# METHODS OF GEOREFERENCING OLD MAPS ON THE EXAMPLE OF CZECH EARLY MAPS

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2 For any transformation method within georeferencing, there is a need of collecting identical points (on the map and in reality). These points for transformation are usually called ground control points (GCPs). There are some important recommendations for GCPs collection: GCPs should be laid out through the whole map image (if possible); GCPs should be represented by stable well-identifiable objects; the more GCPs collected the better input data for georeferencing. The last remark led me to the method of full vector data model of the map, where the map is vectorized at first. Then any vector point from the model identifiable in reality can be used as GCP. Some points can be later omitted (e.g. evident errors made by author of the map). Transformation methods used within georeferencing need brief explanation. There are two main groups of transformations: global, and local. Global transformation methods use two mathematical equations (for two coordinates) for the whole image; local transformation methods use other approach where either the image is cut into areas (e.g. triangles of GCPs) with own equations ( rubber-sheeting method) or any point is transformed with own equations (usually based on interpolation methods such Thin plate spline or Inverse distance weighted ). Local transformations are non-residual where GCPs after transformation fit precisely, but the image can be distorted very ugly. Global transformations use only two equations and are non-residual only for minimal number of GCPs for equation solving. If having more than minimal number of GCPs global transformations are residual. Transformation parameters are then adjusted, usually by Least squares method (LSM). My approach of georeferencing old maps is based on global transformation methods. If georeferencning the map, I am not interested only in overlay the map with other ones, but I am interested in map parameters (precision, mean scale, rotation against graticule, ). These parameters can be computed within the adjustment of enough GCPs using global transformation methods. Local transformation methods deform the original image and are not suitable for such research. Of course, there could be plenty of global transformation methods. For map georeferencing there are suitable only several methods (linear, or low degree polynomials). a) Only map sheet, unknown projection, unknown dimensions This combination is typical for the oldest maps. If we don t know used projection it is proposed to georeference the map in Lat/Long projection (in geographic coordinates). In fact, Lat/Long projection matches equidistant cylindrical projection with undistorted equator (so called Plate Carree). This projection is usually used in GIS software for displaying Lat/Long data (e.g. in ArcGIS). GCPs are collected in Lat/Long (in reality), respectively in pixel coordinates for the image. As the shrinkage of the paper is unknown the used transformation should reduce the distortion. After affine transformation the image can be scaled in both axes and skewed. After second or third order polynomial transformation the image can be bended locally (especially near margins); texts on the map can be damaged. For the whole map sheet transformation I prefer affine transformation. If the aim of transformation is only local area within the map sheet, low order polynomial can be used for better fit of GCPs. Transformations are adjusted by LSM. b) Only map sheet, unknown projection, known dimensions If we know original dimensions of the map (by measurement of print matrices or by other source) the procedure should be little different. Before GCPc collection the image of the map should be reconstructed to its original size. The easiest way is to fit original dimensions to corner points of the map image. As we have four corner points and want to fit these points precisely projective (collinear) transformation is the best solution. It transforms any quadrangle into other quadrangle as non-residual. After having the map image with real size GCPc can be collected. The shrinkage of the map is removed by reconstructing original size. For the whole map sheet transformation here I prefer similarity transformation. Compared to affine transformation, it preserves angles. It consists only of uniform scale, rotation and shift. Different scaling or skew is no longer needed for reconstructed images. c) Only map sheet, known projection, unknown dimensions If we know used projection of the original map georeferencing should be done within this projection. Known projection means known geodetic datum (used ellipsoid or sphere parameters) and cartographic projection with parameters (prime meridian, undistorted parallels, ). GCPs should be collected in this projection either directly in GIS software that can on-the-fly transform the data or it is necessary to transfer coordinates from projection where data were collected into original projection (e.g. using software package PROJ.4). Then affine transformation can be used for adjustment by LSM. d) Only map sheet, known projection, known dimensions

