[GRASS-dev] Re: [GRASS GIS] #163: g.transform no longer calculating error for 2nd order transformation

[Hamish]

Michael Barton wrote:
> RMS error reports all 0 for 6 points in a 2nd order
> transformation. But the rectification happens OK. RMS values
> are reported for a 2nd order transformation with more than 6
> points.


right; when you have only the minimum number of points to describe the
transform you have no statistical power to determine how well that matches
the "ideal" transform described by a set containing many many well placed
control points.

once you start to add more points you can begin to see how noisy your GCP
placement is. Note that with a low "n" such as min+1 you can get a very
small RMS by chance, even if they're crap but happen to line up. As you
add enough extra points to get a meaningful RMS, the best obtainable RMS
you can achieve will asymptote to some smaller value but never reach 0.0
(due to limits GPS accuracy; width of line on map vs scale; etc)


With the RMS you are testing how well the points fit each other (as
described by a polynomial fn), not how well they fit reality. So RMS error
is an abstract thing which primarily just gives you confidence in your
digitization consistency, and AFAIU the back-transformed RMS gives you an
idea how much of a difference that error makes after the projection step.
** i.e. you should be georeferencing into a location/projection which is
the same as the original map scan, and not try e.g. to georeference a lat/
lon (plate carree) map directly into a projected location. **
Use [i.rectify] + r.proj as a two step process if the projection will
change.


as I understand it,
Hamish