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Please Note: the e-mail address(es) and any external links in this paper were correct when it was written in 1995, but may no longer be valid.
Gernot
Westphalen
e-mail:
gwestpha@astro.uni-bonn.de
Radioastronomisches Institut der Universität Bonn (RAIUB), Auf dem Hügel 71, 53121 Bonn, GERMANY
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 X-ray data from the German Röntgensatellit (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.
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 coordinate 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:
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.
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)).
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 X-ray contour is dashed. A clear anticorrelation between
HI and X-ray emission is visible. The positional error of the restored
HI data is less than 4 arcmin, whereas the error for the X-ray 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 
). 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 
, which is much smaller than the resolution of the data. The
fully restored map was used for an overlay with 
data by
Kennicutt et al. (1995).
Digitization: The next step is the digitization of the photocopied contour plot template 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: 
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.
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, conserving 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 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.
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 extrema, 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):
where 
is the value of the uphill plateau, 
that of the lower
and 
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 function 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 smoothing 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 physical 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 
pixels.
).
).
)
within 
(
) and of small ones (
) within
(
).
Two applications as shown in Figures 2 and 3.
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.
Table 1: Summary of restored maps