Cryptography Reference
In-Depth Information
In this section, examples are provided to illustrate the effectiveness and
tradeoff of the introduced methods. Constructions of 3-out-of-3 halftone VSS
schemes are illustrated. The secret image to be encoded is the logo of the
University of Delaware. Three grayscale natural images, Lena, Earth, and
Baboon are provided to generate the shares. The size of the share is 513513
and the size of the secret image is 171 171. For illustrative purposes, image
Lena is shown in
Figure 1.9(a).
The VSS pixel expansion of the secret pixel is = 4 and the size of the
halftone cell is q = 33. The number of ABPs for each halftone cell is x = 2
and the quality index is s = 1=3. The distributions of SIPs and ABPs for each
share are decided before halftone shares are generated. The jointly optimized
distribution of SIPs and ABPs over a local region in one share is shown in
Figure 1.9(b) where the gray pixels indicate SIPs and the black pixels indicate
ABPs. We use the Floyd-Steinberg error filter shown in
Figure 1.2
for the error
diffusion. For robust error diffusion, output-dependent threshold modulation
is employed and the threshold t(m;n) at the point (m;n) is given by:
t(m;n) = 0:25 + 0:33 0:25 [g(m;n 1)
+ g(m;n 2) + g(m;n 3)]:
The threshold modulation tries to adjust the current threshold by using the
information of three preceding halftone pixels. For error diffusion, the error
diusion constant is set to = 0:8 to avoid error diusion instability.
Three output shares are shown in
Figure 1.10(a)
to Figure 1.10(c), re-
spectively, where the corresponding perceived errors are also shown. When
calculating the perceived error , an alpha stable human visual system model
proposed in [9] is used. All shares show visually pleasing halftone images where
the image details can be clearly recognized. The resultant shares do not show
either residue image of the encoded image or any residue image of other shares.
Figure 1.10(d) shows the reconstructed image when shares 1 to 3 are "stacked"
together with the OR operation. The content of the reconstructed image is
clearly recognizable with a contrast = 1=9. The decoded image does not
bear any residue of any share images.
To illustrate the tradeoff between the share image quality and contrast of
the decoded image, we show another set of simulation results of a 3-out-of-3
halftone VSS scheme. Compared with the previous example, the halftone cell
size is changed to q = 44. The sizes of the shared image and the secret image
are well adjusted to be 512 512 and 128128, respectively. The number of
ABPs for each halftone cell is x = 4 and the quality index increases to s = 1=2.
The three output shares are shown in
Figure 1.11(a)
to Figure 1.11(c), respec-
tively, where the corresponding perceived error is also shown. Figure 1.11(d)
shows the reconstructed image by stacking three shares together, where the
contrast of the decoded image is = 1=16. Shares in the second example have
larger halftone cell size, thus larger s and better image quality than that of
the shares in the first example, as can be seen from Figure 1.11. However, the
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