4 Figure 1. Klaudyan's map of Bohemia (1518) georeferenced and superimposed with Czech republic borders Criginger s map (1568) is the second known map of Czech lands. Its size is approximately 51 by 34 cm. The map was vectorized as well; 319 point features were used as GCPs. After removing 5 points (errors by author) the map was georeferenced using affine transformation into Lat/Long projection with RMSE 14.0 km in reality. Other parameters such mean scale or rotation of the map were computed as well. Both maps after georeferencing show similar errors. After deeper study I found out many similarities between both maps. It can be assumed that Criginger s map was based on the older Klaudyan s map. Map series are represented by Müller s map of Moravia (1712, 4 map sheets with unknown projection), Müller s map of Bohemia (1720, 25 map sheets with unknown projection, but known dimensions of map sheets), selection of sheets of 1st Military Mapping Survey of Austria-Hungary ( , with unknown projection and size of map sheets) and selection of sheets of 2nd Military Mapping Survey of Austria- Hungary ( , with known projection and size of map sheets). Müller s map of Moravia and maps of 1st Military Mapping Survey were georeferenced using the same method adjusted affine transformation for each sheet with constraints of edge adjacency. After collecting GCPs for all map sheets the matrix for overall adjustment was filled. For affine transformation the definition of constraints was very simple. Coordinates of corner points from neighboring sheets must have after transformation the same position. These conditions were added to augmented matrix for LSM adjustment with constraints. Results of the adjustment are transformation parameters (6 parameters for every map sheet). After transforming all map sheets they fit precisely. RMSE for Müller s map of Moravia is about 2.1 km in reality, for selected 4 sheets of 1st Military Mapping Survey it is 550 m in reality. Müller s map of Bohemia was firstly transformed to original dimensions of the map sheets. The size of map sheets was determined by measurement of original copperplate print matrices. These are archived in National Technical Museum in Prague. After having right dimensions map sheets were georeferenced using adjusted similarity transformation for each sheet with constraints of edge adjacency. Constraints were defined as in previous case. After transforming all 25 map sheets fit precisely (see Figure 2 and 3). RMSE for Müller s map of Bohemia is about 2.0 km in reality.

5 Figure 2. Müller s map of Bohemia (all 25 georeferenced map sheets) Figure 3. Müller s map of Bohemia (detail of georeferenced map sheets) Maps of 2nd Military Mapping Survey of Austria-Hungary are based on the cadastral mapping and have defined cartographic projection and size of map sheets. It is possible to compute coordinates of corner points in Gusterberg coordinate system (for Bohemia) or St. Stephen coordinate system (for Moravia). Cartographic projection is Cassini-Soldner (transverse cylindrical projection equidistant in cartographic meridians with fundamental points Gusterberg for Bohemia and St. Stephen for Moravia). Thus all corner points of map sheets were computed. After that every map sheet was georeferenced separately using projective transformation with 4 corner points. Precision of these maps was tested by independent control points. RMSE for maps of 2nd Military Mapping Survey of Austria-Hungary was only about 20 m in reality. CONCLUSION AND FUTURE PLANS

6 In this article georeferencing methods for old maps were presented and new method for map series (adjustment with constraints of edge adjacency) was introduced. Used georeferencning methods are based on global transformation methods. It is not the only solution. Local transformation methods can be used for local areas. For better GCPs fitting low order polynomials can be used, but maps are then deformed. Nevertheless, even for polynomial transformations can be defined constraints of edge matching. Another approach to map series could be based on the image processing and automated edge matching during creating joint raster data. I left out these methods because of high hardware demands. For example joint raster of Müller s map of Bohemia (composed of 25 map sheets) exceeded 1GB of data. Such raster is very difficult to work with. Proposed method works only with one map sheet, but guarantee edge fitting. My future plans are focused on 1st Military Mapping Survey. All map sheets will be adjusted together and overall seamless map from the area of Bohemia and Moravia will be created. ACKNOWLEDGEMENT This research has been supported by the GA CR grant No. 205/09/P102.

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