Fitting 3D ellipsoid to a set of 3D data points

Question

I have set of points whose 3D coordinates are x , y and z and I have to determine the best fit ellipsoid to their distribution. What makes it difficult is that my points are not distributed on an ellipsoidal surfaces, but they approximately fill the space defined by a cigar. I usually work with python/C and I know this question has been asked before, but I couldn't find any satisfactory answer. Do you know how I could solve this issue?

Answer 1

A possibility is to: i) take the convex hull of the shape. ii) take only extremal points (ie those lying on the boundary and not inside). iii) use a standard ellipsoid fitting algorithm eg https://github.com/pierre-weiss/FitEllipsoid .

The main difficulty from what I understood, is that ellipsoid fitting algorithms assume points to be on the boundary. Steps i) and ii) would allow discarding the inside points quite easily.