Image Processing Reference
There are several ways in which a test set can be made available. For example:
In practice it is often possible to duplicate a corruption process such as one re-
sulting from a printing operation or fax transmission. A known test image may
then be passed through the process and used to train a filter for use on other
similarly corrupted images where the original is not available.
When presented with a noisy image or sequence to be restored, it is often possi-
ble to identify a clean part of the image and to cut and paste examples of noise
corruption in order to create an ideal and noisy test set. This method has been
used successfully in restoring old video sequences. 2 4
An example of a corrupted image may also be cleaned manually using a soft-
ware package such as Adobe Photoshop. This may then be used as the training
set to design a filter for the automatic restoration of other images.
These methods may seem artificial, but in practice there may be few other options
to solve real-world restoration problems. More theoretical approaches such as
mathematical models can be used to simulate the statistical properties of images
and noise processes. The optimum filters can then be found for these models. In
practice the image and noise characteristics rarely conform to these simple models,
especially in image and film corruption. Once the assumptions of the models are no
longer valid, then the performance of such filters can rapidly decline.
An alternative method is to optimize an image quality criterion, and these do
exist. 5 Most restoration approaches can be adapted to optimize such a criterion
rather than to minimize the error with respect to a training set. In practice these
methods have been found to lead to poorer results compared to training set ap-
This chapter has given insight into the problems associated with filter training. By
definition, the filter must be trained on a different set of images than it is applied to
in practice. The training set must be statistically consistent with the task in hand.
This chapter has considered the effect of changing the size of the filter window and
the associated implications for the size of the training set required. This chapter has
also introduced the two types of error present in filters designed by training;
namely constraint and estimation error. The criteria for whether or not the applica-
tion of a constraint is beneficial have been quantified. Finally, an explanation of
how training sets may be acquired for different classes of problems has been given.
The next chapter considers one of the most commonly used forms of constraints,
that of restricting the filter to increasing functions. This results in filters that have
an interpretation in terms of mathematical morphology.