thesis_draft1

CHAPTER 1

INTRODUCTION

Over the past few years, there has been tremendous growth in computer networks

and more specifically, the World Wide Web demonstrating the commercial potential

of offering multimedia resources through the digital networks. This phenomenon,

coupled with the exponential increase of computer performance, has facilitated the

distribution of multimedia data such as images [1-6]. Since commercial interests seek

to use the digital networks to offer digital media for profit, a strong interest in

protecting the ownership rights arises. Publishers, artists, and photographers,

however, are unwilling to distribute pictures over the internet due to a lack of

security; images can be easily duplicated and distributed without the owner’s

consent. Digital watermarks [4,14,26], have been proposed as a way to tackle these

issues. The digital watermarks could discourage copyright violation, prevent

duplication and authenticate the contents.

The aim of watermarking [7,8,13,18,26] is to include subliminal information (i.e.,

imperceptible) in a multimedia document to ensure a security service or simply a

labeling application. It would be then possible to recover the embedded message at

any time, even if the document was altered by one or more nondestructive attacks,

whether malicious or not. A digital watermark [6] is a digital signal or pattern

inserted into a digital image. Since this signal or pattern is present in each unaltered

copy of the original image, the digital watermark may also serve as a digital

signature for the copies. A given watermark may be unique to each copy (e.g. to

identify the intended recipient), or common to multiple copies (e.g. to identify the

document source). In either case, the watermarking of the document involves the

transformation of the original into another form. This distinguishes digital

watermarking from digital fingerprinting, where the original file remains intact and a

new created file 'describes' the original file's content. The information embedded as a

watermark can be a bit string representing copyright message, serial number,

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grayscale or colored image, plain text, etc. The watermark is not always hidden but

sometimes visible watermarks are used such as a company logo.

Digital watermarking is also to be contrasted with public-key encryption [11-13,26],

which also transforms original files into another form. It is a common practice

nowadays to encrypt digital documents so that they are not viewable without the

decryption key. Unlike encryption, digital watermarking leaves the original image

(or file) intact and recognizable. In addition, digital watermarks, as signatures, may

not be validated without special software. Further, decrypted documents are free of

any residual effects of encryption, whereas digital watermarks are designed to be

persistent in viewing, printing, or subsequent retransmission or dissemination.

It is desirable that the watermark is irremovable from the cover image. However,

several intentional and unintentional operations with the watermarked image may

provide possibility for disabling the watermark. Commonly, these operations

(especially the intentional ones) are referred as attacks [16,26,29,36] against

watermarks.

This thesis presents a performance analysis of digital watermarking techniques in

spatial and transform domain for grayscale image. The work is carried on the

Lena.bmp image. Various techniques of watermark embedding in both the domains

are implemented in MATLAB and their performance is analyzed based on the

following:

1. Computational cost in terms of the time required for embedding and recovery

of the watermark.

2. Imperceptibility in terms of signal to noise ratio.

3. Robustness in terms of ratio of bits of the watermark retrieved correctly.

4. Capacity in terms of allowable size of watermark to be embedded.

5. Tamper resistance in terms of tolerance to geometrical distortions like scaling

and cropping; and in terms of signal processing applications like histogram

equalization, Gaussian noise, median filtering.

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The outline of the thesis is as follows:

Chapter 2 covers the history of watermarking, models, types, characteristics and

applications of watermarking systems focusing on the grayscale images. Various

attacks, intentional and unintentional are also covered in this chapter.

Chapter 3 covers the image watermarking techniques in spatial domain.

Chapter 4 covers the image watermarking techniques in transform domain. The

transform domains covered are Discrete Cosine Transform, Singular Value

Decomposition and Discrete Wavelet Transform.

Chapter 5 gives the performance parameters for which the techniques discussed in

chapter 3 and 4 are analyzed.

Chapter 6 contains the results of implementation of these techniques with analysis

and discussions.

Chapter 7 gives the conclusion of the work with future scope.

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CHAPTER 2

2.0 INTRODUCTION

The general idea of hiding some information in digital content has a wide class of

application. The techniques involved in such applications are collectively referred to

as information hiding techniques. For example, an image printed on a document is

annotated by metadata that could lead a user to its high resolution version. In general,

metadata provides additional information about an image. Usually, when a file is

transformed to another format (e.g., from TIFF to JPEG or to BMP), the metadata is

lost. Similarly, cropping or any other form of image manipulation destroys the

metadata. Also, metadata can only be attached to an image as long as the image

exists in the digital form and is lost once the image is printed. Information hiding

allows the metadata to travel with the image regardless of the file format and image

state (digital or analog).

2.1 HISTORY OF INFORMATION HIDING

The idea of communicating secretly is as old as communication itself. The earliest

allusion to secret writing in the West appears in Homer’s Iliad. Steganographic

methods made their record debut a few centuries later in several tales by Herodotus,

the father of history. Herodotus tells how around 440 B.C. Histiaeus [3,8,11] shaved

the head of his most trusted slave and tattooed it with a message which disappeared

after the hair had regrown. The purpose of this message was to instigate a revolt

against the Persians. Another slave could be used to send a reply.

During the American Revolution, invisible ink [3,8], made from milk, vinegar, fruit

juices and urine, which would glow over a flame was used by both the British and

Americans to communicate secretly. Later, chemically affected sympathetic inks

were developed. This was used in World Wars I and II. German spies hid text by

using invisible ink to print small dots above or below letters and by changing the

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heights of letter-strokes in cover texts. In World War I, prisoners of war would hide

Morse code messages in letters home by using the dots and dashes on i, j, t and f.

Censors intercepting the messages were often alerted by the phrasing and could

change them in order to alter the message. A message reading “Father is dead” was

modified to read “Father is deceased” and when the reply “Is Father dead or

deceased?” came back the censor was alerted to the hidden message. During World

War II, the Germans would hide data as microdots. Microdots are text or

photographic images that are shrunk down to the size and shape of a period or the dot

of an i or j. Microdots were usually sent by writing a letter containing periods, i's, or

j's, and the intended recipient could read the messages using a microscope. Because

of the extremely small size of the microdots the messages typically went unnoticed

by inspectors. FBI director J. Edgar Hoover described the use of microdots as “the

enemy’s masterpiece of espionage”.

A message sent by a German spy during World War II [39,41] read:

“Apparently neutral’s protest is thoroughly discounted and ignored. Isman hard hit.

Blockade issue affects for pretext embargo on by-products, ejecting suets and

vegetable oils.”

By taking the second letter of every word the hidden message retrieved is

“Pershing sails for NY June 1”

2.2 INFORMATION HIDING TERMINOLOGY

Information hiding, steganography and watermarking are three closely related fields

that have a great deal of overlap and share many technical approaches [7,40]. This

section discusses different information hiding terminologies. Figure 2.1 gives the

classification [9] of the information hiding techniques.

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Information hiding [40] is a general term encompassing a wide range of problems

beyond that of embedding messages in contents, the term hiding may refer to either

making the information imperceptible or keeping the existence of information secret.

Information Hiding

Steganography Cryptography Watermarking

Technical Linguistic

Figure 2.1: Classification of information hiding techniques

Steganography

Steganography is the art / science /study of communicating in a way which hides a

secret message in the main information. The origin of steganography is biological

and physiological. The term steganography came into use in 1500’s after the

appearance of Trithemius’ book on the subject “Steganographia”. The word

steganography is derived from two Greek words [39], “Stegos” meaning hidden or

covered and “Graphia” meaning writing. The goal of steganography is to avoid

drawing attention to the transmission of a hidden message. If suspicion is raised, then

this goal is defeated. In steganography an issue of concern is bandwidth for the

hidden message whereas robustness is of more concern with watermarking.

Steganography hides messages in plain sight rather than encrypting the message; it is

embedded in the data and doesn’t require secret transmission. The message is carried

inside data. Steganography is therefore broader than cryptography. Figure 2.2 (a)

shows the model of steganography [4].

The Steganographic techniques are classified as Technical and Linguistic

Steganography. The former, such as invisible ink tries to hide data physically while

the later one uses linguistic or language forms of hidden writing. Linguistic

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Steganography, also called acrostic was one of the popular ancient Steganographic

techniques. The secret messages were encoded [40] as initial letters of sentences or

successive tersest in a poem. These are the semagrams and the open code.

Semagrams hide information by the use symbols or signs. A visual semagram uses

innocent-looking or everyday physical objects to convey a message, such as doodles

or the positioning of items on a desk (or Web site). A text semagram hides a message

by modifying the appearance of the carrier text, such as subtle changes in font size or

type, adding extra spaces, or different flourishes in letters or handwritten text. Open

codes hide a message within a legitimate carrier message in ways that are not

obvious to an unsuspecting observer. The carrier message is sometimes called the

covert communication while the hidden message is the covert communication.

(a)

(b)

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Figure 2.2: (a) Steganography (b) Cryptography

Cryptography

Cryptography is the study of methods of sending messages in distinct form so that

only the intended recipients can remove the disguise and read the message. The

message we want to send is called plain text and disguised message is called cipher

text. The process of converting a plain text to a cipher text is called enciphering or

encryption, and the reverse process is called deciphering or decryption. Encryption

protects contents during the transmission of the data from the sender to receiver.

However, after receipt and subsequent decryption, the data is no longer protected and

is the clear. The schematic representation of the cryptography is given in Fig. 2.2 (b).

Steganography differs from cryptography in the sense that where cryptography is the

practice of scrambling a message to an obscured form to prevent others from

understanding it, steganography is the study of obscuring the message so that it

cannot be seen. Steganography and cryptography are both ways to protect

information from unwanted parties but neither technology alone is perfect and can be

compromised. Once the presence of hidden information is revealed or even

suspected, the purpose of steganography is partly defeated. The strength of

steganography can thus be amplified by combining it with cryptography.

Digital watermarking

A special case of steganography is digital watermarking. Watermarking is the

process that embeds data called a watermark, tag or label into a multimedia object

such that watermark can be detected or extracted to make an assertion about the

object may an image or video or audio may also be text only. A watermark is

perceived as an attribute of the carrier (cover). It may contain information such as

copyright, license and authorship etc. Whereas in case of steganography, the

embedded message may have nothing to do with the cover. The key difference

between steganography and watermarking is the absence of an active adversary. In

watermarking applications like copyright protection and authentication, there is an

active adversary that would attempt to remove, invalidate or forge watermarks. In

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steganography there is no such active adversary as there is no value associated with

the act of removing the information hidden in the content. Nevertheless,

steganography techniques need to be robust against accidental distortions.

2.2.1 DIFFERENCES BETWEEN STEGANOGRAPHY AND DIGITAL

WATERMARKING

Digital Information Hiding is the protection or concealing of digital information.

Steganography and Digital Watermarking are both sub-disciplines of information

hiding. Steganography is a way of hiding pertinent information. An example of

Steganography is sending a message containing invisible ink. The message appears

to be saying one thing but the invisible ink contains the true message. Watermarking

unlike Steganography focuses on the robustness of the information being hidden or

protected. The goal of Watermarking is for the watermarked information to be

irremovable. In fact, although primary focus is on invisible watermarks, this is not a

requirement. Watermarking focuses [15, 31] on protecting digital content and

therefore the watermarked information is always related to the digital content it is

applied to. Steganography does not follow this criterion while it is possible that the

information being hidden is related to the digital content itself, in many cases the

digital content is simply a decoy to hide the pertinent hidden information.

Steganography is usually applied to a one-to-one relationship and it is a two-way

communication. Information is hidden by one individual for another individual to

decode. Watermarking is usually applied to a one-to-many relationship and the

communication is one-way. Information is watermarked by one to prevent the theft

by many.

Thus, to summarize, the differences between Steganography and watermarking are:

Digital Watermarking:

Main goals are copyright protection and information authentication.

Inserts information related either to the host signal or its owner.

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Is either visible or imperceptible.

Is for communications point-to-multiple points.

Capacity is not an important issue.

Robustness is an important issue.

Digital Steganography:

Main goal is covert communication.

Inserts any kind of information.

Must not only be imperceptible but also statistically undetectable.

