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Laser & Optoelectronics Progress, Volume. 59, Issue 18, 1815014(2022)

Improved Calibration Method of Camera Internal Parameters Based on Nonlinear Optimization

Yidong Liu and Zhentang Jia*
Author Affiliations
  • College of Electronics and Information Engineering, Shanghai University of Electric Power, Shanghai 200090, China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (14)
    Equations (21)
    References (18)
    Cited By (1)
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    Figures & Tables(14)
    Main flow of camera calibration

    Fig. 1. Main flow of camera calibration

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    Coordinate transformation of camera imaging

    Fig. 2. Coordinate transformation of camera imaging

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    Improved calibration process of camera

    Fig. 3. Improved calibration process of camera

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    Calibration images at different positions

    Fig. 4. Calibration images at different positions

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    Calibration image after corner extraction

    Fig. 5. Calibration image after corner extraction

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    Optimization results of two PSO algorithms

    Fig. 6. Optimization results of two PSO algorithms

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    Position relationship between actual corner and reprojection corner

    Fig. 7. Position relationship between actual corner and reprojection corner

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    Reprojection error of different calibration methods. (a) Calibration toolbox; (b) Zhang calibration method; （c） proposed method

    Fig. 8. Reprojection error of different calibration methods. (a) Calibration toolbox; (b) Zhang calibration method; （c） proposed method

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    Search performance comparison of four intelligent optimization algorithms

    Fig. 9. Search performance comparison of four intelligent optimization algorithms

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    • Table 1. Linear solution of camera internal parameters

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      Table 1. Linear solution of camera internal parameters

      Parameterfxfyu0v0k1， k2， k3，p1， p2
      Value10214.3310214.33643.25482.5200

    • Table 2. Results of PSO with different iterations

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      Table 2. Results of PSO with different iterations

      ParameterNumber of iterations
      100200300400
      fx10208.0410209.0910207.7810208.23
      fy10205.381.02053810204.8910204.25
      u0644.51644.46645.0140644.72
      v0482.76482.22486.280481.77
      k1-7.72-5.4735-4.1863-3.3107
      k20.1996-2.0780-0.43040.2064
      k3-5.2160-4.9430-4.6964-4.5130
      p1-0.0862-0.0254-0.02610.0006
      p20.11970.08210.06430.0632
      Fitness0.42000.38520.35340.3195

    • Table 3. Results of DWAMPSO with different iterations

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      Table 3. Results of DWAMPSO with different iterations

      ParameterNumber of iterations
      100200300400
      fx10214.3510214.3110214.3110218.25
      fy10219.2910216.5010216.3410217.61
      u0645.5413645.4992645.5005645.4854
      v0481.3720481.4797481.4860481.4947
      k1-0.1778-0.1897-0.1681-0.3372
      k2-4.4974-4.4636-4.4629-4.3837
      k3-8.0918-7.3946-7.5034-9.3731
      p10.00420.00110.00100.00002
      p20.00050..00220.00170.0017
      Fitness0.04600.03720.03700.0368

    • Table 4. Fitness results of different algorithms

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      Table 4. Fitness results of different algorithms

      AlgorithmOptimal fitnessWorst fitness
      DE0.21520.3033
      GA0.15720.2389
      PSO0.31950.4075
      DWAMPSO0.03680.1694

    • Table 5. Convergence rate of different algorithms

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      Table 5. Convergence rate of different algorithms

      AlgorithmFitness10.80.60.40.2
      GDIteration number3643109186
      Running time /s38.905746.1268117.1337197.2784
      DEIteration number184202246278
      Running time /s156.2791171.8147210.1576239.0557
      GAIteration number43125169268351
      Running time /s44.7721129.5620176.4058280.4783368.7568
      PSOIteration number478287147
      Running time /s40.978773.157477.9820142.2541
      DWAMPSOIteration number1212134154
      Running time /s11.628911.628912.538138.088150.2417
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    Yidong Liu, Zhentang Jia. Improved Calibration Method of Camera Internal Parameters Based on Nonlinear Optimization[J]. Laser & Optoelectronics Progress, 2022, 59(18): 1815014

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    Paper Information

    Category: Machine Vision

    Received: Jun. 7, 2021

    Accepted: Aug. 25, 2021

    Published Online: Aug. 22, 2022

    The Author Email: Jia Zhentang (462458081@qq.com)

    DOI:10.3788/LOP202259.1815014

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology