Basic Concepts

This section explains the basic concepts of applying geo-referencing techniques to maps which have been transformed from their original paper state into an image file (raster) by means of a scanner. Although this subject can be applied to any type of maps, this discussion is mainly referring to original Cadastral Maps and the particular problems that can be solved by applying the right geo-referencing transformation.

Raster  image files

As mentioned in CorrMap presentation, the availability of a map as a raster image file permits you to apply specific techniques to the file itself in order to geo-reference, calibrate and rectify the map itself.

 

So, first of all let’s explain what an image raster file is. It is a file format which reproduces an image by dividing it into a grid of points each of which has a specific color. To be more precise, these points, called “pixels”, are actually squares and the smaller their size, the more accurate the image resolution is. The pixels of a raster file are aligned in rows and columns as in a normal table. In fact, when an image raster file is mentioned, usually it’s also accompanied by its size in pixels. For example, if you say that an image raster file is 1024 x 768, it means that it is composed of 1024 columns (width) and 768 rows of pixels (height). The greater these two values are, the bigger is the image and the dimension in bytes of the file. As already mentioned, each pixel has its own color, so by putting together all the pixels you obtain the reproduction of the image, which will appear more or less as the real object (the paper map) depending on its resolution, as we’ll see further on in this section.

 

Digital photographs are a real example of image raster files. There are various formats for this type of file: BMP (bitmap), TIF, JPG, PNG, etc., each of which have been created to optimize specific needs (quality, file compression, etc.).

Why do raster maps need to be geo-referenced?

Before going any further it is worth clarifying the meaning of the term “geo-referencing”. As the two parts of this compound word tell us, geo-referencing means to give a geographic (geo) reference system (referencing) to a map.

But why do we need to give a reference system to a raster file map?

Simply because a non-geo-referenced raster map does not have any reference system.

This is also true when a raster map contains some reference points or grid lines provided with coordinates written on the map, as shown in Fig. BC.1. This is because these coordinates are simply numbers drawn on the map and are not the coordinates of their corresponding points.

 

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Fig. BC.1 – It does not help if the raster map contains reference points or grid lines showing their coordinates, they’re simply numbers drawn on the map.

A non-geo-referenced raster map has no reference system and real units

The easiest way to understand this problem is by importing a raster map into a CAD system which supports raster image files, such as AutoCAD  or ZWCAD . So let’s import into ZWCAD the raster map shown in Fig. BC.3. As soon as you activate the import menu command, the CAD system opens the window to locate the imported file and asks for the following parameters in order to insert the image into your drawing, as shown in Fig. BC.2.

 

1.Insertion point: here the CAD system asks you to specify X-Y-Z coordinates at which to insert the lower-left vertex of the image.

 

2.Scale: this is the scale factor to assign to the image.

 

3.Rotation: this is the rotation angle to apply to the insertion point in case you want to rotate the map instead of inserting it perfectly orthogonal to the drawing axis.

 

 

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Fig. BC.2When inserting a raster image into a Cad system, you are asked to specify insertion point coordinates, scale and rotation - all the values that you don’t know!

 

What values do we provide for these 3 parameters? Obviously we don’t know. Also selecting the Specify on screen option would not help because we still wouldn’t know what insertion point, scale factor and rotation to specify on the drawing.

So, we end up by simply accepting the default values suggested by the CAD system itself in Fig. 2, i.e. 0,0,0 for the insertion point coordinates, 1 for the scale factor and 0 for the rotation.

 

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Fig. BC.3A raster map imported in a Cad software has no real coordinates and measurement units.

 

We can easily verify the result of this operation by showing the coordinates of the map lower-left vertex using the usual CAD command for inquiring the coordinates of a point. As shown in Fig. BC.4, this point has coordinates: X = 0  Y = 0  Z = 0.

 

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Fig. BC.4The map just inserted simply has coordinates 0,0,0 in its lower-left vertex.

 

Then, what about if we ask for the coordinates of a reference point in the map?

For example, let’s ask for the coordinates of the reference point shown in Fig. BC.5. We do not get the real coordinates East = -34600; North = 53600 (*) written on the map, but we obtain the values: X = 831.012  Y = 610.106.

 

icona_nota (*)

All maps shown on this guide belong to the Italian Cadastre which reference system assumes the letter Y as the horizontal axis (Easting) and the letter X as the vertical axis (Northing). In this guide we will invert the two letters so that they match the typical mathematical (and CAD) assumption:

X = horizontal axis (Easting)      Y = vertical axis (Northing).

 

 

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Fig. BC.5The coordinates of any point in the map are simply the number of pixels in horizontal and vertical direction from the lower-left vertex.

 

What are these values then? They are simply the number of pixels in horizontal/vertical direction between the lower-left vertex of the map and that point – quite unusable.

