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1
N mn
n
m
2
˃
=
W m ( |
W m (
i
,
j
) | − μ
m
)
(3.20)
(
i
,
j
)
Also, n and m denote decomposition level and subband orientation, respectively,
N mn is the number of coefficients in the mn -th subband, and W m (
i
,
j
)
is the wavelet
in the subband image W m .
coefficient at location
(
i
,
j
)
3.3.2.2
Feature Extraction from Wavelet Transform/Vector Quantization
Coder
The hybrid wavelet transform/vector quantization (WT/VQ) coders have been
proven to achieve high compression while maintaining good visual quality [ 89 , 353 ].
Figure 3.6 shows the coder and decoder of this coding scheme. Here, a two-
level wavelet decomposition scheme, with a 15-coefficient biorthogonal filter, is
adopted for the analysis of images. The decomposition scheme produces three
subbands at resolution level 1, and four subbands at resolution level 2. To capture the
orientational characteristics provided by the wavelet-based subband decomposition,
a codebook is designed for each subband. This results in a multi resolution codebook
(Fig. 3.6 d) that consists of sub-codebooks for each resolution level and preferential
direction. Each of these sub-codebooks is generated using the Linde-Buzo-Gray
(LBG) algorithm, as well as the bit allocation method (Fig. 3.6 c), to minimize
overall distortion. The codebook design divides a subband belonging to different
images into m
m square blocks and the resulting vectors are used as the training
vectors. Separate codebooks are trained for each resolution orientation subband.
For the encoding of an input image at a total bit rate of 1 b/pixel, the bit
assignment is organized as follows: resolution 1 (diagonal orientation) is discarded;
Resolution 1 (horizontal and vertical orientations) and resolution 2 (diagonal
orientation) are coded using 256-vector codebooks resulting in a 0.5-b/pixel rate,
whereas resolution 2 (horizontal and vertical orientations) is coded at a 2 b/pixel rate
using 256-vector codebooks; and, finally, the lowest resolution is coded by scalar
quantization at 8-b/pixel.
Figure 3.6 b shows the decoding process. The feature extraction is obtained before
vector dequantization. The coding labels are used to constitute a feature vector
via the computation of the labels histograms. Each subband is characterized by
one histogram and represents the original image at a different resolution; thus, the
resulting histograms are called multiresolution histogram indexing (HMI) [ 90 ]. This
method makes use of the fact that the usage of codewords in the sub-codebook
reflects the content of the encoded input subband. For the two-level decomposition,
five subbands containing wavelet detail coefficients are utilized for the construction
of HMI features:
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