Fwd: [gdal-dev] gdalwarp : how many gcp's for -order n?

[Markus Neteler]

here again a FWD for the record:

---------- Forwarded message ----------
From: Helena Mitasova <hmitaso at unity.ncsu.edu>
Date: Wed, Mar 19, 2008 at 6:13 PM
Subject: Re: [gdal-dev] gdalwarp : how many gcp's for -order n?
To: Markus Neteler <neteler at osgeo.org>
Cc: Frank Warmerdam <warmerdam at pobox.com>


It indeed has the basic TPS (no tension, no smoothing) so
 something like this may be added (based on my reading of the code and
 the referenced paper):

 Thin plate spline in the following form is used for interpolation:
 f(x,y) = a +bx + cy + \sum_{j=1}^N \w_j r^2 \ln r^2
 where r^2 = (x_i-x_j)^2 + (y_i-y_j)^2, N is number of points and
 a,b,c,\w_j are coefficients

 Donato and Belongie paper:  www-cse.ucsd.edu/~sjb/pami_tps.pdf

 If the instability becomes annoying it can certainly be improved.

 Helena



 On Mar 19, 2008, at 11:05 AM, Markus Neteler wrote:
 > Helena,
 >
 > thanks for your explanations! the relevant code pieces should be here:
 >
 > http://trac.osgeo.org/gdal/browser/trunk/gdal/alg/gdal_tps.cpp
 > http://trac.osgeo.org/gdal/browser/trunk/gdal/alg/thinplatespline.cpp
 > http://trac.osgeo.org/gdal/browser/trunk/gdal/alg/thinplatespline.h
 >
 > Maybe those files could be enriched with some doxygen style
 > equations or citations.
 >
 > Markus