A Camera Self-Calibration for Machine Vision Based on Kruppa's Equation

Abstract:

A camera self-calibration algorithm based on the Kruppas equation has been put forward by decomposing the fundamental matrix on the basis of computing the geometrical static moment. The fundamental matrix could be estimated through the normalized 8 points algorithm in which the centroid of the irregular polygon was calculated by computing the geometrical static moment. The five intrinsic parameters of a camera were calculated in accordance with the optimal target function established from the simplified Kruppas equation and the linear equation about the five internal parameters of a camera. The experiment showed that the five intrinsic parameters of a camera could be realized by this method.

• Periodical: Applied Mechanics and Materials (Volume 389)
• Pages: 1003-1007
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.389.1003
• Online since: August 2013
• Authors: Zhao Sheng Tao, Da Wei Tu, Sai Sai He, Jin Jie Ye
• Keywords: Camera Self-Calibration, Fundamental Matrix, Geometrical Static Moment, Kruppas Equation

References

[1] Quan L., Faugera O D. The Fundamental Matrix: Theory, Algorithms, and Stability Analysis[J]. International Journal of Computer Vision, 1996, 17(1): 43-76.

[2] Zhang Z Y. A Flexible Technique for Camera Calibration[J]. IEEE Trans. on Pattern Analysis and Machine Intelligence, 2000, 22(11): 1330-1334.

DOI: 10.1109/34.888718

[3] Richard I. Hartley. In Defence of the 8-point Algorithm[C]. Proceedings of the 5th International Conference on Computer Vision(ICCV'95) [C]. Cambridge, MA: IEEE Computer Society Press, 1995: 1064-1070.

[4] Zhang Z Y, Deriche R., Faugeras O., et al. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry[J]. Artificial Intelligence, 1995, 78 (2): 189-196.

DOI: 10.1016/0004-3702(95)00022-4

[5] Luong Q.T., Faugeras O.D. On the determination of epipoles using cross-ratios[C]. Proceeding of Computer Vision and Image Understanding, 1998, 71(1): 1-18.

DOI: 10.1006/cviu.1997.0621

[6] Liu H W. Mechanics of Materials[M]. Beijing: Higher Education Press, 2004. (in Chinese).

[7] HAO Yong-tao, ZHOU Wei, ZHONG Bo-tao. Self-calibration technique based on Kruppa equations obtaining initial solution by translational motion[J]. Computer Engineering and Applications, 2009, 45(22): 38-40. (in Chinese).