Principles of Digital Watermarking

Principles of Digital Watermarking
Ingemar J. Cox, Matt L. Miller, and Jeffrey A Bloom

Course outline Part 1: Introduction and Applications
Part 2: Basic Algorithms and Concepts Part 3: Advanced Watermarking Course outline

Part 1: Definitions and Applications

Definitions and Applications: Outline
Definitions of watermarking Properties of watermarking systems Watermarking applications Conclusions Definitions and Applications

Definitions of watermarking
Without common definitions, various approaches and technologies cannot be compared. Definitions and Applications

Definitions of watermarking: Our definition
Watermarking is the practice of unobtrusively modifying a work of art (image, song, software program, geometric model, etc.) to embed a message about that work. Multimedia watermarking is the practice of imperceptibly altering a work (image, song, etc.) to embed a message about that work. This tutorial will concentrate on multimedia watermarking. We assume that the work is a representation of still or motion imagery or sound. Basic concepts may apply to other types of works. We further illustrate with imagery as that was the easiest to represent in a book. Definitions and Applications

Definitions of watermarking: Basic design of a system
Original work Watermark embedder Watermark detector Watermarked work (looks like original) Detected message Message (regarding work) Definitions and Applications

Definitions of watermarking: Other definitions
Imperceptibility is not always considered essential (allows for visible watermarking). Sometimes more broadly defined as any data hiding (i.e. hidden data need not relate to work). Sometimes more narrowly defined as owner identification (watermarks must indicate identity of owner). Definitions and Applications

Definitions of watermarking: Related terms
Data hiding: any technology for preventing adversaries from perceiving or finding data. Steganography: keeping the existence of messages secret by hiding them within objects, media, or other messages. Modification may be of the file format rather than of the essence of the work. Watermarking is a special case. In watermarking, the secrecy of the message is not essential. Definitions and Applications

Definitions of watermarking: Related terms
Watermarking is the practice of unobtrusively modifying a work of art (image, song, software program, geometric model, etc.) to embed a message about that work. Steganography is the practice of undetectably modifying a work to embed a message.

Unobtrusive Original Undetectable

Definitions and Applications
Properties of systems Understanding, comparing, and selecting watermarking approaches or technologies takes place in the context of system properties. Definitions and Applications

List of properties to be discussed
Embedding effectiveness Fidelity Data payload Blind vs. informed detection False positive rate Robustness Security Definitions and Applications

A note before we begin … When we say “random work”, we mean a work drawn from an application-dependent distribution of works. Examples: x-rays, animation, natural image, classical music, speech, etc. When we say “random watermark”, we mean a watermark message drawn from the set of possible messages. Definitions and Applications

Embedding effectiveness
A system’s embedding effectiveness is the probability it will succeed in embedding a random watermark in a random work. Random work Watermark embedder Watermark detector Message detected correctly? Random message Definitions and Applications

Embedding effectiveness
Why might embedding effectiveness be less than 100 percent? In some cases, it is not possible to embed required amount of information imperceptibly. Actual implementations usually involve some round-off and truncation before watermarked work is stored, which sometimes make watermark undetectable. Definitions and Applications

Properties of systems: Fidelity
A system’s fidelity is the perceptual similarity between marked and unmarked works. Random work works appear sufficiently similar? Watermark embedder Watermarked work Human observer Random message Definitions and Applications

Properties of systems: Data payload
A system’s data payload is the amount of information that it can embed in a single work. … Random message Watermarked work Random work Watermark embedder Definitions and Applications

Blind vs. informed detection
An informed detector requires some information about the original, unwatermarked work. A blind detector does not. Required by informed detector Original work Watermark embedder Watermark detector Message Definitions and Applications

Properties of systems: False positive rate
A system’s false positive rate is the frequency with which it is expected to detect watermarks in unwatermarked works. Watermark detector Random, unwatermarked work Watermark detected? Definitions and Applications

Properties of systems: False negative rate
A system’s false negative rate is the frequency with which it is expected to NOT detect watermarks in watermarked works. Watermark detector Random, watermarked work Watermark detected? Definitions and Applications

Properties of systems: Robustness
A watermark’s robustness is its ability to survive normal processing (e.g. lossy compression, noise reduction, etc.). Random work Watermark embedder Watermark detector Message detected correctly? Random message Normal processing Definitions and Applications

