Chin-Hung Teng,1
Yung-Sheng Chen,2
and Wen-Hsing Hsu1
1C.-H. Teng (tengchinhung@yahoo.com.tw) and W.-H. Hsu (whhsu@ee.nthu.edu.tw) are with the Department of Electrical Engineering, National Tsing Hua University, Taiwan.
2Y.-S. Chen (eeyschen@ee.yzu.edu.tw) is with the Department of Electrical Engineering, Yuan Ze University, Taiwan.
This paper presents a self-calibration algorithm that seeks the camera intrinsic parameters to minimize the sum of squared distances between the measured and reprojected image points. By exploiting the constraints provided by the fundamental matrices, the function to be minimized can be directly reduced to a function of the camera intrinsic parameters; thus variant camera constraints such as fixed or varying focal lengths can be easily imposed by controlling the parameters of the resulting function. We employed the simplex method to minimize the resulting function and tested the proposed algorithm on some simulated and real data. The experimental results demonstrate that our algorithm performs well for variant camera constraints and for two-view and multiple-view cases.
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The symbol denotes the standard deviation of imposed Gaussian white noise.
In this table, τ denotes the camera aspect ratio, α is the camera skew factor, p represents the image principal point, f stands for the focal length, and fi is the focal length of the ith view.
Table 3
Comparison of Proposed Method with Bougnoux's Closed-Form Solutiona
Noise Level
Focal Length
Proposed Method
Bougnoux's Method
View 1
View 2
View 1
View 2
σn = 0.0
Mean
1000.00
1100.00
1000.00
1100.00
St. Dev.
0.00
0.00
0.00
0.00
σn = 0.5
Mean
999.08
1099.27
999.02
1099.25
St. Dev.
30.47
32.33
30.57
32.41
σn = 1.0
Mean
1000.48
1101.27
1000.31
1101.28
St. Dev.
62.12
65.66
62.28
65.87
Ref. 11.
Table 4
Comparison of Proposed Method with the Linear Approacha
The symbol denotes the standard deviation of imposed Gaussian white noise.
In this table, τ denotes the camera aspect ratio, α is the camera skew factor, p represents the image principal point, f stands for the focal length, and fi is the focal length of the ith view.
Table 3
Comparison of Proposed Method with Bougnoux's Closed-Form Solutiona
Noise Level
Focal Length
Proposed Method
Bougnoux's Method
View 1
View 2
View 1
View 2
σn = 0.0
Mean
1000.00
1100.00
1000.00
1100.00
St. Dev.
0.00
0.00
0.00
0.00
σn = 0.5
Mean
999.08
1099.27
999.02
1099.25
St. Dev.
30.47
32.33
30.57
32.41
σn = 1.0
Mean
1000.48
1101.27
1000.31
1101.28
St. Dev.
62.12
65.66
62.28
65.87
Ref. 11.
Table 4
Comparison of Proposed Method with the Linear Approacha
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