[argyllcms] Re: rspl weights
- From: Graeme Gill <graeme@xxxxxxxxxxxxx>
- To: argyllcms@xxxxxxxxxxxxx
- Date: Sat, 30 Jul 2005 11:12:21 +1000
Gerhard Fuernkranz wrote:
Btw, my understanding of thin plate splines (TPS) is, that the scattered
data are basically fitted by a sum of N radial basis functions (r^2*ln(r)),
each of the RBFs centered at one of the N scattered data points (plus
optional linear/polynomial terms and an optional smoothness term). Does this
apply to RSPLs as well, or are there some differences? Does the RSPL grid
simply represent a resampling of the TPS at regular intervals? And is my
assumption correct, that the spline_interp() method does not use the TPS for
interpolation, but only the scattered data fitting involves TPS?
The RSPLs are not related to radial basis functions. The technique is
essentially the fitting of the regular grid to the data. The fitting
is governed by the interpolation error the grid has to the scattered
data points, and the smoothness of the grid (balancing one against
the other.) A multigrid approach is needed to get the fitting to
converge properly.
Radial basis functions are relatively simple to do, but have
lots of problems such as:
Slope being zero at data points.
Value tending towards the average at a distance.
"Shadowing" of one point by another.
Wrinkles and bumps.
Performance inversely proportional to number of scattered data points.
Regularized linear splines seem to be well behaved by comparison, and directly
solves for the representation that the ICC format has in a clut.
Graeme Gill.
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