Properties of systems: Security
A watermark’s security is its ability to resist hostile attacks, specifically designed to defeat the purpose of the watermark. Types of attacks Unauthorized embedding (forgery) Unauthorized detection Unauthorized removal Definitions and Applications

Security – unauthorized embedding
Random work Watermark detector Forged Message detected Watermarked work Unauthorized embedding by an adversary Forged message Definitions and Applications

Security – unauthorized removal
Random work Watermark embedder Watermark detector Message detected correctly? Random message Hostile processing by an adversary Definitions and Applications

Security – unauthorized detection
Original Work Watermark embedder Adversary can detect message? Message Attempt at detection by adversary Definitions and Applications

Watermarking applications
Watermarking may be appropriate for applications in which data about a work must be imperceptibly embedded. Different applications place different requirements on system properties. Definitions and Applications

List of examples discussed
Broadcast Monitoring Owner Identification Proof of Ownership Transaction Tracking Content Authentication Copy Control Definitions and Applications

Broadcast monitoring Original content Content was broadcast! Broadcasting system Watermark embedder Watermark detector Definitions and Applications

Broadcast monitoring Monitor when and whether content is transmitted over broadcast channels, such as television or radio Verify advertising broadcasts (1997 scandal in Japan) Verify royalty payments ($1000 of unpaid royalties to actors per hour of broadcast) Catch instances of piracy Definitions and Applications

Owner identification Alice Original work Alice is owner! Watermark embedder Distributed copy Watermark detector Definitions and Applications

Owner identification Watermark identifies owner of copyright, similar to a copyright notice Help honest people identify rightful owner Notify people of copyright In US, until 1988, such notice was required to retain copyright Since 1988, presence of notice increases possible reward in lawsuits Definitions and Applications

Owner identification The problem with text: this well-known image … Definitions and Applications

Owner identification … is a pirated part of a larger image. Definitions and Applications

Proof of ownership Alice Original work Alice is owner! Watermark detector Watermark embedder Distributed copy Bob Definitions and Applications

Proof of ownership Watermark is used to prove ownership in a court of law Differs from owner identification in two ways Intended to carry burden of proof Watermark need not be detectable by anyone other than owner (allows informed detection) Definitions and Applications

Transaction tracking Alice Watermark A Honest Bob Original work Evil Bob B:Evil Bob did it! Watermark B Watermark detector Unauthorized usage Definitions and Applications

Transaction tracking Watermarks record transaction histories of content, typically identifying first authorized recipient Identifying pirates (DiVX corporation) Identifying information leaks (M. Thatcher, movie dailies) Definitions and Applications

Transaction tracking The MPAA estimates that piracy costs the US film industry $3B per year One source of material is the annual distribution of Oscar screeners to the 5,803 voting members of the Academy

Transaction tracking Thomson system enabled the MPAA to distribute individually-watermarked VHS and DVD screeners to its 5,803 eligible voting members Screeners appeared on the internet The Last Samurai Something's Gotta Give Mystic River Actor Carmine Caridi expelled from MPAA

Content authentication
Watermark embedder Watermark detector Definitions and Applications

Content authentication
Watermark is used to detect modifications applied to cover work Exact authentication: work is inauthentic if even one bit has changed Selective authentication: work is inauthentic only if significantly changed Tell-tale watermarks/localization: identify what changes have been made Definitions and Applications

Copy control Watermarks indicate whether content may be copied Record control: recording devices contain detectors and refuse to record copyrighted material Playback control: players contain detectors and refuse to play pirated material Definitions and Applications

Copy control Compliant player Compliant recorder Legal copy Playback control Record control Non-compliant recorder Illegal copy Definitions and Applications

Conclusions Definitions and Applications

Conclusions: Stuff not covered
Erasability (whether watermark can be perfectly removed) Cipher and watermark keys Modification and multiple watermarks Cost

Conclusions: Take Away
Watermarking may be appropriate for applications in which data about a work must be imperceptibly embedded. Different applications place different requirements on system properties.

