[GRASS-user] r.proj or r.resamp.rst issues

[Glynn Clements]

Bulent Arikan wrote:

> > Cubic interpolation can introduce overshoot, as can other forms of
> > spline interpolation. Linear and nearest-neighbor interpolation don't
> > have this issue.
> >
> > With r.resamp.rst, the problem can be alleviated to a degree by using
> > higher values for the tension= parameter.
> >
> > Also, if your data is noisy, this will tend to exaggerate the
> > gradients, making overshoot more likely. Filtering the data first will
> > reduce the errors.
> 
> That makes sense now. I did not know about the inherent problem of
> overshooting in cubic interpolation. ASTER DEMs I have seem to be pretty
> consistent in terms of data ranges and representation of values (based on
> r.report), so I am not sure about the noise effect in my case. However,
>  does this mean that I am sort of out of "corrective" options if I want to
> use cubic reprojection of imagery from Latlong to UTM? I mean I either use
> nearest method for error-free reprojection or I have to be careful about the
> results of cubic method.

All methods of interpolation introduce artifacts; you just have to
choose which sort of artifacts you prefer. Nearest-neighbour
interpolation produces extreme gradients at sample points and zero
gradient elswhere. Linear interpolation produces extreme curvature at
sample points and zero curvature elsewhere.

Too low (or even negative) values from undershoot aren't any more
inaccurate than too high values from overshoot; they're just more
likely to be noticed (there are several places on earth where negative
altitudes would be correct).

> Finally, when you say "use higher values for
> tension parameter", I guess you mean values lower than default 40. such as
> 30. or 20.

Higher tension values cause less overshoot at the expense of greater
variations in curvature.

-- 
Glynn Clements <glynn at gclements.plus.com>