Abstract
<div class="abstract"><div class="abstract_item"><em>Modern techniques for the map analysis allow for the creation of full or partial geometric reconstruction of its content. The projection is described by the set of estimated constant values: transformed pole position, standard parallel latitude, longitude of the central meridian, and a constant parameter. Analogously the analyzed map is represented by its constant values: auxiliary sphere radius, origin shifts, and angle of rotation. Several new methods denoted as M6-M9 for the estimation of an unknown map projection and its parameters differing in the number of determined parameters, reliability, robustness, and convergence have been developed. However, their computational demands are similar. Instead of directly measuring the dissimilarity of two projections, the analyzed map in an unknown projection and the image of the sphere in the well-known (i.e., analyzed) projection are compared. Several distance functions for the similarity measurements based on the location as well as shape similarity approaches are proposed. An unconstrained global optimization problem poorly scaled, with large residuals, for the vector of unknown parameters is solved by the hybrid BFGS method. To avoid a slower convergence rate for small residual problems, it has the ability to switch between first- and second-order methods. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the projection. Its importance is primarily referred to refinement of spatial georeference for the medium- and small-scale maps, analysis of the knowledge about the former world, analysis of the incorrectly/inaccurately drawn regions, and appropriate cataloging of maps. The proposed algorithms have been implemented in the new version of the <span style="font-family: monospace;">detectproj</span> software.</em></div></div>
Highlights
Maps are an important part of our history and cultural heritage; close attention is paid to their study and research
New methods and techniques for map analysis allow for the creation of full or partial geometric reconstruction of its content
The proposed methods supporting the determination of additional parameters of the map projection as well as the analyzed map were implemented in open-source software detectproj [4]
Summary
Maps are an important part of our history and cultural heritage; close attention is paid to their study and research. There is a need to perform a geometrical reconstruction of the early map involving the establishment of the correct geometric position of the map content in the projected spatial coordinate system. For the georeferencing of maps covering a small territory (large-scale maps), the 1st order transformation is sufficient (projection impact can be neglected). The current and widely applied method based on splitting the map into tiles, applying a transformation to each tile, and restoring the continuous raster image from tiles, is time consuming, tedious, and less accurate This approach could be improved using the proposed method, when a projection of the analyzed map is detected. Based on the results of this research, for successful map projection analysis 5-10 points are sufficient for world maps, 10 points for the medium-scale maps, and 15 for the large-scale maps. The developed software detectproj supports all proposed methods and optimization techniques
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