Estimation of an unknown cartographic projection and its parameters from the map

This article presents a new off-line method for the detection, analysis and estimation of an unknown cartographic projection and its parameters from a map. Several invariants are used to construct the objective function ϕ that describes the relationship between the 0D, 1D, and 2D entities on the analyzed and reference maps. It is minimized using the Nelder-Mead downhill simplex algorithm. A simplified and computationally cheaper version of the objective function ϕ involving only 0D elements is also presented. The following parameters are estimated: a map projection type, a map projection aspect given by the meta pole K coordinates [φk, λk], a true parallel latitude φ0, central meridian longitude λ0, a map scale, and a map rotation. Before the analysis, incorrectly drawn elements on the map can be detected and removed using the IRLS. Also introduced is a new method for computing the L2 distance between the turning functions Θ1, Θ2 of the corresponding faces using dynamic programming. Our approach may be used to improve early map georeferencing; it can also be utilized in studies of national cartographic heritage or land use applications. The results are presented both for the real cartographic data, representing early maps from the David Rumsay Map Collection, and for the synthetic tests.