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version (7.5 KB) by Martti Kesäniemi
Direct fitting of ellipses, ellipsoids, and hyperellipsoids


Updated 16 Apr 2019

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The function HYPERELLIPSOIDFIT.M fits a quadratic surface to given n-dimensional data. It has been written especially for ellipsoid fitting purposes. It contains n-dimensional elaborations of several ellipse fitting methods, and includes a method that is guaranteed to produce an ellipsoidal solution in n-dimensional space regardless of the data. It includes also a regularization method that can be used to force the solutions towards spheres and to solve ill-posed fitting problems.
The implemented methods are described in Kesäniemi-Virtanen, "Direct Least Square Fitting of Hyperellipsoids", IEEE Transactions on Pattern Analysis and Machine Intelligence.
The other function in the package, DEMO.M, uses HYPERELLIPSOIDFIT function to illustrate the 3D results produced by various fitting methods with three different regularization parameter values.

Cite As

Martti Kesäniemi (2019). hyperellipsoidfit (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)

Great tool, thank you!

For ease of use and for traceability of output, recommend making the return a single struct, i.e. foo.Me, foo.oe, foo.succcess, etc.


Fixed a bug in input parameter handling, added possibility to get outputs as struct.

Update for 2017b

Updated for 2017A

Reference update

Fix to demo

Fix to the comments / function help.

MATLAB Release Compatibility
Created with R2019a
Compatible with any release
Platform Compatibility
Windows macOS Linux