Separation of Lanthanides/ Lanthanides and Actinides
Digital Watermarking
1. Digital Watermarking
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Chapter 1
INTRODUCTION
Techniques used to hide the information are:
Information
Hiding
Steganography Cryptography Watermarking
Fig 1.1: Classification of Information Hiding
1.1 Steganography (art of hidden writing)
A term derived from the Greek words “steganos” and “graphia” (The two words mean
“covered” and “writing”, respectively).The art and science of writing hidden messages in
such a way that no one apart from the intended recipient knows of the existence of the
message. The existence of information is secret.
1.2 Cryptography
The conversion of data into a secret code for transmission over a public network.
Today, most cryptography is digital, and the original text ("plaintext") is turned into a coded
equivalent called "cipher text" via an encryption algorithm. The cipher text is decrypted at the
receiving end and turned back into plaintext.
EncryptionDecryption
Plaintext cipher text Plaintext
Fig 1.2: Cryptography
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1.3 Watermarking
A distinguishing mark impressed on paper during manufacture; visible when paper is
held up to the light (e.g. $ Bill)
Physical objects can be watermarked using specialdyes and inks or during paper
manufacturing.
Fig 1.3:Watermarked currency
1.3.1 History of watermarking
The term “watermark” was probably originated from the German term
“wassermarke”. Since watermark is of no importance in the creation of the mark, the name is
probably given because the marks resemble the effects of water on paper. Papers are invented
in China over athousand years ago. However, the first paper watermark did not appear until
1282, in Italy. By the 18th century, watermarks on paper in Europe and America had been
used as trademarks, to record the manufactured date, or to indicate the size of original sheets.
Watermarks are commonly used on bills nowadays to avoid counterfeiting
1.3.2 Advancing to Digital Watermarking
In recent times, due to great developments in computer andinternet technology,
multimedia data i.e. audio, images and video have found wide applications. Digital
watermarking is one of the best solutions to prevent illegal copying, modifying and
redistributing multimedia data. Encryption of multimedia products prevents an intruder from
accessing the contents without a proper decryption key. But once the data is decrypted, it can
be duplicated and distributed illegally. To enforce IP rights and to prevent illegal duplication,
interpolation and distribution of multimedia data, Digital watermarking is an effective
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solution. Copyright protection, data authentication, covert communication and content
identification can be achieved by Digital watermarking. Digital watermarking is a technique
to embed copyright or other information into the underlying data. The embedded data should
maintain the quality of the host signal. In order to achieve the copyright protection, the
algorithm should meet few basic requirements
i) Imperceptibility: The watermark should not affect the quality of the original signal, thus it
should be invisible/ inaudible to human eyes/ ears.
ii) Robustness: The watermarked data should not be removed or eliminated by unauthorized
distributors, thus it shouldbe robust to resist common signal processingmanipulations such as
filtering, compression, filteringwith compression.
iii) Capacity: the number of bits that can be embedded in onesecond of the host signal.
iv) Security: The watermark should only be detected byauthorized person.
v) Watermark detection should be done without referencingthe original signals.
vi)The watermark should be undetectable without prior knowledge of the embedded
watermark sequence.
vii) The watermark is directly embedded in the signals, not ina header of the signal.
All these requirements are often contradictory with each otherand we need to make a
trade-off among them. For exampleincreasing data rate in watermarking system results in
qualitydegradation of the watermarked signal and decreases therobustness against attacks.
Imperceptibility and robustness arethe most important properties for many applications.
Theseconflicting requirements pose many challenges to design ofrobust watermarking.
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Chapter 2
WHAT IS DIGITAL WATERMARKING?
Watermarking can also be applied to digital signals!
(a) Images (b) Video (c) Audio
Fig 2.1
A digital watermark is a pattern of bits inserted into a digitalimage, audio or video file
that identifies the file's copyright information (author, rights, etc.). The name “watermark” is
derived from the faintly visible marks imprinted on organisational stationery.
In addition, the bits representing the watermark must be scattered throughout the file
in such a way that they cannot be identified and manipulated. And finally, a digital
watermark must be robust enough to survive changes to the file its embedded in, such as
being saved using a lossycompressionalgorithm eg: JPEG.
Satisfying all these requirements is no easy feat, but there are a number of companies
offering competing technologies. All of them work by making the watermark appear as noise
that is, random data that exists in most digital files anyway.
