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794 JOURNAL OF SOFTWARE, VOL. 6, NO. 5, MAY 2011 Figure 4. Image fragment Figure 6. Pixel-level image and results First, process Fig. 4 using the first method mentioned in II where T is equal to 400.The results are marked with red box as shown in Fig. 5.. It can be seen that these points are distributed in a 3 × 3 small areas. Second, we use the second method in II to filter the above results. The correlation coefficient of points between I and III is shown in Table 1. From Table I we can see that the maximum value of the correlation coefficient is at (16,15). So we define (16,15) as the corner we want. In Fig. 6, the red cross indicates the final extracted result. It show that algorithm is correct and has a high accuracy © 2011 ACADEMY PUBLISHER A B C Figure 7. Results extracted by AXDA TABLE I. EXTRACTED RESULTS Point Extracted Results Corner Coordinate (15,14) (16,14) (16,15) (17,16) P 0.1632 -0.1085 0.6497 0.4043 Figure 8. Extracted Result (16,15) A. Comparison with Harris corner detection algorithm Red labels in Fig. 7, Fig. 8, Fig. 9and Fig. 10 are detection results processed by AXDA and Harris operator respectively. Numbers of detected corners are listed in Table II. From Fig. 7, Fig.8 and Table II we can see that the performance of the AXDA is much better than that of the Harris operator. The AXDA detects only one corner outside the chessboard. As the general algorithm however, Harris detects large numbers of non-X-corners in the background. These points distribute disorderly and will cause great trouble in the automated calibration.
JOURNAL OF SOFTWARE, VOL. 6, NO. 5, MAY 2011 795 A B C Figure 9. Results extracted by Harris Fig. 9 and Fig. 10 are the local enlargement result images of AXDA and Harris operator respectively. It can be seen clearly that the performance of the AXDA outweighs the Harris operator. Corners detected by Harris in Fig. 9 shifts from the real position and false Figure 10. Results extracted by AXDA corners are detected. But in Fig. 10 the results are more accurate. Figure 8. Results extracted by Harris TABLE II. NUMBER OF POINTS Number of Corners Algorithm Image A Image B Image C Harris 443 382 393 AXDA 157 156 156 © 2011 ACADEMY PUBLISHER Corners AXDA TABLE III. SUB-PIXEL CORNERS Camera Calibration Toolbox for Matlab 1st (287.5431,116.2525) (287.1477,114.9688) 2nd (282.3183,152.3035) (281.4477,151.0909) 3rd (277.3627,186.4973) (276.3348,185.5046) 4th (272.6387,219.0928) (271.3617,217.9590) 5th (268.1781,249.8713) (267.0234,248.7857) 6th (264.0387,278.4330) (262.5504,277.8376) 7th (260.0439,305.9974) (258.6074,305.3773) 8th (256.3077,331.7771) (254.5650,331.1984) 9th (252.7597,356.2584) (251.3006,355.5708) 10th (249.4266,379.2563) (247.6796,378.6948) 11th (246.2785,400.9786) (244.7730,400.3725) 12th (243.3301,421.3226) (241.7335,420.8897) B. Precision comparison on sub-pixel level Corners detected by intersection of straight line fitting and corners detected by Matlab calibration toolbox are compared on the sub-pixel level. Take the detection results of the fourth column in Fig.7.A as an example, comparisons from the top to the bottom are shown as Fig.11 and Tab.III.
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