Is for communications point-to-point.

Capacity is an important issue.

May be robust (not necessary).

2.3 THE PRISONER’S PROBLEM: MODERN FORMULATION OF

STEGANOGRAPHY

Watermarking technique has evolved from steganography. The use of watermarks is

almost as old as paper manufacturing. Paper Watermarks have been in wide use since

the late middle Ages. Their earliest use seems to have been to record the

manufacturer’s trademark on the product so that the authenticity could be clearly

established without degrading the aesthetics and utility of the stock. Today most

developed countries also watermark their paper, currencies and postage stamps to

make forgery more difficult. The digitization of our world has expanded our concept

of watermarking to include immaterial digital impressions for use in authenticating

ownership claims and protecting proprietary interests. However, in principle digital

watermarks are like their paper ancestors. They signify something about the token of

a document or file in which they inherit. Whether be the product of paper press or

discrete cosine transformations, watermarks of varying degree of visibility are added

to presentation media as a guarantee of authenticity, quality ownership and source.

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Although steganography is an ancient subject, the modern formulation of it is often

given in terms of the prisoner’s problem [1,6,15,33] proposed by Simmons, where

two inmates, Alice and Bob, wish to communicate in secret to hatch an escape plan.

All of their communication passes through a warden, Wendy, who will throw them in

solitary confinement should she suspect any covert communication. The warden,

who is free to examine all communication exchanged between the inmates, can either

be passive or active [33]. A passive warden simply examines the communication to

try and determine if it potentially contains secret information. If she suspects a

communication to contain hidden information, a passive warden takes note of the

detected covert communication, reports this to some outside party and lets the

message through without blocking it. An active warden, on the other hand, will try to

alter the communication with the suspected hidden information deliberately, in order

to remove the information. The scenario is modeled as in figure 2.3. Alice wants to

send a secret message ‘m’ to Bob. In order to do so, she embeds ‘m’ into a cover

object ‘c’ and obtains a stego object ‘s’, which is sent over a public channel. Thus,

cover object refers to the object used as carrier to embed the secret message into and

the stego object is the object that contains the hidden message. In a pure

Steganographic scenario, the technique for embedding the message is unknown to

Wendy and shared as a secret between Alice and Bob. Sometimes it is considered

that the algorithm for embedding message is known but the key used by the

algorithm is kept as a secret between the two parties. Now Wendy has to find out if

the message sent is a stego object or not? In this context, Steganalysis refers to the

techniques that aid Wendy to distinguish between stego object and cover object,

sometimes even without knowing the algorithm used for embedding the secret

message, just determining a hidden message will do the work.

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Figure 2.3: General model for Steganography

2.4 GENERAL WATERMARKING SYSTEM

Digital Watermarking is a promising solution of content copyright protection in the

global network. It imposes extra robustness on embedded information. To put into

words, digital watermarking is the art and science of embedding copyright

information in the original files, the information embedded is called watermarks.

Digital watermarks don’t leave a noticeable mark on the content and not affect its

appearance. These are imperceptible and can be detected only by proper authorities.

Digital watermarks are difficult to remove without noticeably degrading the content

and are a covert means in situations where cryptography fails to provide robustness.

A watermarking system can be viewed as a communication system [30,34,35]

consisting of three main elements:

an embedder (insertion algorithm),

a communication channel and

a detector (verification or extraction or detection algorithm).

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Watermark information is embedded within the host signal before the watermarked

signal is transmitted over the communication channel, so that the watermark can be

detected at the receiving end, that is, at the detector.

Figure 2.4: A general watermarking system

A watermarking system is illustrated in figure 2.4. The dotted lines represent the

optional components, which may or may not be required according to the

application.

First of all, a watermark Wo is generated by the watermark generator with a secret

watermark generation key Kg. The watermark Wo can be a logo, or a pseudo-random

signal. Instead of directly embedding it into the host signal, the watermark Wo can be

pre-coded to optimize the embedding process, i.e. to increase robustness against

possible signal processing operations or imperceptibility of the watermark. This is

done by an information coder, which may require the original signal S0.

The outcome of the information coding component is denoted by symbol W that,

together with the original signal S0 and a secret key K, are taken as input of the

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embedder. The secret key K is intended to differentiate between authorized users and

unauthorized users at the detector in the absence of Kg. The embedder takes in W, S0

and K, so as to hide W within S0 in a most imperceptible way with the help of K, and

produce the watermarked signal Sw. Afterwards, Sw enters into the communication

channel where a series of unknown signal processing operations and attacks may

take place. The outcome of the communication channel is denoted by the symbol S’w.

At the receiving end, the detector works in an inversely similar way as the embedder,

and it may require the secret key Kg, K, and the original signal S0. Then the detector

reads S´w and decides if the received signal has the legal watermark. Each owner has

a unique watermark or an owner can also put different watermarks in different

objects the marking algorithm incorporates the watermark into the object. The

verification algorithm authenticates the object determining both the owner and the

integrity of the object. A watermark must be detectable or extractable to be useful.

Depending on the way the watermark is inserted and depending on the nature of the

watermarking algorithm, the method used can involve very distinct approaches. In

some watermarking schemes, a watermark can be extracted in its exact form, a

procedure we call watermark extraction. In other cases, we can detect only whether a

specific given watermarking signal is present in an image, a procedure we call

watermark detection. It should be noted that watermark extraction can prove

ownership whereas watermark detection can only verify ownership.

2.5 CLASSIFICATION OF WATERMARKING

A digital watermark [34] is a digital signal or pattern inserted into a digital image.

Since this signal or pattern is present in each unaltered copy of the original image,

the digital watermark may also serve as a digital signature for the copies. A

watermark may be unique to each copy or may be common to multiple copies. In

either case, the watermarking of the image involves the transformation of the original

into another form.

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The classification of watermarks and watermarking techniques is very broad. These

are divided into various categories [8, 11, 12] based on different criterions as shown

in figure 2.5.

Figure 2.5: Types of watermarking techniques

According to the type of Document

Watermarking techniques can be divided into four categories according to the type of

document [18] to be watermarked as follows.

Image Watermarking

Video Watermarking

Audio Watermarking

Text Watermarking

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According to the prior exchange of data

The watermarking system is said to be pure watermarking system [33,35,37] if it

does not require prior exchange of data like shared secret keys while it is said to be

shared-key or shared-secret watermarking system if there is required a prior

exchange of keys. Depending on the exchange and availability of keys these shared

key systems are further classified. Public- key steganography [29, 31,35, 37] does

not rely on shared-key exchange. Instead it is based on the public-key cryptography

principle in which there are two keys, one being the public key which can be usually

obtained from a public database and the other a private key. Usually in this case the

public key is used in the embedding process and the private key in the decoding

process. A typical watermarking system is a shared-secret system. Private-key

steganography no public key and the intended recipient is to be supplied with the

key separately.

According to how watermark is detected and extracted

Many of the watermarking algorithms initially published required that the original

data be available to the detector. It would typically be subtracted from the

watermarked data to reveal the watermark itself. These are referred to as private

watermarks [29]. Watermark detection and extraction that do not depend on the

availability of original image are referred to as Blind watermarking [12,31,35]

techniques. The drawback is when the watermarked image is seriously destroyed;

watermark detection will become very difficult. Nonblind-extracting [12,29,35]

watermark can only be detected by those who have a copy of original image. It

guarantees better robustness but may lead to multiple claims of ownerships.

According to the domain for watermark embedding

On the basis of domain used for watermarking the techniques fall in two categories:

those which use spatial domain and those which use transform domain. Spatial-

domain watermarking [12,18] technologies change the intensity of original image or

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gray levels of its pixels. This kind of watermarking is simple and with low

computing complexity, because no frequency transform is needed. However, there

must be tradeoffs between invisibility and robustness, and it is hard to resist common

image processing and noise. Transform-domain watermarking [12,18] embeds the

watermark into the transformed image. It is complicated but has the merits which the

former approach lacks.

According to the ability of watermark to resist attack

Fragile watermarks [12,18,29,35] are ready to be destroyed by random image

processing methods. The change in watermark is easy to be detected, thus can

provide information for image completeness. Robust watermarks [12,18,29,35] are

unaffected under most image processing methods and can be extracted from heavily

attacked watermarked image. Thus it is preferred in copyright protection.

According to the human perception

According to the human perception [8,11,18,35], the digital watermarks can be

divided into different types as follows.

Visible watermark

Invisible-Robust watermark

Invisible-Fragile watermark

Dual watermark

Visible watermark is a secondary translucent overlaid into the primary image. The

watermark appears visible to a casual viewer on a careful inspection. The invisible-

robust watermark is embedded in such a way that an alternation made to the pixel

value is perceptually not noticed and it can be recovered only with appropriate

decoding mechanism. The invisible-fragile watermark is embedded in such a way

that any manipulation or modification of the image would alter or destroy the

watermark. An invisible robust private watermarking scheme requires the original or

reference image for watermark detection; whereas the public watermarks do not. The

class of invisible robust watermarking schemes that can be attacked by creating a

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counterfeit original is called invertible watermarking scheme. .Dual watermark [42]

is a combination of a visible and an invisible watermark .In this type of watermark an

invisible watermark is used as a back up for the visible watermark as clear from the

following diagram shown in figure 2.6.

Figure 2.6: Schematic representation of dual watermarking

According to the application

From application point of view digital watermark is either source based or

destination based. Source-based watermark are desirable for ownership identification

or authentication where a unique watermark identifying the owner is introduced to all

the copies of a particular image being distributed. A source-based watermark could

be used for authentication and to determine whether a received image or other

electronic data has been tampered with. The watermark could also be destination

based where each distributed copy gets a unique watermark identifying the particular

buyer. The destination -based watermark could be used to trace the buyer in the case

of illegal reselling.

2.6 APPLICATIONS OF WATERMARKING

The requirements that a watermarking system needs to comply with depends upon

the specific type of application. A few most common applications [2,3,15,38]

involve:

1. Owner Identification: The owner identification [2,3,15,18] can be printed on the

covers or mentioned somewhere on the item. Examples are the identification mark of

an audio company on the CD case or the mark of the paper manufacturer on top

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corner of the paper. These types of watermarks can be easily removed by cropping

the image or by tearing the part that has the identification. Digital watermarking

helps to overcome this problem by embedding the watermark in the form of bits and

forming an integral part of the content. The device reads the CD and identifies the

watermark. For having further access to the CD the owner should have a license or

he should have paid a fee to access the copyrighted work.

2. Copy Protection: To prevent the data from being copied [3,15,18] a watermark

can be introduced in the data with a copy protect bit. When the copying device reads

the data, the watermark detecting circuitry should detect the watermark and stop

recording. This would need all the copying machines to have the watermark circuitry

to identify the watermark and act accordingly.

3. Broadcast Monitoring: A commercial advertisement may be watermarked

putting a unique watermark in each video or sound clip prior to broadcast [3].

Automated monitoring systems can then receive broadcasts and check for these

watermarks, identifying when and where each clip appears. This proves very helpful

for the advertisers as they actually pay for only the number of times the

advertisement was actually relayed.

4. Medical applications: Names of the patients can be printed on the X-ray reports

and MRI scans using techniques of visible watermarking. The medical reports play a

very important role in the treatment offered to the patient. If there is a mix up in the

reports of two patients this could lead to a disaster.

5. Fingerprinting: A fingerprinting [15] technique can be used to trace the source of

illegal copy. Every copy available can be watermarked with a unique bit sequence.

Now, if a copy is made illegally the source can be easily tracked since each original

copy had a unique bit sequence embedded into it.

6. Data Authentication: A given set of data (images) can be easily tampered

without even being detected. To avoid this [18] and maintain the originality of the

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image a watermark like signature, a set of words, may be embedded into the image.

If the image is now being tampered it can be easily detected as the pixel values of the

embedded data would change and not match the original pixel values. If the image is

being copied it would lose its authentication as the embedded data would not be

copied along with the image.

Different types of watermarks are used for different applications depending upon

their characteristics as follows.

