Ph.D. thesis defense

Digital watermarking methods applied to non-additive channels Ph.D. candidate: M. Scagliola Tutor: P. Guccione Research Doctorate Course in Information Engineering

Introduction to digital data hiding
Quantization-based data hiding methods
Providing invariance to power-law attack for quantization-based data hiding
Data hiding robust to linear filtering for colored hosts
Conclusions
Michele Scagliola, DEE – Politecnico di Bari Torino , February 25 2010 Outline

At a very general level digital watermarking, or data hiding, is a way of hiding a message (the watermark ) within a multimedia content (the host signal )
Applications
Copyright protection
Authentication
Compression
Covert communications
Broadcast monitoring
ecc.
Typical requirements for a watermarking system:
Imperceptibility of the watermark
Capacity: the amount of emebedded information
Robustness: the watermark is resistant to attacks
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Digital watermarking: a brief introduction

Definition: watermarking is a mechanism to create a communication channel that is multiplexed into original content By adopting a communication point of view: Watermark signal Watermarked signal Attacked signal Estimated message Host signal Error probability Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Watermarking as communications Message

According to a communication approach: MSE-based metrics Data to Watermark Ratio: Watermark to Noise Ratio: being Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Distortion measures

Filtering
Compression
Related with the content type
(images, audio, video, ecc.)
Attacks to robustness: every processing applied to the marked content that increases the probability of error of the data hiding channel Constraint: the attacked content has an acceptable perceptual quality
Examples:
AWGN
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Attack channel

It aims to change the reference of the watermarked signal, so that the decoder is no more able to retrieve the hidden information
Theoretical model:
Offset
Amplitude scaling
Gamma correction
LTI filtering
Weak perceptual effect but heavy impact on watermark retrieving Achieving robustness to desynchronization is an important challenge Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Desynchronization attack channel

Realizes side-informed data hiding exploiting the knowledge of the host signal at the embedder to minimize the introduced distortion
Dither modulation:
embedding is realized through host data quantization
decoding based on minimum Euclidean distance
2 Δ Δ m=1 m= -1 m=-1 m=1 Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Quantization-based data hiding

Pros:
“ Provably good” methods no decoding errors for
Robust to AWGN channel
High capacity capability
Host signal fidelity is preserved
Cons:
Extreme sensitivity to valumetric distortions
applied pointwise to all the host samples modifying the original value, i.e. gain scaling Decoding errors occur for Δ m=-1 m=1 Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Quantization-based data hiding

It can be considered somewhat solved in literature by various approaches, such as Rational Dither Modulation (RDM) RDM uses a variable quantization step-size which scales according to the gain on the channel. Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Fixed gain attack and RDM

RDM asymptotically approaches the BER of DM but being also invariant to constant gain scaling Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Fixed gain attack and RDM

The power-law attack consists of a constant exponentiation and a constant gain scaling of the amplitudes of the watermarked signal: Open problem: Coping with nonlinear distortions The power-law attack models common processings such as gamma compression Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Power-law attack

Mapping to hyperbolic angle:
Quantization-based technique invariant to gain scaling are well-known in literature (RDM)
Hyperbolic RDM: using hyperbolic mapping in conjunction with RDM, the decoder output is expected to be intrinsically invariant to both gain scaling and exponentiation. Gain is cancelled out by the ratio Exponent becomes a gain scaling The idea: perform the embedding in a power-law attack invariant domain Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Providing robustness to power-law attack

k-th host sample Function computed on the previous watermarked samples The k-th sample in the hyperbolic angle representation results Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Hyperbolic RDM: hyperbolic mapping The function h belongs to the set : The geometric mean belongs to this set:

Inverse mapping: Host signal Watermaked signal Transformed domain h RDM encoder Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Hyperbolic RDM: embedding

The information bits are retrieved applying the RDM decoder to the estimated marked samples in the hyperbolic angle domain: The decoder output results intrinsically invariant to the power-law attack: RDM decoder h Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Hyperbolic RDM: decoding

For large memory vectors, the Data to Watermark Ratio has been analytically evaluated: Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Performance analysis: DWR

Under the hypothesis of Gaussian host, high DWRs and memory vectors going to infinity, the error probability has been analytically evaluated Additive noise in hyperbolic domain results in having pdf the error probability has been computed from Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Performance analysis: bit-error rate

The DM and the RDM outperform the hyperbolic RDM
Noise sensitivity can be ascribed to logarithmic transformation
For Gaussian i.i.d. distributed host samples and DWR = 25 dB Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results: AWGN channel

The BER of hyperbolic RDM is not varied by the power-law attack
The BER of other DM-based techniques is roughly a half
For Gaussian host, DWR = 25 dB, and Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results: power-law attack

Quantization-based data hiding schemes are not designed to cope with desynchronization channels, such as filtering LTI filtering attack: Linear time invariant (LTI) filtering adds to the watermarked signal a host-dependent noise that increases with the host power Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 LTI filtering attack Discrete Fourier Transform – Rational Dither Modulation (DFT-RDM) was designed to cope with LTI filtering attack Attack filter is totally unknown at both the embedder and the decoder

