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I am wondering how to decompose the data[x,y] into several elliptic-shaped functions, i.e. $f[x,y]=\frac{H}{(1+(\frac{x-x1}{a1})^2+(\frac{y-y1}{b1})^2)^{3/2}}$.

I could follow in 1D case, decomposition data[x] into $\frac{H}{1+((x-x1)/a1)^2}$, by just following (with modification) How to perform a multi-peak fitting? , but I cannot perform in 2D case.

Does anyone have a good idea?

Thank you.

Ui-Jin Kwon
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  • Possibly helpful? https://mathematica.stackexchange.com/questions/207812/finding-a-parametric-curve-fitting-a-two-dimensional-dataset – MelaGo Feb 05 '20 at 07:11
  • @MelaGo Thank you for helping me. But actually the data is three dimension in graph, and even determining the number of basis functions is not trivial. – Ui-Jin Kwon Feb 05 '20 at 07:20

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