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BABEL --- A method for digitization and
restoration of contour maps
By G e r n o t W e s t ph a l en
e­mail: gwestpha@astro.uni­bonn.de
Radioastronomisches Institut der Universit¨at Bonn (RAIUB), Auf dem H¨ugel 71, 53121 Bonn,
GERMANY
We have developed BABEL as a method for digitization and restoration of contour maps. The
results of the comparison between restoration and template are encouraging and first applications
are proving very useful. The restoration method is now quite flexible and fast. The result
is available as a standard fits file, so that the restored map can be transferred into various
coordinate systems and projections and can be used for further digital processing, e.g. for
comparison of older radio data with new infrared or X­ray data. So far we have digitized
various HI line and 11.1 cm continuum contour maps, for which we know that the original
digital data were lost or did never exist in a machine readable format.
1. Introduction
The idea behind the whole approach is to acquire digitized maps from data, which have
been published in the form of contour plots, to compare the restored data with either
new data, or also with restored data from other sources. Initially we wanted to compare
newly measured X­ray data from the German R¨ontgensatellit (ROSAT) with older Hi
(atomic hydrogen) surveys, i.e. to make a detailed comparison of certain objects observed
at different wavelengths (e.g. Herbstmeier et al. (1993), Mebold et. al (1993), Snowden
et al. (1991)).
The difficulty lies in the fact that some original survey data are completely lost, whereas
other are not obtainable quickly. However, published contour plots are free at everyone's
disposal. So digitizing and restoring Hi contour plots seemed to be a good idea in order
to save hard to get telescope time. Obviously, for maps restored with the developed
method it is quite irrelevant what the contours actually stand for. They could mean
anything from yearly rainfall to the rate of cancer deaths. Naturally the quality of the
restored maps is limited, but completely sufficient for many applications. More details
about the quality and the uncertainties of BABEL can be found in Westphalen (1993).
The method described here relies almost entirely on existing software and hardware. As
a result the process is easy to install on various system configurations, although there
are a few items to be refined and optimized. With the introduction of a scanner, we have
now two choices for the digitization and, after the purchase of PhotoStyler, three ways
of restoration.
2. A quick walk through BABEL
A number of aspects had to be considered, should the method be useful for a wide
range of applications. The possibility of transferring the restored map into various co­
ordinate systems and projections is an obvious one. Another one is the restoration and
interpolation of values between the contours for quantitative results. We settled on the
following three objectives:
1

2 G. Westphalen: Restoration of contour maps
ffl Defining every pixel's coordinates
ffl Defining an intensity for every pixel
ffl A transportable and transformable format
To achieve these objectives a couple of problems had to be solved:
ffl Digitization
ffl Conversion into a ``flat'' projection
ffl Manipulation and cleansing (Initial Restoration)
ffl Rotation into pixel parallel coordinates
ffl Definition of the coordinates
ffl ``Gauging'' of the intensity (Final Restoration)
2.1. Digitizing the original data
Copying: A block diagram of the process is shown in Figure 1. First the published
contour maps are photocopied. This is necessary to avoid substantial distortions (caused
by the unhandy hardcover format) either when taking the pictures with a CCD camera
or scanning the plots directly from the original. A drawback in doing so are small but not
avoidable --- and sadly not correctable --- distortions caused by the photocopier. These
distortions are found to be negligible (Westphalen (1993)).
Digitization: The next step is the digitization of the photocopied contour plot tem­
plate by using a CCD camera or a scanner. In the first case the result is an image with
more then 60,000 colours and more or less strong vignetting (according to the size of the
image). In the latter case we get a black--and--white image of considerable size (according
to the chosen resolution).
Independent of the way of digitization there is a soft limit on the size of the digitized
images: 1280 \Theta 1024 pixels. The reason is that manipulation and transformation of larger
images may result in substantial loss of information (see Westphalen (1994), chapter 2
for details.).
Preparation: The following step is only necessary when using a CCD camera. In
that case we have to correct for vignetting and illumination. This is done by flatfielding
the image with the corresponding routine in the IRAF package.
We also have to reduce the number of colours to a useful amount. Useful means that
we have to choose a number which is not too small (loss of information) and not too
large (artificial details from the structure of the paper and printing). In the first case
one would degrade the final resolution, while in the second one the process of restoration
would be complicated considerably. The reduction is done with a small ULTRIX script,
utilizing functions of the PBM Plus package.
2.2. Initial restoration
The initial restoration consists mainly of erasing all artefacts, colouring the plateaus
between the contour lines with specific colours, conserving the coordinate information
and transferring the map into a ``flat'' projection. The result is called ``map'' in Figure 1.
All of this is done with a paintprogram on a PC.
Producing a grid: In case of a rectangular or ``flat'' projection of the template, con­
serving the coordinate information can easily be achieved by duplicating the unrestored
image and drawing a mesh of coordinate lines onto the duplicate (``grid'' in Figure 1). In
the coloured image (``map'' in Figure 1) we mark a point of origin, so that the coordinate
information is preserved.
However, if the original sky projection is not a flat plane (e.g. Aitoff) one needs to
transform the coordinates at some point. In case the precise projection formula is known,
one can do the transformation at any stage. Usually this is not so. Then, provided the

