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Audio Watermarking
Charalampos Laftsidis
Artificial Intelligence and Information Analysis Lab
Aristotle University of Thessaloniki
February 2001
The technique’s motiv
Due to contemporary technology, there are
broadly available tools in order to reproduce and
retransmit multimedia data.
Potential of both legal and unauthorized
manipulation
The objective of the watermarking technique
Protection against data piracy.
(Unauthorized copying and redistribution of data).
Rightful ownership authentication
A watermarking system provides owner authentication. It processes the claim of whether the person under
consideration is the owner of the digital data (hypothesis testing).
The output of the system is therefore binary:
Rightful owner or not.
Probabilities of false detection and of false alarm (pfd, pfa).
Watermarking: a data hiding technique(method for secretly and imperceptibly embedding signals
into digital data)
Watermarking system’s requirements
Inaudible watermarks
Statistically invisible watermarks
Similarity of the watermark’s compression characteristics as those of the original signal
Reliable detection scheme
Robustness to deliberate attacks
Robustness to signal manipulation
(filtering, compression, resampling, requantization, cropping, noise corruption, D/A - A/ etc.)
The system’s algorithm should be available to users
The system’s performance should be independent from the signal
Audio masking
The effect of a stronger sound on the loudness and hearing threshold of a weaker one, when the latter lies in the frequency or temporal neighborhood of the former one.
– Masker (host signal)
– Maskee (embedded signal)
The human auditory system is a frequency analyzer consisting of a set of 24 bandpass filters.
Frequency masking
Temporal masking
Different watermarking methods
Watermark embedding in the time domain
Watermark embedding in the frequency domain (temporal masking is unavoidable)
Watermarking MPEG audio streams
Echo-hiding techniques (also used for multi-bit information embedding)
Phase coding method
Modules of a watermarking system
Watermark-signal generation module
Watermark embedding module
Watermark detection module
Watermark generation
Use of a chaotic map (recursive calls of a function).
Thresholding the produced values.
Formulation of a vector of 1 and –1 (actual watermark).
The use of a chaotic map is significant in order to prevent the inverse calculation of the watermark.
Watermark embedding
Segmentation of the original sound data in blocks of N samples.
Generation of a watermark w(i) of length N using a seed (starting point).
Modulation of the watermark, thus producing a signal dependent watermark w’(i):
or
where denotes a superposition law, which can be addition, multiplication, exponential law.
1,,0,1,,0)()( NkNiiNkxixk
10,10),()(' sk NkNiiwaiw
)()()(' iwixaiw kk
Watermark embedding
Filtering of w’(i) through a lowpass filter (a Hamming filter of order L with bl coefficients for example):
Adding the resulting watermark to the original data:
1
0
''' )()(L
lklk liwbiw
)()()( '' iwixiy kkk
Test signal: segment from Vivaldi’s “L’amoroso” concerto for violin.Signal to Noise Ratio (SNR)=22dB
Watermark detection
CorrelationSimple correlation
Circular correlation
The latter case can be calculated through the Fourier transform:
1,,0,)()()(1
0
NnniyixncN
i
)mod)(()()(1
01 Nniyixnc
N
i
)()()( *1 kYkXkC
Watermark detection
Calculation of the filtered watermark vector w’(i) (filtering just the series of 1 and -1)
Calculation of the circular correlation between the test signal and the watermark:
If the signal is watermarked, then:
1
0
)(')mod)((1
)(N
ikk iwNniy
NnS
))(')mod)(()(')mod)(((1
)(1
0
''1
0
N
ik
N
ikk iwNniwiwNnix
NnS
Watermark detection
Definition of a scaling factor:
Calculation of the detection ratio:
If E(w’(i)) is not equal to 0, then
where:
1
0
''' )()mod)((1
)(N
ikk iwNniw
NnT
)(
)()(
nT
nSnr
k
kk
)(
)()()()(
nT
nSNw
wsignnSnr
k
kk
k
1
0
' )(N
i
iww
Watermark detection
Fusion (average) of the detection ratios for all periods:
Calculation of the final detection value:
Comparison of R to a predefined threshold
1
0
)()(sN
kk nrnR
))(max( nRR
Detection results
Receiver operating characteristics (ROC):Choice of threshold’s positionProbability of False Acceptance (Pfa)Probability of False Rejection (Pfr)Plotting Pfa versus Pfr (in logarithmic scale)Definition of the Equal Error Rate (EER)
Parameters
Segment’s size N.Smallest number of segments permitted.Power of the watermark (SNR).Watermark generation map.Watermark’s filtering.Type of embedding:
Multiplicative:Additive:
Fusion among periods.
