BCSE323L

DIGITAL WATERMARKING AND

STEGANOGRAPHY
Dr. Saritha Murali
(SCOPE, VIT Vellore)

Module 1 – Fundamentals of Digital Watermarking

Importance of Watermarking - Application and Properties of
Watermarking - Models of Watermarking
Assessments
• CAT-1 : 15
• CAT-2 :15
• Project : 30
• FAT : 40
Text Books
1. Frank Y. Shih, Digital Watermarking and Steganography Fundamentals and
Techniques, 2020, 2nd Ed. CRC Press, United States. (ISBN No. : 9780367656430)

2. J. Fridrich, Steganography in Digital Media: Principles, Algorithms, and Applications,

2010, 1st Ed. Cambridge: Cambridge University Press, United Kingdom

Reference Books
1. I. J. Cox, M. L. Miller, J. A. Bloom, T. Kalker, and J. Fridrich, Digital Watermarking and
Steganography, 2008, 2nd Ed. Amsterdam: Morgan Kaufmann Publishers In, United
States.

2. P. Wayner, Disappearing Cryptography: Information hiding: Steganography and

Watermarking, 2008, 3rd ed. Amsterdam: Morgan Kaufmann Publishers In, United
States. (ISBN No. : 978-0-08-092270-6 )
Digital Watermarking
 Terminology
• Information hiding (or data hiding) can refer to either making the
information imperceptible (as in watermarking) or keeping the
existence of the information secret.

• Steganography - derived from the Greek words steganos (“covered”)

and graphia(“writing”)

• Steganography is the art of concealed communication. The very

existence of a message is secret.
 Watermarking
• Process of imperceptibly embedding a message into a cover.
• Main properties
1. watermark is hidden from view during normal use, only becomes
visible using a special viewing process
2. carries information about the object in which it is hidden
• Message – Portrait/logo
• Cover – paper/electronic signals/Fabrics/garment labels/product
packaging
• Electronic representations of music, photographs, and video are
common signals that can be watermarked.
 Example: Paper
Watermark
• First, the watermark is hidden from
view during normal use
• only becomes visible by a special
viewing process (here, holding the
currency up to the light).
• Second, the watermark carries
information about the object in
which it is hidden (here, the
watermark indicates the
authenticity of the currency).
 • Digimarc's watermark on products – to replace barcodes

https://www.digimarc.com/press-releases/2020/09/08/digimarc-center-pan-european-development-digital-watermarking-improved
 Steganography Example
• Ancient Romans used to write between
lines using invisible ink with natural
substances such as fruit juices and milk.
• children play spies and write secret
messages that appear only when heated.
• In steganography, the hidden message is
unrelated to the content of the letter,
which only serves as a decoy or cover to
hide the very presence of sending the
secret message.

https://www.sciencephoto.com/media/111171/view/steganography
 Generic watermarking(steganography)
system

Secret message determines

/Watermark whether a
payload is
present
 Oldest example of
steganography
• Herodotus mentioned about a
slave(messenger) who shaved his
head and had a secret message be
tattooed on his scalp during the
Persian Wars.
• He grew his hair back and traveled
to the recipient of the message.
• His head was shaved again to
reveal the message.
• Message: to start a revolt against
the Persian king
• Here, the message is of primary
value and the slave is simply the
carrier of the message
https://www.tattoolife.com/the-soaring-eagles/
Let's modify the story…

• Message on the slave’s head: “This slave belongs to Histiæus.”

• Here, Message refers to the slave (cover Work). If someone else
claimed possession of the slave, Histiæus could shave the slave’s head
and prove ownership.
• Here, the slave (cover Work) is of primary value, and the message
provides useful information about the cover Work.