G. Westphalen: Restoration of contour maps 3
The Process of Restoration
Copy of the contour maps
CCD Camera (*)
Scanner (&)
Digitized image
IRAF (*)
Flatfield Correction (*)
PBM Plus (*)
Reducing to n colours (*)
Best (irreducible) image
Dr. Halo (*)
Paintbrush (&)
PhotoStyler (&)
Restoration
Restored, cleaned map
and map with grid
grid
map
anglegrid
Calculation of rotation angle
and grid spacings
SAOimage
Restored, cleaned map
with known levels, grid spacings
and rotation angle
GIPSY
(fits­Format)
Anything you like ...
Intensity Correction
Rotation (*)
Header Fixing
Map with correct intensity
and coordinates values
Figure 1. The diagram shows an overview of BABEL. On the left side you find the working step,
while the corresponding result is indicated on the right. Used software packages are displayed
inside the hatched frames. (*) and (&) indicate the digitization via CCD Camera or Scanner.
The curved arrow with circles is supposed to symbolize the processing of the digitized image.
Anything you like: : : refers to the fits format which allows to transport and transform the map
freely.

4 G. Westphalen: Restoration of contour maps
Figure 2. Four maps of the HVC MI: The two upper ones are grey scale reproductions of
Hi contour plots from Giovanelli et al. (1973). In the lower left the completely restored map
is shown, which has been transferred from equatorial into Galactic coordinates and integrated
over all channels. In the lower right an overlay with ROSAT--Survey data is shown in Aitoff
projection. The lowest X­ray contour is dashed. A clear anticorrelation between Hi and X­ray
emission is visible. The positional error of the restored Hi data is less than 4 arcmin, whereas
the error for the X­ray data amounts to more than 24' (only preliminary data was available).
This overlay was used for selecting sky positions for pointed observations of MI with ROSAT
and for publication in Herbstmeier et al. (1993) and Mebold et. al (1993). For latest results
concerning MI see Herbstmeier et al. (1994).
Figure 3. The contour plot on the left of the SMC was published by Hindman (1967) and
shows the integrated brightness in the Hi line (contour unit is 3:5 \Theta 10 \Gamma17 W m \Gamma2 sr \Gamma1 ). As the
projection formula is not given by Hindman (1967) we had to ``unproject'' the map ``by hand''.
On the right the result is displayed with a positional error of \Sigma2 0 , which is much smaller than
the resolution of the data. The fully restored map was used for an overlay with Hff data by
Kennicutt et al. (1995).

