• Acta Optica Sinica
  • Vol. 43, Issue 13, 1315001 (2023)
Ping Wang1,2,4,*, Dengyin Yao1, Rui Qiao3, Tao Zhang4, and Pengpeng Yao5
Author Affiliations
  • 1College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
  • 2Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou 730050, Gansu, China
  • 3College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China
  • 4Suzhou Focus Technology Co., Ltd., Suzhou 215000, Jiangsu, China
  • 5Zhuhai Fudan Innovation Institute, Zhuhai 519031, Guangdong, China
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    DOI: 10.3788/AOS221724 Cite this Article Set citation alerts
    Ping Wang, Dengyin Yao, Rui Qiao, Tao Zhang, Pengpeng Yao. Estimation Method of Lens Distortion Parameters Based on Two Lines[J]. Acta Optica Sinica, 2023, 43(13): 1315001 Copy Citation Text show less
    Distribution curve of undistorted points. (a) Along xu direction; (b) along yu direction
    Fig. 1. Distribution curve of undistorted points. (a) Along xu direction; (b) along yu direction
    Source image
    Fig. 2. Source image
    Distorted images and corrected images. (a)-(c) Pincushion distorted images and corrected images; (d)-(f) barrel ditorted images and corrected images
    Fig. 3. Distorted images and corrected images. (a)-(c) Pincushion distorted images and corrected images; (d)-(f) barrel ditorted images and corrected images
    Choice of two lines with two kinds of constraint rules. (a)-(e) Corresponding edge of two lines should be as close to center of image as possible; (f)-(j) corresponding edge of two lines should be as far away from center of image as possible
    Fig. 4. Choice of two lines with two kinds of constraint rules. (a)-(e) Corresponding edge of two lines should be as close to center of image as possible; (f)-(j) corresponding edge of two lines should be as far away from center of image as possible
    Average estimation errors when different edges are selected. (a) Mean absolute error; (b) mean relative error
    Fig. 5. Average estimation errors when different edges are selected. (a) Mean absolute error; (b) mean relative error
    Average errors when noise level varies. (a) Errors of principal point; (b) errors of radial distortion
    Fig. 6. Average errors when noise level varies. (a) Errors of principal point; (b) errors of radial distortion
    Correction of real distorted images. (a)-(e) Different scene images
    Fig. 7. Correction of real distorted images. (a)-(e) Different scene images
    SequenceSelected edgesReal parameterProposed methodBukhari et al16
    CxCyλCx'Cy'λ'Cx'Cy'λ'
    (a)R1,R4(320,240)3×10-6(319.99,240.05)2.99×10-6(320.49,240.05)2.99×10-6
    (b)R5,C5(310,230)1×10-6(310.11,229.91)1.01×10-6(312.22,229.91)1.01×10-6
    (c)R1,C1(300,220)6×10-7(300.06,220.75)6.03×10-7(307.49,220.75)6.03×10-7
    (d)R1,R5(330,250)-3×10-6(330.01,249.98)-2.99×10-6(330.05,249.98)-2.99×10-6
    (e)R2,R5(340,260)-1×10-6(339.75,259.56)-1.01×10-6(339.78,259.56)-1.01×10-6
    (f)R1,C2(350,270)-6×10-7(349.64,268.85)-6.08×10-7(353.56,268.85)-6.08×10-7
    Table 1. Estimated results of distortion parameters
    Sequence(a)(b)(c)(d)(e)(f)
    Proposed methodDis /pixel0.050.140.750.010.281.19
    Rel /%0.100.120.590.040.491.34
    Bukhari et al16Dis /pixel0.502.117.430.040.503.92
    Rel /%0.100.120.590.040.491.34
    Table 2. Estimated errors of distortion parameters
    SequenceImage sizeDistortion centerDistortion parameter
    (a)256×256CxCy)=(130.92,131.59)λ=-1.6814×10-5
    (b)720×480CxCy)=(333.64,258.33)λ=-1.1934×10-5
    (c)800×600CxCy)=(369.90,271.13)λ=-1.7466×10-6
    (d)1024×680CxCy)=(490.33,308.66)λ=-2.4160×10-6
    (e)2560×1920CxCy)=(1228.90,942.75)λ=-1.0704×10-6
    Table 3. Estimated results of real distorted images