XSET - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 83

ation with a certain distortion Λ is decoded from the bitstream by the entropy decoding
process. The VFWs were not encoded during the entropy encoding process, since it would
increase the amount of stored data. A possible solution is to embed these weights α ( ν , r )

into . Thus, our goal is to recover the α ( ν , r ) weights only using the information from the

bitstream, namely, from the Forward quantized coefficients . Thus, our goal is to recov-
er the α ( ν , r ) weights only using the information from bitstream, namely, from the forward
quantized coefficients
The reduction of the dynamic range is uniformly made by the perceptual quantizer, thus

the statistical properties of I are maintained in .

Therefore, our hypothesis is that an approximation

of α ( ν , r ) can be recovered applying CBPF to , with the same viewing conditions used

in I . That is, is the recovered e-CSF. Thus, the perceptual inverse quantizer or the

recovered introduces perceptual criteria to inverse scalar quantizer and is given by

(3)

3.2 Startup Considerations
(1) Hilbert space-filling Curve : The Hilbert curve is an iterated function, which can be repres-
ented by a parallel rewriting system, more precisely an L-system. In general, the L-system
structure is a tuple of four elements:
(a) Alphabet : the variables or symbols to be replaced.
(b) Constants : set of symbols that remain fixed
(c) Axiom or initiator : the initial state of the system.
(d) Production rules : how variables are replaced.
In order to describe the Hilbert curve alphabet let us denote the upper left, lower left, lower
right, and upper right quadrants as W , X , Y , and Z , respectively, and the variables as U ( up ,
W-X-Y-Z), L (left, W-Z-Y-X), R ( right , Z-W-X-Y ), and D ( down , X-W-Z-Y ). Where - indicates
a movement from a certain quadrant to another. Each variable represents not only a traject-
ory followed through the quadrants, but also a set of 4 m transformed pixels in m level. The
structure of the proposed Hilbert Curve representation does not need fixed symbols, since
it is just a linear indexing of pixels. It is appropriate to say that the original work made by
David Hilbert [ 7 ], proposes an axiom with a D trajectory ( Figure 2(a) ) , while it is proposed