by Manuel Claeys Boùùaert

This code was built to analyse distortion in old maps.

Old, historical maps can be inaccurate for many reasons (primitive techniques, surveying errors, mixed inputs, conservation, etc). A distortion represents a loss in geographic information, but, by its specific origin, yields new historical information. Hence the study of distortions in old maps.

This code takes as input a set of common ground control points, identified both on the old map and on a modern reference map. Based on these points, an interpolation is constructed between both maps. From this interpolation, the distortions are computed using common distortion visualisation techniques, including displacement vectors, distortion grids, Tissot indicatrices and a new technique called Differential Distortion Analysis.

The output consists of a set of .WKT files representing the displacement vectors, distortion grid and Tissot indicatrices, and a .csv file with the values of distortion measures, such as the area distortion log2sigma and angular distortion 2Omega, computed at a number of mesh points and ground control points.

For further interpretation, visualise the output documents in a (web-)GIS application. For optimal visualisations, interpolate the point-wise results of the .csv file to create a continuous distortion raster image. As an example: the visualised outputs for the sample data look like this:

Displacement vectors

Distortion grid

Indicatrices of Tissot

Differential Distortion Analysis: area distortion log2sigma

Differential Distortion Analysis: angular distortion 2Omega

Bonus: this code can also be used in similar settings where 2D objects are warped, such as abstracted maps (e.g. transit maps), mental maps, maps of deformed terrain (glaciers, tectonics), etc. Feel inspired!

The .m code is fully Matlab and Octave compatible.

In order to build the interpolation, you should have access to either the Octave splines package or Matlab CurveFitting Toolbox. (The Octave splines package can be installed using pkg install -forge -global -auto splines)

The example.m file demonstrates how to load data, set optional parameters and call the main function distortionAnalysis.m.

Manuel Claeys Boùùaert wrote this code in 2015 for a project analysing distortion in the 1777 'Carte de Cabinet' of the Austrian Netherlands by count de Ferraris.

If you want use this code for scientific work, please refer to the following publication:

Claeys Boùùaert, M., De Baets, B., Vervust, S., Neutens, T., De Maeyer, P., Van De Weghe N., 2016. Computation and visualisation of the accuracy of old maps using differential distortion analysis. International Journal of Geographical Information Science.
http://dx.doi.org/10.1080/13658816.2015.1127377

The 'Author’s Original Manuscript (AOM)' of this article is also part of this repository.

If you want to learn more about the application of this technique on Farraris's 1777 Carte de Cabinet, read the following article:

Vervust, S., Claeys Boùùaert; M., De Baets; B., Van de Weghe, N., De Maeyer, P., 2018. A Study of the Local Geometric Accuracy of Count de Ferraris's Carte de cabinet (1770s) Using Differential Distortion Analysis. The Cartographic Journal
https://doi.org/10.1080/00087041.2017.1323148

The sample data map is courtesy of swisstopo (map collection, LT K BL 1798).
The sample data ground control points are courtesy of Martin Rickenbacher (Bern).

This sample data is similar to the one used in the MapAnalyst software by Bernhard Jenny, which has inspired us during our work.

The splines package for GNU Octave is written by Nir Y. Krakauer and others. It features the commands used in this code since version 1.2.9.