Image Processing Reference
In-Depth Information
Figure 2.1
Corrupted text document. This document contains 10% additive salt-and-pepper
noise.
should remove only black pixels to restore the image to its original state. Unfortu-
nately, the median treats both equally, so it cannot simply remove black pixels
while leaving white unchanged. The second disadvantage is that the median filter
carries out exactly the same operation for all images and all noise distributions.
Therefore, it cannot possibly be the best filter in all these cases. There must be
better filters possible, and it would be reasonable to assume that these will be differ-
ent for images with different structure and corrupting noise.
This leads to the second approach above: heuristic methods. This is basically
designing by guesswork—a human designer tries out different filters to improve
the quality of the resulting image. A typical approach might be to observe that the
noise in the image consists of isolated black pixels and hypothesize that if these
pixels could be identified and switched to white, most of the noise would be re-
moved.
This would constitute a rule such as: “Switch a black pixel to white if it has
more than
N
white neighbors,” where
N
could be anything from 1 to 8. Another rule
might include structural details. For example, “Switch every black pixel to white
that has a white pixel immediately above and below it.” These rules may give some
improvement especially in simple cases. However, they may be difficult to formu-
late in more complex images especially in areas where the noise and signal detail
are very similar. It would also be impossible to know if the filter obtained was the
best one out of all available filters or whether it might be improved.
The third approach is to use statistics to determine the
optimum
filter. Consider
the following very simple pair of images shown in Fig. 2.2 with the original image
I
o
on the left and the noise corrupted version
I
n
on the right.
The ideal image consists of a number of horizontal bars. The noisy image has
been corrupted by a random noise process that has both added pixels to the back-