2.6.1 Applications of visible watermark

Visible watermarks can be used in following cases:

Visible watermarking for enhanced copyright protection [35]. In such

situations, where images are made available through Internet and the content

owner is concerned that the images will be used commercially (e.g. imprinting

coffee mugs) without payment of royalties. Here the content owner desires an

ownership mark, that is visually apparent, but which does not prevent image

being used for other purposes.

Visible watermarking used to indicate ownership [35] originals. In this case

images are made available through the Internet and the content owner desires to

indicate the ownership of the underlying materials (library manuscript), so an

observer might be encouraged to patronize the institutions that own the material.

2.6.2. Applications of invisible robust watermark

Invisible robust watermarks find application in following cases.

Invisible watermarking to detect misappropriated images [35]. In this

scenario, the seller of digital images is concerned, that his, fee-generating images

may be purchased by an individual who will make them available for free, this

would deprive the owner of licensing revenue.

Invisible watermarking as evidence of ownership [35]. In this scenario, the

seller that of the digital images suspects one of his images has been edited and

published without payment of royalties. Here, the detection of the seller’s

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watermark in the image is intended to serve as evidence that the published image

is property of seller.

2.6.3 Applications of Invisible fragile watermarks

Following are the applications of invisible fragile watermarks.

Invisible watermarking for a trustworthy camera. In this scenario, images are

captured with a digital camera for later inclusion in news articles. Here, it is the

desire of a news agency to verify that an image is true to the original capture and

has not been edited to falsify a scene. In this case, an invisible watermark is

embedded at capture time; its presence at the time of publication is intended to

indicate that the image has not been attended since it was captured.

Invisible watermarking to detect alternation [35] of images stored in a digital

library. In this case, images (e.g. human fingerprints) have been scanned and

stored in a digital library; the content owner desires the ability to detect any

alternation of the images, without the need to compare the images to the scanned

materials.

2.7 ATTACKS ON WATERMARKS

A watermarked image is likely to be subjected to certain manipulations [3,18,21,40],

some intentional such as compression and transmission noise and some intentional

such as cropping, filtering, etc. They are summarized in figure 2.7.

Lossy Compression: Many compression schemes like JPEG and MPEG can

potentially degrade the data’s quality through irretrievable loss of data.

Geometric Distortions [3]: Geometric distortions are specific to images videos

and include such operations as rotation, translation, scaling and cropping.

Common Signal Processing Operations: They include the followings.

o D/A conversion

o A/D conversion

o Resampling

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o Requantization

o Dithering distortion

o Recompression

o Linear filtering such as high pass and low pass filtering

o Addition of a constant offset to the pixel values

o Addition of Gaussian and Non Gaussian noise

o Local exchange of pixels

Other intentional attacks:

o Printing and Rescanning

o Watermarking of watermarked image (rewatermarking)

o Collusion: A number of authorized recipients of the image should not be

able to come together (collude) and like the differently watermarked

copies to generate an un-watermarked copy of the image (by averaging all

the watermarked images).

o Forgery: A number of authorized recipients of the image should not be

able to collude to form a copy of watermarked image with the valid

embedded watermark of a person not in the group with an intention of

framing a 3rd party.

22

Figure 2.7: Attacks on watermarks

These attacks may also be classified as active attacks, passive attacks, collusion

attacks and forgery attacks.

Active Attacks: Here, the hacker tries deliberately to remove the watermark or

simply make it undetectable. This is a big issue in copyright protection,

fingerprinting or copy control for example.

Passive attacks: In this case, the attacker is not trying to remove the watermark but

simply attempting to determine if a given mark is present or not. As the reader

should understand, protection against passive attacks is of the utmost importance in

23

covert communications where the simple knowledge of the presence of watermark is

often more than one want to grant.

Collusion attacks: In collusive attacks [3], the goal of the hacker is the same as for

the active attacks but the method is slightly different. In order to remove the

watermark, the hacker uses several copies of the same data, containing each different

watermark, to construct a new copy without any watermark. This is a problem in

fingerprinting applications (e.g. In the film industry) but is not the widely spread

because the attacker must have access to multiple copies of the same data and that

the number needed can be pretty important.

Forgery attacks: This is probably the main concern in data authentication. In

forgery attacks, the hacker aims at embedding a new, valid watermark rather than

removing one. By doing so, it allows him to modify the protected data as he wants

and then, re-implants a new given key to replace the destructed (fragile) one, thus

making the corrupted image seems genuine.

These four types of malicious attacks are only a categorization of what has been

encountered in the past. Of course, a lot of new attacks can be designed and it is

impossible to know what will come out next from hackers’ imagination. To those

malicious attacks, one must add all signal processing operations involved in the

transmission or storage of data, which can naturally degrade the image and alter the

watermarked information to the point of not being detectable anymore. In fact, the

identification and classification of attacks, as well as the implantation of a standard

benchmark for robustness testing is of great importance and will be a key issue in the

future development of watermarking.

2.8 DESIRED CHARACTERISTICS OF WATERMARKS

This section focuses on a number of watermarking system requirements

[13,15,18,21,38] as well as the tradeoffs among them.

24

Security: The security requirement of a watermarking system can differ slightly

depending on the application. Watermarking security implies that the watermark

should be difficult to remove or alter without damaging the host signal. As all

watermarking systems seek to protect watermark information, without loss of

generality, watermarking security [2] can be regarded as the ability to assure

secrecy and integrity of the watermark information, and resist malicious attacks.

Imperceptibility: The imperceptibility [2, 3] refers to the perceptual

transparency of the watermark. Ideally, no perceptible difference between the

watermarked and original signal should exist. A straightforward way to reduce

distortion during watermarking process is embedding the watermark into the

perceptually insignificant portion of the host signal. However, this makes it easy

for an attacker to alter the watermark information without being noticed.

However, other techniques, such as spread spectrum [3], can be used to add

imperceptible or unnoticeable watermarks in perceptually significant regions.

Capacity: Watermarking capacity [2] normally refers to the amount of

information that can be embedded into a host signal. Generally speaking,

capacity requirement always struggle against two other important requirements,

that is, imperceptibility and robustness as shown in figure 2.8. A higher capacity

is usually obtained at the expense of either robustness strength or

imperceptibility, or both.

Figure 2.8: The tradeoffs among imperceptibility, Robustness, and capacity

Robustness: Robustness[2,3,18] actually comprises two separate issues:

1) Whether or not the watermark is still present in the data after distortion.

2) Whether the watermark detector can detect it.

25

For example, watermarks inserted into images by many algorithms remain in the

signal after geometric distortions such as scaling, but the corresponding detection

algorithms can only detect the watermark if the distortion is first removed. In this

case, if the distortion cannot be determined and/or inverted, the detector cannot

detect the watermark even though the watermark is still present albeit in a

distorted form. Apart from malicious attacks, common signal processing

operations can pose a threat to the detection of watermark, thus making it

desirable to design a watermark that can survive those operations. For example, a

good strategy to robustly embed a watermark into an image is to insert it into

perceptually significant parts of the image. Therefore, robustness is guaranteed

when we consider the case of lossy compression which usually discards

perceptually insignificant data, thus data hidden in perceptual significant portions

is likely to survive lossy compression operation. However, as this portion of the

host signal is more sensitive to alterations, watermarking may produce visible

distortions in the host signal. The exact level of robustness an algorithm must

possess cannot be specified without considering the application scenario. Not all

watermarking applications require a watermark to be robust enough to survive all

attacks and signal processing operations. Indeed, a watermark needs only to

survive the attacks and those signal processing operations that are likely to occur

during the period when the watermarked signal is in communication channel. In

an extreme case, robustness may be completely irrelevant in some case where

fragility is desirable.

Tamper-resistance: Watermarks are often required to be resistant to signal

processing that is solely intended to remove them, in addition to being robust

against the signal distortions that occur in normal processing. We refer to this

property as tamper-resistance [3]. Tamper-resistance can be visualized in the

same way that we visualize robustness.

Key restrictions: An important distinguishing characteristic is the level of

restriction placed on the ability to read a watermark. The watermarks in which

the key is available to a very large number of detectors are described as

26

“unrestricted-key” watermarks, and those in which keys are kept secret by one or

a small number of detectors are described as “restricted-key” watermarks. Some

watermarking methods create a unique key for each piece of data that is

watermarked. Such algorithms can be used for restricted-key applications, where

the owner of the original data can afford to keep a database of keys for all the

data that has been watermarked. But they cannot be used for unrestricted-key

applications, since this would require every detector in the world having a

complete list of all the keys. Thus, algorithms for use as unrestricted-key systems

must employ the same key for every piece of data.

Computational cost: The speed requirements are highly application dependent.

In general, there is often an asymmetry between the requirement for speed of

insertion and speed of detection. This is particularly true when watermarks need

to be inserted or detected in real-time video or audio. Another issue to consider in

relation to computational cost is the issue of scalability [3,18]. It is well known

that computer speeds are increasing and it is therefore very desirable to design a

watermark whose detector and/or inserter is scalable with each generation of

computers.

2.8.1 Desired characteristics of visible watermarks [15]

A visible watermark should be obvious in both color and monochrome images.

The watermark should spread in a large or important area of the image in order to

prevent its deletion by clipping.

The watermark should be visible yet must not significantly obscure the image

details beneath it.

The watermark must be difficult to remove. Rather, removing a watermark

should be more costly and labor intensive than purchasing the image from the

owner.

The watermark should be applied automatically with little human intervention

and labor.

27

2.8.2 Desired characteristics of invisible robust watermarks [15]

The invisible watermark should neither be noticeable to the viewer nor should

degrade the quality of the content.

An invisible robust watermark must be robust to common signal distortions and

must be resistant to various intentional tampering solely intended to remove the

watermark.

Retrieval of watermark should unambiguously identify the owner.

It is desirable to design a watermark whose decoder is scalable with each

generation of computer.

While watermarking high quality images and art works the amount of pixel

modification should be minimum.

Insertion of watermark should require little human intervention or labor.

The robust watermark must be able to reliably carry higher number of

information bits in the presence of attacks.

2.8.3 Desired characteristics of invisible fragile watermarks [15]

The invisible watermark should neither be noticeable to the viewer nor should

degrade the quality of the content.

An invisible fragile watermark should be readily modified when the image pixel

values have been altered.

The watermark should be secure. This means that it is impossible to recover the

changes, or regenerate the watermark after image alternations, even when the

watermarking procedure, and/or the watermark itself is known.

For high quality images, the amount of individual pixel modification should be as

small as possible.

2.9 IMAGE STEGANOGRAPHY

28

There have been a number of image steganography algorithms proposed which find

wide use in the image watermarking domain. These algorithms could be categorized

in a number of ways [6,35]:

1. Spatial or Transform, depending on redundancies used from either domain for

the embedding process.

2. Model based or ad-hoc, if the algorithm models statistical properties before

embedding and preserves them, or otherwise.

3. Active or Passive Warden, based on whether the design of embedder-detector

pair takes into account the presence of an active attacker.

2.9.1 SPATIAL DOMAIN WATERMARKING

The techniques for spatial domain watermarking [21] insert the watermark into the

intensity values of the predefined regions of the image. The best widely known

watermarking algorithm is based on modifying the least significant bit layer of

images, hence known as the LSB technique. This technique makes use of the fact

that the least significant bits in an image could be thought of random noise and

changes to them would not have any effect on the image. Although the image seems

unchanged visually after the LSBs are modified, the statistical properties of the

image changes significantly. In the LSB technique, the LSB of the pixels is replaced

by the message to be sent. The message bits are permuted before embedding, this has

the effect of distributing the bits evenly, thus on average only half of the LSB's will

be modified. Different tools vary in their approach for hiding information. Some

algorithms change LSB of pixels visited in a random walk, others modify pixels in

certain areas of images, or instead of just changing the last bit they increment or

decrement the pixel value.

Spatial domain technique for watermarking can also be applied using color

separation. In this way, the watermark appears in only one of the color bands. This

renders the watermark visibly subtle such that it is difficult to detect under regular

viewing. However, the mark appears immediately when the colors are separated for

29

printing. This renders the document useless for the printer unless the watermark can

be removed from the color band. This approach is used commercially for journalists

to inspect digital pictures from a photo-stock house before buying unmarked

versions.