Key properties include Embedding effectiveness Fidelity Data payload Blind vs. informed detection False positive rate Robustness Security

Digression: The politics of DRM
Why does Hollywood care about piracy? Loss in revenue But some level of piracy actually stimulates sales Evidence that peer-to-peer file sharing affects sales is mixed But has been used to control the evolution of the digital market

Digression: The politics of DRM
Why do computer and consumer electronics companies care about DRM? Need content owners to provide content in new digital formats Conflict of interests Customers don’t want DRM Legal and business contracts impose DRM

Course outline Part 1: Definitions and Applications
Part 2: Basic Algorithms and Concepts Part 3: Informed Watermarking Course outline

Part 2: Basic Algorithms and Concepts

Basic Algorithms and Concepts: Outline
Algorithmic building blocks Robustness issues Security issues Conclusions

Algorithmic building blocks
Over the past 5 to 10 years of research, several ideas have emerged as basic building blocks of watermarking systems.

A simple watermark embedder
Given … Watermark pattern, w Cover image co Embedding strength a Compute watermarked image, cw, as Basic Algorithms and Concepts

A watermarked version of this …
Basic Algorithms and Concepts

Basic Algorithms and Concepts
…looks like this Basic Algorithms and Concepts

Informed detection Given Possibly watermarked image c Original cover image co Subtract original to obtain watermark pattern (if present) Basic Algorithms and Concepts

Linear correlation test
Use linear correlation to determine whether Linear correlation defined as If c = co + n, then 0 If c = co + aw + n, then azlc(w,w) Basic Algorithms and Concepts

Blind detection If w is chosen so that zlc(co,w) is likely to be close to 0, then zlc zlc(wn,w). No need to subtract out co before computing linear correlation. White noise pattern tends to have low- magnitude correlation with any image. Basic Algorithms and Concepts

Interpreting system geometrically
Media space – a high-dimensional space in which each point corresponds to a work. 256 256 grayscale image -> 65,536 dimensions (one for each pixel). 5 second mono audio clip, sampled at 44,100Hz -> 220,500 dimensions (one for each sample) Basic Algorithms and Concepts

2d pictures of media space
Several possible interpretations Abstraction of high-dimensional space (just pretend media space is really 2d) Projection of media space Slice of media space Basic Algorithms and Concepts

Picture of media space Basic Algorithms and Concepts

Algorithmic building blocks: Watermark in media space

Geometric interpretation of zlc()
zlc(c,w) is just dot product of c and w divided by N Dot product of c and w is cosine of angle between them, times their magnitudes If |w| = 1, then dot product is projection of c onto direction of w Comparing zlc(c,w) against a threshold leads to detection region with planar boundary Basic Algorithms and Concepts

Geometric interpretation of zlc()

Now that we have a basic system …
… let’s consider a problem: What happens when we change the contrast of the image? cwn = ncw , where n is some scalar value zlc(cwn,w) = n zlc(cw,w) If n < 1, detection value might drop below threshold Basic Algorithms and Concepts

Solution: normalized correlation
Normalize correlation by magnitudes of vectors Scaling has no effect on znc(c,w) Basic Algorithms and Concepts

Geometric interpretation of znc()
znc(c,w) correlation is just cosine of angle between c and w Comparing znc(c,w) against a threshold is equivalent to comparing angle against a threshold Result: detection region with conical boundary Basic Algorithms and Concepts

Geometric interpretation of znc()
acos( znc(c,w) ) w Basic Algorithms and Concepts

Another problem What happens if the image is spatially shifted a little? Detection value will depend on autocorrelation function of watermark pattern. White noise pattern has close to zero autocorrelation. \ Watermark is unlikely to be detected. Basic Algorithms and Concepts

Possible solution Watermark Fourier-magnitude instead of pixel values Fourier-magnitudes are invariant to translation Basic Algorithms and Concepts

Possible solution To embed Take FFT of image and compute magnitudes Add w to magnitudes Scale FFT coefficients of image to new magnitudes and take inverse FFT To detect Compute normalized correlation between magnitudes and w Basic Algorithms and Concepts

Watermark extraction We can view the preceding system as comprising two basic parts A watermark extraction process that maps points in media space to points in some marking space (Fourier-magnitude space, in this case) A simple watermarking system that operates in marking space Basic Algorithms and Concepts

Reasons for watermark extraction
Increase robustness Project into distortion invariant space Invert distortions Reduce noise Reduce computational cost Increase security Key-based extraction Basic Algorithms and Concepts

