| ARANZ's
FastRBFTM
software is very useful for interpolating irregularly sampled
data in 2 and 3
dimensions. However, due to the presence of noise,
it is not always desirable to exactly interpolate at
the data points. Approximation is often prefered. FastRBF's spline smoothing fitter lets users
specify a smoothing parameter when fitting which strikes a
compromise between smoothness of the interpolant and fidelity to the data.
The following
example illustrates 2D interpolation of a bivariate function -
the well-known Matlab 'peaks' function (a). This
function is a sum of scaled and translated Gaussian
distributions. The height depicted in (a) is a
function of X & Y. The function was randomly sampled over the
domain depicted in (b). To simulate scattered
data more typical of the real world, white noise has then been
added to the sampled function values in (c). The
magnitude of the noise component is 10% that of the maximum range
of values in the 'peaks' function.
Figures
(e) and (g) illustrate exact and
approximating RBF fits to the data, respectively. In (g) a smoothing parameter determines how closely the RBF
fits the data. The basic function in both cases is the thin-plate
basis. A compromise between interpolating the data exactly and
achieving a smooth (low-energy) fit is achieved in
(g).
Figures
(f) and (h) illustrate the differences
between the fitted data and the original, noise-free, signal (a) - which is usually not
known.
Further information can be found on the following ARANZ web pages:
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