• Example of Watermarking
 Importance of Watermarking
• Risk of piracy - concern over copyright protection of content
• Cryptography for protecting digital content: Encrypted content + a decryption
key is provided to those who have purchased legitimate copies. But encryption
cannot help the seller monitor how a legitimate customer handles the content
after decryption.
• How to protect content even after it is decrypted?
• Watermarking can fulfill this because it places information within the content
where it is never removed during normal usage
• Decryption, re-encryption, compression, digital-to-analog conversion, and file
format changes -- a watermark can be designed to survive all these processes.
APPLICATIONS OF WATERMARKING
 Owner
Identification
Proof of
Ownership

Legacy Applications Transaction

Enhancement
of Tracking

Watermarking

Device Content
Control Authentication
Copy
Control
Broadcast Monitoring – for advertisers to ensure that they receive all
of the air time they purchase from broadcasters
• Passive monitoring systems: try to directly recognize the content being
broadcast
• Active monitoring systems: place the identification information in a
separate area of the broadcast signal
• Watermarking: coding identification information within the content
itself, rather than exploiting a particular segment of the broadcast
signal
Owner Identification

For visual works, ©

For sound recordings, ℗

• Since watermarks can be made imperceptible and inseparable from

the Work that contains them, they are likely to be superior to text
for owner identification.
• If users of Works are supplied with watermark detectors, they
should be able to identify the owner of a watermarked Work, even
after the Work has been modified in ways that would remove a
textual copyright notice.
Proof of Ownership
Original Image (Image A)
• Alice creates an original artwork - e.g., a digital painting of a forest (Image A).
She saves the original high-resolution file with all layers intact, which only she
has access to.
Derived Image (Image B)
• Instead of just placing a watermark like © 2001 Alice on Image A and posting it
online, Alice creates a new version - Image B by modifying the Image A
• She posts Image B on her website along with a public timestamp and copyright
notice: “© 2001 Alice — derived from original work held privately.”
Transaction Tracking(fingerprinting)
• The watermark records the recipient in each legal sale or distribution
of the Work. The owner of the Work would place a different
watermark in each copy. If the Work were misused, the owner could
find out who was responsible.

• person responsible for misuse of a Work is referred to as a traitor,

whereas a person who receives the Work from a traitor is a pirate
 Transaction Tracking(fingerprinting)

https://eeweb.engineering.nyu.edu/~yao/EE4414/memon_F05_v2.pdf
Content Authentication
• Digital signatures are metadata that must be transmitted along with the
Works they verify. e.g., an image authentication system with metadata
in a JPEG header field. If the image is converted to another file format
that has no space for a signature in its header, the signature will be
lost. The Work can no longer be authenticated.
• Solution is to embed the signature directly into the Work using
watermarking. Such an embedded signature is called as an
authentication mark. e.g., Epson has this feature on its digital cameras
• Authentication marks designed to become invalid after even the
slightest modification of a Work are called fragile watermarks.
 Example of
Fragile
watermark

https://eeweb.engineering.nyu.edu/~yao/EE4414/memon_F05_v2.pdf
Copy Control
• aims to prevent people from making illegal copies of copyrighted
content.
Overcome an encryption mechanism
• Decrypt a copy without a valid key - Theoretically infeasible
• Obtain a valid key – by reverse-engineering
• Legally obtain a key and pirate the decrypted content
• The content must be decrypted before it is used, but all protection is
lost once decrypted!
• Watermarking in copy control:
• Combine every content recorder with a watermark detector
• compliant devices – have watermarking and decryption
• A legal, encrypted copy of a Work(e.g., a DVD purchased from a
video store), can be played on a compliant player, but not on a
noncompliant player, because the noncompliant player cannot decrypt
it.
• The output of the compliant player cannot be recorded on a compliant
recorder, because the recorder would detect the watermark and shut
down.
• But, such output can be recorded on a noncompliant recorder, resulting
in an unencrypted, illegal copy of the Work.
• This copy can be played on a noncompliant player, because it is not
encrypted, but it cannot be played on a compliant player, because the
player would detect the watermark and prohibit playback.
Device Control
• Digimarc’s mobile system embeds a unique identifier into printed and
distributed images such as magazine advertisements, packaging,
tickets, etc.
• After the image is recaptured by a mobile phone’s camera, the
watermark is read by the software on the phone and the identifier is
used to direct a web browser to an associated web site.
• Automatically turning on/off functions related to special contents. E.g
Including watermark to skip advertisements
Legacy Enhancement
• upgrading a system should make the new system backward compatible
(i.e., continue to work with the existing system)
• e.g., from analog to digital TV
• When MP3 players attempt to display the lyrics of songs in synchrony
with the music. One solution is to embed the lyrics directly into the
audio signal using watermark technology
• The legacy application, which doesn't know about the watermark, still
functions as before, while new applications or modules can utilize the
embedded information.
PROPERTIES OF WATERMARKING
 PROPERTIES OF WATERMARK EMBEDDING