Detection threshold.
)()()(' iwixaiw kk )()(' iwaiwk
Subjective quality evaluation
Presentation of the original and watermarked versions to a set of listeners.
1st test: try to find the watermarked version among 3 presentations: original, watermarked, original
or original, original, watermarked
2nd test: mark the quality of the watermarked version as: 5. Imperceptible
6. Perceptible, but not annoying
7. Slightly annoying
8. Annoying
9. Very annoying.
Present versions that contain multiple watermarks.
Frequency masking (MPEG-1 psychoacoustic model)
Modification of the watermark according to the spectral characteristics of the original signal.
Calculation of the spectrum
and normalization by a constant value.
(s(n): original signal, w(n): predefined window)
21
010 )2exp()()(
1log10)(
N
n N
nkjnwns
NkS
Frequency masking (MPEG-1 psychoacoustic model)
Identification of tonal components:
where j defines a neighborhood around k and can be up to 6, depending on the value of k.Division of the frequency axis into 24 critical bands, according to the perceptual model of the human ear. The bandwidth of each of those critical bands is defined as 1 Bark.
)1()()1()( kSkSandkSkS
dBjkSkS 7)()(
Frequency masking (MPEG-1 psychoacoustic model)
Calculation of non-tonal components for every critical band from the remaining signal energy.
Calculation of the absolute hearing threshold.
Removal of components that fall below the absolute hearing threshold or of those that are separated by more than 0.5 Barks.
Calculation of individual and global masking thresholds.
Topics to be investigated
The deadlock problem: the method cannot easily distinguish which watermark was embedded first, if a pirate embeds his own one on watermarked data.
Special attacks on the watermark.
Watermarking of short segments of sounds that may be used.
Inability to use the full properties of a high-pass (especially) chaotic generators, because of filtering the watermark during the embedding procedure.
Bibliography
P. Bassia, I. Pitas, N. Nikolaidis “Robust audio watermarking in the time domain”, Dept. of Informatics, University of Thessaloniki, November 2000.L. Boney, A. H. Tewfik, K. N. Hamdy, “Digital watermarks for audio signals”, in Proc. of EUSIPCO ’96, September 1996, vol. III, pp.1697-1700.M. D. Swanson, B. Zhu, A. H. Tewfik, L. Boney, “Robust audio watermarking using perceptual masking”, Elsevier Signal Processing, Sp. Issue on Copyright Protection and Access control, vol. 66, no. 3 , pp.337-355, 1998.W. Kim, J. Lee, W. Lee, “An audio watermarking scheme robust to mpeg audio compression”, in Proceedings NSIP ’99, Antalya, Turkey, June 1999, vol. I, pp.326-330.I. J. Cox, J. Kilian, F. T. Leighton, T. Shammon, “Secure spread spectrum watermarking for multimedia”, IEEE Transactions on Image Processing, vol. 6, no. 12, pp. 1673-1687, 12 1997.K. Nahrsted, “Non-invertible watermarking methods for mpeg video and audio”, in Multimedia and Security Workshop, ACM Multimedia ’98, Bristol, UK, September 1998.D. Gruhl, A. Lu, W. Bender, “Echo Hiding”, in Proceedings of 1st Information Hiding Workshop, Cambridge, U.K., May 1996, pp. 295-316.W. Bender, D. Gruhl, N. Morimoto,, A. Lu, “Techniques for data hiding”, IBM Systems Journal, vol. 35, no. 3 and 4, pp. 313-335, 1996.F. A. Peticolas, R. J. Anderson, “Weaknesses of Copyright Marking Systems”, in Multimedia and Security Workshop, ACM Multimedia ’98, pp. 55-61, Bristol, UK, September 1998.
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