Digital Watermarking works by concealing information within digital data, such that
it cannot be detected without special software with the purpose of making sure the concealed
data is present in all copies of the data that are made whether legally or otherwise, regardless
of attempts to damage/remove it.
Thepurposeofdigitalwatermarksis toprovidecopyrightprotection for intellectual
property that is in digital format.
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Fig 2.2
As seenabove in Fig 3.2,Alicecreatesan original image and watermarks it
beforepassingittoBob.IfBobclaims the image and sells copies to
otherpeopleAlicecanextracther watermarkfromtheimageproving her copyright to it.
ThecaveathereisthatAlicewillonlybeabletoprovehercopyright
oftheimageifBobhasn’tmanagedtomodifytheimagesuchthat thewatermarkisdamagedenough
to be undetectable or added his own watermark such that it is impossible to discover which
watermark was embedded first.
2.1How Watermarking is Different from Steganography and
Cryptography.
2.1.1Steganography vs. Watermarking
The main goal of steganography is to hide a message m in some audio or video
(cover) data d, to obtain new data d', practically indistinguishable from d, by people, in such a
way that an eavesdropper cannot detect the presence of m in d'.
The main goal of watermarking is to hide a message m in some audio or video (cover)
data d, to obtain new data d', practically indistinguishable from d, by people, in such a way
that an eavesdropper cannot remove or replacem in d'.
It is also often said that the goal of steganography is to hide a message in one-to-one
communications and the goal of watermarking is to hide message in one-to-many
communications.
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Shortly, one can say that cryptography is about protecting the content of messages,
steganography is about concealing its very existence.
Steganography methods usually do not need to provide strong security against
removing or modification of the hidden message. Watermarking methods need to to be very
robust to attempts to remove or modify a hidden message.
2.1.2Cryptography vs. Watermarking
Watermarking is a totally different technique from cryptography. Cryptography only
provides security by encryption and decryption. However, encryption cannot help the seller
monitor how a legitimate customer handles the content after decryption. So there is no
protection after decryption. Unlike cryptography, watermarks can protect content even after
they are decoded.
Other difference is cryptography is only about protecting the content of the messages.
Because watermarks are inseparable from the cover in which they are embedded, so in
addition to protecting content they provide many other applications also, like copyright
protection, copy protection, ID card security etc.
2.2 Characteristics of Digital Watermarking
Invisibility: an embedded watermark is not visible.
Robustness: piracy attack or image processing should not affect the embedded
watermark.
Readability: A watermark should convey as much information as possible. A
watermark should be statisticallyundetectable. Moreover, retrieval of the digital
watermark can be used to identify the ownership and copyrightunambiguously.
Security: A watermark should be secret and must be undetectable by an unauthorized
user in general. Awatermark should only be accessible by authorized parties. This
requirement is regarded as a security and thewatermark is usually achieved by the use
of cryptographic keys. As information security techniques, the details of adigital
watermark algorithm must be published to everyone. The owner of the intellectual
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property image is the onlyone who holds the private secret keys. A particular
watermark signal is related with a special number usedembedding and extracting. The
special number is kept secretly and is used for confirming legal owners of
digitalproducts later. If we lay strong stress on robustness, and then invisibility may
be weak. If we put emphasis oninvisibility, then vice versa. Therefore, developing
robustness watermark with invisibility is an important issue.
2.3 History of digital watermarking
The first watermarking example similar to thedigital methods nowadays appeared in
1954.The Muzak Corporation filed a patent for“watermarking” musical Work.
Anidentification Work was inserted in music byintermittently applying a narrow
notch filtercentred at 1KHz.
About 1995, interest in digital watermarking began to mushroom.
The water marking fever
Fig 2.3: Annualnumber ofpaperspublishedonwatermarking
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Chapter 3
WATERMARKING CLASSIFICATION
Digital Watermarking techniques can be classified in a number of ways depending on
different parameters. Various types of watermarking techniques are enlisted below.
Robust & Fragile Watermarking
Robust watermarking is a technique in which modification to the watermarked
content will not affect the watermark. As opposed to this, fragile watermarking is a technique
in which watermark gets destroyed when watermarked content is modified or tampered with.
Visible & Transparent Watermarking
Visible watermarks are ones, which are embedded in visual content in such a way that
they are visible when the content is viewed. Transparent watermarks are imperceptible and
they cannot be detected by just viewing the digital content.
