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Fig. 13.7
Lena image reconstruction using several sets of Tchebichef moments of various orders:
a
0-9,
b
0-19,
c
0-29,
d
0-39,
e
0-49,
f
0-9,
g
10-19,
h
20-29,
i
30-39 and
j
40-49
For example, the orders' range 0-9 (1st row of Fig.
13.7
) is able to reconstruct a quite
coarse image's content, while by adding the next 10 orders (0-19) some detailed infor-
mation is incorporated. This observation is in agreement with the image's content
described by each moment set (2nd row of Fig.
13.7
), where it is obvious that the
higher order moments sets model the high frequency pixels variations.
Considering the above analysis, the moments of low orders are not so useful in
discriminating patterns which differ slightly, since their differences are described in
the highmoment orders. For example, if a second image of the above Lena benchmark
is constructed with Lena having her eyes closed, the two image patterns could not
be discriminated by the low order moments but high orders are needed.
Therefore, it is evident that the appropriate set of moments, better discriminating
some specified patterns, depends on the application and thus a selection procedure
considering patterns' modalities is inevitable.
13.4 Moment Features Selection
By examining the recent literature in the field of image moments, one can reach the
conclusion that little work has been done towards the moments' selection [
13
,
20
].
The main selection method applied to all the aforementioned works is the
Genetic Algorithm (GA), proved as an efficient wrapper selection technique [
24
]
taking into account the classificationmodel applied to recognize the patterns. Genetic
Algorithms are a great example of evolutionary computation mimicking the evolu-
tionary process that characterizes the evolution of living organisms [
5
]. However,
the main disadvantage of the GA-based selection is the high computation time need
to converge the algorithm to a suitable solution.
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