Cryptography Reference
In-Depth Information
Type-II algorithms [5]-[12] can be partitioned into three offsets. The first
offset based on lossless compression techniques and contains lossless bit-
plane compression methods in the spatial domain [5] and in the Integer
Discrete Wavelet Transform (IDWT) domain [6]. The reversible RS data-
embedding method is given in [7], and the lossless G-LSB data-embedding
method is given in [8]. The second offset contains the algorithm [9] and is
based on histogram shifting techniques. The third offset based on the value
expansion techniques contains Integer Discrete Cosine Transform (IDCT)
based on a bit-shifting method in [10], and the difference expansion meth-
ods are given in [11, 12]. Type-II algorithms can not cause salt-and-pepper
noise, but can achieve higher embedding capacities, albeit at the loss of
the robust properties of the first category.
The chapter is organized as follows. Section 13.2 and Section 13.3 respec-
tively introduce several existing reversible watermarking algorithms of two
categories. In Section 13.4, an introduction about our proposed reversible wa-
termarking techniques is given. Future research is discussed in Section 13.5.
The performance of related techniques is compared and their respective ad-
vantages and disadvantages are also analyzed in this chapter.
13.2 Type-I Algorithms: Robust Spatial Additive
Watermarks
Robust Spatial Additive Watermarks combined with Modulo Addition first
appeared in a patent by Honsinger et al. [1]. It is owned by the Eastman
Kodak Company. Paper [1] utilizes modulo 256 addition to embed the au-
thentication hash to the original image. The embedding method is equivalent
to the arithmetic formula i
w
= i⊕w = 256
i
256
+mod(i+w, 256), where ⊕
denotes modulo 256 addition, i and w respectively indicate any pixel value and
corresponding watermarking bit coming from the hash function of the orig-
inal image. The symbol⌊⌋denotes the truncation operation to the integer
part, and i
w
stands for the watermarked pixel. At the decoder, the water-
marking bits are extracted from the watermarked image. Then, watermarked
bits are subtracted from the watermarked pixel values to restore the original
pixel values according to the operation: i = i
w
⊕(−w). Modulo
256 addition can be represented as the following permutation: 0→1, 1→
2, , 254→255, 255→0. From the above permutation, pixel values
close to the grayscale value 255 are flipped to zeros and vice versa, so water-
marked image would suffer from the disturbing visual artifact resembling the
salt-and-pepper noise. Macq [2] applied modulo additions and the patchwork
algorithm [3] to achieve reversible data embedding. But papers [1, 2] cannot re-
solve the salt-and-pepper noise caused by modulo additions. De Vleeschouwer
et al. [4] proposed a lossless data hiding algorithm based on the patchwork
theory and effectively avoided the salt-and-pepper noise.
−w = i
w
