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.
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The implemented methods are described in Kesäniemi-Virtanen, "Direct Least Square Fitting of Hyperellipsoids", IEEE Transactions on Pattern Analysis and Machine Intelligence.
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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.