Fig. 1. Schematic of fisheye camera imaging
Fig. 2. Orthogonal projection model
Fig. 3. Schematic of scanning bounding box of fisheye image contours. (a) Field of view is 180°; (b) field of view is less than 180°
Fig. 4. Schematic of vanishing points of parallel spatial lines under spherical perspective projection
Fig. 5. Schematic of two types of fisheye cameras to calibrate. (a) TypeⅠ; (b) typeⅡ
Fig. 6. Images by fisheye camera TypeⅠ. (a) Checkerboard calibration image; (b) outdoor scene image
Fig. 7. Images by fisheye camera type Ⅱ. (a) Checkerboard calibration image; (b) indoor scene image
Fig. 8. Schematic of contour bounding box extraction and ellipse fitting of fisheye image. (a) Contour bounding box; (b) fitting ellipses
Fig. 9. Error distributions of re-projection. (a) Camera typeⅠ; (b) camera typeⅡ
Fig. 10. Schematic of test images for camera typeⅠand cubic box expansion. (a)-(d) Edge test images; (e)-(h) cubic box expansion of test images
Fig. 11. Schematic of test images for camera typeⅡand cubic box expansion. (a)(b) Edge test images; (c)(d) cubic box expansion of test images
Fig. 12. Cubic box expansion comparison of fisheye images for indoor and outdoor scenes. (a)(b) Results by toolbox; (c)(d) results by proposed method
Camera | Internal parameters | External parameters |
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(fx, fy) /pixel | (u0, v0) /pixel | (k1,k2) | | (φ, ω, κ) /rad | (tx, ty, tz) /mm |
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TypeⅠ | (589.24,589.24) | (639.68,640.21) | (0,0) | (3.4483,-0.0916,1.589) | (-71.33,-85.38,79.08) | TypeⅡ | (637.56,637.56) | (628.36,489.51) | (0,0) | (3.4876,-0.0432,1.7237) | (-80.57,-89.76,131.25) |
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Table 1. Initial parameters of fisheye cameras to calibrate
Camera | Internal parameters | External parameters | RMSE /pixel |
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(fx,fy) /pixel | | (u0,v0) /pixel | (k1,k2) | | (φ,ω,κ) /rad | (tx,ty,tz) /mm |
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TypeⅠ | (558.76,582.52) | (639.68,640.21) | (2.769×10-8,-1.725×10-13) | (3.1617,-0.0502,1.5716) | (-86.11,-89.26,106.72) | 0.3032 | TypeⅡ | (472.47,626.52) | (628.36,489.51) | (1.950×10-8,-2.201×10-13) | (3.2583, -0.035,1.5872) | (-106.84,-107.0,174.37) | 0.1472 |
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Table 2. Globally optimized parameters of fisheye cameras to calibrate
Corrected image | Middle | Left | Right | Above | Below | Average |
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Error of line fitting | 0.40 | 0.48 | 0.50 | 0.67 | 0.60 | 0.53 |
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Table 3. Calibration parameters and image correction line fitting RMSE of camera typeⅠ
Corrected image | Middle | Left | Right | Average |
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Line fitting error | 0.17 | 0.37 | 0.28 | 0.27 |
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Table 4. Calibration parameters and image correction line fitting RMSE of camera typeⅡ
Camera | (fx, fy) /pixel | (u0, v0) /pixel | (k1, k2, k3, k4) | RMSE /pixel |
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Model 1 | (547.79, 571.06) | (640.03,641.87) | (-0.18741,0.06478,-0.02346,0.00327) | 0.2978 | Model 2 | (340.96, 452.53) | (628.72,489.28) | (0.10739,-0.17992,0.2101,-0.09241) | 0.2621 |
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Table 5. Calibration parameters in online calibration toolbox and their re-projection RMSE
Corrected image | Middle | Left | Right | Above | Below | Average |
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Line fitting error | 0.20 | 1.36 | 0.74 | 1.20 | 1.16 | 0.93 |
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Table 6. Parameters in calibration toolbox for camera typeⅠand image correction line fitting RMSE
Corrected image | Middle | Left | Right | Average |
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Line fitting error | 0.65 | 2.96 | 3.65 | 2.31 |
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Table 7. Parameters in calibration toolbox for camera typeⅡ and image correction line fitting RMSE