# Chapter 6. Geo-reference of the maps

Geo-referring of the maps and cartographic databases means that we give geo-reference to all pixels of the scanned raster data. In the beginning, the pixels of the scanned raster image have only image pixel coordinates, valid in the plane of the image. In this coordinate system, the origin is usually at the upper left corner of the image (this can be different in some GIS software packages) and every pixel means increases one unit both in horizontal and vertical directions.

During the geo-reference, we define GCPs (Ground Control Points), whose image pixel coordinates and grid coordinates are all given.

## 6.1 The geo-reference and the rectification

We can follow different ways while defining our GCPs. The common part of these method is that first we have to define the grid of the target coordinate system: the geodetic datum, the projection type and projection parameters. It is important that – if it is feasible – the native projection and geodetic datum of the original map should be used, and not the one that is required for the result. Also, we have to choose the method, the program should use while fitting the grid coordinate system to the raster image. The most frequently used methods are polynomial ones, with different orders, such as:

• Linear

• Quadratic

• Cubic

In case of the linear fitting, a square grid, usually somewhat rotated, is overlapping to the original image. The quadratic and cubic methods use second and third order polynomial fitting, respectively. Using these methods, better fit at the given GCPs can be achieved, however the errors occurring in between the GCPs can be considerably larger. Besides, these methods need to define more GCPs than the linear one. If possible, choose always the linear fitting method.

Besides the above discussed polynomial methods, the triangulation-based fit is also a frequent option. It provides zero error at the GCPs, while the grid in between them is fit using different linear methods in different triangles, drawn based on the GCP set. Albeit the mathematically optimum accuracy of the method has, the resulted image is usually somewhat awkward.

Fig. 30. Selection of ground control points (GCPs) in a map without coordinates: choose known points, here: cities, with their coordinates.

Fig. 31. The image and projected coordinates of the selected GCPs. If the magnitude of the fitting error (Column named ‘RMS’) is around a few pixels, the fit is acceptable.

Fig. 32. Result of the rectification: a figure of a geological paper on an elevation model.

How to define the ground control points? The most widespread used, however the most uncertain method is to indentify some terrain objects in the scanned map and acquire their coordinates from auxiliary databases (Figs 30, 31 & 32). Why the ambiguity of the method? It is because the terrain points are usually less-exactly positioned in the maps than the geodetic base points, providing the maps’ frame. The positions of the terrain object symbols are also affected by the map generalization; this could result a positional ambiguity of 1-2 millimeters. Moreover, this method provide a ‘temptation’ to omit the original projection of the map, which is a considerably error source, mainly while geo-referring medium or low scale maps.

• If there is a coordinate grid in the map, its crossing points (or the crosshairs, if they are used instead of the full grid), are the ideal control points.

• If no grid lines or crosshairs are indicated, the crossing points of the parallel and meridian lines can be also used. However, in this case we have to compute the projected coordinates of these points from the geographic ones. Most GIS packages can do these calculations (if not, this is the only application in the practice, when we do need the knowledge of the projection equations). Using only the geographic coordinates leads to unacceptably high errors!

• If even the latitude-longitude grid is not provided, we can use the corner points as GCPs if the sheet label bears the geo-reference. This is the case of many Hungarian geological or forestry maps, prior to the introduction of the EOV grid.

• Only if there is no such geo-reference, we can use identified terrain points as GCPs.

Fig. 33. As our map contains coordinate or latitude-longitude grid, its crossings provide the best GPCs. Here: because of the usage of Ferro prime meridian, the longitude values are nor round numbers. The fitting errors are too high because of the ellipsoidal coordinates given for the GCPs.

