Fitting Superellipses

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 measures that can be applied by most superellipse fitting methods.

[1]  Boualem Boashash,et al.  A structural-description-based vision system for automatic object recognition , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[2]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[3]  Andrew W. Fitzgibbon,et al.  Direct Least Square Fitting of Ellipses , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  G. Toussaint Solving geometric problems with the rotating calipers , 1983 .

[5]  N. Yokoya,et al.  Recovery of superquadric primitives from a range image using simulated annealing , 1992, [1992] Proceedings. 11th IAPR International Conference on Pattern Recognition.

[6]  Paul L. Rosin Assessing Error of Fit Functions for Ellipses , 1996, CVGIP Graph. Model. Image Process..

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

[8]  Wen-Hsiang Tsai,et al.  Moment preserving detection of elliptical shapes in gray-scale images , 1990, Pattern Recognit. Lett..

[9]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[10]  Beno Benhabib,et al.  Accurate parameter estimation of quadratic curves from grey-level images , 1991, CVGIP Image Underst..

[11]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[12]  Andrew W. Fitzgibbon,et al.  Training PDMs on models: The case of deformable superellipses , 1999, Pattern Recognit. Lett..

[13]  Paul L. Rosin,et al.  Curve segmentation and representation by superellipses , 1995, IEE Proceedings - Vision, Image, and Signal Processing.

[14]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[15]  Terrance E. Boult,et al.  Error Of Fit Measures For Recovering Parametric Solids , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

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

[17]  Paul L. Rosin Ellipse Fitting Using Orthogonal Hyperbolae and Stirling's Oval , 1998, Graph. Model. Image Process..

[18]  Herbert Süße,et al.  A New One-Parametric Fitting Method for Planar Objects , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Franco P. Preparata,et al.  Computational Geometry , 1985, Texts and Monographs in Computer Science.