Public & Private Watermarking
In public watermarking, users of the content are authorized to detect the watermark
while in private watermarking the users are not authorized to detect the watermark.
Asymmetric & Symmetric Watermarking
Asymmetric watermarking (also called asymmetric key watermarking) is a technique
where different keys are used for embedding and detecting the watermark. In symmetric
watermarking (or symmetric key watermarking) the same keys are used for embedding and
detecting watermarks.
Steganographic &Non-Steganographic watermarking
Steganographic watermarking is the technique where content users are unaware of the
presence of a watermark. In nonsteganographic watermarking, the users are aware of the
presence of a watermark.
Steganographic watermarking is used in fingerprinting applications while
nonsteganographic watermarking techniques can be used to deter piracy.
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Chapter 4
DIGITAL WATERMARKING LIFE CYCLE PHASES
Fig 4.1:Block diagram of a watermarking system.
The information to be embedded in a signal is called a digital watermark, although in
some contexts the phrase digital watermark means the difference between the watermarked
signal and the cover signal. The signal where the watermark is to be embedded is called
the host signal.
A watermarking system is usually divided into three distinct steps
1. Embedding
2. Attack
3. Detection/Extraction
4.1 Embedding
In embedding, an algorithm accepts the host and the data to be embedded, and
produces a watermarked signal.
Fig 4.2: Embedding
Inputs to the scheme are the watermark, the cover dataand an optional public or secret
key. The outputs are watermarkeddata.The key is used to enforce security.
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4.2 Attacks
The watermarked digital signal is transmitted or stored, usually transmitted to another
person. If this person makes a modification, this is called an attack. While the modification
may not be malicious, the term attack arises from copyright protection application,
where pirates attempt to remove the digital watermark through modification. There are many
possible modifications, for example, lossy compression of the data (in which resolution is
diminished), cropping an image or video, or intentionally adding noise.
4.3 Extraction
Extraction is an algorithm which is applied to the attacked signal to attempt to extract
the watermark from it. If the signal was unmodified during transmission, then the watermark
still is present and it may be extracted.
Fig 4.3: Extraction
Inputs to the scheme are the watermarked data, the secret or public key and,
depending on the method, the original dataand/or the original watermark. The output is the
recoveredwatermarked W or some kind of confidence measure indicatinghow likely it is for
the given watermark at the input to be present inthe data under inspection.
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Chapter 5
WATERMARKING TECHNIQUES
Watermarking
Frequency
Spatial Domain
Domain
Watermarking
Watermarking
Discrete
Least SSM- Discrete Cosine
Wavelet
Significant Bit Modulation Transformation
Transformation
Fig 5.1: Watermark Techniques
5.1 Spatial Domain Techniques
Some of the Spatial Techniques of watermarking are as follow.
5.1.1 Least-Significant Bit (LSB)
The earliest work of digital image watermarking schemes embeds watermarks in the
LSB of the pixels. Given an image with pixels, and each pixel being represented by an 8-bit
sequence, the watermarks are embedded in the last (i.e., least significant), bit, of selected
pixels of the image. This method is easy to implement and does not generate serious
distortion to the image; however, it is not very robust against attacks. For instance, an
attacker could simply randomize all LSBs, which effectively destroys the hidden information.
5.1.2SSM-Modulation-Based Technique
Spread-spectrum techniques are methods in which energy generated at one or more
discrete frequencies is deliberately spread or distributed in time or frequency domains. This is
done for a variety of reasons, including the establishment of secure communications,
increasing resistance to natural interference and jamming, and to prevent detection. When
applied to the context of image watermarking, SSM based watermarking algorithms embed
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information by linearly combining the host image with a small pseudo noise signal that is
modulated by the embedded watermark.
5.2 Frequency Domain Techniques
Compared to spatial-domain methods, frequency-domain methods are more widely
applied. The aim is to embed the watermarks in the spectral coefficients of the image. The
most commonly used transforms are the Discrete CosineTransform (DCT), Discrete Fourier
Transform (DFT), Discrete Wavelet Transform (DWT), Discrete LaguerreTransform (DLT)
and the Discrete Hadamard Transform (DHT). The reason for watermarking in the
frequencydomain is that the characteristics of the human visual system (HVS) are better
captured by the spectral coefficients.For example, the HVS is more sensitive to low-
frequency coefficients, and less sensitive to high-frequency coefficients. In other words, low-
frequency coefficients are perceptually significant, which means alterations to those
components might cause severe distortion to the original image. On the other hand, high-
frequency coefficients are considered insignificant; thus, processing techniques, such as
compression, tend to remove high-frequency coefficients aggressively. To obtain a balance
between imperceptibility and robustness, most algorithms embed watermarks in the midrange
frequencies.