Convolution theorem:
Rational Dither Modulation: gain invariant quantization-based method
LTI filtering can be addressed by applying RDM in the Fourier domain
In real applications it is used discrete Fourier transform in a block-by-block basis
Limited computational complexity
Filter effect on received signal is not purely multiplicative
Additive self-noise is produced by the DFT implementation
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM: the key idea

An RDM-like channel is constructed on each DFT channel: Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM

DFT-RDM exhibits low per-channel error probabilities for white Gaussian host But it is also shown that high error probability occurs for non-white, non-Gaussian and non-stationary hosts (audio signals are used as case study) Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Performance analysis of DFT-RDM

We consider non-white Gaussian host signal X modeled by an AR process: Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts Per-channel host signal power Per-channel host watermark power, from the properties of RDM, is

Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts A larger watermark signal is produced on those DFT channels having stronger spectral content Different RDM-like channel have different robustness against additive noise Per-channel host signal power Per-channel host watermark power, from the properties of RDM, is

Received signal: Per-channel multiplication error power Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts Depends on the host psd: multiplication error is a self-noise term Depends on the attack filter

The knowledge of the per-channel host power and of the per-channel multiplication error power allow to analytically predict the per-channel error probability Per-channel BER with N=256 and DWR =25 dB Low-pass attack filter with Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts

We aim at improving the DFT-RDM for non-white hosts
No knowledge about the attack filter
Embed the same watermark power in every DFT channel
Perform DFT-RDM on the host signal after whitening filtering W-DFT-RDM does not incur in any penalty in terms of embedding distortion and payload w.r.t. DFT-RDM W-DFT-RDM for non-white hosts is expected to have the same performance of DFT-RDM for white hosts Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Whitened DFT-RDM

DFT-RDM ( ) has an overall error probability smaller than that of
W-DFT-RDM ( )
N = 256 and DWR = 25 dB
Low-pass filter with cut-off frequency
Whitening does not assure the best BER for every attack filter Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results

W-DFT-RDM ( ) outperforms DFT-RDM ( )
N = 256 and DWR = 25 dB
Band-pass filter
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results

Then we tested W-DFT-RDM with audio clips in order to verify the performance improvement w.r.t. DFT-RDM The whitening filter resembles the psd of an average audio signal Overall error probabilities for band-pass filter The BERs for W-DFT-RDM are always lower than those for DFT-RDM Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results for audio signals

Then we tested W-DFT-RDM and DFT-RDM with a ten-band audio equalizer as attack filter Overall error probabilities for audio equalizer The improvement given by W-DFT-RDM is increased and acceptable BERs are achieved Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results for audio signals

Research activity has been focused on robustness to non-additive channels for quantization based data hiding methods
Hyperbolic RDM has been proposed as a novel quantization-based method invariant to power-law attack
The developed data hiding methods have been validated by theoretical analysis and experiments
The analysis of DFT-RDM has been extended to non-white hosts and Whitened DFT-RDM has been proposed
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Conclusions

Achieve lower BERs for Hyperbolic RDM
Extend DFT-RDM to non-stationary signals through host adaptive and time-varying whitening filter
Combine Hyperbolic RDM with perceptual considerations in order to be applied to “real-world” signals
Deep analysis of W-DFT-RDM for audio files and MP3 compression
Combine DFT-RDM with perceptual considerations
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Guidelines for future works

Scagliola, M. and Guccione, P., “Rotation Invariant Feature Extraction for Watermarking”, Proceedings of International Conference on Signal Processing and Multimedia Applications (SIGMAP 2008) , Porto (Portugal), 26-28 July 2008.
Guccione, P. and Scagliola, M., “Hyperbolic RDM for Nonlinear Valumetric Distortions,” Information Forensics and Security, IEEE Transactions on , vol.4, no.1, pp.25-35, March 2009.
Scagliola, M. and Guccione, P., "Providing invariance to nonlinear valumetric scaling for quantization based watermarking," Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on , vol., no., pp.1489-1492, Taipei (Taiwan), 19-24 April 2009.
Scagliola, M. and Guccione, P., “Geometric distortion resilient watermarking based on a single robust feature for still images”, in Communications in Computer and Information Science , vol. 48, November 2009, pp. 345–357, e-Business and Telecommunications, Springer Berlin Heidelberg.
Scagliola, M., Perez-Gonzalez, F., and Guccione, P. , “High-rate data-hiding robust to linear filtering for colored hosts,” EURASIP Journal on Information Security , vol. 2009, Article ID 914937, 14 pages, 2009.
Scagliola, M., Perez-Gonzalez, F., and Guccione, P. , “An Extended Analysis of Discrete Fourier Transform – Rational Dither Modulation for Non-white Hosts”, Information Forensics and Security, 2009. WIFS 2009. First IEEE International Workshop on , vol., no., pp. 146-150, London (UnitedKingdom), 6-9 Dec. 2009.
Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Publications

Ph.D. thesis defense

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