, Volume 20, Issue 2, pp 241–284

Advanced methods for the estimation of an unknown projection from a map


DOI: 10.1007/s10707-015-0234-x

Cite this article as:
Bayer, T. Geoinformatica (2016) 20: 241. doi:10.1007/s10707-015-0234-x


This article presents three new methods (M5, M6, M7) for the estimation of an unknown map projection and its parameters. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the map projection; it could improve their georeference. The location similarity approach takes into account the residuals on the corresponding features; the minimum is found using the non-linear least squares. For the shape similarity approach, the minimized objective function ϕ takes into account the spatial distribution of the features, together with the shapes of the meridians, parallels and other 0D-2D elements. Due to the non-convexity and discontinuity, its global minimum is determined using the global optimization, represented by the differential evolution. The constant values of projection φk, λk, φ1, λ0, and map constants RXY, α (in relation to which the methods are invariant) are estimated. All methods are compared and the results are presented for the synthetic data as well as for 8 early maps from the Map Collection of the Charles University and the David Rumsay Map Collection. The proposed algorithms have been implemented in the new version of the detectproj software.


Digital cartography Map projection Optimizing Differential evolution Least squares BFGS Early maps Analysis Georeferencing Cartographic heritage History of cartography 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Applied Geoinformatics and Cartography, Faculty of SciencesCharles University in PraguePragueCzech Republic

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