• Laser & Optoelectronics Progress
  • Vol. 59, Issue 18, 1815014 (2022)
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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    DOI: 10.3788/LOP202259.1815014 Cite this Article Set citation alerts
    Yidong Liu, Zhentang Jia. Improved Calibration Method of Camera Internal Parameters Based on Nonlinear Optimization[J]. Laser & Optoelectronics Progress, 2022, 59(18): 1815014 Copy Citation Text show less
    Main flow of camera calibration
    Fig. 1. Main flow of camera calibration
    Coordinate transformation of camera imaging
    Fig. 2. Coordinate transformation of camera imaging
    Improved calibration process of camera
    Fig. 3. Improved calibration process of camera
    Calibration images at different positions
    Fig. 4. Calibration images at different positions
    Calibration image after corner extraction
    Fig. 5. Calibration image after corner extraction
    Optimization results of two PSO algorithms
    Fig. 6. Optimization results of two PSO algorithms
    Position relationship between actual corner and reprojection corner
    Fig. 7. Position relationship between actual corner and reprojection corner
    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
    Search performance comparison of four intelligent optimization algorithms
    Fig. 9. Search performance comparison of four intelligent optimization algorithms
    Parameterfxfyu0v0k1k2 k3p1p2
    Value10214.3310214.33643.25482.5200
    Table 1. Linear solution of camera internal parameters
    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 2. Results of PSO 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 3. Results of DWAMPSO with different iterations
    AlgorithmOptimal fitnessWorst fitness
    DE0.21520.3033
    GA0.15720.2389
    PSO0.31950.4075
    DWAMPSO0.03680.1694
    Table 4. Fitness results 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
    Table 5. Convergence rate of different algorithms
    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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