Steganography in Halftone Images - Visual Cryptography and Secret Image Sharing - page 344

error diffusion [2]. Ordered dithering uses straightforward 1-bit quantization
with fixed pseudo-random threshold patterns to give halftone images with rea-
sonable visual quality. Error diffusion also performs simply 1-bit quantization
but allows the 1-bit quantization error to be fed back to the system and thus
can achieve higher visual quality than ordered dithering.
Sometimes it is desirable to hide watermarking data in halftone images.
Some halftone image watermarks are designed to be fragile and are useful for
authentication and tamper detecting of the halftone images. Some halftone
image watermarks are designed to be robust and are useful for copyright
protection. In some applications, the data are to be embedded into a single
halftone image and some special method can be used to read the hidden
data. In other applications, visual patterns are hidden in two or more halftone
images such that, when they are overlaid, the hidden visual patterns can be
revealed. This kindly visual pattern hiding is also called visual cryptography.
This chapter is about visual cryptography in error diffused halftone images.
The chapter is organized as follows. Section 13.2 introduces the basic error
diffusion technique. Section 13.3 introduces a visual cryptography method
for error diffused images called Data Hiding by Stochastic Error Diffusion
(DHSED) [3]. Section 13.4 introduces an improved method called Data Hiding
by Conjugate Error Diffusion (DHCED) [4]. Section 13.5 gives theoretical and
empirical analysis of DHSED and DHCED. At last, Section 13.6 will give a
summary of this chapter.

13.2 A Review of Error Diffusion
In this section, we will briefly introduce a halftoning method called Error
Diffusion. The method that we will describe is by no means the only way to
achieve halftoning, but is a popular approach that gives good visual quality
while maintaining reasonable complexity. The error diffusion process converts
a multitone image to a halftone one by distributing the error introduced at the
current pixel to a neighborhood of yet unprocessed pixels. The neighborhood,
as well as the weights in the distribution, is described by a set of positions
and weights known as an error kernel. This diffusion of error across a region
allows the local intensity of the halftone image to be preserved approximately.
Consider a multitone image with pixels defined over the range of 0 (black)
to 255 (white). Let h(k;l) be an error kernel dened over a neighborhood N.
For example, the common Steinberg kernel [2] is

1
16

7

3 5 1

dened over the neighborhood N = f(0; 1); (1;1); (1; 0); (1; 1)g. Here we have
used to indicate the location of the current pixel. Let (i;j) be the current