Satellite Image Classification Using Cascaded Architecture of Neural Fuzzy Network - Advanced Techniques in Knowledge Discovery and Data Mining - page 217

tion from both low pass and high pass in columns and in rows, respectively. The
top-right image is from low pass in columns and high pass in rows. Conversely,
the bottom- left image is from high pass in columns and low pass in rows.
The complete discrete wavelet decomposition is obtained by cascading the
outputs of the low-pass filter {h(n)} into the same filter bank as shown in the upper
part of Fig. 8.7. The outputs of each filter are critically sampled. The decomposi-
tion results in a fine-to-coarse representation of the input signal. The scaling coef-
ficients at a given scale are a low-pass-filtered and contracted version of the scal-
ing coefficients at the previous scale. The wavelet coefficients at a given scale
represent the different detail information needed to reconstruct the signal at the
previous finer scale. The scaling function I i () is obtained from {h(n)} only while
wavelets are obtained from {h(n)} and {g(n)} , where \ ki x

, () is the wavelet with

input i and the output at level k .

Do wavelet
column by
column
Low pass +
High pass

Get the
neighbors
from the
point

Do wavelet
row by row
Low pass +
High pass

Stop until
reach the
end of the
image

Select a
point in
ordering

Extend the
size
of the
selected
boundary

Convolution Downsampling Transpose

Fig. 8.5. Procedure of wavelet decomposition.

Fig. 8.6. Result of wavelet decomposition of a channel input.