“Transform domain” watermarking
Many authors categorize watermarking systems by transforms included in their extraction processes, e.g. … “Spatial-domain watermarking” (no transform) “DCT-domain watermarking” “Wavelet-domain watermarking” Etc. But … Basic Algorithms and Concepts

“Transform domain” watermarking
… the transform alone says little about how the system works If T is a linear, energy-preserving transform, then zlc( T(c),w ) = zlc( c,T-1(w) ) Thus a linear-correlation-based system in domain T is the same as a spatial-domain system with a different watermark pattern It is the nonlinearities in the extraction process that distinguish a system’s behavior Basic Algorithms and Concepts

Perceptual shaping Basic idea: amplify watermark in areas where the cover work can mask noise co Perceptual model w cw Basic Algorithms and Concepts

Image before embedding

Without perceptual shaping

With perceptual shaping

Detection after perceptual shaping
Early approach: invert shaping in detector (shown here for informed detector) co Perceptual model c wn Basic Algorithms and Concepts

Detection after perceptual shaping
Not necessary to invert perceptual shaping Distortion of watermark pattern degrades detection value for given watermark scaling value, a, but … … possible to use larger value of a because pattern is better hidden Basic Algorithms and Concepts

Geometric view of perceptual shaping
Region of acceptable fidelity Shaped watermark vector Original (unshaped) watermark vector Basic Algorithms and Concepts

Robustness Issues The robustness of a watermark is its ability to survive normal processing.

Additive Noise Watermarked image is corrupted by additive noise Linear Correlation Linear Correlation (matched filtering) is optimal when noise is AWGN. Basic Algorithms and Concepts

Valumetric Scaling Watermarked image is subjected to a change in contrast Linear Correlation For n < 1, this scaling decreases the detection value. How can we select a threshold? Basic Algorithms and Concepts

Valumetric Scaling Normalized Correlation Independent of vector magnitude Describes the cosine of the angle between the vectors -1  znc  +1 1-n q Unit Sphere Basic Algorithms and Concepts

Quantization Transform Quantization Entropy Coding uncompressed work compressed Quantization noise cannot be modeled as additive white noise There are current efforts to model quantization noise Eggers and Girod Appendix B.5 Canonical Transform Coder Basic Algorithms and Concepts

Synchronization Geometric distortion in imagery translation, rotation, zoom, aspect ratio, skew, perspective distortion, warp Temporal distortion in audio time delay, time scaling Video can suffer from both geometric and temporal misalignments Noise due to synchronization errors is not well modeled as additive white noise. Basic Algorithms and Concepts

Synchronization Approaches
Exhaustive Search Detection applied at all possible temporal/geometric distortions Negative impact on false positive probability Usually requires too much computation Basic Algorithms and Concepts

Synchronization pattern is embedded along with the payload-carrying pattern. Registration to synchronization pattern prior to detection. Negative impact on fidelity and security Basic Algorithms and Concepts

Implicit Synchronization Watermark location in time or space is relative to extracted features Example: audio reference pattern added between salient points Basic Algorithms and Concepts

Invariance Design patterns that are invariant to desynchronization Example: Use of Fourier magnitude in watermark extraction process for shift invariance Basic Algorithms and Concepts

Security Issues The security of a watermark is its ability to resist hostile attacks specifically designed to defeat the purpose of the watermark.

Robustness Security against unauthorized removal requires robustness to any process that maintains fidelity Desynchronization Attacks Noise Removal Attacks Basic Algorithms and Concepts

Mosaic Attack Image is broken into many small rectangular patches Each patch is too small for reliable detection Patches are displayed in a table such that patch edges are adjacent Basic Algorithms and Concepts

Collusion Attacks Many different works, same watermark Many different watermarks, same work Simple example: averaging Average of many different works gives an estimate of the watermark Average of many copies of the same work reduces the strength of each watermark Basic Algorithms and Concepts

Copy Attack Watermark is “copied” from one work to another Unauthorized Embedding Example: apply a watermark removal attack to obtain an estimate of the watermark, add to fake. Basic Algorithms and Concepts

Ambiguity Attack Create the appearance that a watermark has been added to someone else’s work Example: define fake watermark pattern and subtract from the distributed image. This is the fake “original.” Difference between distributed and Bob’s original contains Bob’s watermark Difference between distributed and Alice’s original contains Alice’s watermark Basic Algorithms and Concepts