1. Embedding Effectiveness:
• Probability that the output of the embedder will be watermarked OR Probability of
detection after embedding
2. Fidelity:
• Fidelity of a watermarking system refers to the perceptual similarity between the
original and watermarked versions of the cover Work.
3. Payload:
• Data payload refers to the number of bits a watermark encodes within a unit of
time or within a Work.
• A watermark that encodes N bits is referred to as an N-bit watermark. Such a
system can be used to embed any one of 2N different messages.
 PROPERTIES OF WATERMARK DETECTION
4. Blind or Informed Detection:
• Detectors that require access to the original, unwatermarked Work are called as
informed detectors. (private watermarking systems)
• Detectors that do not require any information related to the original are called blind
detectors. (public watermarking systems)

5. False Positive Rate:

• A false positive detects a watermark in a Work that does not contain one.
• e.g., a global movie distribution platform that uses watermark detectors to prevent
illegal copies by checking if a watermark on copyright protection is present. Millions of
detectors scan millions of videos every day. Consider a public domain movie (e.g.,
Movie X) that is not watermarked at all, but due to a flaw in the detector's algorithm,
it falsely triggers a detection of a watermark every time it is scanned. Users uploading
or viewing Movie X may be penalized for trying to "distribute copyrighted content".
 PROPERTIES OF WATERMARK DETECTION
6. Robustness:
• The ability to detect the watermark after common signal processing operations.
egs., of common operations on images include spatial filtering, lossy compression,
printing and scanning, and geometric distortions (rotation, translation, scaling, and
so on)
• You have a digital image with a copyright watermark (e.g., an invisible pattern or
code embedded into the image's pixels). The image is saved as a low-quality JPEG
to reduce size. A robust watermark should still be detectable after this.
 OTHER PROPERTIES OF WATERMARKING
7. Security:
The security of a watermark refers to its ability to resist hostile attacks. A hostile attack is
any process specifically intended to thwart the watermark’s purpose.
Types of attacks:
• Unauthorized removal - elimination attacks and masking attacks – (active)
• Unauthorized embedding(forgery) - illegitimate watermarks – (active)
• Unauthorized detection – (passive - does not modify the cover Work)
8. Cipher and Watermark Keys
• In cryptography, all n-bits of a cipher key must be determined, and no useful information
is provided by keys that only differ in a few bits
• But in watermarking, an adversary often needs only to find a key that is close enough
 OTHER PROPERTIES OF WATERMARKING
9. Modification and Multiple Watermarks
• You are permitted to make a copy of a broadcast for non-commercial purpose of
watching that broadcast later. But, you are not permitted to make a copy of this
copy.
• In copy control applications, the broadcasted content may be labeled copy-
once and, after recording, should be labeled copy-no-more.
• Example of multiple watermarks:
• During content distribution, a record label might include a watermark for
identifying the copyright owner. The Work might then be sent to many music
websites. Each copy of the Work might have a unique watermark embedded in
it to identify each distributor. Finally, each web site might embed a unique
watermark in each Work it sells for the purpose of uniquely identifying each
purchaser.
 OTHER PROPERTIES OF WATERMARKING
10. Cost
• depends on the speed of embedding and detection; number of embedders and
detectors deployed; and whether implemented as hardware devices or as software
apps or plugins.
• Copy control applications need fewer embedders but millions of detectors
embedded in consumer video and audio devices.
• But, in the transaction-tracking application in which each player embeds a distinct
watermark, there would be millions of embedders and only a handful of detectors.
Models of Watermarking
 Models of Watermarking

