(FWD to list since Helena isn't subscribed)


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From: Helena Mitasova <hmitaso@unity.ncsu.edu>
Date: Wed, Mar 19, 2008 at 3:23 PM

 On Mar 19, 2008, at 9:23 AM, Markus Neteler wrote:
 > (I cc to Helena for TPS insights)
...

  - your references are right, although I wonder whether just plain
 TPS is used or whether at least tension has been added to increase
 the TPS stability. One reason why Lubos has derived the RST function
 which we have in GRASS was that TPS tends to overshoot if you have
 larger gradients as noted in the comments and adding tension and
 smoothing minimizes that problem. Segmentation then solves the
 problem of applying it to large data sets - but do you ever have more
 than 1000 GCPs?
 For the record here are some relevant equations:

 eq 44 is the radial basis function used in plain TPS, eq. 50 is
 spline with tension, eq. 55 is regularized spline (the last two are
 in ArcGIS spatial analyst)
 http://skagit.meas.ncsu.edu/~helena/gmslab/papers/CMA1988.pdf

 and here eq 9 has RST (and some useful comments about the rest of the
 methods)
 http://skagit.meas.ncsu.edu/~helena/gmslab/papers/sint.html

 And this nicely illustrates the "spline goes wild" issue - the blue
 points are given points, the surface is interpolated with changing
 tension and the results with a big blue hole and white peaks is close
 to what you can get with plain TPS:
 http://skagit.meas.ncsu.edu/~helena/gmslab/viz/movies/tension.gif

 smoothing also helps a lot and can even be used to take into account
 the accuracy of GCPs.

 To conclude - it would be nice to put the equations for what is used
 in gdalwarp somewhere to better understand how it works.
 Maybe put a reference to a relevant paper that has the equations into
 the man page.
 I am not sure whether the tps-related problems in gdalwarp are
 significant enough to do some modifications - I would assume most
 transformations are pretty smooth,