Fig. 1. Pixels on circle with radius of 3

Fig. 2. Distributions of pixels on circle in each region. (a) Sum of pixels in any two adjacent regions of circle is half of sum of pixels on circle; (b) pixels at boundary on concentric circle correspond to the same θ

Fig. 3. Distributions of candidate corners before and after iterative refinement. (a) Distribution of candidate corners before iterative refinement; (b) locally enlarged drawing of Fig. 3(a); (c) distribution of candidate corners after iterative refinement; (d) locally enlarged drawing of Fig. 3(c); (e) distribution of candidate corners after eliminating fake corners; (f) locally enlarged drawing of F

Fig. 4. Gradient graphs of candidate corner points

Fig. 5. Flow chart of corner detection

Fig. 6. Contrast experiments of corner detection. (a) Original images; (b) results of corner detection by Matlab Toolbox^[15]; (c) results of corner detection by algorithm in Ref. [11]; (d) results of corner detection by proposed algorithm

Fig. 7. Checkerboard with large distortion. (a) Original images; (b) result of corner detection by Matlab Toolbox^[15]; (c) result of corner detection by algorithm in Ref. [11]; (d) result of corner detection by proposed algorithm

Fig. 8. 10 checkerboard images with different shooting angles

Fig. 9. Re-projection error. (a) Matlab Toolbox^[15]; (b) algorithm in Ref. [11]; (c) proposed algorithm (without refinement); (d) proposed algorithm (with refinement)

Table 1. Number of corner points detected by different algorithms

Table 2. Results of camera calibration