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42 UEC Int’l Mini-Conference No.54

Figure 1: Halftoning structure based on the error diffusion method.

grayscale value and the binarized result—is calcu-
lated as shown in Equation (2). This error is not
discarded; instead, it is propagated to neighbor-
ing unprocessed pixels using a weighted error filter.
This redistribution helps preserve the local intensity
structure of the original image.
(a) (b) (c)

e(i, j) = b(i, j)−u(i, j), (2) Figure 2: Coefficients: (a) Floyd-Steinberg, (b)
The error distribution is controlled by a convolu- Jarvis, (c) Stucki.
tion mask H, which determines how the quantization
error is spread to adjacent pixels. Before quantizing By increasing the diffusion area, these methods
each new pixel, it receives the accumulated influ- offer improved compensation for the local intensity
ence of previously propagated errors, as expressed in loss caused by binarization, which results in more
Equation (3). The choice of filter H directly affects visually accurate halftone representations. Figure 2
the visual quality and tonal accuracy of the resulting illustrates the error propagation patterns of these fil-
halftone image. ters, highlighting how they differ in terms of neigh-
borhood coverage and weight distribution [9].
u(i, j +1) = x(i, j +1)−H ∗e(i, j), (3)

In this equation, the operator ”∗” denotes the con- 2.3 Chaotic Encryption and Checksum
volution between the quantization error e(i, j) and Embedding for Data Integrity
the diffusion kernel H. The value u(i, j + 1) repre-
sents the updated grayscale level of the next pixel To enhance data security and integrity in reversible
in the scanning order, after incorporating the redis- data hiding, Parah et al. proposed a technique that
tributed error from the current pixel. combines chaotic encryption with checksum veri-
The convolution mask H, often referred to as the fication [10]. Chaotic systems, due to their sensi-
error diffusion filter, governs how the quantization tivity to initial conditions and inherent non-linear
error is spread among neighboring pixels. Its co- behavior, provide a robust mechanism for protect-
efficients determine not only the number of affected ing embedded information through pseudo-random
pixels and their relative positions but also the weight sequences. In their method, the Electronic Patient
or influence each receives. The design of H is there- Record (EPR) and a fragile watermark are encrypted
fore crucial, as it directly impacts the smoothness using a logistic map-based chaotic system. This
and tonal accuracy of the halftone image. system dynamically alters the bitstream using log-