Cryptography Reference
In-Depth Information
Algorithm
1. Generate a random grid R
1
with the same size as B.
2. For each pixel B(p), a grid R
2
is determined as below:
<
R
1
(p)
if B(p) = 0
R
2
(p) =
:
:
R
1
(p)
otherwise
Let T and O denote transparent and opaque regions of the original binary
image B so that B(p) = 0j
p2T
and B(p) = 1j
p2O
. The regions T and O
fulfills the following constraints:
= T [O and = T \O;
where stands for the entire region of the original image while represents
the null region, because B is a binary image. Due to the definition of the above
algorithm, random grids R
1
and R
2
satisfies the following relations:
R
1
(p) = R
2
(p)j
p2T
and R
1
(p) = R
2
(p)j
p2O
:
Therefore, R
2
as well as R
1
is a random grid and the average opacity of their
superimposition depends on the regions T and O of the input binary image:
1
2
O((R
1
+ R
2
)(p))j
p2T
=
and O((R
1
+ R
2
)(p))j
p2O
= 1:
The difference of the average opacities of region T and O corresponds to
relative dierence in VSSS.
Figure 4.4
shows an example of random grids
and a reconstructed secret image. The size of all images are 64 64 pixels,
which is the same as that of the original secret images, because Random Grids
are free from pixel expansion, m = 1.
4.3 Fundamentals of Photograph Visual Cryptography
Digital cameras have become very popular and people can easily obtain
continuous-tone digital image data. However, all the schemes explained in the
last section accept binary images as input. Thus, a photograph image must
be converted to a binary image that can be observed similar to the original
image by the human visual system. The algorithm that can achieve such a
conversion is referred as digital halftoning or halftoning in short [38, 18].
4.3.1 Digital Halftoning
There are several approaches to digital halftoning, namely, noise-encoding,
ordered dither, error diffusion, iterative and search-based methods, etc. Here
we explain some of the approaches.
Search WWH ::
Custom Search