• Classified into 2 groups of models

• models based on a communication-based view of watermarking
• models based on a geometric view of watermarking.
 Components of Communications Systems

Standard model of a communication system

m: the message to be transmitted

x: the codeword encoded by the channel encoder
n: the additive random noise
y: the received signal
mn: the received message
 Components of Communications Systems
• We begin with a message, m, to transmit across a communications channel. This
message is encoded by the channel encoder in preparation for transmission over
the channel.
• The channel encoder is a function that maps each possible message into a code
word drawn from a set of signals that can be transmitted over the channel. This
code word is conventionally denoted as x.
• For digital signals, the encoder is usually broken down into a source coder and a
modulator. The source coder maps a message into a sequence of symbols drawn
from some alphabet.
• The modulator converts a sequence of symbols into a physical signal that can
travel over the channel.
• e.g., it might use its input to modulate the amplitude, frequency, or phase of a
physical carrier signal for radio transmission.
 Components of Communications Systems
• Let x be a sequence of real values, x = {x[1] , x[2] , . . . , x[N]}, quantized to some
arbitrarily high precision.
• We also assume that the range of possible signals is limited in some way, usually
by a power constraint that says that

where p is a constant limit on power.

• The signal, x, is then sent over the transmission channel, which is assumed noisy.
So the received signal, denoted y, will be different from x.
• The change from x to y is illustrated here as resulting from additive noise.
 Components of Communications Systems
• At the receiving end of the channel, the received signal, y, enters to the channel
decoder, which inverts the encoding process and attempts to correct for
transmission errors. This function maps transmitted signals into message, mn.
• The decoder is typically a many-to-one function, so that even noisy code words
are correctly decoded.
• If the channel code is well matched to the given channel, the probability that the
decoded message contains an error is negligibly small.
 Classes of Transmission Channels
• In designing a communications system, we usually regard the transmission channel as
fixed. i.e., we cannot design or modify the noise function during transmission.
• The channel can be characterized by a conditional probability distribution, Py|x(y), which
gives the probability of obtaining y as the received signal if x is the transmitted signal.
• Different transmission channels can be classified according to the type of noise function
they apply to the signal and how that noise is applied.
• The channel illustrated is an additive noise channel, in which signals are modified by the
addition of noise signals, y = x + n.
• The noise signals might be drawn from some distribution independent of the signal being
modified.
• The simplest channel to analyze (and perhaps the most important) is a Gaussian channel,
in which each element of the noise signal, n[i], is drawn independently from a Normal
distribution with zero mean and some variance, σ2n.
 Secure Transmission
• Passive adversary: passively monitors the transmission channel and attempts to
illicitly read the message.
• Active adversary: actively tries to either disable the communication or transmit
unauthorized messages.
• Both forms of adversary are common in military communications.
• A passive adversary simply monitors all military communications, whereas an
active adversary might attempt to jam communications on the battlefield.
• Two approaches to defend against attacks:
• Cryptography and
• Spread Spectrum communications.
Secure Transmission with Encryption
 Secure Transmission
Two uses of Cryptography:
• To prevent passive attacks in the form of unauthorized reading of the message.
• To prevent active attacks in the form of unauthorized writing.