5.2.1 Discrete Cosine Transformation (DCT)
DCT like a Fourier Transform, it represents data in terms of frequency space rather
than an amplitude space. This is useful because that corresponds more to the way humans
perceive light, so that the part that are not perceived can be identified and thrown away. DCT
based watermarking techniques are robust compared to spatial domain techniques. Such
algorithms are robust against simple image processing operations like low pass filtering,
brightness and contrast adjustment, blurring etc. However, they are difficult to implement and
are computationally more expensive. At the same time they are weak against geometric
attacks like rotation, scaling, cropping etc. DCT domain watermarking can be classified into
Global DCT watermarking and Block based DCT watermarking. Embedding in the
perceptually significant portion of the image has its own advantages because most
compression schemes remove the perceptually insignificant portion of the image.
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5.2.2 Discrete Wavelet Transformation (DWT)
The Discrete Wavelet Transform (DWT) is currently used in a wide variety of signal
processing applications, such as in audio and video compression, removal of noise in audio,
and the simulation of wireless antenna distribution. Wavelets have their energy concentrated
in time and are well suited for the analysis of transient, time-varying signals. Since most of
the real life signals encountered are time varying in nature, the Wavelet Transform suits
many applications very well.
5.3 Backdrops of above mentioned watermark technique systems
Scope
Tamper Proofing
Inseparability
Transparency / Visibility
Insecurity
5.4 Fast Hadamard Transform (FHT)
FHT Technique/Algorithm has many advantages over above mentioned techniques,
those are
Shorterprocessingtime
Invisibilityofthewatermarkguaranteed
Increasedwatermarkenergyleadstohigherrobustness
5.4.1 2D-Hadamard transform of signal
The 2D-Hadamard transform has been used extensively in image processing and image
compression. In this section, we give a brief review of the Hadamard transform
representation of image data, which is used in the watermarking embedding and extraction
process.
Let [U] represents the original image and [V] the transformed image, the 2D-Hadamard transform
is given by:
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(1)
Where Hnrepresents an N×N Hadamard matrix, N=2n, n=1,2,3…, with element
values either +1 or –1. The advantages of Hadamard transform are that the elements of the
transform matrix Hnare simple: they are binary, real numbers andthe rows or columns of
Hnare orthogonal. Hence the Hadamard transform matrix has the following property:
Hn = Hn* = HT = H-1(2)
Since Hnhas N orthogonal rows HnHn= NI (I is the identity matrix) and HnHn= NHnHn-
1
, thus Hn–1= Hn/N. The inverse2D-fast Hadamard transform (IFHT) is given as
(3)
In our watermarking algorithm, the forward and reverse Hadamard transform is
applied to the sub-blocks of the originalor watermarked images. A two-dimensional FHT of
the segmented 8×8 blocks is performed by applying a one dimensional FHT on the rows first
and then followed by a 1-D FHT on the columns. In the computer implementation, the 8×8
sub-block is first multiplied by Hadamard matrix, and then the resultant matrix is transposed
and multiplied by the Hadamard matrix again. The final matrix is the transformed matrix.
For N=2, the Hadamard matrix, H1, is called a core matrix, which is defined as
(4)
The Hadamard matrix of the order n is generated in terms of Hadamard matrix of
order n-1 using Kroneckerproduct, ⊗, as
Hn=Hn-1⊗H1 (5)
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Or
(6)
Since in our algorithm, the processing is carried out based on the 8×8 sub-blocks of
the whole image, the third orderHadamard transform matrix H3 is used. By applying (5) or
(6), H3 becomes:
(7)
The characteristic of the rows or columns of H3 is sign transitions, which is defined as
a 1 to –1 or –1 to 1 change. In H3, the number of transitions for row 1 to row 8 is 0, 7, 3, 4, 1,
6, 2 and 5 according to equation (7). The number of sign changes is referred to as sequency.
