[GRASSLIST:2385] Re: scan-resolution for maps

GRASS GRASS user
1

"E. Koster" <niwlered@hotmail.com> schrieb am 28.01.04 18:01:40:

I remember from several years ago (grass4.x) there was a document from Cerl
talking about resolution and accuracy of maps. [...] Could you please
send me a reference, or introduce me to any other literature on this
subject?

I don't know that document but it is not too difficult to calculate scan resolution based on some simple assumptions. The only difficulty involved is that most scanners need the resolution in dpi whereas real world units are usually metric.

the map I want to scan was created in 1639 using a copper-plate. The
instrument used to engrave can make lines up to a 0.1 mm in width. The
resolution of the map is 1:2.400.

Actually, 1:2400 is *not* a resolution but a scale. BTW, it is not easy to define resolutions for analog products because these have something like an infinite resolution (but still only a limited accuracy).

At what resolution I should scan not to
have an overkill of information?

You gave two different types of information, so one can define two different formulae to compute a scan resolution. The easier and better one is the line width:

There exists a well know sampling theorem (by Shannon) which states that in order not to loose any vital information, one has to sample with twice the maximum frequency of the data. In your case these are pixels of 0,05 mm size. With 1 in = 25,4 mm the result is 25,4 / 0,05 dpi = 508 dpi.

The other information is the scale of the map that relates the size of real world objects to the size of their cartographical representation. In order to find a scan resolution one has to define the real world area corresponding to one pixel of the result. Let us assume that a pixel size of 50 cm is sufficient to display everything but also necessary for the geometrical precision. This means that one pixel is 50 cm / 2400 = 0,21 mm. According to the above formula this results in 122 dpi.

Now you have got a range of possible scanner settings where you can choose values from. Of course, you'll have to see whether the 50 cm of the second formula make sense for your application. In any case, more than 508 dpi is not necessary to reproduce the map.

HTH,

Wolfgang
______________________________________________________________________________
Erdbeben im Iran: Zehntausende Kinder brauchen Hilfe. UNICEF hilft den
Kindern - helfen Sie mit! https://www.unicef.de/spe/spe_03.php

2

As an addition to Wolfgang's excellent reply: it matters also whether you scan in color, grayscale or black and white. Shannon's theorem is directly applicable to black and white maps. I'm not sure about the theory, but I think that with anti-aliased grayscale and color scans you need a finer resolution. I had this experience with the original cadastral maps of the Netherlands from 1832 (recently available on www.dewoonomgeving.nl). Scanned parcel boundaries are not sharply defined lines: pixel colors gradually flow over from line color to background color. So even if lines on the map are approximately 1 mm wide, a scanning resolution of 0.5 mm is not accurate enough.

FYY, I scanned some twenty historical maps of Amsterdam, mostly black and white at 800 dpi, giving a street resolution of up to 10 cm. This is way beyond Shannon's requirement, but it makes it possible to rectify local parts of them very accurately. For larger overviews you can always resample. BTW, GRASS does a very good job with these large rasters.

Jan

Wolfgang von Hansen wrote:

"E. Koster" <niwlered@hotmail.com> schrieb am 28.01.04 18:01:40:

I remember from several years ago (grass4.x) there was a document from Cerl talking about resolution and accuracy of maps. [...] Could you please send me a reference, or introduce me to any other literature on this subject?

I don't know that document but it is not too difficult to calculate scan resolution based on some simple assumptions. The only difficulty involved is that most scanners need the resolution in dpi whereas real world units are usually metric.

the map I want to scan was created in 1639 using a copper-plate. The instrument used to engrave can make lines up to a 0.1 mm in width. The resolution of the map is 1:2.400.

Actually, 1:2400 is *not* a resolution but a scale. BTW, it is not easy to define resolutions for analog products because these have something like an infinite resolution (but still only a limited accuracy).

At what resolution I should scan not to have an overkill of information?

You gave two different types of information, so one can define two different formulae to compute a scan resolution. The easier and better one is the line width:

There exists a well know sampling theorem (by Shannon) which states that in order not to loose any vital information, one has to sample with twice the maximum frequency of the data. In your case these are pixels of 0,05 mm size. With 1 in = 25,4 mm the result is 25,4 / 0,05 dpi = 508 dpi.

The other information is the scale of the map that relates the size of real world objects to the size of their cartographical representation. In order to find a scan resolution one has to define the real world area corresponding to one pixel of the result. Let us assume that a pixel size of 50 cm is sufficient to display everything but also necessary for the geometrical precision. This means that one pixel is 50 cm / 2400 = 0,21 mm. According to the above formula this results in 122 dpi.

Now you have got a range of possible scanner settings where you can choose values from. Of course, you'll have to see whether the 50 cm of the second formula make sense for your application. In any case, more than 508 dpi is not necessary to reproduce the map.

HTH,

Wolfgang
______________________________________________________________________________
Erdbeben im Iran: Zehntausende Kinder brauchen Hilfe. UNICEF hilft den
Kindern - helfen Sie mit! https://www.unicef.de/spe/spe_03.php