Downside:
• Does not necessarily prevent an adversary from knowing that a message is
being transmitted.
• Provides no protection against an adversary intent on jamming or removing a
message before it can be delivered to the receiver.
 Spread Spectrum

Standard model of a communications channel with key-based channel coding

• Signal jamming (i.e., deliberate effort by an adversary to inhibit

communication between people) is of great concern in military
communications and has led to the development of spread spectrum
communication.
• Here, modulation is performed according to a secret code(key),
which spreads the signal across a wider bandwidth than would
normally be required.
• Here the transmitter broadcasts a
Frequency hopping
message by first transmitting a fraction Spread Spectrum
of the message on one frequency, the
next portion on another frequency, and
so on.
• The pattern of hops from one to another
frequency is controlled by a key that
must be known to the receiver and
transmitter.
• Without this key, an adversary cannot
monitor the transmission.
• Jamming the transmission is also
difficult, since it could only be done by
introducing noise at all possible
frequencies.
 Cryptography vs. Spread Spectrum

• Spread spectrum communications and cryptography are complementary.

• Spread spectrum guarantees delivery of signals.
• Cryptography guarantees secrecy of messages. It is thus common for both
technologies to be used together.
• Spread spectrum can be thought of as responsible for the transport layer, and
cryptography as responsible for the messaging layer.
Communication based Models of Watermarking
 Communication based Models of Watermarking

• Watermarking is a form of communication where we communicate a message

from the watermark embedder to the watermark receiver.
• Ways to incorporate the cover Work into the traditional communications model:
1. The cover Work is considered purely as noise (Basic Model).
2. The cover Work is still considered noise, but this noise is provided to the
channel encoder as side information.
3. Cover Work is not considered as noise, but as a second message that must be
transmitted along with the watermark message in a form of multiplexing.
 Basic Model (informed detector)

Watermarking system with a simple informed detector mapped into a communications model.
(wa : Added pattern, co: Original cover Work, cw: watermarked Work, cwn: noisy watermarked Work)

• Here, watermarking is viewed as a transmission channel through which the

watermark message is communicated. The cover Work is part of that channel.
• Regardless of whether we are using an informed detector or a blind detector, the
embedding process consists of two basic steps.
 Basic Model(contd.)
• First, the message is mapped into an added pattern, wa, of the same type and
dimension as the cover Work, co. e.g., if we are watermarking images, the
watermark encoder would produce a 2D pixel pattern the same size as the cover
image. This mapping might be done with a watermark key.
• Next, wa is added to the cover Work, co, to produce the watermarked Work, cw.
This is a blind embedder because the encoder ignores the cover Work.
• Detection has two steps:
1. co is subtracted from the received Work, cwn, to obtain a received noisy
watermark pattern, wn.
2. Wn is then decoded by a watermark decoder, with a watermark key.
• Since addition of the cover Work in the embedder is exactly cancelled out by its
subtraction in the detector, the only difference between wa and wn is caused by the
noise process.
 Basic Model (blind detector)

Watermarking system with blind detector mapped into a communications model.

(no meaningful distinction between the watermark detector and the watermark decoder)

• Since the un-watermarked cover Work is unknown; it cannot be removed prior to

decoding.
• The received, watermarked Work, cwn, is now viewed as a corrupted version of the added
pattern, wa, and the entire watermark detector is viewed as the channel decoder.
 Applications

• Informed and Blind detector models can be applied in robust watermarking (e.g.,
transaction tracking or copy control), as it requires maximum likelihood that the
detected message is identical to the embedded one.
• In authentication applications, the goal is not to communicate a message but to
learn whether and how a Work has been modified since a watermark was
embedded. For this reason, informed and blind detector models are not typically
used to study authentication systems.
Watermarking as Communications with Side Information at the
Transmitter

