Description 
Generating points along an ellipse or ellipsoid, plotting ellipses and ellipsoids in various parametric representations, and fitting ellipses, ellipsoids or other quadratic curves and surfaces to noisy data occur frequently in fields such as computer vision, pattern recognition and system identification.
This toolbox provides a fairly comprehensive toolset of estimating quadratic curves and surfaces in an errorsinvariables context, with and without constraints. In addition to classical fitting methods such as least squares (with and without curve or surface normals), Taubin's method, direct ellipse fit by Fitzgibbon et al. [1] and direct ellipsoid fit by Qingde Li and John G. Griffiths [4], the toolbox features an estimation algorithm by the author [2,3], based on and extending the work of István Vajk and Jenő Hetthéssy [5]. The proposed quadratic curve and surface fitting algorithm combines direct fitting with a noise cancellation step, producing consistent estimates close to maximum likelihood but without iterations.
REFERENCES
[1] Andrew W. Fitzgibbon, Maurizio Pilu and Robert B. Fisher, "Direct Least Squares Fitting of Ellipses", IEEE Trans. PAMI 21, 1999, pp476480.
[2] Levente Hunyadi, "Estimation methods in the errorsinvariables context", PhD dissertation, Budapest University of Technology and Economics, 2013.
[3] Levente Hunyadi and István Vajk, "Constrained quadratic errorsinvariables fitting", The Visual Computer, 12 pages, in print, available online from October 2013.
[4] Qingde Li and John G. Griffiths, "Least Squares Ellipsoid Specific Fitting", Proceedings of the Geometric Modeling and Processing, 2004.
[5] István Vajk and Jenő Hetthéssy, "Identification of nonlinear errorsinvariables models", Automatica 39, 2003, pp20992107.
CONTACT INFORMATION
Levente Hunyadi
http://hunyadi.info.hu/
Please use my private email address to submit bug reports, which will be addressed upon short notice; reviews, however, are not monitored. Any feedback is most welcome.
