The invention relates to a method and arrangement for extracting data from a host signal. The invention also relates to a method and arrangement for embedding data in a host signal, and to a signal with embedded data.
Blind watermarking is the art of embedding a message in a multimedia host signal, and decoding the message without access to the original, non-watermarked host signal. An example of such a watermarking scheme is disclosed in B. Chen and G. W. Wornell: “Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding”, published in IEEE Transactions on Information Theory, Vol. 47, No. 4, May 2001. The known watermarking scheme is a quantization-based watermarking scheme. The message is embedded in the host signal by quantization of the host signal, using a quantization step size which maps an input sample into an output sample which uniquely identifies a message symbol embedded in the output sample.
It has been shown in literature that blind watermarking withstands additive white Gaussian noise (AWGN) attacks as well as if the decoder had access to the original host signal. However, in practical watermarking applications, attacks are not constrained to AWGN attacks. A particularly interesting class of attacks is amplitude modification. This class of attacks includes scaling of the watermarked signal, e.g. contrast reduction for image data, or addition of a constant DC value. Unlike spread-spectrum watermarking schemes, which are typically believed to survive such attacks without significant losses, quantization-based watermarking schemes are vulnerable to amplitude modifications. This problem is particularly significant in quantization-based watermarking schemes that also use dithering. Dithering is the process of assigning different offsets to different samples of the watermarked signals so as to avoid that the embedded data can be detected by simply inspecting the structure of the watermarked signal. The series of dither values (“dither vector”) is a secret key which is known to the receiver. Without knowledge of the dither vector, it is impossible to extract the message in a reliable manner.
It is an object of the invention to provide a method and arrangement for extracting the data even if the amplitude of the watermarked signal has been modified.
In accordance with the invention, this is achieved by computing the quantizer step size of the received media signal from a histogram of selected signal samples having a predetermined range of dither values. The invention exploits the insight that, in case of an amplitude scaling attack, the quantizer step size used by the watermark embedding algorithm has been scaled by the same factor. It is achieved with the invention that the amplitude scaling factor can be calculated (or at least estimated) as the ratio of the step size computed by the decoder to the step size used by the embedder. This allows the received watermark signal to be re-scaled, and the embedded message to be extracted from the re-scaled signal by a conventional decoder. An embodiment of the decoder extracts the embedded message on the basis of the computed quantizer step size, even if the original quantizer step size (and thus the scaling factor) is unknown.
In a preferred embodiment, the selected signal samples are predetermined signal samples in which a predetermined data symbol has been embedded. This embodiment requires knowledge of the samples having the predetermined data symbol embedded therein. To this end, an embedder in accordance with the invention embeds said predetermined data symbol in predetermined samples of the host signal.
We consider digital watermarking as a communication problem. A watermark message is encoded into a sequence of watermark letters or symbols dn. The elements dn belong to a D-ary alphabet {0,1, . . . ,D-1} of size D. In many practical cases, binary watermark symbols (D=2) will be used.
In practice, the watermarked signal has undergone signal processing, passed through a communication channel, and/or it has been the subject of an attack. This is shown in
In general, the watermark encoder 71 and decoder 72 involve a random codebook that is available at both ends. In the encoder 71, the codebook maps an input sample xn onto an output sample sn, the output sample value being dependent on the message symbol dn and the key kn. The decoder 73 uses the same codebook to reconstruct the message symbol dn from the sample sn. Sub-optimal but more practical versions of the system are based on dithered uniform scalar quantization as will be explained hereinafter.
In the simplest form of scalar quantization, message data is embedded in the media signal by quantizing the signal samples xn (all samples or selected ones) to a selected one of a number of sets of discrete levels, the selected set being determined by the data symbol to be embedded. This simplest form of watermark embedding is illustrated in
The data accommodated in the watermarked signal can easily be detected by inspecting the discrete signal values sn. In low-bit modulation schemes, it even suffices to inspect the least significant bit of sn. If it is 0, then dn=0. If it is ‘1’, then dn=1. In order to provide secure transmission of the message, different offsets are assigned to different output signal samples sn. This is referred to as dithering. In
A mathematical expression of the dithered uniform scalar quantization embedding process can be derived as follows. The output signal sn can be written as:
sn=(Dm+dn)×δ+vnδ (1)
The value sn must be as close as possible to the input value xn, which can be expressed as:
This condition is fulfilled if
Substitution of (2) in (1) yields:
An alternative expression can be obtained by introducing Δ=Dδ and
and denoting the operation
by an operator QΔ{●} to. The latter operator denotes conventional scalar uniform quantization with step size Δ, hence the name of this practical embedding scheme. The data embedding process can now be expressed as:
The data embedding process can even be more generalized. It is not necessary to project xn on discrete points of the sn-axis. The data symbols dn may equally be represented by distinct ranges of values sn, as has been shown in
sn=xn+α(zn−xn)
where zn denotes the discrete points as defined above by equation (4). Accordingly,
yn=QΔ{sn−knΔ}−(sn−knΔ) (6)
As illustrated in
It should be noted that the schematic diagrams of the embedder and detector shown in
Equation (7) can be understood if it is considered that
is the number of times step size δ fits into sn−vnδ (see
In any case, reliable detection requires that besides the secure key kn (or vn) also the step size Δ (or δ) is known. However, as has been shown in
where σw2 represents the embedding distortion.
