[PROJ] Is 16-bit quantization of values / (sub-)millimetric error in grids (sometimes) acceptable ?

[Lesparre, Jochem]

Hi Even,

I will try the clarify the accuracy of the grid shift files for the Netherlands. 

The core control points (CORS) in the Netherlands have a precision of a few millimetres to about a centimetre (depending on what you use as reference). The lower order control points have a precision in the order of a centimetre. 

However, our national coordinate system RD is defined as the transformation from ETRS89 as we publish it. This transformation is therefore perfect. The only inaccuracy comes from numerical issues like iterations etc. in the order of 0.1 mm.

The difference between rdtrans2008.gsb and rdtrans2018.gsb is at maximum 1 cm in on-shore Netherlands. Strictly speaking, this is a redefinition of RD and the 2008 definition should only be used with ETRF2000(R05) coordinates and the 2018 definition only with ETRF2000(R14) coordinates. In practise, the difference doesn't matter to the users, as long as the most precise users do not mix the 2008 and 2018 definition within one project.

The most precise use of RD is in the order of 1 cm. To make sure that implementations of the transformation between RD and ETRS89 are one order of magnitude better, we demand software developers that want to use the trademark RDNAPTRANS to implement the transformation with an accuracy of 1 mm. It is therefore important that when the grid shift file of the Netherlands is converted from NTv2 to another data format, the differences are well below 1 mm, and preferably in the order of 0.1 mm.

The idea behind this is that when surveyors measure with 1 cm precision, the accuracy of the implementation of the transformation they use should be 1 mm. We compare implementations of the transformation in surveying and GIS software with the PROJ. implementation to check if it is within 1 mm. For a fair comparison, the PROJ. implementation should have an accuracy of 0.1 mm and also the different grids we publish should be consistent within 0.1 mm.  

Regards, Jochem 


-----Original Message-----
From: PROJ <proj-bounces at lists.osgeo.org> On Behalf Of Even Rouault
Sent: zondag 8 december 2019 16:10
To: proj at lists.osgeo.org
Subject: [PROJ] Is 16-bit quantization of values / (sub-)millimetric error in grids (sometimes) acceptable ?

Hi,

I'm experimenting with encoding grids with 16-bit integer values, with an offset and scale, instead of using IEEE 32-bit floats. There's some connection with my previous thread about accuracies of NTv2...

Let's for example take the example of egm08_25.gtx. It is 149.3 MB large If converting it into a IEEE 32-bit float deflate-compressed (with floating- point predictor) tiled geotiff, it becomes 80.5 MB large (the compression method and floatin-point predictor are fully lossless. There's bit-to-bit equivalence for the elevation values regarding the original gtx file) Now observing that the range of values is in [-107,86], I can remap that to [0,65535] with an offset of -107 and scale of (86 - -107) / 65535 ~= 0.0029 The resulting deflate-compressed (with integer predictor) tiled GeoTIFF is now
23.1 MB large !

Looking at the difference between the unscaled quantized values and the original ones, the error is in the [-1.5 mm, 1.5 mm] range (which is expected, being the half of the scale value), with a mean value of 4.5e-6 metre (so centered), and a standard deviation of 0.85 mm

After that experimentation, I found this interesting page of the GeographicLib documentation https://geographiclib.sourceforge.io/html/geoid.html
which compares the errors introduced by the gridding itself and interpolation methods (the EGM model is originally a continuous model), with/without quantization. And one conclusion is "If, instead, Geoid were to use data files without such quantization artifacts, the overall error would be reduced but only modestly". Actually with the bilinear interpolation we use, the max and RMS errors with and without quantization are the same... So it seems perfectly valid to use such quantized products, at least for EGM2008, right ?

Now looking at horizontal grids, let's consider Australia's GDA94_GDA2020_conformal.gsb. It is 83 MB large (half of this size due to the error channels, which are set to a dummy value of -1...) Converting it to a compressed tiled Float32 tif (without those useless error channels), make it down to 4.5 MB.
And as a quantitized uint16 compressed tif, down to 1.4 MB (yes, almost 60 times smaller than original .gsb file). The maximum scale factor is 1.5e-7 arcsecond, hence a maximum error of 2.3 micrometre... I'm pretty sure we're several order of magnitudes beyond the accuracy of the original model, right ?
In EPSG this transformation is reported to have an accuracy of 5cm.
The fact that we get such a small scale factor is due to GDA94 -> GDA2020 conformal being mostly a uniform shift of ~1.8 m and that the grids is mentioned to "Gives identical results to Helmert transformation GDA94 to
GDA2020 (1)"

