September 29, 2008 18:14 WSPC/INSTRUCTION FILE LogoMark-IJIG
Optimal Rate Allocation for Logo Watermarking 5
and distributed over the host to maximize the fidelity of the extracted logo, given
the overall host distortion, compared to the close works,
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where the property
of the logo as an image has been generally ignored. It can also be regarded as a
form of side-informed approaches summarized by Cox et al.
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Rather than exploiting
the host side information to optimize the detector design, both host and logo side
information is used to achieve joint redundancy reduction and logo embedding in an
optimal way. The optimality of the proposed scheme is not universal, but under the
rate-allocation framework. The new algorithm is tested to be robust to various types
of attacks. Our prior work on the subject was published as a conference paper.
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Compared to that, this work has a more detailed and articulated presentation
and includes more comparisons with other methods in terms of the fidelity of the
extracted logos for different combinations of host and logo images. Besides, the
extension of the new watermarking approach to the application of image-in-image
embedding is considered in the current paper.
The rest of this paper is organized as follows. In Section 2, the new logo wa-
termarking scheme is introduced. Theoretical derivation is presented in detail in
Section 3. Numerical results are given in Section 4 to verify its improved perfor-
mance over existing methods. Additional experimental results are provided to show
the applicability of the new approach to general image-in-image embedding. Section
5 concludes this paper.
2. The Proposed Logo Watermarking Scheme
In this section, a novel logo watermarking scheme using multi-level reversible
wavelet decomposition to both host and logo images is presented. L is used to
denote the wavelet transform level of the host and h
b
i
, x
b
j
to denote the wavelet
coefficients of the host and logo, respectively, where b is the subband index and i, j
are the coefficient indices.
The central idea of the embedding mechanism is shown in Fig. 1, in which the
suggested decomposition level is L = 4, and the logo is decomposed into L −1 = 3
levels. The low-low frequency band (LL) of the host is not used for hiding since
a small distortion in the LL subband could cause a relatively large artifact in the
watermarked image. Instead, the logo LL subband is embedded into the high-high
subband (HH) of the highest level of the host, as indicated by the top arrow in Fig. 1.
For the remaining subbands, the logo coefficients are inserted into the corresponding
host subbands with the same decomposition level and orientation. In other words,
the logo subband b is associated with the host subband b for b = 0, 1, . . . , (3L −2).
The detail of the logo embedding scheme will be described after a review of RWT
and the HVS model in the following.
2.1. Reversible Wavelet Transform
Reversible wavelet transform (RWT) has been widely used for lossless compression,
especially in JPEG2000,
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which involves only integer-to-integer computation.
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