Cryptography Reference
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distortion points. From the above description, the LGLSB (Lossless G-LSB)
algorithm can operate at a specified distortion value by flexibly modifying
the embedding intensity, or an extension at a given level. The LGLSB also
has an advantage over the RS embedding scheme in embedding capacity for a
comparable distortion, computational complexity. The LGLSB algorithm can
achieve embedding capacities exceeding 1bpp, while RS embeddings capaci-
ties was less than 1 bpp.
13.3.2 Algorithms Based on Histogram Shifting Techniques
Ni et al. [9] proposed a novel reversible algorithm based on histogram shifting
techniques. The algorithm first finds a zero point (no pixel) and a peak point
(a maximum number of pixels) of the image histogram. If zero point does not
exist for some image histogram, a minimum point with a minimum number
of pixels is treated as a zero point by memorizing the pixel grayscale value
and the coordinates of those pixels as overhead information. Paper [9] shifts
peak point towards the zero point by one unit and embeds the data in the
peak point and the neighboring point. The specified embedding process is
illustrated in Fig. 13.7.
Note that original peak point after embedding disappears in the histogram.
Hence, to ensure the reversible restoration, the embedding algorithm needs to
memorize the zero point and peak point as a part of the overhead information.
The algorithm can embed a significant amount of data (5 k to 80 kbits for a
5125128 grayscale image) while keeping a very high visual quality for
all natural images. Specifically, the PSNR of the marked image versus the
original image is guaranteed to be higher than 48 dB.
13.3.3 Algorithms Based on Value Expansion Techniques
Integer DCT Based Bit-Shifting Method
Yang et al.s method [10] is based on the block 88 integer discrete cosine
transform (DCT) domain. It applies the one-bit left shifted operation to all
selected N≤64 AC coe cients, and then embeds watermarking bits in their
LSBs. The parameter selection can be adjusted according to the required vi-
sual quality or embedding capacity. Yang et al. [10] first estimates the pixel
values errors and then sets two thresholds (in the range of [0, 255]) to se-
lect suitable blocks where all pixel values must fall between two thresholds.
These selected blocks are embedded with watermarking bits without concern-
ing overflow or underflow caused by the modification of DCT coe cients. To
differentiate watermarked image blocks from ineligible, or unsuitable blocks,
Yang et al. [10] use additional overhead bits to record the watermarked blocks
locations. These overhead bits are embedded in those blocks, which are proof
against overflows and underflows after doing embedding process twice. The
method is known as a Block Discrimination Method twice-try.
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