If we look at the France' ntf_r93.gsb, which has shifts of an amplitude up to 130m, the maximum error introduced by the quantization is 0.6 mm. I would tend to think this is also acceptable (given the size of that particular file is small, compression gains are quite neglectable, but this is mostly to look if we can generalize such mechanism). What puzzles me is that in https://geodesie.ign.fr/contenu/fichiers/documentation/algorithmes/notice/
NT111_V1_HARMEL_TransfoNTF-RGF93_FormatGrilleNTV2.pdf where they compare the
NTv2 approach regarding their native 3D geocentric correction approach, they underline in red a sample point where the difference between the 2 models is
1.2 mm, as if it had really some importance. For that test point, using the quantized approach would increase this difference to 1.3 mm. But when looking at the accuracy reported in the grid at that point it is 1.6e-3 arc-second (which is the minimum value for the latitude error of the product, by the way), ie 5cm, so it seems to me that discussing about millimetric error doesn't make sense.
In EPSG this transformation is reported to have an accuracy of 1 metre (which is consistent with the mean value of the latitude shift error)

Now, let's look at the freshly introduced BWTA2017.gsb file. 392 MB large As a Float32 compressed geotiff: 73 MB (5.4x compression rate) As a Int16 compressed geotiff: 26 MB (15x compression rate) Maximum error added by quantization for latitude shift: 0.25 mm Minimum error value advertized for latitude shift: 1.61e-5 arc-second (not completely sure about the units...), ie 0.5mm Mean error value advertized for latitude shift: 6.33e-5 arc-second, ie 1.9mm Interestingly when looking at the ASCII version of the grid, the values of the shifts are given with a precision of 1e-6 arcseconds, that is 0.03 mm !

For Canadian NTv2_0.gsb, on the first subgrid, the quantization error is
0.9 mm for the latitude shift. The advertized error for latitude is in [0,
13.35 m] (the 0.000 value is really surprising. reached on a couple points only), with a mean at 0.27 m and stddev at 0.48 m. In EPSG this transformation is reported to have an accuracy of 1.5 metre

~~~~~~~~~~~~~

So, TLDR, is it safe (and worth) to generate quantized products to reducte by about a factor of 2 to 3 the size of our grids compared to unquantized products, when the maximum error added by the quantization is ~ 1mm or less ? 
or will data producers consider we damage the quality of products they carefully crafted ? do some users need millimetric / sub-millimetric accuracy ?

Or do we need to condition quantization to a criterion or a combination of criteria like:
- a maximum absolute error that quantization introduces (1 mm ? 0.1 mm ?)
- a maximum value for the ratio between the maximum absolute error that quantization introduces over the minimum error value advertized (when known) below some value ? For the BWTA2017 product, this ratio is 0.5. For ntf_r93.gsb, 0.012. For NTv2_0.gsb, cannot be computed given sothe min error value advertized is 0...
- or, variant of the above, a maximum value for the ratio between the maximum absolute that quantization introduces  over the mean of the error value advertized (when known). For the BWTA2017 product, this ratio is 0.13. For ntf_r93.gsb, 5.5e-4. For NTv2_0.gsb, 3.3e-3
- and perhaps consider that only for products above a given size (still larger than 10 MB after lossless compression ?)

~~~~~~~~~~~~~~~~

Jochem mentionned in the previous thread that the Netherlands grids have an accuracy of 1mm. I'm really intrigued by what that means. Does that mean that the position of control points used to build the grid is known at that accuracy, both in the source and target systems, and that when using bilinear interpolation with the grid, one remains within that accuracy ? Actually both the rdtrans2008.gsb and rdtrans2018.gsb grids report an accuracy of 1mm, but when comparing the positions corrected by those 2 grids, I get differences above 1mm.

echo "6 53 0" | cct -d 9 +proj=hgridshift +grids=./rdtrans2008.gsb
   5.999476046    52.998912757

echo "6 53 0" | cct -d 9 +proj=hgridshift +grids=./rdtrans2018.gsb
   5.999476020    52.998912753

echo "52.998912757 5.999476046 52.998912753 5.999476020" | geod -I 
+ellps=GRS80
-104d18'21.49"	75d41'38.51"	0.002

That's a difference of 2 mm. I get that difference on a few other "random" 
points.

If applying the quantization on rdtrans2018.gsb, we'd add an additional maximal error of 0.6 mm. The grid being 1.5 MB uncompressed, and 284 KB as a losslessly compressed TIFF, quantization isn't really worth considering (reduces the file size to 78 KB)

Even

--
Spatialys - Geospatial professional services http://www.spatialys.com _______________________________________________
PROJ mailing list
PROJ at lists.osgeo.org
https://lists.osgeo.org/mailman/listinfo/proj


Disclaimer:
De inhoud van dit bericht is uitsluitend bestemd voor geadresseerde.
Gebruik van de inhoud van dit bericht door anderen zonder toestemming van het Kadaster 
is onrechtmatig. Mocht dit bericht ten onrechte bij u terecht komen, dan verzoeken wij u 
dit direct te melden aan de verzender en het bericht te vernietigen. 
Aan de inhoud van dit bericht kunnen geen rechten worden ontleend.

Disclaimer:
The content of this message is meant to be received by the addressee only.
Use of the content of this message by anyone other than the addressee without the consent 
of the Kadaster is unlawful. If you have received this message, but are not the addressee, 
please contact the sender immediately and destroy the message.
No rights can be derived from the content of this message