Cryptography Reference
In-Depth Information
index of the halftone share and is represented as:
s =
qx
q
;
(1.11)
where q is the halftone cell size, x is the number of ABPs in a cell, and is the
number of SIPs in a cell. A large s leads to good image quality of the halftone
share. However, s cannot be arbitrarily large and it can be shown that:
s (
k 1
n
)(
q
q
) < 1:
(1.12)
Thus, the best image quality of a halftone share that can be achieved depends
on k, n and the halftone cell size q. If k, n, and s are the design parameters,
then q is calculated as:
q = d
(k 1)
kns 1
e:
(1.13)
Consider the 2-out-of-2 scheme. Assume q = 4, then it is calculated that
x = 1 and s = 0:25. Since s is small, the image quality of the share is not
high. If q is larger, then better image quality can be expected. Furthermore,
as q !1, s approaches 0:5. However, a larger q leads to worse contrast loss
of the reconstructed image. As will be shown later, the contrast loss of the
reconstructed image can be improved by filtering.
The quality of each share depends on the quality index s. We can compare
the share image with the halftone image generated from the grayscale image
without encoding any secret information and then compute the perceived
error between the coded and uncoded halftone image. The perceived error is
calculated by employing an appropriate human visual system (HVS) model.
See [11, 9] for details.
For the second method, it is dicult to determine the proportion of pixels
that carry visual information of the shares. However, it is clear that for n 1
in a n-of-of-n scheme, the quantity s approaches:
s =
q
q
;
(1.14)
which indicates potentially good image quality for a suciently large q.
Compared with methods in [26] and [22], the requirement of a comple-
mentary pair is removed and all shares generated carry natural images. From
(1.12), it is clear that for the first method, the quality index is more correlated
to fk;ng in the VSS scheme. A visually pleasing halftone image share can be
obtained if n 1 and nk is small, and if the HVC expansion q is su-
ciently large. If small image quality discrepancy of the share is tolerable, then
we should first consider the first method, especially if we have the flexibility
to choose the grayscale images. If the grayscale images are carefully chosen,
n 1, and nk is small, then the distortion due to image quality discrep-
ancy will be hardly noticeable. Otherwise, only the first method should be
considered since it is the only method that guarantees uniform image quality
of the shares without using complimentary shares.
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