Image Processing Reference
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where α ( ν , r ) is the e-CSF weighting function that tries to reproduce some perceptual proper-
ties of the HVS. The term α ( ν , r ) ω s , o is considered the perceptual wavelet coefficients of image I
when observed at distance d .
(2) Forward quantization ( F -pSQ): Quantization is the only cause that introduces distortion
into a compression process. Since each transform sample at the perceptual image I ρ (1) is
mapped independently to a corresponding step size either Δ s or Δ n , thus I ρ is associated
with a specific interval on the real line. Then, the perceptually quantized coefficients Q ,
from a known viewing distance d , are calculated as follows:
Unlike the classical techniques of visual frequency weighting (VFW) on JPEG2000, which ap-
ply one CSF weight per subband [ 1 , Annex J.8], perceptual quantization using CBPF (pSQ)
applies one CSF weight per coefficient over all wavelet planes ω s , o . In this section, we only
explain forward perceptual quantization using CBPF (F-pSQ). Thus, Equation (2) intro-
duces perceptual criteria of the perceptual images (1) to each quantized coefficient of the
dead-zone scalar quantizer [ 1 , Annex J.8]. A normalized quantization step size Δ = 1/128 is
used, namely, the range between the minimal and maximal values at I ρ is divided into 128
intervals. Finally, the perceptually quantized coefficients are entropy coded, before forming
the output code stream or bitstream.
(3) Inverse quantization ( I -pSQ): The proposed perceptual quantization is a generalized method,
which can be applied to wavelet-transform-based image compression algorithms such as
EZW, SPIHT, SPECK, or JPEG2000. In this work, we introduce both forward (F-pSQ) and
inverse perceptual quantization (I-pSQ) into the H i -SET coder [ 4 - 6 ] . An advantage of in-
troducing pSQ is to maintain the embedded features not only of H i -SET algorithm but also
of any wavelet-based image coder. Thus, we call CBPF quantization + H i -SET = CH i -SET or
Both JPEG2000 and XSET choose their VFWs according to a final viewing condition. When
JPEG2000 modifies the quantization step size with a certain visual weight, it needs to ex-
plicitly specify the quantizer, which is not very suitable for embedded coding. By contrast,
XSET needs neither to store the visual weights nor to necessarily specify a quantizer in or-
der to keep its embedded coding properties.
The main challenge underlies in to recover not only a good approximation of coefficients Q
but also the visual weight α ( ν , r ) (Equation 2 ) that weighted them. A recovered approxim-
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