Visual Cryptography from Halftone Error Diffusion - Visual Cryptography and Secret Image Sharing - page 16

visible distortion. In this way, the SIPs and ABPs are seamlessly embedded
into the halftone shares generated and the halftone share is structured taking
meaningful visual information.
Much like the methods in [26, 25], the above procedure can be extended
to an arbitrary access structure ( Qual ; Forb ). The security of the introduced
halftone VSS scheme is guaranteed by the properties of the underlying visual
secret sharing scheme.
1.4 Halftone VSS Construction Using Parallel Error
Diusion
In the previous method, uniformly distributed auxiliary black pixels are intro-
duced to satisfy the contrast condition of image decoding. The current method
exploits the fact that halftoning of the grayscale images alone may generate a
sucient number of black pixels to block the shared visual information from
showing on the decoded image.
As in the previous method, in the current method, the shares are also di-
vided into nonoverlapping halftone cells of size q = v 1 v 2 . pixels within
the halftone cell are SIPs carrying the secret visual information. A method
based on error diffusion is used to generate the distribution of SIPs. To this
end, a constant-value grayscale image of gray level z 0 = =q, having the same
size of a share image is first produced. This grayscale image is then halftoned,
producing a distribution of "1"s, denoted by Z 0 . Z 0 determines the distri-
bution of the SIPs. To ensure that there are exactly "1"s in each halftone
cell, the error diffusion is constrained such that the values of some pixels are
preset and are not modied by the error diusion. The error e(m;n), which is
the difference between the input to the thresholding block and the resultant
pixel value, is still calculated for the preset pixels and then diffused away to
neighboring grayscale pixels through the error filter. In this constrained er-
ror diusion mechanism, if the current halftone cell already contains "1"s,
the rest of the pixels in the halftone cell are prefixed and constrained to be
"0"s. The quantization error is accumulated and diused to grayscale pixels
in neighboring cells. If the current halftone cell contains t < "1"s, and the
error diusion already proceeds to the (q t)th pixel of the current cell,
then the rest of the t pixels in that cell are all constrained to be "1"s. This
procedure guarantees that there are exactly SIPs in each halftone cell. Since
the errors are always diffused to neighboring grayscale pixels, a homogeneous
distribution of SIPs is produced, where most of the SIPs are well separated
from each other. The assignment of SIPs are predetermined using the same
approach as described previously.
Then, the current method halftones the grayscale images in parallel to
produce the halftone shares. Within the error diffusion process, all the shares