Well, this is the first problem of a non-geo-referenced raster map: we cannot obtain the real map coordinates of the points we are interested in.

But there is also another problem: the unit of measurement of the raster map is pixels, not the real units (meters in this example). This implies that we cannot obtain real distances from the map either.

For example, the map we are treating contains grid lines at an interval of 200 meters. But if we inquire about the distance between two consecutive grid lines, as shown in Fig. BC.6, we do not obtain 200 but a totally different value: 788.132.

 

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Fig. BC.6Also we cannot obtain real distances from a non-geo-referenced map.

 

The reason for this difference is the same as previously noted: the value we get is simply the number of pixels, not meters, between the two grid lines. We will understand the ratio between the real distance (200 m) and the value in pixels (787.965) in the Transformations | Affine section when we’ll explain the scale factor calculated by this transformation.

The map deformation

So far, you might think that the non-corresponding coordinates and measurement units of a non-geo-referenced map is the only problem we need to solve, but unfortunately this is not the case.

There is another more important problem: the original paper map has been subjected to a deformation from its original state. And if the paper map has been deformed, its raster image (file) is therefore deformed too. This means that, in order to obtain correct geometric information from a raster map, we also need to resolve this deformation and thus rectify the map itself.

But let’s first describe the possible factors of a map deformation:

 

1.Graphical errors during creation: actually this factor is not a deformation issue but it is due to human errors that might have occurred when the map had been manually drawn on the paper. Of course these errors depend on the age of the map: the older a map is, the bigger graphical errors it potentially contains because of the poor quality of the instruments used. Referring to the Italian Cadastral Maps, for example, one of these types of errors is the following: the first stage for Cadastral Technicians who created the maps was to trace the grid lines at an interval of 10 cm, i.e. 200 m for scale 1 : 2000. Then they assigned the real coordinates to these grid lines and proceeded to insert each map point by measuring its coordinates from the grid. This process had a drawback: if two consecutive grid lines were not traced at the exact interval of 10 cm, but at a slightly greater or lesser distance, let’s say 9.9 or 10.1, the map points inserted from these lines had been affected by this error, and are therefore incorrect (a graphical error of just 1 millimeter for a scale 1 : 2000 implies a real error of 2 meters). Fig. BC.7 shows this possible error in a Cadastral Map, even though we cannot tell for sure if it is totally due to map creation or deformation, as we see here below.

 

2.The wearing effect of time: if the map is quite old, this is the main deformation reason and it’s obviously caused by physical factors such as temperature and humidity changes, paper degradation, etc.

 

3.The scanner: raster maps are obtained by scanning original paper maps. But this process does not lack errors. The accuracy of a scanned map obviously depends on the quality of the image scanner used, even top quality scanners have an average tolerance between 0.5 to 1 mm for the diagonal of a sheet sized 100 x 70 cm. So this is another deformation factor. However, the scanning process can also generate a slight rotation of the map as we’ll explain here below.

 

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Fig. BC.7 - The first deformation factor depends on the accuracy applied during map creation.

 

The deformation of a map due to these factors not only affects map distances, it can also generate a rotation of the map. For example, see the vertical grid lines shown in Fig. BC.7. At first sight they appear to be perfectly vertical, i.e. pointing to the real North direction of the map. But we must assume that the map has been deformed, so those lines are no longer straight but might be wavy and therefore they don’t point in a Northerly direction.

But there is another reason why we must assume that the map has been subjected to a rotation: the scanning process. Why?

Because the operation of positioning a paper map on a (plane) scanner is performed by an operator whose task is to align the lower border of the map with a horizontal line traced on the scanner itself. This line guarantees the orthogonality, hence the exact North direction of the resulting image. Of course, even if this operator takes the maximum care in doing this, he/she will always be subjected to a little positioning error which causes a slight rotation of the image obtained (not to mention when a rolling scanner is used, because this instrument significantly magnifies the positional error in the direction of rolling).

The rotation error is very subtle because it is usually very small, and therefore virtually invisible to the naked eye but, being an angle, it causes significant linear errors for map points which are located far from the rotation pole.

What does it exactly mean to geo-reference a raster map?

Well, so far we have seen all the reasons why a non-geo-referenced map is not suitable for usual surveying tasks. Then it is now clear that the goal of geo-referencing a map is to solve the problems and remove the limitations described in the previous paragraph, this means:

 

1.Assign to the raster map its real map coordinates.

 

2.Transform the measurement units from pixel into meters (or whatever unit).

 

3.Rectify the deformation of the map.

 

4.Correct the orientation error (rotation).

 

In the following chapters of this section we’ll see how the different geo-referencing techniques (*) allow us to reach this goal.

 

icona_nota (*)

In the rest of this guide we will refer to any geo-referencing technique as a “transformation”.