• From the basic model, much more effective embedding algorithms can be made if we
allow the watermark encoder to examine co before encoding the added pattern wa.
• Figure shows a model of watermarking that allows wa to be dependent on co.
• The model is almost identical to Blind Detector, with the difference that here co is
provided as an additional input to the watermark encoder.
• Allows the embedder to set cw to any desired value by simply letting wa= cw - co
 Watermarking as Multiplexed Communications

Watermarking as simultaneous communications of two messages using a blind watermark

detector (An informed detector would receive the original cover Work as additional input)

• Cover Work is a second message to be transmitted along with the watermark

message in the same signal, cw.
• The watermark embedder combines m and co into a single signal, cw.
• The two messages, co and m, will be detected and decoded by two different
receivers: a human being and a watermark detector, respectively.
 Watermarking as Multiplexed Communications
• When viewing cwn the human should perceive something close to the original
cover Work, with no interference from the watermark.
• When detecting a watermark in cwn the detector should obtain the original
watermark message, with no interference from the cover Work.
• If the watermark detector is informed, it receives the original cover Work, or a
function of the cover Work, as a second input
Geometric Models of Watermarking
 Geometric Models of Watermarking
Watermarking algorithms can be conceptualized in geometric terms
Media space:
• To view a watermark system geometrically, imagine a high-dimensional space in
which each point represents one Work
• Works are points in an N-dimensional media space
• The dimensionality of a media space, N, is the number of samples used to
represent each Work
• For monochrome images, N is the number of pixels
• For RGB images, N is 3*the number of pixels
• For continuous and temporal content(audio and video), N is the number of samples in the
fixed segment in which the watermark is embedded
• Each sample is quantized and bounded
• Implying a finite but huge set of possible Works, arranged in a rectilinear lattice in media
space
 Distribution of
unwatermark Describing how likely each Work is
ed Works

Region of
A region in which all Works appear essentially
acceptable
identical to a given cover Work
Viewing fidelity

Geometrically Detection
Describing the behavior of the detection algorithm
region

Embedding
distribution Describing the effects of an embedding algorithm
/region

Distortion Indicating how Works are likely to be distorted

distribution during normal usage
 Different works have different likelihoods of entering a
watermark embedder or a detector

• In audio, watermarks are more likely to be embedded

into music than into pure static
Distribution of • In video, watermarks are more likely to be embedded in
images of scenes than in video "snow"
Unwatermarked
When estimating the properties of a watermarking system
Works (false positive rate, effectiveness, etc.), it is important to
model the a priori distribution of the content we expect
the system to process
• Elliptical Gaussian distribution, Laplacian or generalized
Gaussian distribution, Or result of random, parametric
processes
 The distribution of
unwatermarked content is
application dependent
Distribution of e.g., satellite images are drawn from a
Unwatermarked different distribution than news
photographs
Works
Accuracy of performance
estimation relies on correct
choices of distributions of Works
Region of • The region of media space vectors that are
indistinguishable from the cover Work Co is called as
Acceptable the region of acceptable fidelity.
Fidelity • We approximate by setting a threshold on some
measure of perceptual distance

e.g., Mean Square Error, DMSE= ∑ (C₁[i]-C2[i])2/ N

• where C₁ and C₂ are N-vectors in media space. If a

limit TMSE is set on this function, the region of
acceptable fidelity becomes an N-dimensional ball of
radius NTMSE
 Region of Acceptable Fidelity

• MSE is not very good at predicting the perceived differences between Works
• e.g., if C2 is slightly left shifted version of image C1 , the two Works will
appear almost identical, but the MSE might be enormous.

• Some perceptual distance functions are asymmetric (e.g., DSNR). Let the first
argument be original Work and the second be a distorted version of it.

• Reciprocal of the SNR to measure how noisy C2 is in relation to C1

DSNR=Σ (C2[i]- C₁[i])² / Σ C₁[i]²
 The detection region for a given message and a
Detection watermark key is the set of Works in media space
that will be decoded by the detector as containing
Region that message

Detection measure: A threshold on the measure of

the similarity between the detector's input(e.g., a
watermarked image) and a pattern that encodes the
message(e.g., an expected watermark).