Ambiguity Attack Alice is owner! Alice’s original (real) Alice Alice’s detector Distributed copy Bob is owner! Bob’s “original” (fake) Bob Bob’s detector Basic Algorithms and Concepts

Ambiguity Attack Solution to ambiguity attack: Alice uses system that cannot be hacked May be possible to implement by making watermark dependent on cryptographic hash of original work Strictly-speaking, provides proof of ancestry, rather than proof of ownership Basic Algorithms and Concepts

Sensitivity Analysis Technique for removing watermark when adversary has black box detector Estimate the normal to the detection region surface boundary at some point Assume that this normal indicates a short path out of the detection region Basic Algorithms and Concepts

Sensitivity Analysis Find a work that lies on the detection boundary Approximate the normal to the detection boundary Scale and add the normal to the watermarked work Detection region work A attacked work watermarked work w Basic Algorithms and Concepts

Conclusions Basic Algorithms and Concepts

Conclusions: Major stuff not covered
Message-coding for multi-bit watermarks Non correlation-based watermarking “Constraint-based” watermarking (can usually be recast as correlation-based) Quantization-based watermarking (will be covered in part 3) Authentication methods ROC Curves Basic Algorithms and Concepts

Linear correlation (matched filtering) is optimal for detecting a signal in AWGN Most processing is not well modeled as AWGN Normalized correlation provides robustness to amplitude changes Helpful to think of a work as a point in a high dimensional space Basic Algorithms and Concepts

Watermark extraction: project a work to another space for embedding and/or detection Perceptual modeling can improve fidelity and allow for stronger embedding Robustness to desynchronization is an difficult problem Collusion attacks and sensitivity analysis are significant security challenges Basic Algorithms and Concepts

Outline Part 1: Definitions and Applications
Part 2: Basic Algorithms and Concepts Part 3: Informed Watermarking

Part 3: Informed watermarking

Informed watermarking: Outline
Idea of informed watermarking Informed shaping Informed coding Conclusions Informed watermarking

Idea of informed watermarking
Informed watermarking is the practice of using information about the cover work during watermark coding and shaping. Informed watermarking

Informed watermarking
Blind coding & shaping Original Work Watermark embedder Blind shaping (scaling) Blind coding Watermarked Work Message Informed watermarking

Informed shaping Original Work Watermark embedder Blind coding Informed shaping Watermarked Work Message Informed watermarking

Informed coding & shaping
Original Work Watermark embedder Informed coding Informed shaping Watermarked Work Message Informed watermarking

Central insight Watermarking with informed embedder and blind detector = communication with side information at the transmitter Shannon’s model: transmitter has knowledge of channel’s noise characteristics In watermarking, cover Work = (part of) noise Theoretical results for this type of channel should apply to watermarking Informed watermarking

Consequences Informed shaping alone Allows more precise control of fidelity/robustness tradeoff Informed coding + informed shaping Greatly increases payload for a given fidelity/robustness performance Alternatively, improves fidelity/robustness performance for a given payload Informed watermarking

Informed shaping The cover work can be used to inform perceptual shaping. It can also be used to adjust watermark pattern for maximal robustness. Informed watermarking

Basic approach Design detector (we’ll use the linear-correlation detector from Part 2) Treat detection algorithm and parameters as given Design best embedder we can Informed watermarking

Embedding problem The embedder is capable of producing any image Objective: produce an image within the intersection of a region of acceptable fidelity and the detection region Informed watermarking

Embedding problem Region of acceptable fidelity Any point in this area is a successful embedding w Informed watermarking

Embedding problem Several possible approaches Maximize robustness for a given fidelity Maximize fidelity for a given robustness Either approach requires Estimate of fidelity Estimate of robustness Informed watermarking

Simple embedding method
Assume MSE indicates fidelity (better estimates lead to perceptual shaping) Assume robustness is monotonic function of linear correlation Under these assumptions, blind embedding achieves maximum “robustness” for given “fidelity” Alternatively … Informed watermarking

Simple embedding method
… we can minimize fidelity impact while embedding for a constant “robustness” Informed watermarking

Estimating robustness
Simple assumption: robustness is monotonic function of detection value True for linear correlation Not true for other detection measures For normalized correlation, we have obtained good results by estimating amount of white noise that may be added before watermark is likely to be lost Informed watermarking

