Visual Cryptography from Halftone Error Diffusion - Visual Cryptography and Secret Image Sharing - page 17

are checked at each non-SIP position to see if a sucient number of black
pixels have been produced. If a sucient number of black pixels have not yet
been generated, black pixels are deliberately inserted at that position. The
SIPs are again preserved and not changed.
In a k-out-of-n scheme, if only < nk + 1 black pixels are generated
by halftoning at a non-SIP location (i;j), then = n k + 1 shares
with the smallest magnitudes of halftone error at (i;j) are selected and black
pixels are inserted at (i;j) on these shares. Thus, the contrast condition of
image decoding is guaranteed. The quantization error caused by the inserted
black pixels will be diffused away to neighboring grayscale pixels and pleasing
halftone shares can be obtained. Since far fewer black pixels are deliberately
introduced, the second method imposes fewer constrains on the error diffusion
and thus it has the potential to achieve better image quality than that of the
first method. However, to achieve uniform image quality of the whole share,
we need to choose the grayscale images in a selective way.
It is clear that the decision to insert a black pixel or not depends on the
image content of the shares. Thus, the inserted black pixels are not evenly
distributed. In some regions of the image, the error diffusion mechanism is
constrained by the SIPs. In some other regions, error diffusion is constrained
not only by the SIPs but also by the inserted black pixels. Therefore, the im-
age quality on some regions in the image may be better than the image quality
on some other regions that exhibit more artifacts. The parallel approach may
thus generate shares whose image quality is not consistent over the whole im-
age. Such quality discrepancy may cause visible distortions. To mitigate such
visible distortion, we need to minimize the number of black pixels inserted.
An obvious way to mitigate the distortion is to select grayscale images where
the contents of some images tend to be complimentary to those of the others.
For example, if there is one bright (white) region on one image, there should
be corresponding dark region(s) in some other image(s). Then the halftoning
of the grayscale images will generate most of the black pixels needed and the
number of inserted black pixels will be greatly reduced, which leads to visually
pleasing halftone shares. In a n-out-of-n scheme, if n 1, then this approach
is especially effective and the visible distortion is less likely to happen.
1.5 Quality of Halftone Shares
In this section, we focus on the quality analysis of the halftone shares for the
first method. The analysis also helps to evaluate the share image quality of the
second method. With the exception of the SIPs and the ABPs, all pixels in the
halftone share produced by the first method are assigned freely to carry the
shared visual information. The proportion of these pixels governs the image
quality of the resultant halftone shares. The quantity s is called the quality