The concept of sequency is analogous to its Fourier counterpart frequency. Zero sign
transitions correspond to DC and a large number of sign transitions correspond to high
frequency. In Hadamard matrix H3, the elements are not arranged in increasing sequency,
such that the number of transitions is 0, 1, 2, 3, 4, 5, 6and 7. If the order of rows is in
ascending of sequency, this transform matrix is called a Walsh transform matrix. A Walsh
transform may cause the transformed matrix to have DC value at upper left corner and AC
coefficients arrange in Zigzag order from low frequency components to high frequency
components. The Walsh transform is not used here because the middle and high frequency
AC components, which could be watermarked has shown to be somewhat unreliable and the
performance worse than existing DCT watermarking algorithms. On the contrary, the
Hadamard transform matrix H3 has its AC components in Hadamard order. It is possible that
in the watermarking process, some of the watermark information can be embedded into the
low frequency AC components. This increases the mark reliability and makes it more
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difficult to attack and remove. Moreover, Hadamard transform has more useful middle and
high frequency bands available, for hiding the watermark, as compared to other high coding
gain transforms like DCT and DWT, at high noise environment. It has been shownthat
transforms including DCT and sub-band transforms are suitable for watermarking when the
channel noise is low. But low channel noise condition is not usually the case. For low quality
JPEG or wavelet compression as well as some linear or nonlinear filtering such as Gaussian
filtering and median filtering, the processing noise approachesinfinity for the middle and high
frequency bands. In these cases, the high gain transform watermarking methods are not very
robust. But middle and high frequency Hadamard transform coefficients have components
equivalent to where many DCT low-frequency AC coefficients are located. So it is more
likely that in high noise environment the Hadamard transform bands would remain and
unscathed and immune to the channel noise.
Furthermore, low quality JPEG and wavelet compression could normally affect the
high frequency components of DCTor DWT based watermarked image than the high
frequency components in the Hadamard bands. Watermark information embedded in these
components of DCT and DWT may be removed by these compressions. However, Hadamard
transform would survive the compression as some of the watermark energy is embedded into
the equivalent low frequency components of DCT and DWT domain. Therefore,
decompositions that are not so efficient for compression, such as the Hadamard transform,
would provide more immunity to channel noise than decompositions with high coding gain
transform.
Another advantage of using the FHT is that it has a shorter processing time and its
ease of hardware implementation than many commonly used orthogonal transforms. An
efficient FHT hardware structure has been reported. Based on the radix-2 algorithm, the
structure can be implemented with shift register and controllable adder/subtracters for high
processing throughput. This makes it possible for the real-time implementation of a digital
watermarking system.
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5.4.2Experiment Results and Discussions
The experiment for the watermarking system is performed using the MATLAB 6
platform. Two container test images consist of lenna.bmp cameraman.bmp are selected for
the experiment. All these images are of sizes of 512×512×8bit, grayscale intensity images.
For the robustness test, we use the Stirmark benchmarking software that
consistsapproximately 90 different types of image manipulations or attacks. The Stirmark
attacks destroy the synchronization required in information retrieval via applying some small
random geometrical transforms in such a way that the distortion is not visually perceivable.
Some Stirmark attack examples such as cropping, changing aspect ratio, rotation and JPEG
compression are shown in figure 5.2:
(a)Original watermarked (b) image Cropping 50% (c) Rotation 30°
(d)Changing aspect ratio(e) 3×3 median filtering (f)JPEG compression
x-1 y-0.8 factor 35
Fig 5.2: Stirmark attack examples on watermarked image lenna.bmp
For our algorithm, a maximum image size of 256×256×8bit can be hidden into the container
digital image of size512×512×8bit. In the experiment, a grayscale image dmt.bmp with size
64×64×8bit is used. The original and watermarked image examples are shown in figure 5.3:
(lenna.bmp marked with image dmt.bmp)
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(a) Original image (b) Watermarked image
(c) Original watermark (d) Extracted watermark
Fig 5.3:Original and watermarked images for image embedded algorithm
Results show that there were no perceptually visible degradations on the watermarked
images. The extracted watermarkis also highly correlated with the original watermark with
correlation factor 0.989. Results using benchmarking softwareStirmark are shown in Table 1:
(lenna.bmp is marked with image dmt.bmp)
Table 5.1: Results of some Stirmark tests for image-in-image embedding algorithm
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Chapter 6
ANALYSIS OF ROBUSTNESS
The similarity measurement between original watermark and extracted watermark is
obtained through Normalized Correlation (NC) coefficient and Accuracy Rate (AR).