Another approach for embedding in spatial domain is that, noise that statistically

resembles common processing distortion, e.g., scanner noise, or digital camera noise,

is introduced to pixels on a random walk. The noise is produced by a pseudo random

noise generator using a shared key. A parity function is designed to embed and detect

the message signal modulated by the generated noise. These are referred to as

Correlation based techniques. The next chapter discusses different spatial domain

watermark embedding techniques in detail.

2.9.2 TRANSFORM DOMAIN EMBEDDING

Another category for embedding techniques for which a number of algorithms have

been proposed is the transform domain [2,21,30] embedding category. Most of the

work in this category has been concentrated on making use of redundancies in the

DCT (discrete cosine transform) domain, which is used in JPEG compression.

Embedding in DCT domain is simply done by altering the DCT coefficients [6,30].

Although changing the DCT coefficients will cause unnoticeable visual artifices,

they do cause detectable statistical changes. But there have been other algorithms

which make use of other transform domains, such as the frequency domain, by

quantizing the coefficients in the frequency domain in order to embed messages.

Since high frequencies will be lost by compression or scaling, the watermark signal

is applied to lower frequencies, or better yet, applied adaptively to frequencies that

contain important information of the original picture. Since watermarks applied to

the frequency domain will be dispersed over the entirety of the spatial image upon

inverse transformation, this method is not as susceptible to defeat by cropping as the

spatial technique. However, there is more a tradeoff here between invisibility and

decodability, since the watermark is in effect applied indiscriminately across the

spatial image. The other important and upcoming methods use Discrete Wavelet

30

Transform, Fast Wavelet Transform and Singular Value Decomposition. The basic

principle of use of these transforms remains the same. The transform coefficients are

altered.

Some other transforms used are Radon Transform, Hartley Transform [22], Discrete

Laguerre Transform[25], Steerable Pyramid Transform[26]. There are many more

algorithms proposed lately which use more than one transform[23] i.e. there exists a

class of hybrid techniques to embed a watermark. The simplest example is modifying

Singular Values of the Discrete Cosine Transform of an image to put in watermark

secretly.

The table 2.1 shows the comparison of the spatial domain and Transform domain

watermarking techniques depending upon various characteristics. The data is

practically evaluated in Chapter 6.

Characteristics Spatial Domain Transform Domain

Computation Cost Low High

Robustness Fragile More robust

Perceptual quality High Control Low control

Capacity High(depends on image size) Low

Example of Application Mainly authentication Copyright

Table 2.1: Comparison between watermarking techniques

2.9.3 MODEL BASED TECHNIQUES

Unlike previously discussed techniques, model based techniques [6,24] try to model

statistical properties of an image, and preserve them in the embedding process. For

example, the transformed image coefficients are divided into two parts and the

perceptually insignificant component is replaced with the coded message signal.

Another model based technique proposed to process the message signal so that it

31

would exhibit the properties of an arbitrary cover signal. This approach is called data

masking.

As argued if Alice wants to send an encrypted message to Bob, the warden Wendy

would be able to detect such a message as an encrypted stream since it would exhibit

properties of randomness. In order for a secure channel to achieve covertness, it is

necessary to preprocess the encrypted stream at the end points to remove randomness

such that the resulting stream defeats statistical tests for randomness and the stream

is reversible at the other end.

CHAPTER 3

IMAGE WATERMARKING IN SPATIAL DOMAIN

The most straight-forward method of watermark embedding would be to embed the

watermark into the least-significant-bits of the cover object. This technique lies

under spatial domain watermarking techniques.  Given the extraordinarily high

32

channel capacity of using the entire cover for transmission in this method, a smaller

object may be embedded multiple times. Even if most of these are lost due to attacks,

a single surviving watermark would be considered a success. The resulting

watermark may be visible or invisible depending upon the value (large or small,

respectively) of the watermark intensity.

3.1 SIMPLE LSB SUBSTITUTION

A naive algorithm for LSB substitution would be to take the first M cover pixels

where M is the length of the secret message to be hidden in bits. And then every

pixel's last bit is replaced [1,2,6,13] by one of the message bit because this has

negligible effect to the appearance of the carrier message. This can be observed in

figure 3.1.

Image 1 grayscale pixel value=128

Image 2 grayscale pixel value=129

Image 3 grayscale pixel value=000

Figure 3.1: Effect of changing LSB and MSB on grayscale pixel value

Consider that the grayscale value at any arbitrary pixel is 128 represented with 8 bits

as 10000000. Now, if LSB is changed from zero to one, the grayscale pixel value

changes from 128 to 129, which is undetectable to human eye. However if MSB is

changed, the change in gray level is from 128 to 0 which is a significant change to be

detected by human eye. This is the simplistic case; we could get away with replacing

more than one bit also.

X w = 0 1

…………

7 = 0111 y = 6 = 0110 7 = 0111

1 0 0 0 0 0 0 0

1 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0

33

D = 1 = 0

8 = 1000 y = 8 = 1000 9 = 1001

D = 0 = 1

…………

Table 3.1: Distortion for R=1

x w = 00 01 10 11

…………..

4 = 0100 y=4=0100 5=0101 6=0110 7=0111

D = 0 = 1 = 2 =3

5 = 0101 y=4=0100 5=0101 6=0110 7=0111

D = 1 = 0 = 1 =2

6 = 0110 y=4=0100 5=0101 6=0110 7=0111

D = 2 = 1 = 0 =1

7 = 0111 y=4=0100 5=0101 6=0110 7=0111

D = 3 = 2 = 1 =0

8 = 1000 y=8=1000 9 = 1001 10=1010

11=1011

D = 0 = 1 = 2 = 3

9 = 1001 y=8=1000 9 = 1001 10=1010

11=1011

D = 1 = 0 = 1 = 2

10 = 1010 y=8=1000 9 = 1001 10=1010

11=1011

D = 2 = 1 = 0 = 1

11 = 1011 y=8=1000 9 = 1001 10=1010

11=1011

D = 3 = 2 = 1 = 0

………….

Table 3.2: Distortion for R = 2

If we assume the set of permissible gray levels is represented with B number of

bits, the number of bit used for message embedding as R and the value of bit(s) as w,

then say the gray level changes from x to y. Then the distortion [13] introduced due

34

to change in LSB can be given with the help of the following tables. From table 3.1

[13], for R=1 the distortion is and from table 3.2 [13], for R= 2 the average

distortion is .

To recover the watermark, the LSB of the watermarked image are extracted. LSB

substitution however despite its simplicity brings a host of drawbacks. Although it

may survive transformations such as cropping, any addition of noise or lossy

compression is likely to defeat the watermark. An even better attack would be to

simply set the LSB bits of each pixel to 1 or 0 fully defeating the watermark with

negligible impact on the cover object. Furthermore, once the algorithm is discovered,

the embedded watermark could be easily modified by an intermediate party.

This technique is a pure watermarking technique as it does not require a key to be

shared between the sender and the receiver but only the number of bits used for

hiding the data. One solution to improve the robustness of the watermark is to use a

pseudo random number generator [4] to determine the pixels to be used for

embedding. This is discussed in the following section. The security is increased but it

does require a key or a password to be sent with the image or shared between the

users.

3.2 VISITING PIXELS IN A RANDOM WALK FOR LSB SUBSTITUTION

An improvement on basic LSB substitution would be to use a pseudo-random

number generator [2,4,12] to determine the pixels to be used for embedding based on

a given “seed” or key.

Security of the watermark would be improved as the watermark could no longer be

easily viewed by intermediate parties. The algorithm however would still be

vulnerable to replacing the LSBs with a constant. Even in locations that were not

used for watermarking bits, the impact of the substitution on the cover image would

be negligible. LSB modification proves to be a simple and fairly powerful tool for

35

stenography, however lacks the basic robustness that watermarking applications

require.

To recover the watermark, the same key is used to regenerate the pseudo-random

number generator to determine the pixel where watermark was embedded. Extracting

the LSB of these pixels gives back the watermark.

3.3 OTHER LSB SUBSTITUTION TECHNIQUES

Many other LSB substitution techniques are found in the literature where different

coding schemes like Hamming Codes and Golay Codes for example are used as they

affect the LSB of each gray scale symbol. These techniques find the modified forms

in literature with the use of ternary embedding [13]. These methods have lower

distortion rates.

3.4 ADVANTAGES AND DISADVANTAGES OF LSB SUBSTITUTION

Advantages:

1. It is a well-rounded method and lends itself to a variety of information hiding

applications.

2. A large quantity of embedded information can be included in even the most

modestly sized images.

3. LSB can also allow for the hiding of photographic images and even audio

recordings.

4. Calculation complexity is relatively low.

Disadvantages [12]:

1. Any attack or noise distortion of the composite image will seriously damage

the imbedded data.

2. Cropping or translation of the composite image will destroy an equal portion

of the imbedded image.

3. Robustness limits the overall effectiveness.

36

3.5 CORRELATION BASED TECHNIQUES

These techniques for watermark embedding exploit the correlation properties of

additive pseudo-random noise patterns as applied to an image [11]. Pseudo-

random noise sequences are a good tool for watermarking because

of the following reasons:

PN generator produces periodic sequences that appear to be

random.

PN sequences are generated by an algorithm that uses an

initial seed.

The PN sequence generated is actually not statically random

but will pass many tests of randomness.

Unless the algorithm and seed are known, the sequence is

impractical to predict.

A pseudo-random noise (PN) pattern, W(x,y) is added to the cover image, I(x,y)

according to the equation shown below

, 3.1

Where, k is the gain factor, and is the watermarked image. Increasing k increases

the robustness of the watermark at the expense of the quality of the watermarked

image. To retrieve the watermark, the same pseudo-random noise generator

algorithm is seeded with the same key, and the correlation between the noise pattern

and possibly watermarked image computed. If the correlation exceeds a certain

threshold T, the watermark is detected, and a single bit is set. This method can easily

be extended to a multiple-bit watermark by dividing the image up into blocks, and

performing the above procedure independently on each block.

37

This basic algorithm can be improved in a number of ways. First, the notion of a

threshold being used for determining a logical “1” or “0” can be eliminated by using

two separate pseudo-random noise patterns. One pattern is designated a logical “1”

and the other a “0”. The above procedure is then performed once for each pattern,

and the pattern with the higher resulting correlation is used. This increases the

probability of a correct detection, even after the image has been subject to attack.

We can further improve the method by pre-filtering the image before applying the

watermark.   If we can reduce the correlation between the cover image and the PN

sequence, we can increase the immunity of the watermark to additional noise. By

applying the edge enhancement filter shown below in figure 3.2, the robustness of

the watermark can be improved with no loss of capacity and very little reduction of

image quality.

. 3.2

Figure 3.2: FIR edge enhancement pre-filter

Rather then determining the values of the watermark from “blocks” in the spatial

domain, we can employ CDMA spread-spectrum techniques to scatter each of the

bits randomly throughout the cover image, increasing capacity and improving

resistance to cropping. The watermark is first formatted as a long string rather then a

2D image. For each value of the watermark, a PN sequence is generated using an

independent seed. These seeds could either be stored, or themselves generated

through PN methods. The summation of all of these PN sequences represents the

watermark, which is then scaled and added to the cover image.

To detect the watermark, each seed is used to generate its PN sequence, which is then

correlated with the entire image. If the correlation is high, that bit in the watermark is

set to “1”, otherwise a “0”. The process is then repeated for all the values of the

watermark. CDMA improves on the robustness of the watermark significantly, but

requires several orders more of calculation.

38

3.6 EMBEDDING CHECKSUM IN LSB

Another variation in the approach for exploiting the spatial domain for information

hiding can be to hide the checksum [5, 30] for the cover image divided into blocks

instead of the binary logo or file directly. A checksum is the modulo-2 addition of a

sequence of fixed-length binary words; it is a special type of hash function. The

technique divides the cover image into blocks and for each block then selects a

pseudorandom group of pixels according to a secret key. The checksum is calculated

by summing the numbers determined by the seven most significant bits of selected

pixels which is then embedded in the LSB. As proposed in [5], the checksum can be

calculated using all the pixels in the block and selecting a large integer N using the

following equation.

