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Issue No.06 - June (2009 vol.31)
pp: 1147-1152
D. Shane Barwick , Rocky Mound Engineering , Macon
ABSTRACT
Many machine vision tasks require objects to be delineated during image segmentation that have shapes that are well approximated by circles or ellipses. Due to their computational efficiency least-squares, algebraic methods are a popular choice for fitting an elliptic primitive to noisy image data when real-time processing is required. These methods, however, suffer from biased estimates and sensitivity to outlier data. In this paper a real-time, least-squares method is proposed that provides an indirect geometric fit based on the quadratic polynomial form of parallel chord lengths. The algorithm is shown to be more computationally efficient and more easily made robust to outlier data than algebraic methods. Experimental results also suggest that it provides estimates that suffer less from bias error.
INDEX TERMS
Segmentation, Edge and feature detection, Least squares methods, Shape
CITATION
D. Shane Barwick, "Very Fast Best-Fit Circular and Elliptical Boundaries by Chord Data", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 6, pp. 1147-1152, June 2009, doi:10.1109/TPAMI.2008.279
REFERENCES
[1] A. Talukder, J.M. Morookian, S. Monacos, R. Lam, C. LeBaw, and J. Lambert, “Eye-Tracking Architecture for Biometrics and Remote Monitoring,” Applied Optics, vol. 44, no. 5, pp.693-700, Feb. 2005.
[2] Y. Nagawaka and A. Rosenfeld, “A Note on Polygonal and Elliptic Approximation of Mechanical Parts,” Pattern Recognition, vol. 11, pp.133-142, 1979.
[3] P.L. Rosin and G.A. West, “Nonparametric Segmentation of Curves into Various Representations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 12, pp.1140-1153, Dec. 1995.
[4] F. Bookstein, “Fitting Conic Sections to Scattered Data,” Computer Graphics and Image Processing, vol. 9, pp.56-71, 1979.
[5] K. Kanatani, “Statistical Bias of Conic Fitting and Renormalization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 3, pp.320-326, Mar. 1994.
[6] P.D. Sampson, “Fitting Conic Sections to Very Scattered Data,” Computer Graphics and Image Processing, vol. 18, pp.97-108, 1992.
[7] G. Taubin, “Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp.1115-1138, Nov. 1991.
[8] A.W. Fitzgibbon, M. Pilu, and R.B. Fisher, “Discrete Least Square Fitting of Ellipses,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp.476-480, May 1999.
[9] R. Halir and J. Flusser, “Numerically Stable Least Squares Fitting of Ellipses,” Proc. Sixth Int’l Conf. in Central Europe on Computer Graphics, Visualization, and Interactive Digital Media, vol. 1, pp.125-132, 1998.
[10] E.S. Maini, “Enhanced Direct Least Squares Fitting of Ellipses,” Int’l J. Pattern Recognition and Artificial Intelligence, vol. 20, no. 6, pp.939-953, 2006.
[11] R. Halir, “Robust Bias-Corrected Least Squares Fitting of Ellipses,” Proc. Eighth Int'l Conf. in Central Europe on Computer Graphics, Visualization, and Interactive Digital Media, vol. 1, 2000.
[12] A. Fitzgibbon and R.B. Fisher, “A Buyers Guide to Conic Fitting,” Proc. Sixth British Conf. Machine Vision, vol. 2, pp.513-522, 1995.
[13] D. Bertsekas, Nonlinear Programming. Athena Scientific, 1999.
[14] J.V. Beck and K.J. Arnold, Parameter Estimation in Engineering and Science. John Wiley and Sons, 1977.
[15] H. Theil, “A Rank-Invariant Method of Linear and Polynomial Regression Analysis,” Nederlandse Akademie Wetenchappen Series A, vol. 53, pp.386-392, 1950.
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