It should be recalled that generation of the intermediate signal yn requires knowledge of the quantizer step size and the secure key kn. The quantizer step size of the attacked signal r, which is now Δr=gΔ due to the scaling by the factor g, has to be estimated from the received data r. Note that estimation of Δr is equivalent to estimation of g when Δ is known. Here, the more general point of view is taken, and estimation of Δr is considered.
An estimation of Δr (and an estimation of the offset roffset, if any), can be obtained by analyzing a histogram of received samples rn. However, as mentioned before, dithering has been applied to avoid that the embedded data can be easily detected by simply inspecting the signal samples. Because of the dithering, there is no structure in the received samples. The histogram of received samples is more or less a continuous graph in practice.
Recall that dithering has been created by assigning offsets knΔ (or vnδ) to the samples sn. Due to the scaling by the factor g, the offsets of the received samples rn are knΔr, (or vnδr). These offsets are unknown at the receiver end because g is unknown. The key kn, however, is known. Therefore, in accordance with one aspect of the invention, the histogram is derived from only those samples that have a given predetermined key value kn assigned thereto. Reference numeral 91 in
Creating a statistically reliable histogram from only those samples that have a given predetermined key kn assigned thereto requires a large number of samples having that key to be collected. This may take a too long time. This disadvantage is mitigated in an embodiment in which one or more histograms are created for signal samples with keys k, in a range:
The histograms (or histograms) thus obtained will show wider peaks with the relative distance δr. Moreover, the peaks are shifted to the right because the offset ranges are positive.
In a further embodiment, the histogram is created from samples rn having a predetermined data symbol dn embedded therein. Such an embodiment has the advantage that the peaks will have a larger relative distance Δr (D times the distance δr of the previous embodiment), and larger maximum-to-minimum ratios. This embodiment allows the step size Δr to be calculated more accurately. In order to render it possible that the receiver can select samples having the predetermined data symbol, the embedder is arranged to embed a “pilot” sequence of said data symbols in the signal. The predetermined pilot symbol, further referred to as dpilot, is one of the available data symbols {0,1, . . . D-1}, for example dpilot=0. The pilot sequence is dithered like the normal signal samples and thus securely embedded. Without knowing the secure key k, no structure in the watermarked signal is visible.
The pilot sequence can be. accommodated in the signal, inter alia, by embedding a pilot symbol dpilot in every kth sample of the input signal, or by (preferably repeatedly) inserting a fixed-length series of pilot symbols in the embedded message. Relevant to the invention is only that the receiver knows which samples r, have an embedded pilot symbol. As far as histogram analysis is concerned, only the samples rnhaving the embedded pilot symbol will be considered hereinafter.
Again, the histogram is generated from those samples having a given predetermined key value kn (for example, kn=0) or a predetermined range of key values as defined by equation (8).
The histogram 100 is derived from one third of the pilot samples (M=3). Similar histograms can be derived for m=1 (0.33≦kn<0.67) and m=2 (0.67≦kn<1), so that all samples of the pilot sequence are taken into account for the histogram analysis. They are denoted 101 and 102 in
In case a pilot sequence is used, a selection signal S is applied to the histogram analysis circuit to identify the signal samples rn having the embedded pilot symbols dpilot. At the transmitting end, a switch 76 being controlled by the same selection signal S is used to apply either a message symbol m or a pilot symbol dpilot to the embedder 71.
The system shown in
A practical embodiment of the histogram analysis circuit will now be described for application in the embodiment using a pilot sequence. It can be implemented in hardware or software. First, the whole range of sample values rmin≦rn≦rmax is divided into Lbin bins. For each bin, the histograms pr,m(b) are computed, where bε{0,1,.. .,Lbin-1} is the bin index, and mε{0,1, . . . ,M-1} indicates the considered range of key values kn. For M=3, this will yield 3 “conditional” histograms per bin that resemble the histograms 100, 101, and 102 shown in
For Gaussian distributed rn, but also for other typical signal distributions, empty and almost empty bins occur mainly at the tails of the histograms. Therefore, it is useful to also weight the normalized histograms with a window function W(b) that gives a different weight to the tails. In that case, the Fourier spectra are computed in accordance with:
All M spectra can be combined in an elegant way since it is known that the maxima in the different conditional histograms are shifted against each other by Δr/M. This shift corresponds to a multiplication by
in the Fourier domain so that the overall spectrum can be obtained as:
where LDFT is the length of the discrete Fourier transform. The offset roffset can be derived from the argument arg{A(f0)} of the complex Fourier spectrurn.
Disclosed are a method and arrangement for embedding data (dn) in a host signal (xn) using dithered quantization index modulation (71), and extracting said data from the watermarked signal. A problem of this embedding scheme (71) is that the amplitude of the watermarked signal (sn) may have been scaled (72) unintentionally (by a communication channel) or intentionally (by a hacker). This causes the quantization step size (Δr) of the received signal (rn) to be unknown to the extractor (73) which is essential for reliable data extraction. The invention provides making a histogram (74) of those signal samples that have substantially the same amount of dither, and analyzing said histogram to derive an estimation of the step size (Δr) therefrom. In a preferred embodiment, a pilot sequence of predetermined data symbols (dpilot) is embedded (76) in selected (S) samples of the host signal.
Number | Date | Country | Kind |
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01204888.0 | Dec 2001 | EP | regional |
Filing Document | Filing Date | Country | Kind |
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PCT/IB02/04898 | 11/20/2002 | WO |