Resolving the Alignment Problem in Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 311

According to Lemma 3, for one-dimensional deviation, it is evident that if
R 0 W R W and R 0 B R B , the whiteness of the white secret pixel is whiter
and the darkness of the black secret pixel is darker when using the large
subpixels. We can conclude that the large subpixels have better misalignment
tolerance than that of small subpixels. Actually, for two-dimensional deviation,
the conclusion also holds. However, the proof is rather complex; we omit the
proof here. Readers also can reach this conclusion via simulations, for example
the Figure 11.6, and more simulations for two-dimensional deviation can be
found in [16].
FIGURE 11.6
Recovered secret image for a (2; 2)-VCS using two dierent-sized subpixels
and (d x ;d y ) = (0:5; 0:5), (s 1 =s 2 ) = 2: (a) the small subpixel and (b) the large
subpixel; two secret image (a printed text "VSS" and a halftoned Lena image)
are tested.
From the preceding description and the results in Figure 11.5 and Fig-
ure 11.6, unfortunately, there exists another dilemma of using the large or
small subpixels. Together with previous comparisons in Table 11.1, we sum-
marize the advantages and disadvantages of large and small subpixels in
Table 11.5.
In order to bring these conflicting goals in a kind of balance, we prop-
erly distribute two-sized subpixels in shares to develop their specialities and
simultaneously avoid corresponding disadvantages. Our method is based on
the trade-off between the usage of large and small subpixels. Both two-sized
subpixels create a trade-off, which a large size subpixel leads to the high mis-
alignment tolerance but the low resolution, while the small subpixel has the
opposite properties. Finally, we successfully reduce the diculty of aligning
shares. Designing our misalignment tolerant VCS therefore delivers the fol-