Steganography in Halftone Images - Visual Cryptography and Secret Image Sharing - page 369

1.2

L=1
L=5
L=10
Theoretical value

1

0.8

0.6

0.4

0.2

0

−0.2

0 50 100 150 200 250 300

R w- w a i of X

FIGURE 13.27
Contrast of Y in Figure 13.24 vs row-wise average intensity of X in Figure
13.14 (Ramp).

the theoretical behavior predicted by (13.43) and (13.44). It can be observed
that the empirical intensity curves and contrast curves are similar to the
corresponding theoretical curves, as expected. Again, the choice of L has little
eect.
Comparing DHCED and DHSED, they have the same Y 1 . For their Y 2 ,
their pixel values are identical in W w but different in W b . On overlaying the
corresponding Y 1 and Y 2 , the Y of both DHCED and DHSED are identical in
W w , but DHCED has lower E[y(i;j)] in W b than DHSED such that the black
patterns of W would look darker in DHCED than in DHSED as predicted by
Figure 13.29. And, the contrast of the revealed W in DHCED is higher than
that in DHSED as predicted by Figure 13.30.

13.6 Summary
In this chapter, we introduce two ways to achieve steganography in halftone
images, namely DHSED and DHCED. Both methods can embed a binary
secret pattern into two halftone images that come from the same multitone
image. When the two halftone images are overlaid, the secret pattern is re-
vealed. DHCED can further embed a binary secret pattern into two halftone
images from two different multitone images. DHSED operates by introducing
different stochastic phases in the two images. DHCED operates by favoring
certain conjugate values for each pixel and taking on the values only if the
implied distortion is small enough. Both theoretical analysis and simulation