G. Westphalen: Restoration of contour maps 5
coordinate information (i.e. the tickmarks or coordinate mesh) in the template is ``dense''
enough, one can transform the coordinates ``by hand'' with the program PhotoStyler
(see Westphalen (1994), chapter 3.3.3.). In Figure 3 an example for this transformation
is displayed.
2.3. Final restoration
Rotation angle and gridspacings: The second image (``grid'' in Figure 1) is used to
determine the rotation angle (this is only necessary for CCD images) and the and the
correct gridspacings. This is done by displaying the ``grid'' and reading out the pixel
coordinates of points with known physical coordinates by hand. Program anglegrid
then calculates the rotation angle and the gridspacings. In the case of rotation it checks
whether the size of a chosen subset is small enough for rotation with the GIPSY package.
``Gauging'' the intensity: The only ``original'' data preserved in the contour plots
are the values at the position of the contour lines. However, these data are already
interpolated themselves. Nevertheless, they constitute a lower limit to the real data.
To construct a surface there are generally two approaches: either one uses local ex­
trema, or one utilizes a regular grid of fixed points (Press et al. (1987)). However, with
the contours as the only fixed points we neither have a regular grid (apart from the
pixels) nor local extrema.
Under the assumption that the actual values between the contour lines increase almost
linearly one can assign to each colour (i.e. to each plateau) a corresponding value. In
other words: adding half the difference between the values of two contours to that of
the lower one and assigning the resulting value to the uphill plateau has been shown to
approximate the real situation quite well (for a more detailed discussion see Westphalen
(1993), chapters 3.6 & 3.7):
ynm = yn + ym \Gamma yn
2 (2.1)
where ynm is the value of the uphill plateau, y n that of the lower and ym that of the
higher contour.
By smoothing this plateau map we produce some ``realistic'' intermediate values for the
points between the contour lines. Using a 2--dimensional Gaussian as a smoothing func­
tion is a very simple way of interpolating on the grid defined by the pixels of the image.
Although it was a crude guess when it was first tried and by no means a mathematically
exact undertaking, it does work very well. This is the heart of BABEL.
Final handling and quality of the restored maps: After fixing the image header
(point of origin, gridspacings, etc), possible rotation, intensity ``gauging'' and final smooth­
ing we give the restored map an extensive history (positional error and resolution) and
write it into fits format, so that anyone can use it easily --- even for plotting contour
maps!
As the restoration works on a pixels basis, the errors are given in these units. The phys­
ical errors have to be calculated individually for every image according to the gridspacings
etc. The equivalent percentages in brackets refer to a typical image of 1000 \Theta 1000 pixels.
ffl BABEL will cause a loss in resolution, which is equivalent to smearing with a Gaus­
sian of 9--10 pixels halfwidth ( “
ú1:0%).
ffl It may also cause an additional positional error of up to 3 pixels ( “
ú0:3%).
ffl BABEL reproduces the area integral of large structures (? 10pix 2 ) within \Sigma5%
(90% ! orig ! 100%) and of small ones (! 10pix 2 ) within \Sigma13% (74% ! orig ! 100%).
ffl Restored maps obviously have no noise (anymore).
Two applications as shown in Figures 2 and 3.

6 G. Westphalen: Restoration of contour maps
Hi­line maps
HVC complexes CIB, MI, MII [Giovanelli et al. 1973, A&AS 12, 209]
LMC, SMC [Mathewson & Ford 1984, IAU Symposium, 108, 125]
SMC [Hindman 1967, Aust.J.Phy., 20, 152]
LMC/SMC intercloud region [Mathewson et al. 1979, IAU Symposium, 84, 547]
Magellanic Stream [Morras 1983, AJ, 88, 62 & 1985, AJ, 90, 1801]
NGC 3198, 7331, 2903, 5033, 2841 [Begeman 1988, PhD thesis, 28, 62, 87, 88, 106]
11.1 cm continuum maps
NGC 315, 3C 236, DA 240, 3C 326 [Stoffel & Wielebinski 1978, A&A, 68, 307]
Table 1. Summary of restored maps
3. Conclusions
With the quality achieved (see Section 2.3), BABEL is an effective tool for digitizing
and restoring contour maps --- data which would be ``lost'' otherwise. So far we have
digitized various Hi line and 11.1 cm continuum contour maps, for which the original
digital data are not available anymore. A listing of these maps is displayed in Table 1.
They have fits format and are available on request at the RAIUB.
The development of BABEL is a good example for teamwork. I want to thank all
the people at the RAIUB who have contributed to BABEL and I am especially grateful
to: Prof. Dr Ulrich Mebold who had the initial idea to ``restore a published contour
plot''; Dr Peter Kalberla for the help with the installation and configuration of the
diverse software; Sven Kohle for introducing the digitization via scanner and Dr Uwe
Herbstmeier for everyday all­round support.
REFERENCES
Giovanelli R. and Verschuur G.L. & Cram T.R., 1973, A&AS, 12, 209.
Herbstmeier U., Moritz P., Engelmann J., Kerp J. & Westphalen G., 1993, in Back to the Galaxy,
Proceedings of the 3rd annual Maryland Astrophysics Conference.
Herbstmeier U., Mebold U., Snoden S.L., Hartman D., Moritz P., Kalberla P.M.W. & Egger R.,
1994, A&A, in press.
Hindman J.V., 1967, Aust.J.Phy., 20, 152.
Kennicutt R.C., Bresolin F., Bomans D.J., Bothun G.D. & Thompson I.B., 1995, AJ, in press.
Mebold U., Kerp J., Herbstmeier U., Moritz P. & Westphalen, G., 1993, in Recent results in
X--ray and EUV astronomy, eds Tr¨umper J., Bowyer et al.
Press W.H., Flamery B.P., Teukolsky S.A. & Vetterling W.T., 1987, Numerical Recipes.
Snowden S.L., Mebold U., Hirth W., Herbstmeier U. & Schmitt J.H.M.M., 1991, Science, 252,
1529.
Westphalen G., 1993, Diploma thesis, (University of Bonn).
Westphalen G., 1994, BABEL --- A Method for Digitization & Restoration of Contour Plots,
(University of Bonn).