We now illustrate the practical use of the method on two specific, very different examples.
Figure 3 (click here) displays a wide-field
(9
5) CCD image of comet P/Halley obtained
on 17 April 1986 at the European Southern Observatory in Chile
(Lamy et al. 1987). The camera consisted of a cooled, large-format CCD
pixels behing a Canon f/2.8, 100 mm lens.
This particular image was obtained with a B filter and with an exposure
time of 15 minutes.
In April 1986, the comet was crossing the southern Milky Way resulting in a
very rich star-field surperimposed onto the comet.
The fast f-number led to a non-negligible distortion
of the star images which are further slightly trailed due to an imperfection
of the guiding. Several star images are saturated, the most severe ones
presenting the characteristic linear extension along a column.
The quantitative
analysis of the dust tail to retrieve for instance the physical properties
of the dust and its production rate, requires the removal of all star images
to perform its accurate photometry.
Following the classical processing of CCD images (bias removal, flat-fielding
...) and specific corrections for vignetting and atmospheric
transmission, we started applying our method by taking the log of the intensity.
Figure 4 (click here) shows the (k1, k2) diagram of principal curvatures. The characteristic features discussed in Sect. 3 (click here) are present: the butterfly pattern and the two blobs on the k1 and k2 axis. Note the conspicuous angular offset of the A wing from the bissector (k1 = k2), to be compared to the closeness of the B wing to the k2 axis, offset produced by the trailed star images.
Figure 5 (click here) represents the histogram of the modulus of the curvature k = (k21 + k22)1/2.
Figure 5: The histogram of the modulus of the curvature and the selected
threshold value k = 0.09
Figure 6 (click here)a displays the first mask generated with a discrimination level of k > 0.09. The few, heavily saturated stars produced flat tops which were not properly detected. A second mask was generated by applying a threshold to the intensity to cope with this problem.
Figure 6 (click here)b display the final mask resulting from previous masks
(OR operation) and the
morphological operation described in Sect. 4 (click here). The percentage of invalid
pixels amounts to 
which ensured a good restitution of the background.
Figure 7 (click here)a shows the intensity of the final, ``restored" image of comet P/Halley with an intensity range similar to that of the original image (Fig. 3 (click here)).
Figure 7 (click here)b is similar to Fig. 8 (click here) except for a streched intensity range to visualize the full extent of the dust tail. The effenciency of the method is excellent: only traces of the few most intense (saturated) stars are persisting although at very faint levels.
This method was successfully applied to a set of 32 wide-field images of comet P/Halley.
Figure 8 (click here) displays a CCD image of the solar corona obtained on 4 May 1996 with
the LASCO/C3 externally-occulted coronagraph aboard the SOHO spacecraft
located at the Sun-Earth L1 Lagrangian point.
This instrument has an effective focal length of 77.6 mm and an effective
f-number of 9.3.
The 
pixels image has been extracted from an original
pixels image centered on the Sun and obtained with a
blue filter (450-520 nm bandpass) with an exposure time of 10 minutes.
The 8 8 field-of-view includes the outer
K and F coronae
(the Sun and inner corona are blocked by the occulter), comet Hyakutake,
a few stars and numerous impacts of cosmic rays.
The application of our method was quite straightforward in this case. The mask was only modified to retain the comet (whose head is slightly saturated) and the bright fringe surrounding the occulter.
Figure 9 (click here) displays the final result after correction,
and Fig. 10 (click here), the difference
with the original image.
All artifacts and star images have been removed, including very faint ones
which were hardly noticeable on the original image.
This method has been implemented in the routine processing of the
images produced daily by the LASCO experiment.