Camera Calibration Based on 2D-plane - Academy Publisher

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B. Solve camera parameter matrix The solution of the camera parameter matrix can be seen Literature[6]. III. EXPERIMENT AND RESULTS A. Experiment materials KOKO camera; Image gathering card; Computer; Tripod; 7×9 the black and white interaction's chess discoid grid 2D plane target (as shown in Figure 1), each grid size for 28×28 millimeter; Horizontal iron sheet Figure 2. <strong>Calibration</strong> with the 25 images Figure 1. 2D plane for camera calibration B. Experiment procedure 1) Prints a calibration template to paste on the horizontal iron sheet; 2) moves plane or camera to shot some template images (more than or equal 20)from different angle; 3) detects characteristic point of the image; 4) obtains each image the unitary matrix H ; 5) computes camera's internal parameter by using matrix H extracted in the premise of the distortion factor being zero; 6) obtains a group of precision higher camera's internal parameter by Further optimizing using the counter-projection, simultaneously calculating each distortion factor. C. Experimental results 1) Lens' internal parameter As shown in Figure 2, obtains internal parameter by Carrying on the demarcation to the load 25 charts. Figure 5-8 shows the spatial distribution situation for the 25 images. The intrinsic parameters after camera calibration is Focal Length: f = c [3419.27498 3260.81444 ] ±[88.56950 99.83080] Principle Point: cc = [383.50000 287.50000] ± [0.00000 0.00000] Skew: alpha_c = [0.00000] ± [0.00000] Figure 3. The spatial distribution for the 25 images Distortation: kc = [-0.41925 -46.21000 -0.00466 -0.02250 0.00000] ± [0.77140 78.34200 0.01162 0.00423 0.00000] Pixel error: err = [0.36731 0.79805] 2) Computation of the extrinsic parameters We put the plane pattern on the ground and shoot a image. Use this image to compute the extrinsic parameters. Extrinsic parameters: Translation vector: ⎡-77.629688 ⎤ T = ⎢ -98.708815 ⎥ ⎢ ⎥ ⎢⎣ 1755.086388⎥⎦ Rotation vector: ⎡ 0.019894 0.999776 -0.007244⎤ R = ⎢ 0.433706 -0.015158 -0.900927 ⎥ ⎢ ⎥ ⎢⎣ -0.900835 0.014781 -0.433911⎥⎦ Pixel error: err = [0.32229 0.69439] 3) Experiment test 366
TABLE I. THE COORDINATE OF MARKED POINTS AND THEIR CALIBRATION ERROR Marked points Image coordinate Real world coordinate Computational world coordinate u( pixels ) v( pixels ) x( cm ) ycm ( ) xˆ( cm ) ycm ˆ( ) x direction( cm ) error y direction ( cm ) 1 26 281 23.5 -9.5 21.74 -8.90 -1.76 0.60 2 47 354 32 -7.5 29.39 -7.42 -2.61 0.08 3 50 126 3 -10 3.00 -9.08 0.00 0.92 4 60 195 13.5 -8.5 11.85 -8.00 -1.65 0.50 5 81 496 46.5 -5 42.50 -5.17 -4.00 -0.17 6 104 76 -4.5 -7.5 -3.86 -6.73 0.64 0.77 7 183 258 20.5 -1.5 19.44 -1.85 -1.06 -0.35 8 208 163 9 -1 8.12 -1.00 -0.88 0.00 9 231 103 0 0 0.20 -0.03 0.20 -0.03 10 235 402 37 1.5 34.32 0.82 -2.68 -0.68 11 366 267 22 7.5 20.74 6.55 -1.26 -0.95 12 367 435 40 7.5 37.55 6.34 -2.45 -1.16 13 367 62 -6.5 7.5 -5.37 7.00 1.13 -0.50 14 370 206 14.5 8 13.72 6.85 -0.78 -1.15 15 373 122 3 8 3.06 7.18 0.06 -0.82 16 375 559 52 7.5 48.02 6.48 -3.98 -1.02 17 431 346 31 10.5 29.16 9.25 -1.84 -1.25 18 535 238 18 16 17.74 14.46 -0.26 -1.54 19 544 96 -1 17.5 -1.74 16.00 -0.74 -1.50 20 552 395 36 16 34.11 14.21 -1.89 -1.79 21 588 166 9.5 19.5 9.18 17.57 -0.32 -1.93 22 689 82 -3 26 -1.86 23.61 1.14 -2.39 23 721 430 40 23.5 37.58 20.98 -2.42 -2.52 24 723 295 25 25 24.34 22.51 -0.66 -2.49 25 725 515 48 23 44.92 20.34 -3.08 -2.66 26 730 164 9 27 9.18 24.51 0.18 -2.49 In order to verify the calibration algorithm’s accuracy, we keep the camera’s position and orientation is unchangeable. The world coordinate system establishment is as the same as the Z. Zhang [6.]. 26 marked points are pasted on the laboratory ground. Figure 4 is the primary image shot by the camera. All the marking points’ world coordinate can be obtained by measuring, and the corresponding image coordinates can be got by image processing. Fig. 5 show the centroid coordinates of the marked point. We first use the image coordinate of the 26 points to reconstruct their world coordinate, and then compare them to the real world coordinate. Their corresponding error is the experimental error. The error can be evaluated by the following expression: m 2 2 ( ∑ ( x ˆ ) ( ˆ i − xi + yi − yi) i= 1 Qk = (6) m where , ( xi, y i) , ( i = 1,2, , m) is the real world coordinate of the marked point, ( xˆ, y ˆ) , ( i = 1,2, , m) is the computed world coordinate by calibration method, m is the number of marked points. The experimental results can be seen from table 1. The overall error of world coordinates is: Figure 3. Marked points image Figure 4. Extracted centroid of marked points 367
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Camera Calibration Based on 2D-plane - Academy Publisher

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