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2 Georeferencing procedure

Once the XY location with the raw map and the target location with the projection have been created, we are ready to georeference the raw map as follows:

1. Indicate the name of the map and image data that are to be transformed into a newly created image group.

   i.group

   • Assign names for this group: e.g. "map".
   • Select the map(s) to be imported with an "x".

2. Indicate the target location (target) and mapset (e.g. a Gauß-Krüger location) in which the map and image data shall be transferred.

   i.target

   • The target location should not be zoomed. Otherwise the end-product is only transferred to the zoomed cutout because GRASS always works with the current region. Reset the standard resolution (in the target location) as follows: g.region -dp

3. Start a GRASS monitor: d.mon start=x0

4. Assign the Gauß-Krüger coordinates to the four edges or coordinate-crosses of the region to be transformed (see chapter: 6.2.1).

   i.points (Related to raster maps)
   i.vpoints (Related to vector maps)

   • Indicate the image group to be transformed (for this example "map").

1 Choosing control points

The imported map/image is clickably displayed in the GRASS monitor on the left hand side. There are two possibilities for georeferencing: either (A) using reference coordinates or (B) using an existing reference map in the target location.

Figure 14: Searching control points of a scanned topographical map with the GRASS module i.points

(A): If control points for georeferencing are known, e.g. from an available analog paper map, clearly identifiable points such as Gauß crosses or indicated edge coordinates are chosen by clicking on the imported map, and entering the coordinates in X term (separated by a space).

(B): If a georeferenced map exists in the target location, which exhibits distinctive points (such as crossroads or buildings) and which can also be found in the map to be referenced, the georeferenced map can be loaded into the right window with the 'PLOT RASTER' function. Thus, it is possible to find and to mark corresponding reference points in both monitor windows. The 'ZOOM' function allows exact placement of control points (see Figure 14).

The control points should be evenly distributed throughout the map. The RMS error can be determined via the 'ANALYSE' function, which should not be higher than half of the raster resolution of the target location. All partial RMS errors are calculated to an overall error. Where required, it is possible to ignore or reassign an inexactly assigned control point by double clicking on the point in the 'ANALYSE' function window. Points can be disconnected in this way to reduce the RMS error or to redistribute the points more evenly.

An even distribution of points with "suboptimal" RMS error can produce an overall lower error than a poor distribution of points with "optimal" RMS error.

The module i.points is exited after the successful assignment of the control and reference points. The coordinate assignments are automatically saved on exit. This also applies to previously assigned points, from prior executions of i.points. With a new call you can continue working on the same location.

Depending on the original data and the selected polynomial degree of the equalization to be performed, the module i.rectify is started when sufficient points for georeferencing have been set. In this context the group of images to be equalized must first be indicated. The query follows whether the map

1. shall be transformed into the 'current region' of the target location (complies with the currently set parameters (cutout, resolution) of the target location);
2. or in the 'minimal region' (GRASS independently calculates the range in the target location).

If in this menu point 1 'current region' is chosen, it is important to ascertain again before referencing that the current settings of the target location (cutout and resolution) are correctly chosen. Due to the fact that all data are automatically saved it is no problem to leave the module i.rectify and GRASS again, to verify the current settings of the target location or to change if necessary, and to call the XY location and i.rectify again.

2 Determining the correct transformation

The correct transformation is defined by the polynomial degree. This depends on the degree of distortion (at central perspective aerial views e.g. by the relief energy existing in the project region) as well as on the quorum of available control points. The greater the image-internal distortion the higher the needed polynomial degree and the more control points are needed for an exact georeferencing (see table 9). Too high polynomial degrees are however mathematically not reasonable.

As a rule of thumb correct internal image geometry (e.g. scanned topographical maps, as orthogonal projection) requires a minimal quantity of control points and therefore a minimal polynomial degree. Otherwise, distorted internal image geometry (e.g. historical map) needs a higher quantity of control points and therefore a higher polynomial degree.

Table 9: Polynomial degrees for georeferencing

Polynomial degree	Minimum number of	Module
	Control points
1	3
2	6	i.rectify
3	10
4	15

If too few reference points are set for a chosen polynomial degree, GRASS does not start the rectification. A guide for determining the minimum number of control points needed by polynomial degree is given in table 9. Polynomial degrees of first to third order are proven of value. Whereby at polynomial degrees of third order more than 10 control points are required.