Detection Linear correlation: Zlc(c, wr) = c. wr / N

measure
Orthogonal projection of the N-vector c onto the
N-vector wr

The set of all points for which this value is greater

than the threshold is the set of all points on one
side of a plane perpendicular to wr
Illustrating Regions
in the Media Space
• All points within the circular
region of acceptable fidelity
and to the right of the
planar edge of the detection
region corresponds to
versions of Co that are within
an acceptable range of
fidelity and that will cause
the detector to report the
presence of the watermark
 A watermark embedder is a function that maps
Embedding a Work, a message, and possibly a key into a
new Work
Distribution
or Region It is generally a deterministic function(for any
given original Work, Co, message, m, and key, k,
the embedder always outputs the same
watermarked Work, Cw)
The probability that a given Work Cw will be
output by the embedder is the probability that
a Work leads to it, Co is drawn from the
distribution of unwatermarked Works.
If several unwatermarked Works map into Cw ;
the probability of Cw is the sum of the
probabilities of those Works. The resulting
probability distribution is called as Embedding
distribution
 Embedding Distribution or Region
• Some embedding algorithms define an embedding distribution in which every
point has a non-zero probability (assuming every point in media space has non-
zero probability of entering the embedder)
• Even images outside the detection region can be arrived by applying the
embedding algorithms into some other images
media vectors before embedding
media vectors after embedding

blind embedding embedding with side info

 p(Cwn|Cw) - Distortion distribution
Distortion around Cw
• Probability of obtaining a distorted work
Distribution Cwn , given that undistorted watermarked
work was Cw
Distortion distribution is usually
modeled as additive Gaussian noise
• Simplified, not close to reality
• A few distortions are even random, most
are in general deterministic functions
• Noise added is highly dependent on the
content
• Distortion distribution is multi-modal,
unlikely to be produced by a Gaussian
noise process.
 Marking Spaces
• For sophisticated algorithms, analysis is difficult in media space. So we consider
projection or distortion of media space into a marking space.
• Watermark detectors using marking space:
• Step1: Watermark extraction, applies one or more preprocesses to the content, such as frequency
transforms, filtering, block averaging, geometric or temporal registration, and feature extraction. The
result is a vector called as extracted mark (a point in marking space)-of possibly smaller
dimensionality than the original.
• Step 2: Determine whether the extracted mark contains a watermark and decode the embedded
message by comparing the extracted mark against one or more predefined reference marks.
 Marking Spaces
• Watermark embedders using marking space:
• Step1: map the unwatermarked Work into a point in marking space.
• Step2: choose a new vector in marking space that is close to the extracted mark and will
be detected as containing the desired watermark. We refer to the difference between this
new vector and the original, extracted mark as the added mark.
• Step3: Invert the extraction process, projecting the new vector back into media space to
obtain the watermarked Work.
 Marking Spaces
• Our aim here is to find a Work that will yield the new vector as its extracted mark. If marking
space has the same dimensionality as media space, this projection can be performed in a
straightforward manner.
• However, if marking space has smaller dimensionality than media space, each point in marking
space must correspond to many points in media space.
• Thus, there will be many Works that all yield the new vector as their extracted marks. Ideally, we
would like to choose the one perceptually closest to the original Work.
• In systems designed according to Figures, one purpose of the extraction function is to reduce the
cost of embedding and detection.
• A second purpose is to simplify the distribution of unwatermarked Works, the region of acceptable
fidelity, and/or the distortion distribution so that simple watermarking algorithms will perform
well.
 Reference:
I. J. Cox, M. L. Miller, J. A. Bloom, T. Kalker, and J. Fridrich, Digital
Watermarking and Steganography, 2008, 2nd Ed. Amsterdam: Morgan
Kaufmann Publishers In, United States.

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