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of image watermarking depends only on a secret key
during extraction when the entire embedding algorithm
may be known. These features of image watermarking
algorithms are essential for the copyright protection of
digital images [1,4].
Many researchers have made great effort in devel-
oping robust watermarking algorithms. Cox et al. [5]
suggested embedding the watermark into the perceptu-
ally significant portion of the whole DCT transformed
image. This watermarking scheme was shown to be
robust against common attacks such as compression,
filtering and cropping. Kunder et al. [6] employed
multiresolution fusion techniques and incorporated a
model of the human visual system (HVS) for water-
mark embedded into the wavelet domain. Barni et al.
[7] proposed a watermarking algorithm based on mask-
ing the watermark according to the characteristics of
the HVS. Nevertheless, these methods are not desir-
able because they are non-blind watermarking.
In general, blind methods are more useful than non-
blind methods, because the original image may not be
available when the detection process is applied. More-
over, blind methods are very suitable for Internet com-
munication scenarios against the attack of IBM [8].
Langelaar et al. [9] proposed the differential energy
watermarking algorithm for JPEG/MPEG streams in
the domain of discrete cosine transform. A set of several
8× 8 DCT blocks were composed and divided into two
parts in order to embed a watermark bit. Wang et al. [10]
proposed a wavelet-based blind watermarking scheme.
The wavelet coefficients of the host image are grouped
into so-called super trees. The watermark is embedded
by quantizing super trees. The trees are quantized in
such a way that they exhibit a large enough statisti-
cal difference, which will later be used for watermark
extraction. Lin et al. [11] improved this watermark-
ing algorithm by using the local significant difference
based on the block-based wavelet coefficients. Every
seven non-overlapping wavelet coefficients of the host
image are grouped into a block, and the watermark
bit is embedded into a block by quantizing the dif-
ference between two maximum wavelet coefficients.
The embedding capacity is constrained by the block
size. On this basis, Run et al. [12] proposed a blind
watermarking method based on wavelet tree quantiza-
tion which can embed a watermark bit in the maximum
wavelet coefficient of a wavelet tree. The watermark
bit is embedded by scaling the magnitude of the signif-
icant difference between the two largest wavelet coeffi-
cients in a wavelet tree to improve the robustness of the
watermarking. During extraction, an adaptive thresh-
old value is designed. A watermark bit 1 is extracted
if the significant difference is greater than the adap-
tive threshold value; otherwise, a watermark bit 0 is
extracted. It is not constrained in a block size and can
promote the capacity of embedding. However, these
algorithms have fatal drawbacks in the security. Once
they are published, the embedded watermarks will lose
their protection.
In the past decade, the chaotic maps have been
used to improve the uncertainty of watermarking.
Yen [13] reported a watermarking scheme based on
chaotic binary sequence. The peak signal-to-noise ratio
(PSNR) is larger than 44 dB, and the extracted water-
marks are still recognizable when the compression ratio
reaches 39 %. Tefas et al. [14] firstly introduced Markov
chaotic sequences into digital watermarking technique
and analyzed the statistical properties of watermark-
ing based on chaotic sequences. Keyvanpour et al. [15]
presented a robust watermarking scheme based on a
chaotic mapping and a dynamic blocking, operating
in the DWT domain. Both watermark embedding and
detection were accomplished without using the origi-
nal image. Ghebleh et al. [16] proposed a robust blind
wavelet domain watermarking scheme based on chaotic
maps. The black and white watermark was embedded
in the mid-band components of a host image accord-
ing to a discrete wavelet transform. The security and
robustness of the proposed scheme were improved at
the cost of embedding capacity. In these literatures, the
chaotic map is regarded as a spread spectrum signal
and used only for watermark detection. However, in
fact, the combination watermarking with chaotic maps
could enable the watermarked image to be resistant to
various attacks as well as to facilitate its performance
such as imperceptibility and security.
In this paper, we propose a new blind watermark-
ing method based on chaotic maps to simultaneously
meet various criteria such as robustness, invisibility
and security in the practical applications. A watermark
bit is embedded in the approximation coefficients of a
wavelet block. The proposed method is different from
those in Run et al. [12], Lin et al. [11] and Wang et
al. [10] which use two trees to embed a watermark
bit. We employed the chaotic maps and embedded the
watermark by scaling the difference of approximation
coefficients in the same block to improve the security
and robustness of the watermarked image. The approx-
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