Extended Visual Cryptography for Photograph Images - Visual Cryptography and Secret Image Sharing - page 105

times smaller than the original pixel if the image size is fixed to that of
the original image. This results in diculty of alignment so that transparen-
cies with smaller subpixels are more dicult to be stacked properly. Mis-
aligned transparencies cannot reconstruct the secret image. This cannot be
neglected because one of the most important characteristics of visual cryp-
tography is the capability that the secret information is revealed by simply
stacking transparencies without any computation.
Relative dierence () It is obvious that contrast is also one of the most
important parameters related to image quality. An image with low contrast
is obscure and dicult to see its details. Furthermore, there exists a certain
tradeoff between contrasts of shadow and secret images in case of extended
visual cryptography. It is impossible to increase both contrasts of a secret
image and shadow images simultaneously.
4.3.3 Photograph Visual Cryptography with Basic Schemes
The straightforward way to incorporate photograph images into visual cryp-
tography is as below:
1. Convert photograph (continuous-tone) images to binary images by
halftoning.
2. Encrypt a secret image by one of the schemes explained in Section
4.2.
Of course the quality of resulting images may be changed by the halfton-
ing algorithm. But here we would like to focus on the differences among the
encryption schemes.
Table 4.1 summarizes the characteristics of visual cryptography with pho-
tograph images according to the encryption schemes, i.e., Visual Secret Shar-
ing Scheme (VSSS), Extended Visual Cryptography Scheme (EVCS), and
Random Grids (RG), in the case of (2; 2). Since all three schemes assume that
shadow images are printed on transparencies and stacked together, the super-
imposition (stacking operation) can be seen as Boolean "OR" in mathematical
sense. The basic properties of VSSS and RG are very similar except for the
pixel expansions. The pixel expansion of (2; 2) VSSS is m = 2 (it would be 4 if
one wants to preserve the aspect ratio of a image), while RG's pixel expansion
is m = 1. VSSS and RG have no extended capability. They cannot incorporate
photograph images into shadow images in order to conceal the existence of
"secret," which means the original shadow images are simple monotone images
("mono.") and encrypted results are random-dot binary images ("rand."). In
other words, the relative difference of shadow images is S = 0. However,
they can accept a continuous-tone image ("cont.") as a secret image. A re-
constructed secret image is a halftoned binary image ("half.") whose relative
difference is R = 2 . Only EVCS among the three basic schemes can incorpo-
rate continuous-tone images into shadow images. The resulting shadow images