Fast and Numerically Stable Circle Fit

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less than 10 iterations to converge, on average.

[1]  Nikolai I. Chernov,et al.  Statistical efficiency of curve fitting algorithms , 2003, Comput. Stat. Data Anal..

[2]  I. Vaughan L. Clarkson,et al.  A statistical analysis of the Delogne-Kåsa method for fitting circles , 2006, Digit. Signal Process..

[3]  J. Crawford.  A non-iterative method for fitting circular arcs to measured points , 1983 .

[4]  U. M. Landau,et al.  Estimation of a circular arc center and its radius , 1987, Comput. Vis. Graph. Image Process..

[5]  Sung Joon Ahn,et al.  Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space , 2004, Lecture Notes in Computer Science.

[6]  Pong C. Yuen,et al.  A novel method for parameter estimation of digital arc , 1996, Pattern Recognit. Lett..

[7]  Fitting circular arcs by orthogonal distance regression , 2004 .

[8]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[9]  S. H. Joseph.  Unbiased Least Squares Fitting of Circular Arcs , 1994, CVGIP Graph. Model. Image Process..

[10]  V. Karimdki.  Effective circle fitting for particle trajectories , 2002 .

[11]  William H. Press,et al.  Numerical recipes in C , 2002 .

[12]  N. N. Chan.  On Circular Functional Relationships , 1965 .

[13]  W. A. Perkins,et al.  A Model-Based Vision System for Industrial Parts , 1978, IEEE Transactions on Computers.

[14]  Yves Nievergelt,et al.  A finite algorithm to fit geometrically all midrange lines, circles, planes, spheres, hyperplanes, and hyperspheres , 2002, Numerische Mathematik.

[15]  Craig M. Shakarji,et al.  Least-Squares Fitting Algorithms of the NIST Algorithm Testing System , 1998, Journal of research of the National Institute of Standards and Technology.

[16]  Yves Nievergelt,et al.  Perturbation analysis for circles, spheres, and generalized hyperspheres fitted to data by geometric total least-squares , 2004, Math. Comput..

[17]  W. Gander,et al.  Least-squares fitting of circles and ellipses , 1994 .

[18]  I. Kasa.  A circle fitting procedure and its error analysis , 1976, IEEE Transactions on Instrumentation and Measurement.

[19]  N. Chernov.  Circular and Linear Regression: Fitting Circles and Lines by Least Squares , 2010 .

[20]  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..

[21]  L. Trefethen,et al.  Numerical linear algebra , 1997 .

[22]  Nikolai I. Chernov,et al.  Least Squares Fitting of Circles , 2005, Journal of Mathematical Imaging and Vision.

[23]  S. Ahn.  2. Least-Squares Orthogonal Distance Fitting , 2004 .