Resolving the Alignment Problem in Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 295

11.3 Misalignment with Integer Number of Subpixels
According to the traditional view, the subpixels of the transparencies should
be aligned precisely. Here, we point out that, to recover the secret image
visually, it is not necessary to align the subpixels precisely. In this section, we
will only consider the misalignment with integer number of subpixels.
We will show that, by shifting one of the shares by some number (at
most m 1) of subpixels to the right (resp. left), one can still recover the
secret image visually, for the reason that the average contrast 6= 0. This
result can naturally be extended to the case when more than one share is
shifted. However, we leave the numerical analysis of this case to the interested
readers. So, in this section, we will only consider the case with only one share
(transparency) being shifted by some number of subpixels. And we call the
scheme with a share being shifted the shifted scheme, and the basis matrices
and share matrices of the shifted scheme are called the shifted basis matrices
and shifted share matrices.
We first give an example to show this phenomenon.

Example 1 We take the (2; 2)-DVCS as an example, where the basis matrices
of the scheme are,

100
100

100
010

M 0 = and M 1 =

FIGURE 11.1
The stacking results of the (2,2)-DVCS (a) when no share is shifted; (b) when
one share is shifted by one subpixels; (c) when one share is shifted by two
subpixel. A printed-text "CRYPTO" is tested.

Figure 11.1 are the experimental results of the recovered secret image,