Image Processing Reference
In-Depth Information
the evolutionary process by the application of
crossover
and
mutation
. Two chro-
mosomes were chosen at random as “parents” from the population and were used to
“breed” two child chromosomes. This was carried out using crossover, which in-
volves the swapping of sections of genetic material at random. The premise is that
two well-performing parents may produce an even better-performing child. Further
variation was introduced by a process known as mutation, in which small changes
to the chromosome are made with random probability.
The operation of the GA continued over several generations during which time
the less-well-performing chromosomes were purged from the population. Eventu-
ally, a steady state was reached in which no further improvement could be seen.
Inherent in the above process is the requirement for a performance metric to
evaluate how well the filter resulting from each chromosome was performing. This
property is known as “fitness.” In this case, the fitness is a measure of the similarity
of the filtered and clean images. The work here compares two different measures of
fitness. The first measure used a weighted combination of the mean-absolute error
(weighted at 0.6) and the mean-square error (weighted at 0.4). The second used a
structure similarity (SSIM) index.
10
The SSIM is a metric developed for use in esti-
mating the effect of subjective viewing of structural integrity. In all other respects,
the details of the training process were identical.
Once the fitness of the different filters resulting from the child chromosomes
had been measured, the best fifteen filters were kept and others discarded. The re-
maining chromosomes were then subjected to the GA techniques of crossover and
mutation to create new chromosomes from which to generate new filters. These
measures were used in an attempt to create new filters containing the desirable fea-
tures of the successful filters and combine them to get closer to a near-optimal filter.
The use of mutation introduces “new” information to the filter chromosomes. It al-
lows areas of the search space to be reached that were not accessible using cross-
over alone.
The training runs were initially set to terminate after 30 minutes. After this
time, the GA had completed 35 iterations. Figure 9.7 shows the improvement made
on two examples of the training data by the best filter found using the MAE/MSE
measured after 35 iterations. Clearly the SMF has led to an improvement, but there
is still significant noise in one of the images. The GA was then set to run for 500 it-
erations.
The results from the filter produced after 500 iterations using the MAE/MSE
hybrid as the error measure is shown in Fig. 9.8. The final error measure at the end
of the training run was 0.996. The results of the filter created by using the SSIM as
the fitness measure is shown after 35 iterations in Fig. 9.9 and 500 iterations in
Fig. 9.10. The final error after 500 iterations was 0.991. Table 9.1 summarizes the
quality differences between the images and the clean data by showing the improve-
ment in the two quality measures after 35 and 500 iterations of the GA are applied
to the training set.
It should be pointed out that the absolute values of the two measures are not di-
rectly comparable since the SSIM is much more closely related to the way in which
