Fitting an ellipsoid to 3D data points

Question

I have a large set of 3D data points to which I want to fit to an ellipsoid.

My maths is pretty poor, so I\'m having trouble implementing the least squares method withou

Answer 1

I ported Yury Petrov's least-squares Matlab fitter to Java some time ago, it only needs JAMA: https://github.com/mdoube/BoneJ/blob/master/src/org/doube/geometry/FitEllipsoid.java

Answer 2

If you want the minimum-volume enclosing ellipsoid, check out this SO answer for a bounding ellipsoid.

If you want the best fitting ellipse in a least-squares sense, check out this MATLAB code for error ellipsoids where you find the covariance matrix of your mean-shifted 3D points and use that to construct the ellipsoid.

Answer 3

We developed a set of Matlab and Java codes to fit ellipsoids here: https://github.com/pierre-weiss

You can also check our open-source Icy plugin. The following tutorial can be helpful: https://www.youtube.com/endscreen?video_referrer=watch&v=nXnPOG_YCxw

Note: most of the existing codes fit a generic quadric and do not impose an ellipsoidal shape. To get more robustness, you need to go to convex programming rather than just linear algebra. This is what is done in the indicated sources.

Cheers, Pierre