• Acta Optica Sinica
  • Vol. 42, Issue 16, 1612004 (2022)
Min Zhao*, Xiaogang Li, Zepeng Su, and Lingjian Zhu
Author Affiliations
  • School of Mechanical and Precision Instrument Engineering, Xi′an University of Technology, Xi′an710048, Shaanxi , China
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    DOI: 10.3788/AOS202242.1612004 Cite this Article Set citation alerts
    Min Zhao, Xiaogang Li, Zepeng Su, Lingjian Zhu. Camera Parameter Calibration Based on Directional Layered Target[J]. Acta Optica Sinica, 2022, 42(16): 1612004 Copy Citation Text show less
    Pinhole imaging model
    Fig. 1. Pinhole imaging model
    Results of camera calibration by using target with different sizes. (a) Focal length; (b) horizontal coordinates of principal points
    Fig. 2. Results of camera calibration by using target with different sizes. (a) Focal length; (b) horizontal coordinates of principal points
    Results of focal length calibration by using different number of targets
    Fig. 3. Results of focal length calibration by using different number of targets
    Results of camera calibration with complete and incomplete targets. (a) Focal length; (b) horizontal coordinates of principal points
    Fig. 4. Results of camera calibration with complete and incomplete targets. (a) Focal length; (b) horizontal coordinates of principal points
    Directional layered target
    Fig. 5. Directional layered target
    Flow chart of target recognition and matching algorithm
    Fig. 6. Flow chart of target recognition and matching algorithm
    Numbering sequence of targets
    Fig. 7. Numbering sequence of targets
    Identification and matching of directional targets. (a) Sketch of combined coordinate system; (b) marker map of target matching on axis
    Fig. 8. Identification and matching of directional targets. (a) Sketch of combined coordinate system; (b) marker map of target matching on axis
    Target matching for partial target deficiency. (a) Experimental picture I; (b) matching result of experimental picture I; (c) experimental picture II; (d) matching result of experimental picture II
    Fig. 9. Target matching for partial target deficiency. (a) Experimental picture I; (b) matching result of experimental picture I; (c) experimental picture II; (d) matching result of experimental picture II
    Experimental pictures of camera calibration. (a) Small view (groups 1 and 2); (b) large view (groups 3 and 4)
    Fig. 10. Experimental pictures of camera calibration. (a) Small view (groups 1 and 2); (b) large view (groups 3 and 4)
    Distributions of reprojection error. (a) Group 1; (b) group 2; (c) group 3; (d) group 4
    Fig. 11. Distributions of reprojection error. (a) Group 1; (b) group 2; (c) group 3; (d) group 4
    Proportion of target in camera field

    Focal length

    fx /mm

    Focal length

    fy /mm

    Horizontal coordinate of principal point /pixelVertical coordinate of principal point /pixel
    1/160.31960.309745.025046.0966
    1/80.16440.164524.840824.9445
    1/40.07200.071811.573211.6927
    1/20.03700.03715.36565.7319
    Table 1. Standard error of calibration results of camera parameters under different target sizes
    Number of targets

    Focal length

    fx /mm

    Focal length

    fy /mm

    Horizontal coordinate of principal point /pixelVertical coordinate of principal point /pixel
    3×30.12680.126718.276718.4984
    5×50.07690.077414.279013.9455
    7×70.03980.039011.113910.7524
    9×90.03170.031310.15629.9529
    Table 2. Standard error of calibration results of camera parameters under different number of targets
    Target

    Focal length

    fx /mm

    Focal length

    fy /mm

    Horizontal coordinate of principal point /pixelVertical coordinate of principal point /pixel
    Complete target0.04240.042610.213310.3020
    Incomplete target0.04500.045410.154410.5856
    Table 3. Standard error of calibration results of camera parameters for complete and incomplete targets
    Group No.

    Focal

    length /mm

    Principal point

    u0,v0)(unit:pixel)

    Radical distortion coefficientTangential distortion coefficient

    Reprojection

    error /pixel

    k1k2p1p2
    153.25(1315.2,993.7)-0.065-3.2440.00100.076
    253.37(1317.1,990.1)-0.064-3.2660.00100.073
    352.57(1328.0,995.0)0.170-3.4370.00100.108
    451.33(1317.5,991.2)0.177-3.1220.00100.072
    Table 4. Results of camera parameter calibration
    Target

    Focal

    length /mm

    Principal

    point(u0,v0)(unit:pixel)

    Radical distortion

    coefficient

    Tangential distortion

    coefficient

    Reprojection

    error /pixel

    Measuring

    error /mm

    k1k2p1p2
    I16.50(788.0,485.3)-0.505-11.851-0.0020.0010.2080.009
    II16.56(791.3,477.6)-0.533-10.044-0.00200.2000.008
    I34.48(816.6,453.4)3.036-867.3840.0080.0150.8320.054
    II32.16(768.2,494.6)0.734-189.812-0.0010.0110.2170.008
    Table 5. Results of camera calibration and measurement
    Min Zhao, Xiaogang Li, Zepeng Su, Lingjian Zhu. Camera Parameter Calibration Based on Directional Layered Target[J]. Acta Optica Sinica, 2022, 42(16): 1612004
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