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Fitting Superellipses
July 2000 (vol. 22 no. 7)
pp. 726-732

Abstract—In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the nonlinear nature of the problem. This paper describes and tests several fitting techniques which provide different trade-offs between efficiency and accuracy. In addition, we describe various alternative error of fit (EOF) measures that can be applied by most superellipse fitting methods.

[1] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions. U.S. Government, 1964.
[2] A.H. Barr, "Global and Local Deformations of Solid Primitives," Computer Graphics (Proc. Siggraph), Vol. 18, No. 3, July 1984, pp. 21-30.
[3] M. Bennamoun and B. Boashash, “A Structural Description Based Vision System for Automatic Object Recognition,” IEEE Trans. Systems, Man, and Cybernetics, Part B, vol. 27, no. 6, pp. 893–906, 1997.
[4] A. Fitzgibbon, M. Pilu, and R.B. Fisher, “Direct Least Square Fitting of Ellipses,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 476-480, May 1999.
[5] A.D. Gross and T.E. Boult,“Error of fit for recovering parametric solids,” Second Int’l Conf. Computer Vision, pp. 690-694,Tampa, Fla., 1988.
[6] W. Knowlton, R.A. Beauchemin, and P.J. Quinn, Technical Freehand Drawing and Sketching. McGraw-Hill, 1977.
[7] R. Lee, P.C. Lu, and W.H. Tsai, “Moment Preserving Detection of Elliptical Shapes in Gray-Scale Images,” Pattern Recognition, vol. 11, pp. 405–414, 1990.
[8] Y. Nakagawa and A. Rosenfeld, “A Note on Polygonal and Elliptical Approximation of Mechanical Parts,” Pattern Recognition, vol. 11, pp. 133–142, 1979.
[9] A.P. Pentland,“Automatic extraction of deformable part models,” Int’l J. Computer Vision, vol. 4, pp. 107-126, 1990.
[10] M. Pilu and R.B. Fisher, “Training PDMs on Models: The Case of Deformable Superellipses,” Pattern Recognition Letters, vol. 20, no. 5, pp. 463–474, 1999.
[11] F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
[12] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vettering, Numerical Recipes in C. Cambridge Univ. Press, 1990.
[13] P.L. Rosin, “Assessing Error of Fit Functions for Ellipses,” Graphical Models and Image Processing, vol. 58, pp. 494–502, 1996.
[14] P.L. Rosin, “Ellipse Fitting Using Orthogonal Hyperbolae and Stirling's Oval,” Graphical Models and Image Processing, vol. 60, pp. 209–213, 1998.
[15] P.L. Rosin and G.A.W. West, “Curve Segmentation and Representation by Superellipses,” Proc. IEE: Vision, Image, and Signal Processing, vol. 142, pp. 280–288, 1995.
[16] R. Safee-Rad,I. Tchoukanov,B. Benhabib,, and K.C. Smith,“Accurate parameter estimation of quadratic curves from grey levelimages,” CVGIP: Image Understanding, vol. 54, pp. 259-274, 1991.
[17] M. Stricker, “A New Approach for Robust Ellipse Fitting,” Proc. Int'l Conf. Automation, Robotics, and Computer Vision, pp. 940–945, 1994.
[18] G.T. Toussaint, “Solving Geometric Problems with the Rotating Calipers,” Proc. IEEE Mediterranean Electrotechnical Conf. '83, A10.02, pp. 1–4, 1983.
[19] K. Voss and H. Süße, “A New One-Parametric Fitting Method for Planar Objects,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 646–651, 1999.
[20] N. Yokoya,M. Kaneta,, and K. Yamamoto,“Recovery of superquadric primitives from a range image using simulated annealing,” Int’l Conf. Pattern Recognition, vol. 1, pp. 168-172, The Hague, 1992.

Index Terms:
Curve, superellipse, fitting, error measure.
Paul L. Rosin, "Fitting Superellipses," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 7, pp. 726-732, July 2000, doi:10.1109/34.865190
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