6.1 Normalized Correlation (NC)
The Normalized correlation Coordinate (NCC) computes the similarity measurement
of original watermark and extracted watermark, which is defined as
Where N×N is the size of watermark, W(i,j) and W’(i,j) represents the watermark and
recovered watermarkimages respectively.
6.2 Accuracy Rate (AR)
The Accuracy Rate (AR) is used to measure the difference between the
originalwatermark and the recovered one. AR is computes as follows:
AR= CP/ NP
Where NP is the number of pixels in the original watermark and CP is the number of
correct pixels obtained by comparing the pixels of the original watermark to the
corresponding ones of the recovered watermark.
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Chapter 7
APPLICATIONS OF WATERMARKING
7.1 Security
In the field of data security, watermarks may be used for certification, authentication,
and conditional access.
7.1.1 Certification
It is an important issue for official documents, such as identity cards or passports.
Digital watermarking allows to mutually link information on the documents. That means
some information is written twice on the document, for instance, the name of a passport
owner is normally printed in clear text and is also hidden as an invisible watermark in the
photo of the owner. If anyone would intend to duplicate the passport by replacing the photo,
it would be possible to detect the change by scanning the passport and verifying the name
hidden in the photo does not match any more the name printed on the passport.
7.1.2 Authentication
The goal of this application is to detect alterations and modifications in an image.
Suppose we have picture of a car that has been protected with a watermarking technology.
And if, the same picture is shown but with a small modification, say, the numbers on the
license plate has been changed. Then after running the watermark detection program on the
tampered photo, the tampered areas will be indicated in different color and we can clearly say
that the detected area corresponds to the modifications applied to the original photo.
7.1.3 Conditional access
For example conditional access to confidential data on CD-ROMs may be provided
using digital watermarking technology. The concept consists of inserting a watermark into
the CD label. In order to read and decrypt the data stored on the CD, the watermark has to be
read since it contains information needed for decryption. If someone copies the CD, he will
not be able to read the data in clear-text since he does not have the required watermark.
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7.2 Copyright Protection
Copyright protection inserts copyright information into the digital object without the
loss of quality. Whenever the copyright of a digital object is in question, this information is
extracted to identify the rightful owner. It is also possible to encode the identity of the
original buyer along with the identity of the copyright holder, which allows tracing of any
unauthorized copies.
7.3 Copy protection
Copy protection attempts to find ways, which limits the access to copyrighted
material and/or inhibit the copy process itself. Examples of copy protection include encrypted
digital TV broadcast, access controls to copyrighted software through the use of license
servers and technical copy protection mechanisms on the media. A recent example is the
copy protection mechanism on DVDs. However, copy protection is very difficult to achieve
in open systems, as recent incidents (like the DVD hack) show.
7.4 Other applications
Digital watermarks can also serve as invisible labels and content links. For example,
photo development laboratories may insert a watermark into the picture to link the print to its
negative. This way is very simple to find the negative for a given print. All one has to do is
scan the print and extracted the information about the negative. In order to distinguish
between different copies, different watermarks are embedded into different copies of the
same document. These marks are also called "digital fingerprints".
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CONCLUSION
Digital watermarking has rapidly advanced from theory to practice. This report
focuses on how watermarking techniques are advantageous over stegnography, cryptography
and also focuses on different types and domains of digital watermarking techniques.
A common application requirement for the watermarks is that they resist attacks that
would remove it. Some of the watermarks being attack-resistant may be accidentally removed
by unintended attacks such as cropping, reduction, or compression. There are also other
techniques like blind watermarking (which uses multiple watermarks and also no need of
original image at the of watermark recovery), which uses watermark nesting and encryption.
Nesting means it embeds an extra watermark into the main watermark and then embeds the
main watermark into the cover image.
This report has presented a hybrid watermarking technique for embedding characters
or grayscale image watermark into a container digital image based on the FHT for copyright
protection. Although Hadamard transform has lower energy compaction capability than other
high gain transforms, it was found to be more suitable for watermarking application because
the watermark energy could spread over the whole workspace and more likely to survive
under various attacks compared to other high gain transform domain such as DCT.
The experimental results showed that the proposed method is robust against most of
the Stirmark attacks and Checkmark non-geometric attacks. It was also shown to be more
robust than DCT algorithm under the same malicious attacks. Moreover, the Hadamard
transform offers a significant advantage in shorter processing time and ease of hardware
implementation than commonly used DCT and DWT techniques.
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