Additional map features: generic or specific?

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One of the characteristics of the cadastral maps is the local grid. In the end of the eighteenth century and the beginning of the nineteenth century, geodesy (surveying on a national scale, in regards to the curvature of earth) became introduced. In France, this was instigated by Casini. In Belgium, the Austrian-Hungarian overlords gave it a shot to extend the work from Casini, but failed miserably, ending up with an extremely complex system of linked-up areas, resulting in huge stacking errors. It is not a pretty sight, although the resulting Ferraris-maps are visually beautiful.

In The Netherlands, Kraijenhof succeeded in following the principles of Casini for The Netherlands. During the periode the cadaster was founded, discussions arose about how to deal with the issue of national triangulation. It was decided (for Belgium and The Netherlands alike) that that national scale was of no importance for de cadastre, because in essence it was a national system, but only applied locally. That goes for the entire rhetoric; the taxation was established for each municipality individually. So was the land-surveying, with the exception of some small clusters of municipalities that organised things on a cantonal level.

The idea for the Triangulation was setting out a triangulation grid in each municipality (canévas trigonometrique) and then together with the compass (boussole) the direction of north was established, deviating a consistent number of degrees per municipality. The technical scale (échelle) was determined by measuring 1 “base” in the municipality three times, with a (established in the Recueil Methodique) fixed maximum error of 1 promille. length-wise. And indeed, when working with these maps, you can easily establish the actual map-scale, being just a bit different from the declared 1 in 2500, again, consistent throughout the entire municipality. In the image, you can see all of the triangulation-points for a municipality in The Netherlands (Diepenheim).

So, in theory, that would allow you to stitch together all of the maps for 1 municipality, and then apply a single georeference to that municipal file. This approach works extremely well in some cases. However, not for others. There are 2 complications.

The first is that this approach leans on a perfect triangulation. If there are deviations in that local triangulation, there is a problem. For most municipalities this works fine, but in some cases (and you only know afterwards which ones) the shape of the municipalities led surveyors to cut corners and to not establish sufficient checks and balances for a certain point. This does lead to some very large deviations in a limited (but nevertheless existing) set of municipalities.

The second issue is that in the earliest maps, the triangulated grid was added to the maps afterwards. In those cases, this was not always done in a decent manner. As you can see in the example below (one map being blue, the neighbouring map red) lining out these maps based on the grid is disastrous. The maps however fit together nicely. The grids don’t.

However, besides being of importance for stitching these maps together per municipality, these grid lines serve a different goal as well. If you have these lines as a set of line-equations per map (very easy to do with CV), you can establish the actual map scale after georeferencing (this all can be done with IIIF-annotations, see https://allmaps.org/).

Then, you can calculate the mean map scale for each municipality, and let this be a parameter in the least-squares regression / best fit of a similarity-polynomial-transformation for georeferencing each map. This should not be underestimated, as the actual map-scale is one out of only three values that need to be calculated for georeferencing a map (translation, rotation and scale). The translation-part consists of a X and a Y part, so 4 numbers in total. If you allow for affine deformation (which I would advise against), the rotation and scale also can differ for the x and y component, thus resulting in the 6 parameters of a classical transformation. These 6 parameters are better known as the six lines in a worldfile for georeferencing an image (.wld in general, or .tfw of .jgw for the format-specific extension, but all are the same six lines). That affine-deformation allows for a rectangle to be transformed into a parallelogram. If you don’t allow that deformation, you end up with a world-file with also 6 parameters, of which 2 sets are identical, so indeed 4 unique numbers.

Georeferencing cadastral maps from the early nineteenth century is often a very big challenge, because of two main reasons. Firstly, cities expanded massively, and all of the suburbs bear no resemblance to the earlier landscape, and thus are extremely difficult to georeference. Secondly, because of the pre-modern / early-modern time-period, a lot of the areas have been “ontgonnen” (dutch) / exploité / developed. This is especially true for areas with extensive heath / fenns / bog / mire / bruyère. Those as well bear no resemblance to the original cadastral maps.

All of that taken into account, it is very desirable if any progress can be made, and even small gains like the establishing of a common scale for the entire municipality has enormous (positive) consequences for the quality of the georeferencing, and thus also for the useability of automatically processed maps.

Therefore, I think we should include those grid-lines as an extension of the more generic map-annotation-models, almost as metadata, because of the importance for the actual processing possibilities. This should not be underestimated, and might even be crucial for the feasibility of automatic processing for those maps in general.

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