, 3.3

where, M is the number of pixels in each block, ai is pseudorandom sequence of M

integers comparable in size to N and g(pi) is the gray level of pixel determined by the

seven MSBs. Further before embedding this checksum, the binary form of it is

encrypted. The checking process is similar to the embedding process. It consists of

comparing, for each block, the check-sum determined by the MSB of the tested

image with the original check-sum value recovered from the LSB. The main

advantages of this method are that it does not produce visible changes in the image

and provides a very high probability of tamper detection. For example, if we swap

only two pixels of any block, the check-sum will be modified because each pixel pi

of the block is multiplied by a different coefficient ai . Furthermore the random walk

of the pixels pi and the coefficients ai are block dependent, thus making it impossible

to swap or duplicate entire blocks without making undetected changes.

Advantages

39

1. Embedding W only changes (on average) half of the pixels covered by W. This not

only reduces visual distortion but also increases security.

2. An image may hold many W as long as they do not overlap.

3. This method is very fast.

Disadvantages

1. This watermarking method is fragile. Any change to either the image data itself or

the embedded checksum can cause the verification procedure to fail.

2. The checksum method does not detect pixel swaps or similar attacks. A forger

could replace a section of watermarked block with one of equal size and checksum.

3. An attacker could remove the entire watermark by replacing the LSB plane.

3.7 SPATIAL WATERMARKING USING BITMAP PARITY CHECKING

APPROACH

This approach [19] does not directly embed the information in the LSB but does so

with a certain criterion. This is achieved by using the mean gray value and bitmap in

the block to hide the logo in a secret, undetectable and unambiguous way. The

technique is fragile and blind in nature. In this technique the image f(x,y) is broken

down into blocks and the corresponding bitmaps are obtained by comparing the pixel

values with the block mean value according to the following equations:

. 3.4

The pixel values may be modified to embed logos by checking the even or odd parity

of the block bitmap using sum (S) of the binary values of the bitmap and a random

number R such that the following relation is satisfied for each block, k.

. 3.5

40

A secret key and a random number generator are used to enhance the logo in a secret,

undetectable, and unambiguous way. If sum does not satisfy the above relation, a

pixel with value f(x,y) is chosen and is modified to f’(x,y)

, 3.6

where, is pre-selected random value between 0 and standard deviation for each

block. By choosing a modified pixel near to the mean value of the block and

diffusing the errors of modifications the neighborhood pixels, we can obtain the

smallest value of the mean absolute error in the watermarked image. For retrieving

the watermark, the watermarked image is divided into the same sized non-

overlapping blocks as for embedding process. For each block the bitmap and the sum

is calculated and using the following relation the watermark bit is decided.

, 3.7

where, R produced by a random number generator using the original secret

key.

41

CHAPTER 4

IMAGE WATERMARKING IN TRANSFORM DOMAIN

An advantage of the spatial domain techniques discussed in the previous chapter is

that they can be easily applied to any image regardless of subsequent processing

(whether they survive this processing however is a different matter entirely). But the

disadvantage of spatial techniques is they do not allow for the exploitation of this

subsequent processing in order to increase the robustness of the watermark.

In addition to this, adaptive watermarking techniques are a bit more difficult in the

spatial domain. Both the robustness and quality of the watermark are improved if the

properties of the cover image are exploited. For instance, it is generally preferable to

hide watermarking information in noisy regions and edges of images, rather then in

smoother regions. The benefit is two-fold; Degradation in smoother regions of an

image is more noticeable to the Human Visual System (HVS), and becomes a prime

target for lossy compression schemes.

Taking these aspects into consideration, working in a transform domain becomes

very attractive. The classic and still most popular domain for image processing is that

of the Discrete-Cosine-Transform, or DCT. Although changing the DCT coefficients

will cause unnoticeable visual artifices, they do cause detectable statistical changes.

Another transform domain which is being exploited is Singular Value

Decomposition (SVD) due to its simplicity in implementation and attractive

mathematical features. It is one of the most powerful numerical analysis technique

and used in various applications. Some SVD based algorithms are purely SVD based

in a sense that only SVD domain is used to embed watermark into image. Recently

some hybrid SVD algorithms have been proposed where different types of

transforms are used including discrete Cosine Transform, Discrete Wavelet

Transform and Fast Hadamard Transform. There are two types of pure SVD based

42

algorithms where in some watermarking schemes watermark is embedded into the

whole cover image and in some other schemes the cover image is divided into

several blocks and the watermark is embedded into each block of the cover image

separately.

Another domain exploited for embedding the watermark is the wavelet domain. The

DWT (Discrete Wavelet Transform) separates an image into a lower resolution

approximation image (LL) as well as horizontal (HL), vertical (LH) and diagonal

(HH) detail components. The process can then be repeated to computes multiple

“scale” wavelet decomposition.

One of the many advantages over the wavelet transform is that that it is believed to

more accurately model aspects of the HVS as compared to the FFT or DCT.  This

allows us to use higher energy watermarks in regions that the HVS is known to be

less sensitive to, such as the high resolution detail bands {LH, HL, HH). Embedding

watermarks in these regions allow us to increase the robustness of our watermark, at

little to no additional impact on image quality

4.1 DISCRETE COSINE TRANSFORM

The transform domain watermarking techniques use a DCT to transform successive 8

X 8 pixel blocks of the image into 64 DCT coefficients each. The DCT coefficients

F(u, v) of an 8 X 8 block of image pixels f(x, y) are given by

, 4.1

where C(x) = 1/√2 where x equals to zero and C(x) is 1 otherwise.

The corresponding inverse DCT transformation is given by

43

. 4.2

The DCT allows an image to be broken up into different frequency bands, making it

much easier to embed watermarking information into the middle frequency bands of

an image. The middle frequency bands are chosen such that they have minimize they

avoid the most visual important parts of the image (low frequencies) without over-

exposing themselves to removal through compression and noise attacks (high

frequencies), FL is used to denote the lowest frequency components of the block,

while FH is used to denote the higher frequency components. FM is chosen as the

embedding region as to provide additional resistance to lossy compression

techniques, while avoiding significant modification of the cover image,

Figure 4.1: Definitions of DCT regions

Embedding in DCT domain is simply done by altering the DCT coefficients, for

example by changing the least significant bit of each coefficient as for JSteg

algorithm [7]. One of the constraints of embedding in DCT domain is that many of

the 64 coefficients are equal to zero, and changing two many zeros to non-zeros

values will have an effect on the compression rate. That is why the number of bit one

could embed in DCT domain, is less that the number of bits one could embed by the

LSB method. Also the embedding capacity becomes dependent on the image type

used in the case of DCT embedding, since depending on the texture of image the

number of non-zero DCT coefficients will vary. The two methods using the above

discussed statistical anomalies are F5 and Outguess [6, 7].

44

A widely accepted point now is the frequency-domain watermark should be

embedded into the mid-band of the transformed host image. Watermarks in high

frequency band tend to have less influence on the quality of original image, while

watermarks in low band will achieve a better robustness (since a large portion of

high frequency components may be quantized to zero under JPEG compression, as

shown in figure 4). And the mid-bind scheme is right a tradeoff between the

imperceptibility and robustness.

4.1.1 USEFUL PROPERTIES OF DCT

1. The cosine transform is real and orthogonal.

2. The cosine transform is fast transform. The cosine transform of a vector of N

elements can be calculated in O(N log2 N) operations via an N-point FFT.

4.1.2 EMBEDDING WATERMARK IN HIGH FREQUENCY BANDS OF

DCT

The simplest algorithm to hide a watermark using DCT is to directly embed the DCT

coefficient of the watermark into the high frequency band of the DCT coefficient

matrix of the cover image. The important thing is that, that the size of watermark

should be small as compared to the cover image. For a cover image of size 2nX2n,

the watermark size should at most be nXn. As previously discussed, most of the

components in the DCT coefficient matrix are zero and thus a small sized watermark

is easily embedded in this high frequency band of DCT coefficient as shown in the

figure 4.2.

45

Figure 4.2: Embedding watermark into the high frequency bands of DCT coefficient matrix of

cover image

The DCT of watermark is though flipped during embedding so that its low frequency

components fall to the high frequency side of the DCT matrix of cover image. The

watermark is recovered by taking the DCT of the lower right square of the

watermarked image. This works well if 8 bit image is hidden in a 16 bit image.

4.1.3 WATERMARK EMBEDDING USING COMPARISON OF MID BAND

COEFFICIENT OF DCT

The DCT allows an image to be broken up into different frequency bands, making it

much easier to embed watermarking information into the middle frequency bands of

an image. The middle frequency bands are chosen such that they have minimize they

avoid the most visual important parts of the image (low frequencies) without over-

exposing themselves to removal through compression and noise attacks (high

frequencies).

One such technique utilizes the comparison of middle-band DCT coefficients to

encode a single bit into a DCT block. The middle-band frequencies (FM) of an 8x8

DCT block as shown below in figure 4.1.

Next, two locations Bi (u1, v1) and Bi (u2, v2) are chosen from the FM region for

comparison. Rather then arbitrarily choosing these locations, extra robustness to

compression can be achieved if we base the choice of coefficients on the

recommended JPEG quantization table for a blocksize of 8 X 8 shown below in table

4.1. If two locations are chosen such that they have identical quantization values, we

can be sure that any scaling of one coefficient will scale the other by the same factor

preserving their relative size.

16 11 10 26 24 40 51 61

12 12 14 19 26 58 60 55

46

14 13 16 24 40 57 69 56

14 17 22 29 51 87 80 62

18 22 37 56 68 109 103 77

24 35 55 64 81 104 113 92

49 64 78 87 103 121 120 101

72 92 95 98 112 100 103 99

Table 4.1 - Quantization values used in JPEG compression scheme

Based on the table, we can observe that coefficients (4,1) and (3,2) or (1,2) and (3,0)

would make suitable candidates for comparison, as their quantization values are

equal. The DCT block will encode a “1” if Bi(u1,v1) > Bi(u2,v2); otherwise it will

encode a “0”. The coefficients are then swapped if the relative size of each

coefficient does not agree with the bit that is to be encoded. 

The swapping of such coefficients should not alter the watermarked image

significantly, as it is generally believed that DCT coefficients of middle frequencies

have similar magnitudes. The robustness of the watermark can be improved by

introducing a watermark “strength” constant k, such that Bi(u1,v1) - Bi(u2,v2) > k.

Coefficients that do not meet this criteria are modified though the use of random

noise as to then satisfy the relation. Increasing k thus reduces the chance of detection

errors at the expense of additional image degradation.

4.1.4 WATERMARK EMBEDDING USING THRESHOLD BASED

CORRELATION FOR DCT BLOCK

Another possible technique is to embed a PN sequence W into the middle

frequencies of the DCT block. We can modulate a given DCT block using the

following equations.

47

. 4.3

For each 8x8 block of the image W(x,y), the DCT for the block is first calculated

IW(x,y)(u,v). In that block, the middle frequency components FM are added to the pn

sequence W(x,y) (u,v), multiplied by a gain factor k. Coefficients in the low and middle

frequencies are copied over to the transformed image unaffected. Each block is then

inverse-transformed to give us our final watermarked image IW.

The watermarking procedure can be made somewhat more adaptive by slightly

altering the embedding process to the following method

. 4.4

This slight modification scales the strength of the watermarking based on the size of

the particular coefficients being used. Larger k’s can thus be used for coefficients of

higher magnitude in effect strengthening the watermark in regions that can afford it;

weakening it in those that cannot. 

For detection, the image is broken up into those same 8x8 blocks, and a DCT

performed. The same PN sequence is then compared to the middle frequency values

of the transformed block. If the correlation between the sequences exceeds some

threshold T, a “1” is detected for that block; otherwise a “0” is detected. Again k

denotes the strength of the watermarking, where increasing k increases the

robustness of the watermark at the expense of quality.

