Steganography in Halftone Images - Visual Cryptography and Secret Image Sharing - page 348

which has a larger support than the Steinberg kernel. A typical image, Lena,
is shown in Figure 13.2. The corresponding halftone images generated by
Steinberg and Jarvis kernels are shown in Figures 13.3 and 13.4 respectively.
It can be observed that different error diffusion kernels give rise to different
textures in the halftone images. In general, Jarvis gives images with higher
contrast while the Steinberg kernal gives smoother texture. Both are capable
of generating halftone images that mimic the original images when viewed
afar, though tiny details of the original image such as Lena's hair tend to be
masked by the halftone image texture generated by the error kernel.
The size of all the images in this chapter are 512512. Due to limited space,
all remaining halftone figures are generated by the Jarvis kernel only, though
the methods described in the chapter are applicable to any error diffusion
kernels.
13.3 Data Hiding by Stochastic Error Diffusion (DHSED)
Data Hiding for halftone images is quite different from that for multitone
images due to the fact that halftone pixels can take on only two values: 0 and
255. They contain high frequency noise but resemble the original multitone
images when viewed afar. As such, normal data hiding techniques such as
least significant bit (LSB) embedding technique [6] would not work on them
because the resulting stego-images will be effectively the watermark image
and would not resemble the original multitone images even when viewed afar.
Thus, it is necessary to develop special data hiding techniques for halftone
images. Although several data hiding technologies for halftone images have
been proposed before, Data Hiding by Stochastic Error Diffusion (DHSED) is
the first visual cryptography method based on error diffusion.
DHSED is a method that embeds a binary secret pattern into two halftone
images derived from the same underlying multitone image. The binary pattern
should be revealed when the two halftone images are superimposed. The idea
of DHSED is to stochastically create a texture phase shift between the two
halftone images at locations where the watermark is "active" or black (binary
pattern value being zero). The resulting mismatch allows the watermark to
become visible while maintaining the original halftone background. Let X be
the original multitone image and W the binary secret pattern of the same
size. Let Y 1 be a halftone image obtained by applying regular error diffusion
to X. Let Y 2 be the halftone image obtained through DHSED. The problem,
then, is to obtain Y 2 such that W is revealed when Y 1 and Y 2 are overlaid.
We denote the individual pixels at location (i;j) of both halftone images as
y 1 (i;j) and y 2 (i;j), respectively.
The second image Y 2 is generated by applying regular error diffusion to
certain areas in X, but with different error conditions. These areas are ob-