A Buyer's Guide to Conic Fitting

In this paper we evaluate several methods of fitting data to conic sections. Conic fitting is a commonly required task in machine vision, but many algorithms perform badly on incomplete or noisy data. We evaluate several algorithms under various noise and degeneracy conditions, identify the key parameters which affect sensitivity, and present the results of comparative experiments which emphasize the algorithms' behaviours under common examples of degenerate data. In addition, complexity analyses in terms of flop counts are provided in order to further inform the choice of algorithm for a specific application.

[1]  F. Bookstein.  Fitting conic sections to scattered data , 1979 .

[2]  Azriel Rosenfeld,et al.  A note on polygonal and elliptical approximation of mechanical parts , 1979, Pattern Recognit..

[3]  W. Gander.  Least squares with a quadratic constraint , 1980 .

[4]  PAUL D. SAMPSON,et al.  Fitting conic sections to "very scattered" data: An iterative refinement of the bookstein algorithm , 1982, Comput. Graph. Image Process..

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  John Porrill,et al.  Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter , 1990, Image Vis. Comput..

[7]  William H. Press,et al.  Numerical recipes , 1990 .

[8]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  David A. Forsyth,et al.  Invariant Descriptors for 3D Object Recognition and Pose , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Linda G. Shapiro,et al.  Computer and Robot Vision , 1991 .

[11]  Paul L. Rosin.  Ellipse fitting by accumulating five-point fits , 1993, Pattern Recognit. Lett..

[12]  Paul A. Beardsley,et al.  Robust Vision , 1994, BMVC.

[13]  Kenichi Kanatani,et al.  Statistical Bias of Conic Fitting and Renormalization , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Emanuele Trucco,et al.  Computer and Robot Vision , 1995 .