Suppose we are getting random points in 2D (or 3D) which tend to be on ellipse (or ellipsoid). We can't guarantee points are uniformly distributed over ellipse (ellipsoid surface).
The task is to determine ellipse (ellipsoid) parameters, i.e. center location and semi-axes.
We can't take average, because it will be weighted. I mean if points will come preliminary from one side of ellipse, averaging will give wrong results.
So the question is how to
UN-weight the average?
I think in the case of ellipse, the parameters can be determined by statistical quantities like moments. Can they?