For further modification to increase the robustness of the watermark, instead of one,

two highly uncorrelated pn sequences for zero and one respectively are used. The

procedure can be given by the following equation set.

48

. 4.5

For recovering the watermark, the same pn sequences for zero and one are used. For

every 8 X 8 block obtained by taking the DCT of the same block of the watermarked

image, a pn sequence is generated using the mid band coefficients. The correlation of

this pn sequence is calculated with those for zero and one respectively. Whichever

has higher correlation, that bit is assigned to the recovered watermark.

4.2 SINGULAR VALUE DECOMPOSITION

Singular Value Decomposition (SVD) is a mathematical tool used to analyze

matrices. In SVD, a matrix is decomposed into three matrices of same size. Let A be

M X N matrix with M ≥ N. One form of singular value decomposition of A is

A= UDVT. 4.6

Here U and V are orthogonal and D is square diagonal. That is, UUT = Irank(A), VVT=

Irank(A), U is rank(A) X M, V is rank(A) X N and D is a rank(A) X rank(A) diagonal

matrix.

. 4.7

49

These diagonal entries σi' s are called singular values of A and their number is equal

to the rank of A. These singular values satisfy the relation

σ 1 ≥ σ 2 ≥ σ 3......σrank ( A) > 0. 4.8

Each singular value specifies [16, 17] the luminance of an image layer while the

corresponding pair of singular vectors specifies the geometry of the image. For

majority of the attacks, the change in the largest singular value is very small. The

columns of U are called the left singular vectors of A, and the columns of V are

called the right singular vectors of A.

This decomposition is known as the Singular Value Decomposition (SVD) of A, and

can be written as

SVD(A) = [U D V ]. 4.9

SVD (A) = λ1U1V1T + λ 2U2V2

T + ...... + λ U V

A' =UDVT. 4.10

4.2.1 PROPERTIES OF SVD

The properties of SVD [16] are reviewed below which make the technique useful for

watermarking.

1. If AЄRmxn , then there exist orthogonal matrices U = [u1,...,um ] Є Rmxn and V

= [v1,...,vn ] Є Rmxn such that UTAV = diag (σ1 σ2 …..σp)Where, p = min (m, n)

= rank (A), σ1 ≥σ 2 ≥ ...σ p ≥ 0. σ i, i=1,2,…p are the singular values of A. The

singular values are the square roots of the Eigen values λi of AAH or AHA,

that is σi = √λi.

2. The stability of singular value indicates that, when there is a little disturbance

with A, the variation of its singular value is not greater than 2-norm of

disturbance matrix. 2-norm is equal to the largest singular value of the matrix.

50

3. If the singular values of Amxn are σ1, σ 2, ...σ k , the singular values of α *Amxn

are σ1* ,σ 2

* ,...σ k*, then . This is referred

to as scaling property of SVD.

4. If P is a unitary and rotating matrix, the singular values of PA (rotated matrix)

are the same as those of A. This is referred to as rotation invariance property.

5. The translation invariance property states that the original image A and its

rows or columns interchanged image have the same singular values.

6. Transposition Invariance property of SVD states that if AATu = u, then

AATv = v, so that A and AT have same singular values.

These properties of stability, scaling, rotation invariance, translation invariance and

transposition invariance are much desirable in watermarking. When the watermarked

image undergoes rotation, scaling or noise addition, these properties enable the

watermark embedded in the SVD to be retrieved effectively. This makes the

techniques robust against these attacks.

4.2.2 DITHER QUANTIZATION

In an ideal watermarking scheme, one signal (a digital watermark) is embedded

within another signal (host image) signal to form a third signal (watermarked image)

signal. The embedding should be done in such a way that minimizes the distortion

between the host signal and watermarked signal and maximizes the information

embedding rate and robustness of the embedding. All the three requirements are

usually conflicting, and hence embedding process must be designed to efficiently

tradeoff these requirements. In the Dither quantization[16,17] based watermarking

schemes, the embedded information modulates a dither signal and the host signal is

quantized with an associated dithered quantizer. Dither quantization based schemes

have considerable performance advantages over conventional spread spectrum based

schemes [16]. The conventional spread spectrum embedding function combines the

51

host image and the watermark image in a linear way, and hence the watermark image

can be extracted with ease. In contrast, dither quantization based schemes effectively

hide the exact value of the host signal.

The concept of dither quantization[16,17] was introduced to digital watermarking

community by Chen and Wornell. Dither quantizers are set of basic quantizers. Each

quantization cell in the set is constructed from a basic quantizer. The basic quantizer

is shifted to get the reconstruction point. The shift depends on the watermark bit. The

basic quantizer is a uniform scalar quantizer with a fixed step size T.

4.2.3 NON-BLOCK BASED PURE SVD ALGORITHMS

Many of the earlier algorithms, based on SVD, used to embed the watermark signal

directly into the SVD domain. The simplest approach is where the watermark image

is embedded directly in the SVD domain. A single image is used as watermark which

is embedded in the whole image. This method is blind but requires the singular

values or the orthogonal matrices for retrieving the watermark. This algorithm is

resistant to some of the attacks like compression, filtering, cropping etc. but is not

robust against the attacks including rotation and translation.

Another algorithm uses basic M-sequence as the watermark[17]. Considering the

visible quality and robustness criteria, watermark has been embedded in middle

singular values maintaining the original order. This algorithm is blind i.e. does not

require the original image or any other information of original singular values to

detect the watermark. This method can resist some attacks like JPEG compression,

median filtering, rescaling, Gaussian low-pass filtering but is not robust against some

other attacks including rotation, cropping etc.

4.2.4 BLOCK BASED PURE SVD ALGORITHMS

A naïve block based pure SVD algorithm divides the original image into blocks and

then embed the watermark in the singular values of each blocks separately. The

52

watermark can be a pseudorandom number or an image. The method was found to be

robust against attacks like JPEG compression, cropping, Gaussian noise, resizing and

rotation. However this method could not resist translation. If the cover image size is

not fully divisible by the block size, then it requires adjustments before embedding

the watermark. The following part discusses a few of block based SVD algorithms.

4.2.5 EMBEDDING WATERMARK IN ‘D’ MATRIX

The main idea is to find the SVD of the image and modify its singular values to

embed the watermark. The largest coefficients of these block SVD transformations

are so modified according to the message bits such that the image quality is not

degraded.

Two Dither quantizers [16] were used to shift the quantization levels to T/2 with

respect to each other. The largest coefficients of the D matrices of 8X8 blocks are

quantized using either quantizer1 or quantizer 2 depending upon the watermark bit to

be embedded. The number of 8X8 blocks in the host image partition should be equal

to the size of the watermark. The entire range of these largest coefficients is divided

into ‘n’ number of bins with a step size of T as shown in table 4.2. Each of the

coefficients is modified either to or

depending on the value of the watermark bit which is

either 0 or 1 respectively.

Bin Number dlow dhigh

1 dmin-T dmin

2 dmin dmin+T

….. ….. …..

bn-1 dmax-T dmax

bn dmax dmax+T

53

Table 4.2: Quantization table for n bins with step size T

Here, low (n) and high (n) represent the low and high levels of the bin ‘n’ to which

each coefficient belongs. The new quantized value is the center of the quantizer.

After the modification of the singular values, inverse SVD is applied.

For retrieving the embedded watermark the block SVD transformation on the

watermarked image is applied and the largest coefficients of these matrices are

extracted and checked for the bin position in the quantization table. Now if the

coefficient value lies in the range the watermark bit is

suggestively 1 or if it lies in the range the

corresponding watermark bit is 0.

Robustness of the method against attacks and imperceptibility can be improved with

the number of bins and decrease in the step size. Security can be enhanced by using a

secret key for permuting the watermark before embedding and then using the same

key at the retrieving side to permute the watermark obtained to obtain the original

watermark.

A modified approach was proposed in [17] by using edge detector before taking the

block SVD transformation. Canny edge detector was applied on the entire cover

image and then number of edges was calculated for all 8 X 8 non overlapping blocks.

Now using a threshold

4.2.6 EMBEDDING WATERMARK IN ‘U’ MATRIX

A modification is proposed in the algorithm presented in [16] for embedding the

watermark in U matrix of SVD. The image is divided into 8 X 8 blocks and

watermark image is embedded in the columns of each block of U matrix. For each

block of U matrix the first row, first column element and second row, first column

elements are modified based on their difference compared with a threshold.

54

The difference of these two elements is found and modified according to the

following proposed equations.

If watermark bit is 1 and the difference is greater than a threshold or watermark bit is

0 and the difference is less than the threshold,

. 4.11

And, . 4.12

If watermark bit is 1 and the difference is less than threshold or watermark bit is 0

and the difference is less than the threshold,

. 4.13

And, . 4.14

After the coefficients of the U matrix are modified, the inverse SVD is applied to

each block. To recover the embedded watermark, SVD transformation is applied on

each block of the watermarked image. The number of blocks in which the

watermarked image is divided at the retrieving end should be same as that used at the

embedding end. For each block, the first row, first column and the second row, first

column elements are compared. The watermark bit is suggestively 1 if the first row,

first column element is greater and is not the watermark bit is suggestively 0.

To increase the security, the watermark can be permuted before embedding using a

secret key[16]. The same key is used at the other end to recover the original

watermark. To increase the robustness of the algorithm discussed in section 4.2.5, the

edge detector[17] can be first applied to the image blocks to choose the block to

embed the watermark in, according to some threshold value based on number of

edges present in each block..

55

4.3 DISCRETE WAVELET TRANSFORM

Although the Fourier Transform has been the mainstay of transform based image

processing, but the Wavelet Transform makes it even easier to compress, transmit

and analyze many images. Discrete Wavelet Transform (DWT) allows images to be

viewed and processed at multiple resolutions and provides a powerful insight into an

image’s spatial and frequency characteristics. It separates an image into a lower

resolution approximation image (LL) as well as horizontal (HL), vertical (LH) and

diagonal (HH) detail components. The process can then be repeated to computes

multiple “level” wavelet decomposition [12], as in the level 2 wavelet transform

shown below in figure 4.3.

Figure 4.3: Level 2 Discrete Wavelet Transform

The term Discrete Wavelet Transform refers to a class of transformations that differ

not only in the transformation kernels employed, but also the fundamental nature of

those functions and in the way in which they are applied. Since the DWT

encompasses a variety of unique but related transformations, a single equation cannot

completely describe it. Instead each DWT is characterized by a transform kernel pair

or set of parameters that defines the pair. The basis functions of DWT are based on

small waves, called wavelets, of varying frequency and limited duration.

The Fast Wavelet Transform (FWT) is a computationally efficient implementation of

the DWT that exploits the relationship between the coefficients of the DWT at

adjacent scales.

4.3.1 WAVELETS

56

The first recorded mention of what we now call a "wavelet" seems to be in 1909, in a

thesis by Alfred Haar. The attention of researchers gradually turned from frequency-

based analysis to scale-based analysis when it started to become clear that an

approach measuring average fluctuations at different scales might prove less

sensitive to noise.

Any discussion of wavelets begins with Haar wavelet, the first and simplest. Haar

wavelet is discontinuous, and resembles a step function.

Ingrid Daubechies, one of the brightest stars in the world of wavelet research,

invented what are called compactly supported orthonormal wavelets -- thus making

discrete wavelet analysis practicable. The names of the Daubechies family wavelets

are written dbN, where N is the order, and db the "surname" of the wavelet. The db1

wavelet is the same as Haar wavelet.

The third family of wavelets, called biorthogonal wavelets, exhibits the property of

linear phase, which is needed for signal and image reconstruction. By using two

wavelets, one for decomposition and the other for reconstruction instead of the same

single one, interesting properties are derived.

4.3.2 PROPERTIES OF DISCRETE WAVELET TRANSFORM

The DWT kernels possess the following general properties:

1. Separability, scalability and translatability:

The kernels can be represented as three separable 2-D wavelets,

, 4.15

57

where , and are called horizontal, vertical and

diagonal wavelets respectively and one separable 2-D scaling function

. 4.16

Each of these 2-D functions is the product of two 1-D real, square-integrable

scaling and wavelet functions

. 4.17

Translation k determines the position of these 1-D functions along the x-axis,

scale j determines their width along x and 2j/2 controls their height or amplitude.