As the control points are defined (and switched on) in the rectification algorithm, the software provides their errors: the horizontal difference between their defined position and their calculated position based on the fitted grid (Figs 33, 34 & 35). The error is usually given in pixel units; errors below one – or, maximum two – pixel(s) can be accepted. In case of historical maps, the acceptable error range can be somewhat higher. However, if we have blunders at some or more GCPs, first we should check, whether we typed wrong grid coordinates or changed the easting and northing values. If the error still remains, check the identification of the used terrain objects. The dislocation of the GCPs is also important: they can’t be in or near one line in the map. The aim is to have 4-6 (in case of quadratic or cubic fit, much more) GCPs, well spread in the map area and with low error.

Fig. 34. The ellipsoidal coordinates are transformed to projected ones (here: in Mercator projection), and the errors are almost eliminated.

The next step is the rectification. This is a resampling method: the computer puts the grid, calculated from the image and grid coordinates of the GCPs, on the image and gives the raster values in this new image from the original one. The result is a raster image, whose rows and columns follow the east and north directions of the target grid. The resampling itself can be done by three methods:

• Nearest neighbor (NN)

• Bilinear

• Cubic convolution

The NN methods means that the pixels of the result image obtain their values from the original image pixel, whose center is the nearest to the target pixel center. This is the fastest procedure of all the three ones. This algorithm guarantees that there will be no other pixel values in the resulted images than they were represented in the original one. Therefore, if the pixel values refer to categories (e.g. classes in classified images) we shall choose this method for the rectification.

Fig. 35. Result of the rectification: the 1754 map of Arabia by Bellin (credit: David Rumsay Map Collection) on the Google Earth. Errors indicates the accuracy of the survey behind the map.

The bilinear algorithm means that the target pixel value is given by a bilinear interpolation, based on the original pixel values around it. This is the advised method, when the resolution of rectified image is considerable higher than the original one.

The convolution method provides the target pixel values based on territorial averages of the pixel fragments connected to them in the original image. In case of images with continuously varying pixel values (e.g. scanned images or satellite imagery), this method provides finer but slower solution than the NN-resampling, if the target pixel size is around or larger than the original one.

The GIS software packages stores the position of the resulted image in its coordinate system, usually in their own format. However, there is a quasi-standard description format, known by many GIS packages, this is the World File. The World File can be used to describe the position of TIFF or JPEG-type images, or even of compressed files e.g. MrSID or ECW. The very simple structure of this file is the following. It contains six values:

• The Easting increase while step one pixel to the right

• The Easting increase while step one pixel down

• The Northing increase while step one pixel to the right

• The Northing increase while step one pixel down

• Easting value of the upper left image corner

• Northing value of the upper left image corner

There is no absolute rule for the file extension. For a JPG image, it is a file with a same name and an extension of JPW or JGW. For TIFs, it is TFW, for SID, it is SWF. The World File does not contain any meta-data: neither the map grid and datum, nor their code are not stored. Therefore we have to know ourselves these pieces of information. Also, we have to mention that using the first four data segments, the rotation of the coordinate frame can be also handled.

As a metadata, the target coordinate grid and geodetic datum should be stored for the rectified (resampled) image. Using this, the GIS packages are able to convert to another map grid, assuming that its projection and datum parameters are known to it, according to the Chapters 4 & 5.

Example: let’s assume that we have a map in the Warsaw Pact Gauss Krüger (Zone 34, Pulkovo 1942 datum) grid, and we need to convert it the the Hungarian EOV system. The following steps are to be taken:

1. set the coordinate system for the ground control points (Pulkovo 1942 datum, Gauss-Krüger Zone 34 grid);

2. define the ground control points with their grid and image coordinates;

3. rectify the scanned image to the Gauss-Krüger coordinate system, and

4. transform the result image to the EOV coordinate system.

We shall discuss again, that it would be incorrect, leading to considerable error, if we used GCPs with EOV grid coordinates. In the Gauss-Krüger system, the points of the lines, that are straight in the EOV system, form curves. If our target area is relatively small, e.g. a few kilometers, this is almost undetectable. However, at several ten or hundred kilometers distance, this deflection could be up to several ten meters and cannot be corrected or calculated. Following the above steps a)-d), this error can be avoided.