[gdal-dev] downsampling geotiff with a low-pass filter

[Kay F. Jahnke]

On 16.11.18 10:07, Even Rouault wrote:
>> Upsampling is well
>> covered: cubicspline and lanczos are reasonably sophisticated upsampling
>> filters,
> 
> Did you actually try them for downsampling ? They are for sure widely used in
> that case already, for example when using gdaladdo to create overviews. For
> example cubicspline has a filter radius of 2. If you downsample by a factor of
> X, the effective radius will be 2 X.

I did try them, and the result looks 'okay', but I have reservations. I 
come from a DSP background. If my understanding of the mathematics 
involved is correct, evaluating a spline over a data set will produce 
values which are appropriate at a given resolution. If you use these 
values at a lower resolution, you may get aliasing if the initial signal 
has high frequency content. Aliasing always happens if there is high 
frequency content and you resample with a lower sampling rate. You can 
only avoid it by using a low-pass filter before resampling. So I'm 
trying to find out if this does happen here.

If I understand this correctly, the effective radius signifies the 
number of spline coefficients contributing to the interpolated value, it 
does not imply a low-pass filter. If the spline (and I suspect it's a 
B-spline) is created by first prefiltering the data and then evaluating 
the spline at the desired target locations, the interpolation criterion 
is fulfilled and there is no smoothing.

Omitting the prefiltering and using the original data as spline 
coefficients does some smoothing, but from a cubic spline the effect is 
small and does not vary with the scale of the downsampling, so it would 
not work equally well for different scale changes.

Maybe you can point me to the place in the source code where the 
relevant math happens? I had a look but it's very complex and I did not 
find my way in easily.

 > They are for sure widely used

This doesn't automatically make them correct. If my suspicions are 
founded, then there may be room for improvement.

Kay