Evaluating/Fitting an ellipse from scattered points

Question

Here is the deal. I have multiple points (X,Y) that form an \'ellipse like\' shape.

I would like to evaluate/fit the \'best\' ellipse possible and get its properties

Answer 1

The ellipse fitting method proposed by:

Z. L. Szpak, W. Chojnacki, and A. van den Hengel. Guaranteed ellipse fitting with a confidence region and an uncertainty measure for centre, axes, and orientation. J. Math. Imaging Vision, 2015.

may be of interest to you. They provide estimates of both algebraic and geometric ellipse parameters, together with covariance matrices that express the uncertainty of the parameter estimates. They also provide a means of computing a planar 95% confidence region associated with the estimate that allows one to visualise the uncertainty in the ellipse fit.

A pre-print version of the paper is available on the authors websites (http://cs.adelaide.edu.au/~wojtek/publicationsWC.html). A MATLAB implementation of the method is also available for download: https://sites.google.com/site/szpakz/source-code/guaranteed-ellipse-fitting-with-a-confidence-region-and-an-uncertainty-measure-for-centre-axes-and-orientation