Two-Decoding-Option Image Sharing Method - Visual Cryptography and Secret Image Sharing - page 461

the secret image I is a 512 512 gray-level image. Lin and Lin's TiOISS (2,

m
w

4) scheme needs a compression ratio R = = 32=(2

2:585) = 6:19. We rst compress the gray-level secret image I to a compressed
image I C to obtain the less embedded bits. Notice that even though jI C j has a
lesser file size (the embedded bits), it has the same physical size of the original
image jIj. Finally, the shadow size of Lin and Lin's (2, 4)-TiOISSS is 1024 1024
(note: mjI 0 j), and the pixel expansion is m (C)

8n k log 2

LIN = m = 4. On the other hand,
we need a 15361536(9jIj) halftone image for Jin et al.'s (2, 4)-TiOISSS.
The shadow size of Jin et al.'s (2, 4)-TiOISSS is 3072 3072(9mjIj), and
the pixel expansion is m JIN = 9m = 36.

2

17.4 A New(k;n)-TiOISSS
The VCS and PISSS have their respective features. As is known, the VCS has
the vague reconstructed image and PISSS has a perfect reconstruction. The
VCS has the distinctive stacking-to-see capability, while PISSS spends the
computation for reconstruction. It is reasonable to adopt the stacking-to-see
property of the VCS into PISSS to achieve a two-in-one scheme where the
secret image is revealed both by stacking the transparencies and by compu-
tation. Our new TiOISSS [20] is also a combination of the VCS and PISSS,
which is somewhat similar to Lin and Lin's scheme, but the way is completely
dierent to that in Lin and Lin's scheme.
Jin et al.'s TiOISSS is a lossless version (i.e., no distortion in the secret
image) but has a large pixel expansion. Lin and Lin's TiOISSS is a compress-
ible version. It compresses the secret image such that the shadow size has
enough space to hide the information of a compressed image. Although Lin
and Lin's scheme reduces the pixel expansion of Jin et al.'s scheme, the re-
constructed image has distortion. Obviously, Lin and Lin's approach can be
extended to the lossless version by expanding the halftone image with the size
jI 0 j = (n=k) jIj 8=log 2

m
w

to hide the original secret image. For the

lossless version of Lin and Lin's TiOISSS, the pixel expansion m (L)

LIN is

m
w

m (L)

LIN = (n=k) m 8=log 2

: (17.7)

For example, the pixel expansion of Lin and Lin's (2, 4)-TiOISSS in Example
2 (i.e. k = n = 2, m = 4, w = 2) is m (L)

LIN =24.76.
Jin et al.'s scheme cannot be used in a compressible version because it
uses a look-up table to recover the grayscale value of the pixel. The proposed
TiOISSS has two versions|the lossless version and the compressible version.