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Fig. 13.6 Basis images of the discrete orthogonal dual Hahn ( a = c = 0 , b = 8) moments
The local behaviour of the Krawtchouk and dual Hahn moments is obvious from
the above basis images of the discrete orthogonal moments. This constitutes the most
advantageous property of these moments, since they localize the window of interest
in a specific image portion. The previous analysis considering the basis images of
the orthogonal moments highlights the different representation capabilities of each
moment type for different moment orders. According to this study each moment
carries different image's content and therefore the selection of the moments that
better discriminate some patterns seems to be a reasonable and inevitable process.
13.3 Is There a Need for Moments' Selection?
Apart from the previous analysis of moments' representation capabilities, the exe-
cution of a certain experiment regarding moments' description ability, would be
constructive to further highlight the need for selection of the most appropriate
moment sets.
For this purpose the well known Lena benchmark image with 64
64 pixels
size in grayscale format, is reconstructed with various sets of Tchebichef moments
having different orders. The reconstruction results for moment sets consisting of 10
different orders are depicted in Fig. 13.7 . It has to be noted that in each reconstructed
image the intensities are normalized into the [0, 255] range for illustration purposes.
From the reconstructed images of Fig. 13.7 , it can be deduced that as the
moment order increases more detailed information of the image's content emerges.
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