Computation and visualisation of the accuracy of old maps using differential distortion analysis

ABSTRACT

The accuracy of old maps can hold interesting historical information, and is therefore studied using distortion analysis methods. These methods start from a set of ground control points that are identified both on the old map and on a modern reference map or globe, and conclude with techniques that compute and visualise distortion. Such techniques have advanced over the years, but leave room for improvement, as the current ones result in approximate values and a coarse spatial resolution. We propose a more elegant and more accurate way to compute distortion of old maps by translating the technique of differential distortion analysis, used in map projection theory, to the setting where an old map and a reference map are directly compared. This enables the application of various useful distortion metrics to the study of old maps, such as the area scale factor, the maximum angular distortion and the Tissot indicatrices. As such a technique is always embedded in a full distortion analysis method we start by putting forward an optimal analysis method for a general-purpose study, which then serves as the foundation for the development of our technique. Thereto, we discuss the structure of distortion analysis methods and the various options available for every step of the process, including the different settings in which the old map can be compared to its modern counterpart, the techniques that can be used to interpolate between both, and the techniques available to compute and visualise the distortion. We conclude by applying our general-purpose method, including the differential distortion analysis technique, to an example map also used in other literature.

KEYWORDS:

• Historical cartography
• thin plate spline
• differential distortion analysis
• area scale factor
• maximum angular distortion
• Tissot indicatrices

Acknowledgements

Manuel Claeys Boùùaert is a Fellow of the Fund for Scientific Research–Flanders (FWO–Vlaanderen). The author would like to thank Prof. F. Canters (VUB, Brussels) for his inspiring lectures on map projections. We also thank swisstopo and Martin Rickenbacher for allowing us to use the map of the Basel and Frickthal region and the ground control points, respectively.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. A MATLAB/Octave implementation of the general-purpose distortion analysis method proposed in Section 2.5, including thin plate spline interpolation and differential distortion metrics, is available at: https://github.com/mclaeysb/distortionAnalysis.