Informed coding Significantly larger data payloads can be embedded if the mapping between messages and watermark patterns is dependent on the cover work. Informed watermarking

Informed coding: Outline
Writing on dirty paper (problem studied by M. Costa) Dirty-paper codes Application of dirty-paper codes to watermarking Experimental results Conclusions Informed watermarking

Informed coding: Writing on dirty paper
M. Costa studied a “dirty-paper channel” Obtain a piece of paper with normally-distributed dirt Write a message using limited ink Send message, acquiring more dirt along the way Recipient cannot distinguish dirt from ink How much information can we send? Informed watermarking

Informed coding: The dirty-paper channel
First noise s Second noise n m Transmitter Receiver m’ x y x limited by power constraint: Informed watermarking

Informed coding: Costa’s result
First noise has no effect on channel capacity Informed watermarking

Informed coding: Dirty-paper codes
Basic idea Dirty-paper code = code in which each message is represented by several alternative code vectors From the set of vectors that represent the desired message, choose the one, u, that is closest to the first noise, s Transmit a function of u and s, for example x = u - s Informed watermarking

Coding for a simplified channel
Consider a simplified version of the dirty-paper channel First noise has only two possible values, s1 and s2 (i.e. there are only two possible patterns of dirt on the paper) Remainder of channel is the same If s1 is sufficiently different from s2, then Costa’s result is easy to obtain Informed watermarking

Coding for a simplified channel
This group of code vectors centered on s2 A B C D E A B F G C D E This group of code vectors centered on s1 F G Informed watermarking

Informed coding: Dirty-paper codes
For full dirty-paper channel: Try to design a dirty-paper code in which, within the power-constraint around every possible s, there is at least one code vector for each message. Informed watermarking

Coding for full dirty-paper channel
Code must ensure that, within the power- constraint around every possible s, there is at least one code vector for each message. Capacity cannot be achieved transmitting x = u – s. Costa transmits x = u – as, where a is a carefully-chosen constant Informed watermarking

Application to watermarking
Costa’s proof does not translate directly to watermarking In watermarking, noise is not Gaussian Non-Gaussian noise necessitates non-spherical detection regions (e.g. cones) Lessons from Costa Use dirty-paper codes Use non-trivial informed embedding Informed watermarking

Practical dirty-paper codes
Costa’s code is generated randomly Requires exhaustive search during encoding and decoding Practical for only very small data payloads Lattice code is most-studied practical code Chen & Wornell (“Dither Index Modulation”, “Quantization Index Modulation”) Eggers, Su, & Girod (“Scalar Costa Scheme”) Informed watermarking

Informed coding: Lattice codes
Each dimension in marking space encodes one symbol, usually one bit Bit encoded by choosing between two quantization points 1 1 1 Informed watermarking

Properties of lattice codes
Typically much higher capacity than correlation- based systems (> 1000 bits) Not usually as robust as correlation-based systems Correlation-based systems have better payload/robustness tradeoff when noise is high Lattice codes susceptible to changes in image brightness or audio volume Informed watermarking

Conclusions Informed watermarking

Conclusions: Stuff not covered
Informed-embedding for multi-bit watermarks Syndrome coding Application of informed-coding to correlation- based systems Informed watermarking

Informed shaping Embedder may choose any point in the detection region for the desired message Best to base choice on an estimate of robustness Informed coding Define several patterns for each message, and embed the one that’s closest to the cover work In theory, capacity of watermarking might be unaffected by distribution of cover works Informed watermarking

Future directions

Future directions Research Informed coding Robustness
Quantization index modulation Syndrome coding Trellis coding Robustness Non-random processes Esp. geometric distortions

Future directions Research Security Collusion attacks Others …

Future directions Commercial applications Transaction tracking
Movie screeners Digital cinema Broadcast monitoring Metadata Lyrics in MP3 files

Future directions Commercial applications Authentication
Cameras Surveillance video Medical imagery Enhancements to legacy systems 3D HDTV – Benoit Macq

Future directions Commercial applications? Copy control
Proof of ownership

Future directions Commercial applications
Must be based on a service or product Not technology Similar to commercial applications of cryptography

Principles of Digital Watermarking

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