We constructed 10 training samples in different regions and for different
plates. For these samples the objects are classified, by eye, as
Star, Galaxy and Unknown.
From the corresponding matrix of pixels of classified objects we
calculated many parameters and systematically plotted them two by two.
We found that the dispersion of pixel optical densities
(i.e. standard deviation of the pixel intensities)
plotted versus the inverse of the surface area gives a diagram in which
galaxies and stars are well separated in two distinct zones as in Fig. 2.
The surface area is simply the number of pixels having an intensity I larger
than the sky background intensity
.
The dispersion of pixel density,
,
is calculated as the standard
deviation of the pixel intensities through the classical equation:
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(1) |
These diagrams were plotted for each plate (i.e., 1443 diagrams)
and a polynomial separation curve was
fitted manually to each of them.
Three examples of these diagrams are given in Figs. 3 to 5,
from the best to the worst.
In Fig. 3 the frontier between Stars and Galaxies is a straight line.
Stars and Galaxies are well separated.
The frontier separating stars from galaxies is often quite linear as
in Fig. 3, but
not necessarily. Indeed, it is also common that the separation curve bends down
for large objects (small 1/S) as in Fig. 4.
This seems to be due to the saturation of pixel
intensities in either the central part of galaxies or in the halo of bright stars.
This phenomenon has also been seen in the source extraction from I-band CCD
images of the DENIS survey (Mamon, private communication).
In regions of low galactic latitude the separation is more difficult
as shown in Fig. 5 for a fields located
at .
Thus, at low galactic latitude (i.e.,
)
the separation between stars and galaxies becomes more
difficult especially for small objects (i.e. large values of the
inverse of the surface area) because the two zones are progressively
mixing with each other.
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Figure 3:
Example of the diagram of dispersion of density versus the
inverse of the surface area (
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Figure 4:
Another example of a diagram of dispersion of density versus the
inverse of the surface area (
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Figure 5:
Another example of diagram
![]() ![]() |
This first discrimination step produces a catalogue with
galaxy candidates and
star candidates.
Hereafter, only the galaxy candidates will be considered.
Nevertheless, our process did not remove every star from the galaxy candidate sample.
A visual inspection showed that bright stars are sometimes counted as galaxy
candidates because of their extended halo as explained above.
The construction of a completeness curve is a general way to check
if a catalogue obeys the expected increase of object number with distance.
If we assume that the number of galaxies within a sphere centered
on the observer and of radius r increases as r3, it can be shown
that the number N of galaxies with an apparent diameter larger
than a given limit
follows the law:
.
Generally, this completeness curve is used to check if a sample is complete
up to a given apparent diameter. Here, it is used to check if the
number of galaxy candidates is homogenously distributed in space, as
expected. Note that this curve is insensitive to the angular coverage of
the catalogue or to the galactic extinction.
The over-sampling of large objects is confirmed by the completeness curve
(Fig. 6), which shows an excess of large galaxies. Here,
is the equivalent diameter defined from the surface
area
in arcsec-2. In this paper the surface
area S is expressed in number of pixels. Thus, from the pixel size 1.7
it results:
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Figure 4:
Completeness curve
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Now, we have to clean up our galaxy candidate catalogue. This is the target of the next section.
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