      q2-0.00780.0001-0.0013
      q3-0.0102-0.0071-0.0068
      tx /mm-111.3109-111.3639-111.3772
      ty /mm-73.5315-73.5921-73.7384
      tz /mm609.4127609.3972609.3762

      Reprojection

      error /pixel

      0.70830.67940.4499
    • Table 2. Calibration results of USB camera

      View table

      Table 2. Calibration results of USB camera

      ParameterZhang's methodUKFEKFAEKF
      ax /pixel1149.03841149.02591149.04001149.0490
      ay /pixel1149.21401149.22331149.20871149.2018
      u0 /pixel628.0821628.1140628.0701628.0812
      v0 /pixel378.5566378.5508378.5822378.5690
      q00.99970.99820.70540.7059
      q10.0217-0.00280.02770.0113
      q20.0022-0.0191-0.0004-0.0072
      q3-0.0100-0.0097-0.0065-0.0069
      tx /mm-103.9589-103.8969-103.9813-103.9627
      ty /mm-79.8024-79.8154-79.7535-79.7688
      tz /mm605.5485605.5545605.5555605.5527
      Reprojection error /pixel0.82840.52640.63810.3217
    • Table 3. Calibration results of industrial camera

      View table

      Table 3. Calibration results of industrial camera

      ParameterZhang's methodUKFEKFAEKF
      ax /pixel2789.38762789.37802789.37802789.3807
      ay /pixel2791.25962791.26922791.25662791.2603
      u0 /pixel935.3057935.3159935.3499935.3353
      v0 /pixel566.0097565.9948566.0444566.0195
      q00.99930.99920.70470.7047
      q1-0.0134-0.0187-0.0121-0.0153
      q2-0.0311-0.0379-0.0286-0.0282
      q30.01830.01820.01250.0126
      tx /mm-111.0329-110.9932-110.8443-110.9072
      ty /mm-70.6943-70.7783-70.5493-70.6525
      tz /mm659.3553659.3533659.4082659.3814
      Reprojection error /pixel1.05630.92890.95320.9277
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    Xin Lai, Xiao Yang, Qican Zhang. Adaptive EKF-Based Camera Calibration Optimization Method[J]. Acta Optica Sinica, 2023, 43(23): 2315002

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    Paper Information

    Category: Machine Vision

    Received: Jun. 15, 2023

    Accepted: Sep. 6, 2023

    Published Online: Dec. 12, 2023

    The Author Email: Zhang Qican (zqc@scu.edu.cn)

    DOI:10.3788/AOS231144

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