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.