[SciPy-user] Fitting sphere to 3d data points

David Huard david.huard at gmail.com
Thu Jan 25 08:31:10 CST 2007

Hi James,

As a first guess, I'd say the center of the sphere is simply the mean of
your data points, if they're all weighted equally. With only one parameter
left to fit, it should be easy enough. However, you may want to look at the

Werman, Michael and Keren, Daniel
A Bayesian method for fitting parametric and nonparametric models to noisy
Ieee Transactions on Pattern Analysis and Machine Intelligence, 23, 2001.

They write that the Mean Square Error approach overestimates the radius in
the case of circles. They don't talk about the 3D case, but I'd guess
similar problems arise. They provide a method to fit parametric shapes with
some robustness to data errors.



2007/1/25, James Vincent <jjv5 at nih.gov>:
> Hello,
> Is it possible to fit a sphere to 3D data points using
> scipy.optimize.leastsq? I'd like to minimize the residual for the distance
> from the actual x,y,z point and the fitted sphere surface. I can see how to
> minimize for z, but that's not really what I'm looking for. Is there a
> better way to do this? Thanks for any help.
> params = a,b,c and r
> a,b,c are the fitted center point of the sphere, r is the radius
> err = distance-to-center - radius
> err = sqrt( x-a)**2 + (y-b)**2 + (z-c)**2) - r
> ----
> James J. Vincent, Ph.D.
> National Cancer Institute
> National Institutes of Health
> Laboratory of Molecular Biology
> Building 37, Room 5120
> 37 Convent Drive, MSC 4264
> Bethesda, MD 20892 USA
> 301-451-8755
> jjv5 at nih.gov
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