A Stable Least Squares Ellipses Fitting Algorithm Based on Zernike Moments

Abstract:

This paper presents a stable least squares ellipses fitting algorithm based on Zernike orthogonal moments. The algorithm uses Zernike orthogonal moments for sub-pixel edge detection, and a mask of seven multiply seven was derived in the meantime. The optimal ellipse parameters were computed according to the data points extracted previously. This stable, robust and non-iterative algorithm can be easily implemented. The experiment results show that the proposed algorithm is effective in various situations.

• Periodical: Advanced Materials Research (Volume 142)
• Pages: 199-203
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.142.199
• Online since: October 2010
• Authors: Xiang Lin Meng, Wan Tao He, Can Zhao
• Keywords: Edge Detection, Ellipse Fitting, Least Square (LS), Zernike Moment

References

[1] S. Tsuji, F. Matsumoto: IEEE Transactions on Computers, vol. 27 (1978), pp.777-781.

[2] D.H. Ballard: Pattern Recognition, vol. 13 (1981), pp.111-122.

[3] Andrew Fitzgibbon, Maurizio Pilu, Robert B. Fisher: IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21 (1999), pp.476-480.

DOI: 10.1109/34.765658

[4] M.R. Teague: J. Opt. Soc. Amer, vol. 70 (1980), pp.920-930.

[5] Simon. X, Liao: Electrical and Computer Engineering, IEEE Canadian Conference on 2 (1997), pp.700-703.

[6] I.S. Duff, A.M. Erisman and J.K. Reid: Direct Methods for Sparse Matrices, Oxford University Press (1986).

[7] A. Khotanzad, Y.H. Hong: Pattern Analysis and Machine Intelligence, IEEE Transactions on, Vol. 12 (1990), pp.489-497.

DOI: 10.1109/34.55109

[8] Information on http: /mathworld. wolfram. com.