2. Multiresolution compatibility:

The 1-D scaling function satisfies the following requirements of multiresolution

analysis:

(a) is orthogonal to its integer translates.

(b) The set of functions that can be represented as a series expansion of

at low scales or resolutions is contained within those that can be

represented at higher scales.

(c) The only function that can be represented at every scale is f(x) = 0.

(d) Any function can be represented with arbitrary precision as .

When these conditions are met, there is a companion wavelet , that together

with its integer translates and binary scalings, spans the difference between any

two sets of representable functions at adjacent scales.

3. Orthogonality:

58

The expansion function forms an orthonormal or biorthogonal basis for the set of

1- D measurable, square integrable functions. To be called a basis, there must be

a unique set of expansion coefficients for every representable function.

4.3.2 ADVANTAGES AND DISADVANTAGES OF DWT OVER DCT

Advantages of DWT over DCT [12]

1) Wavelet transform understands the HVS more closely than the DCT.

2) Wavelet coded image is a multi-resolution description of image. Hence an image

can be shown at different levels of resolution and can be sequentially processed from

low resolution to high resolution.

3) Visual artifacts introduced by wavelet coded images are less evident compared to

DCT because wavelet transform doesn't decompose the image into blocks for

processing. At high compression ratios blocking artifacts are noticeable in DCI;

however, in wavelet coded images it is much clearer.

4) DFT and DCI are full frame transform, and hence any change in the transform

coefficients affects the entire image except if DCT is implemented using a block

based approach. However DWT has spatial frequency locality, which means if signal

is embedded it will affect the image locally. Hence a wavelet transform provides

both frequency and spatial description for an image.

Disadvantages of DWT over DCT

1) Computational complexity of DWT is more compared to DCT' . As Feig (1990)

pointed out it only takes 54 multiplications to compute DCT for a block of 8x8,

unlike wavelet calculation depends upon the length of the filter used, which is at least

1 multiplication per coefficient.

4.3.3 EMBEDDING CDMA WATERMARK INTO HORIZONTAL AND

VERTICAL SUB-BAND

59

Figure 4.3: model to embed watermark into the DWT coefficients.

The main idea of embedding CDMA watermark is to embed randomly generated PN

sequence into the horizontal, vertical or diagonal components [21] of the DWT

coefficients as shown in figure 4.3.

The PN sequences are embedded into the horizontal and vertical component

coefficients with certain gain k, when the watermark bit is zero, according to the

following equation:

Hz = Hz + k * PN sequence for horizontal component

Vz = Vz + k * PN sequence for vertical component

where, Hz represents the coefficients of horizontal component and Vz represents the

coefficients of vertical component.

The method used for recovery of the watermark is also very simple. The two PN

sequences for horizontal and vertical component respectively are regenerated and

their correlations with the horizontal and vertical component coefficients are found.

If the average correlation crosses the threshold set at the mean correlation, the

watermark bit is assumed to be 0 else 1.

4.3.4 WATERMARK EMBEDDING USING SECOND LEVEL DWT

DECOMPOSITION

Some of the conventional DWT watermarking techniques as discussed in section

4.3.2, embeds the watermark in the coefficients of first level DWT. The second level

decomposition [36] is performed by either decomposing the approximation sub-band

obtained from the first level decomposition as shown in figure 4.4 (a) or it is

60

performed on the detail sub-band resulting from the first level decomposition as

shown in figure 4.4 (b). Here, L represents the approximation sub-band, HL

represents the horizontal sub-band, LH represents the vertical, and HH represents

diagonal sub-band.

(a) (b)

Figure 4.4: (a) Second level decomposition of approximation sub-band. (b) Second level decomposition of horizontal sub-band.

To embed the watermark in the horizontal sub-band [36] of the second level

decomposition, the horizontal detail information is obtained by decomposing the

image using DWT. These horizontal details are further decomposed using DWT.

Now, as for CDMA technique, a PN sequence is generated and whenever the

watermark bit is 0, the PN sequence is added to these coefficients with some gain, k.

Lastly, Inverse DWT is taken twice to obtain the watermarked image.

To recover the watermark [36] back, the watermarked image is decomposed using

DWT and the obtained horizontal detail is decomposed again. PN sequence is

generated and its correlation with the horizontal detail coefficients is computed. If

the correlation is greater than a threshold the watermark bit is set to 0, else 1.

Horizontal sub-band [36] is chosen because embedding in the approximation sub-

band produces perceptible artifacts in the watermarked image. The technique can be

made secure by using a secret key for embedding and recovery of the watermark.

4.4 HYBRID WATERMARK EMBEDDING TECHNIQUES

61

Many techniques have been proposed using two or more of the transforms. [23] gives

an algorithm which uses DCT and SVD together to watermark the image, such that

the watermark is embedded in all frequencies of DCT. After applying the DCT to the

cover image, we map the DCT coefficients in a zig-zag order into four quadrants as

shown in figure 4.5, and apply the SVD to each quadrant. These four quadrants

represent frequency bands from the lowest to the highest. The singular values in each

quadrant are then modified by the singular values of the DCT-transformed visual

watermark.

Figure 4.5: Mapping of DCT coefficients into the 4 blocks.

The four sets of modified DCT coefficients are mapped back to their respective

positions and inverse DCT is calculated to obtain watermarked image.

For recovery of the four watermarks, the coefficients of the DCT transformed

watermarked image are mapped into the four quadrants and SVD are calculated for

each. The DCT coefficients of the four watermarks are obtained using the the

singular vectors and inverse DCT is obtained.

Another example of hybrid watermarking technique is presented in [22] which uses

Discrete Cosine Transform and Discrete Hartley transform along with edge

detection. The technique divides the image into non-overlapping blocks and then

these blocks are sorted in decreasing order of the number of edges present. The

watermark is embedded block by block in different blocks of the image. The decision

whether to embed in DHT domain or in DCT domain is based on the number of

edges which exist in a given block in the image to be watermarked.

Yet another variation in the combination of techniques used is presented in [27],

which combines the spatial domain LSB technique with the transform domain DCT

and compression technique on raw images to increase the security of the payload.

62

Initially, the LSB algorithm is used to embed the payload bits into the cover image to

derive the stego image which is then transformed from spatial domain to the

frequency domain using DCT. Finally quantization and run length coding algorithms

are used for compressing the stego image to enhance the security.

CHAPTER 5

PERFORMANCE ANALYSIS OF

WATERMARKING TECHNIQUES

Each of the watermarking technique discussed so far has its own pros and cons.

However to judge the performance of these, they should be analyzed on the same

platform. The performance evaluation is based on various performance metrics.

5.1 Measuring Imperceptibility

Imperceptibility of an embedded watermark can be expressed either as fidelity or

quality measure. Fidelity represents a measure of similarity between the original and

watermarked cover.

An important way of evaluating watermarking algorithms for fidelity is to compare

the amount of distortion introduced into a host image by a watermarking algorithm.

The widely used peak signal-to-noise ratio (PSNR) measurement [8,12,40] which

measures the maximum signal to noise ratio found on an image is used as an

objective measure for the distortions introduced by the watermarking system. The

PSNR is given by [8,12]:

5.1

where MSE is mean square error between the original image Iorg and the watermarked

one Iw. The MSE is defined as [8]:

63

5.2

Where, M and N are the image dimensions. When SNR approaches infinity, the

original image and output image are totally the same. SNR provides only a rough

approximation of the quality of the watermark as it does not take into account, the

Human Visual System (HVS). The evaluation relies strictly on the observations

under varied conditions.

5.2 Measuring Robustness

Some of the early literature considered a binary robustness metric that only allows

for two different states (the watermark is either robust or not). However, it makes

sense to use a metric that allows for different levels of robustness. The use of the bit-

correct ratio (BCR) has become common recently, as it allows for a more detailed

scale of values. The bit correct ratio (BCR) is defined as the ratio of correct extracted

bits to the total number of embedded bits and can be expresses using the formula:

5.3

Where, l is the watermark length, Wn corresponds to the nth bit of the embedded

watermark and W'n corresponds to the nth bit of the recovered watermark.

5.3 Measuring Execution Time

Another important tool for evaluating algorithms is measurement of the amount of

time required to embed a watermark into a host image, and then extract it afterwards.

The actual time in CPU cycles will be used as a measure of execution time.

5.4 Measuring Payload

64

Payload or capacity simply refers to the size of watermark that can be embedded in

the cover image. The size is in terms of bits. Payload or capacity is another important

characteristic because it has a direct negative impact on the robustness.

CHAPTER 6

RESULTS AND DISCUSSIONS

Various techniques were discussed in the previous chapters of the thesis for spatial

domain and transform domain watermarking. The first part of the thesis is to

implement these techniques in MATLAB and then in the second part, based on the

results obtained; these algorithms are analyzed for their performance based on the

performance metrics discussed in chapter 5.

6.1 IMAGES USED

The cover image used as cover object is a 512 X 512, 8-bit, .bmp image with 256

gray levels, Lena.bmp as shown in figure 6.1(a). The different images used as

watermark are shown in figure 6.1 (b)-(d). These are the versions of the copyright

image differing in their sizes. The image shown in figure 6.1 (b)-(d) are binary

images of sizes 512 X 512, 20 X 50 and 9 X 12 respectively.

65

(a) (b)

(c) (d)

Figure 6.1: Images (a) cover image (b) copyright large (c) copyright (d) copyright small

The choice of watermark image for each algorithm depends upon the capacity of the

data the technique can hide in a given sized cover object.

6.2 SPATIAL DOMAIN TECHNIQUES

Based on the discussions about different spatial domain techniques in chapter 3,

following algorithms are implemented in MATLAB.

1. Simple LSB substitution.

2. LSB substitution with a random walk.

3. Comparison based correlation.

4.

6.2.1 ALGORITHM 1: SIMPLE LSB SUBSTITUTION

Embedding:

Input: cover image, watermark

66

Output: watermarked image

1. Read watermark.

2. Convert the watermark into binary.

3. Read the cover image.

4. Set the LSB plane of cover image (i,j) to the value of watermark (i,j).

Recovery:

Input: watermarked image

Output: retrieved watermark

1. Read watermarked image.

2. Extract the LSB plane from the watermarked image.

Results for algorithm 1

(a) (b) (c)

(d) (e) (f)

67

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 275

80

85

90

95

100

scaling factor-->

BC

R--

>

(h)

Figure 6.2: (a) Cover image watermarked with simple LSB substitution. (b) Recovered

watermark. (c) Recovered watermark from watermarked image attacked by histogram

equalization. (d) Recovered watermark from watermarked image attacked by median filter

(3X3). (e) Recovered watermark from watermarked image attacked by Gaussian noise. (f)

Recovered watermark from cropped watermarked image. (g) Change in BCR with scaling of

watermarked image.

The watermark is chosen as copyright_large of the same size as image because of

high data handling capacity of the technique. The technique allows embedding the

message at every bit position of the LSB plane. Any change in the visual quality of

the original image is hardly visible. The time elapsed for embedding is 0.6094

seconds with the PSNR of 1.2212e+005 and MSE of 0.4996. The watermark is

recovered correctly in 0.4688 seconds with a BCR of 100 % as shown in figure

6.2(b). The technique fails to pass the test of robustness. The recovered watermarks

from the watermarked image attacked by histogram equalization, rotation, median

filtering, Gaussian noise and cropping are shown in figure 6.2 (c)-(g). The watermark

is totally lost when the watermarked image undergoes histogram equalization or the

LSB plane is set either to 0 or 1. However median filtering resulted in a BCR of

88.0814% but the addition of Gaussian noise removed the watermark completely.

The technique is able to tolerate cropping completely but scaling is tolerable within

limits as shown in figure 6.2 (h). BCR comes out to be 81.004 % for scaling factor of

75% and drops to 78.6057 for scaling factor of 50%.

68

Table 6.1 summarizes the effects of attacks on the image watermarked using

algorithm 1.

