Resolving the Alignment Problem in Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 317

Use the deviations (0; 0), (0:5; 0), (1; 0), (1:5; 0) and (2; 0) to test the
misalignment tolerance of the following four schemes: (a) p B = 0%, (b)
p B = p S = 50%, M reg , (c) p B = p S = 50%, M ran and (d) p B = 100%.
Notice that (a) and (d) are just the traditional VCS with all small subpix-
els and large subpixels, respectively. The first scheme has the best resolution
when aligning correctly, as shown in Figure 11.9 (a1), but the secret on the
recovered secret image diminishes quickly when the deviation increases. The
secret becomes invisible when the deviation is large enough (see Figure 11.9
(a5)). Comparing Figure 11.9 (a) and (d), the small subpixel gives the high
resolution (see Figure 11.9 (a1) and (d1)), whereas the large subpixel enhances
the misalignment tolerance. For example, the deviation is (d x ;d y ) = (2; 0), the
secret in Figure 11.9 (a5) becomes invisible but we still visually view the secret
"VSS" in Figure 11.9 (d5). As shown in Figure 11.9 (a3) and (a4), the secret
image is recovered by its complementary color. This interesting phenomenon
is compatible with the result in Section 11.3 and Section 11.4. From these
stacked results, our two-sized subpixel approach actually provides the mis-
alignment tolerance. Also, it is observed that Figure 11.9 (b) (M reg ) has the
better visual quality than Figure 11.9 (c) (M ran ). This result is anticipated
because the random arrangement of subpixels will introduce additional noise
to the recovered secret image.
Example 6 Consider the rst scheme in Example 5 (a (2; 2) misalignment
tolerant VCS that the large and small subpixels are half used, respectively,
and regularly arranged in a share). Three size ratios, 2 = 4, 16, and 64, are
tested. The printed-text "VSS" is used as a secret image.
FIGURE 11.10
Recovered secret images for a (2; 2) misalignment tolerant VCS using p B =
p S = 50%, M reg and three size ratios: (a) 2 = 4, (b) 2 = 16 and (c) 2 = 64,
horizontal deviations: 0, 0:5, 1, 1:5, 2, 2:5, 3, and 3:5 are tested (unit: small
subpixel).