Image Processing Reference
Figure 7.19 Multimask aperture filters.
from grouping similar patterns together, therefore unseen patterns will have a better
estimate than if the signal was trained by the standard aperture.
Another approach is the multimask approach 15 where the overall filter window
is decomposed into a number of differently shaped subwindows known as masks.
The masks are designed to represent commonly occurring shapes within the signal.
An example of the masks are given in Fig. 7.19.
The multimask filter was compared to the standard aperture and the median fil-
ter in terms of its ability to remove random noise. The training and test set were as
described above but the number of examples was increased from 1024 to 61,440
training pairs. This test was carried out because the median can be used to place the
aperture to collect the observations. The results show how, by selecting the output
by conditional expectation, the multimask filter improves the decision made by the
median filter. Although the two filters are effective for noise removal, the median
filter tends to remove small features whereas the multimask learns to preserve by
estimation from the training set. The domain of the multimask and standard aper-
ture filters was 7 × 7 points and the median filter was also computed over seven
Figure 7.20 shows the error performance of the multimask aperture filter (in
this case it is the MSE that is used) compared with both the single mask aperture fil-
ter and the median filter. It can be seen that the multimask aperture outperforms
both filters. Although neither the multimask nor the single mask apertures have
fully stabilized in terms of estimation error, even at 60,000 training examples the
difference in MSE between these two designs is large enough to show the improve-
ment that can be obtained using the multimask design.
7.6 Grayscale Applications
7.6.1 Film archive restoration
Morphological filters may be trained for removal of noise from film and video foot-
age. This has been successfully applied to old film archive restoration using