Linear Least Squares Fit of Sphere to Points

Question

I\'m looking for an algorithm to find the best fit between a cloud of points and a sphere.

That is, I want to minimise

where C is the centre

Answer 1

You may be interested by the best fit d-dimensional sphere, i.e. minimizing the variance of the population of the squared distances to the center; it has a simple analytical solution (matrix calculus): see the appendix of the open access paper of Cerisier et al. in J. Comput. Biol. 24(11), 1134-1137 (2017), https://doi.org/10.1089/cmb.2017.0061 It works when the data points are weighted (it works even for continuous distributions; as a by-product, when d=1, a well-known inequality is retrieved: the kurtosis is always greater than the squared skewness plus 1).