Human Object Classification Using Dual Tree Complex Wavelet Transform and Zernike Moment - Transactions on Large-Scale Data-and Knowledge-Centered Systems - page 90

level 1 down samplers in tree b pick the opposite sample to those in tree a . then it is
found that to get uniform intervals between samples from the two trees below level 1 ,
the filter in one tree must provide delays that one half of a sample different from those
in the opposite tree.

(a)

(b)

Fig. 1. Dual tree of the real filters for the complex wavelet transform (DTCWT), giving real
and imaginary parts of the complex coefficients

For inverse of Dual tree complex wavelet transform each tree of Fig. 1(a) is invert-
ed separately using biorthogonal filter G , specially designed for perfect reconstruction
with analysis filter H in the 2-band reconstruction block in Fig. 1(b). The results of
each of the 2- inverse function are averaged to give reconstructed signal. This system
is a wavelet frame with redundancy two; and if the filters are designed such that the
analysis and re-construction filters have very similar frequency responses, then it is an
almost tight frame, which means that energy is approximately preserved when signals
are transformed into the DT-CWT domain.

2.2 Zernike Moment

Zernike moment was firstly introduced by Teague [19] to overcome the shortcomings
of information redundancy present in Geometric moments [19]. Zernike moment can
represent the properties of an image with no redundancy or overlap of information