Visual Cryptography from Halftone Error Diffusion - Visual Cryptography and Secret Image Sharing - page 26

ated by comparing its shares with those of the first method. Figure 1.12(a){(c)
show three shares produced using the second method in a 3-out-of-3 scheme
where the size of the image is 512512 and the size of the halftone cell is 44.
Here, images Lena, Tank, and Baboon are used. It is obvious that all halftone
shares show images with fine details. The reconstructed image is shown in Fig-
ure 1.12(d), which preserves all the secret information. Compared with Figure
1.12(a), Figure 1.11(a) is generated using the first method, showing less image
details and appearing dark due to the added ABPs.
We should point out that the second method does not necessarily pro-
duce visually pleasing halftone shares if the grayscale images are not carefully
selected. As an example, Figure 1.13(a){(c) shows another set of shares gen-
erated by Lena, Earth, and Baboon using the second method with the same
scheme. Careful inspection shows these shares present more artifacts due to
the cross interference between the shares. The reason is that the contents of
the three grayscale images are not complementary to each other. Comparing
Figure 1.13(a) with Figure 1.11(a) and Figure 1.12(a), local geometric distor-
tion can be observed in Figure 1.13(a). The texture of the distorted region
is quite different from that of the neighboring regions, which causes visible
artifacts. On the other hand, Figure 1.11(a) and Figure 1.12(a) both show
smooth images with uniform image quality. Thus, it is important to choose
appropriate grayscale images for the second method.
1.8 Conclusion
In this chapter, HVC construction methods based on error diffusion are in-
troduced, which can generate shares with pleasing visual information. In the
introduced methods, the pixels that carry the secret information are preset
before a halftone share is generated from a grayscale image. Error diffusion is
used to construct the shares so that the noise introduced by the preset pixels
is diffused away when halftone shares are generated. The secret information
is then naturally embedded into the halftone shares. The homogeneous and
isotropic distribution of the preset pixels imposes the least noise in the er-
ror diffusion, thus leading to shares with high image quality. Our introduced
methods follow the basic principle of VC, thus the security of the construction
scheme is guaranteed. The introduced HVC constructions apply not only to
VSS but also to VSS used in the context of visual authentication and encryp-
tion.
For the first method, by using auxiliary black pixels, the contrast condition
of the decoded image is satisfied. Furthermore, the shares do not suffer any
interference from other shares. When auxiliary black pixels are employed, blue
noise multitone error diffusion is used to generate the distributions of the secret
information pixels and black auxiliary pixels. The second method exploits the
fact that halftoning of the graycale images alone can generate most of the black