Type of attack BCR (%) for retrieved watermark

Histogram equalization 43.6890

Median filtering 88.0814

Gaussian noise 49.8917

Cropping 100

Table 6.1: effects of attacks on image watermarked with algorithm 1

According to the classification in chapter 2, the technique is a pure, blind, invisible

and fragile spatial domain image watermarking technique.

6.2.2 ALGORITHM # 2: LSB SUBSTITUTION WITH A RANDOM WALK

Embedding:

Input: cover image, watermark, key

Output: watermarked image

1. Read the secret key, cover image and the watermark.

2. Reshape the watermark into a message vector.

3. Using the key, generate a sequence of pixel locations to be visited randomly.

4. While visiting each location according to the random sequence, replace the

LSB with the bit in the “message vector”.

Recovery:

Input: watermarked image, key

Output: retrieved watermark

1. Read the watermarked image and key.

2. Using the key, generate a sequence of pixel locations to be visited randomly.

69

3. Extract the LSB of each pixel during visit and reshape it into the size of the

image.

Results for algorithm 2:

(a) (b) (c)

(d) (e) (f)

(h)

Figure 6.3: (a) Cover image watermarked with LSB substitution with a random walk.

(b) Recovered watermark. (c) Recovered watermark from watermarked image attacked by

histogram equalization. (d) Recovered watermark from watermarked image attacked by

70

median filter (3X3). (e) Recovered watermark from watermarked image attacked by Gaussian

noise. (f) Recovered watermark from cropped watermarked image. (g) Change in BCR with

scaling of watermarked image.

Similar to algorithm 1, the watermark is chosen as copyright_large. This technique

also allows embedding the message at every bit position of the LSB plane. Hardly

any change in the visual quality is visible when the watermark is embedded. The

time elapsed for embedding is 0.5938 seconds with the PSNR of 1.2200e+005 and

MSE of 0.5001. The watermark is recovered correctly as shown in figure 6.3(b), in

0.4844 seconds with a BCR of 100 %. The technique is highly affected by the

attacks. The watermark is totally lost when the watermarked image undergoes

median filtering, Gaussian noise addition, histogram equalization or the LSB plane is

set either to 0 or 1. The recovered watermarks after histogram equalization, median

filtering and Gaussian noise are shown in figure 6.3(c)-(e). Unlike algorithm 1, this

technique is unable to tolerate cropping and the watermark is lost as shown in figure

6.3 (f). The effect of scaling on BCR is shown in figure 6.3 (g), where the BCR falls

to around 80% when the watermarked image is shrunk to half or expanded to twice.

The technique is highly intolerant to rotation.

According to the classification in chapter 2, the technique is a shared key, blind,

invisible and fragile spatial domain image watermarking technique.

6.2.3 ALGORITHM # 3: COMPARISON-BASED CORRELATION

Embedding:

Input: cover image, watermark, key

Output: watermarked image

1. Read the secret key, cover image and the watermark.

2. Set the gain factor k and the block size used for each bit of the water mark.

3. Reshape the watermark into a message vector and pad it with ones if required

to the maximum message size.

4. Reset MATLAB PN generator to state "key".

71

5. Find two highly uncorrelated PN sequences for "1" and "0" respectively.

6. Construct the global watermark mask.

For each block (kk) of size blocksize X blocksize

if (message bit = zero)

add PN sequence to that portion of mask

else

mask is filled with zeros.

7. Add watermark mask to cover image using gain factor ‘k’ such that,

Watermarked image=cover image + k* watermark mask.

Recovery:

Input: watermarked image, key, watermark

Output: retrieved watermark

1. Read watermarked image, key and original watermark.

2. Set the block size same as that for embedding.

3. Reset MATLAB PN generator to state “key’.

4. Find two highly uncorrelated PN sequences for “1” and “0” respectively.

5. Generate a message vector of maximum size (=size of image/blocksize2) with

all elements as one.

6. For each message vector bit

a. Find the correlation of each corresponding block with the PN

sequences for 1 and 0.

b. If ((correlation of the block with PN sequence for 1) > (correlation of

the block with PN sequence for 0))

Message vector bit = 1

else

Message vector bit = 0

c. Move to next block

7. Reshape the message vector according to the size of original watermark.

Results for algorithm 3:

72

The capacity of this technique is low as compared to the previous two techniques,

since each block of the image has a single bit embedded into it. Thus if the image

size is (Mo, No) and blocksize is (Mb,Nb) then the maximum message length is

(Mo*No)/(Mb*Nb). Here, the maximum message size is 64 X 64. Figure 6.4(a)

shows the cover image watermarked using algorithm 3. The time elapsed for

embedding the watermark is 0.3750 seconds with the PSNR of 2.6538e+004 at gain,

k = 2. The technique is fairly resistant to histogram equalization and recovers the

watermark with 92.1% correctness in 1.3594 seconds. The retrieved watermark after

histogram equalization is shown in figure 6.4 (c). On adding Gaussian noise or using

median filtering, the technique fails to recover the watermark properly as shown in

figure 6.4 (d) and (e) respectively. The BCR falls to 72.6% and 70.2 in the respective

cases. The technique is intolerant to cropping. The retrieved watermark is shown in

figure 6.4(f) with 73.1481% correctness. The algorithm does not impact the visual

quality if gain factor is kept small as depicted by figure 6.4(g) which shows a plot

between the gain and PSNR. High PSNR is obtained for small values of gain and the

value of BCR at these small gain values is quite low. The time elapsed for recovery

of the watermark is 1.2656 with a BCR of 90.4% at the same gain. Table 6.2 shows

the summary of these results.

Type of attack BCR(%) for retrieved watermark

Histogram equalization 92.1

Median filtering 70.2

Gaussian noise 72.6

Cropping 73.1481

Table 6.2: Effects of attacks on image watermarked with algorithm 3

The technique is a shared key, blind, invisible and fragile spatial domain image

watermarking technique.

73

(a) (b) (c)

(d) (e) (f)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5x 10

5

PS

NR

-->

gain(k)-->0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

75

80

85

90

95

100

BC

R--

>

(g)

Figure 6.4: (a) Cover image watermarked with comparison based correlation technique.

(b) Recovered watermark. (c) Recovered watermark from watermarked image attacked by

histogram equalization. (d) Recovered watermark from watermarked image attacked by

Gaussian noise. (e) Recovered watermark from watermarked image attacked by median filter

(3X3). (f) Recovered watermark from cropped watermarked image. (g) Variation of PSNR and

BCR with gain (k).

6.2.4 ALGORITHM # 4: THRESHOLD BASED CORRELATION

Embedding:

Input: cover image, watermark, key

Output: watermarked image

74

1. Read the secret key, cover image and the watermark.

2. Set the gain factor k and the block size used for each bit of the water mark.

3. Reshape the watermark into a message vector and pad it with zeros to the

maximum size.

4. Filter the cover image using edge enhancement filter.

5. Reset MATLA PN generator to state "key".

6. Generate PN sequence equal to the size of one block.

7. Construct the global watermark mask.

if (message bit = zero)

add PN sequence to that portion of mask.

else

mask is filled with zeros.

8. Add watermark mask to cover image using gain factor ‘k’ such that,

Watermarked image=cover image + k* watermark mask.

Recovery:

Input: watermarked image, key, watermark

Output: retrieved watermark

1. Read watermarked image, key and original watermark.

2. Set the block size same as that used for embedding.

3. Reset MATLAB PN generator to state “key’.

4. Generate a PN sequence of size of one block.

5. Generate a message vector of size of original watermark with all elements as

ones.

6. For each block of image

if (image block = PN sequence)

set correlation=1.

else

find correlation between the image block and the PN

sequence.

75

if (correlation > average correlation)

Set retrieved watermark bit = 0.

else

Set retrieved watermark bit = 1.

7. Reshape the message vector according to the size of original watermark.

Results for algorithm 4:

(a) (b) (c)

(d) (e) (f)

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2x 10

6

PS

NR

-->

gain(k)-->0 5 10 15 20 25 30 35 40

50

60

70

80

90

BC

R--

>

(g)

Figure 6.6: (a) Cover image watermarked with threshold based correlation technique (k=40).

(b) Recovered watermark. (c) Recovered watermark from watermarked image attacked by

76

histogram equalization. (d) Recovered watermark from watermarked image attacked by

Gaussian noise. (e) Recovered watermark from watermarked image attacked by median filter

(3X3). (f) Recovered watermark from cropped watermarked image. (g) Variation of PSNR and

BCR with gain (k).

The capacity of this technique is low as compared to the algorithm 1 and algorithm 2

due to the same reason as for algorithm3. The time elapsed for embedding the

watermark of size 50 X 20 is 0.2969 seconds with the PSNR of 1.0353e+004. The

watermarked image, with gain set at 25 is shown in figure 6.4 (a). The time elapsed

for recovery of the watermark is 0.9688 seconds with a BCR of 84.4%. The effects of

attacks on the watermarked image are clearly visible in figure 6.4 (c)-(f) which show

the retrieved watermarks. Table 6.3 gives the results for test of robustness for gain

25. The algorithm does not impact the visual quality if gain factor is kept small as

depicted by figure 6.4(g) which shows a plot of PSNR and BCR with respect to gain.

High PSNR is obtained for small values of gain. But, at very low values of gain the

BCR is too low to be accepted.

Type of attack BCR for retrieved watermark

Histogram equalization 84.2

Median filtering 76.8

Gaussian noise 63.7

Cropping 74.0741

Table 6.3: Effects of attacks on image watermarked with algorithm 4

6.2.5 ALGORITHM 5: CDMA BASED WATERMARKING

Embedding:

Input: cover image, watermark, key

Output: watermarked image

1. Read the cover image, watermark and key.

2. Set the gain factor k.

3. Reshape the watermark into a message vector.

77

4. Reset MATLAB PN generator to state "key".

5. For each watermark bit

Generate a PN sequence

if (watermark bit = zero)

Add PN sequence with gain k to that portion of mask.

Recovery:

Input: Watermarked image, watermark, key.

Output: Retrieved watermark.

1. Read the watermarked image, watermark and key.

2. Set the MATLAB random generator to state “key”.

3. Generate a message vector of all ones of size same as original watermark.

4. For each bit of message vector

i. Generate PN sequence.

ii. If (watermarked image = PN sequence)

Set correlation=1.

Else

Find the correlation between watermarked

image and PN sequence..

5. Set the threshold as mean correlation.

6. For each message vector bit

if (correlation>threshold)

retrieved watermark bit = 0.

7. Reshape the message vector into image of dimensions same as for original

watermark.

Results for algorithm 5:

78

(a) (b) (c) (d) (e) (f)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6x 10

4

gain(k)-->

PS

NR

-->

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 570

80

90

100

BC

R--

>(g)

Figure 6.7: Image watermarked using CDMA technique. (b) Retrieved watermark (c)

Recovered watermark from watermarked image attacked by histogram equalization. (d)

Recovered watermark from watermarked image attacked by Gaussian noise. (e) Recovered

watermark from watermarked image attacked by median filter (3X3). (f) Recovered watermark

from cropped watermarked image. (g) Variation of PSNR and BCR with gain (k).

Figure 6.7(a) shows the watermarked image using the technique of CDMA on the

cover image with small watermark of size 9 X 12.The retrieved watermark is shown

in figure 6.4(b). The time elapsed for embedding and recovery is 5.6406 and 8.9531

seconds respectively. The PSNR at gain = 0.5 is 1.94941e+004 and the BCR during

recovery is 100%.

79

Type of attack BCR for retrieved watermark

Histogram equalization 100

Median filtering 70.3704

Gaussian noise 99.0741

Cropping 45.3704

Table 6.4: Effects of attacks on image watermarked with algorithm 5.

Table 6.4 clearly suggests that the technique is resistant to histogram equalization

and Gaussian noise. But, median filtering and cropping defeat the watermark. The

graph shown in figure 6.4 (g) depicts the variations in PSNR and BCR as a function

of gain. Increasing the gain increases the probability of correct watermark retrieval

but at the expense of imperceptibility.

6.3 TRANSFORM DOMAIN TECHNIQUES

The following algorithms use either Discrete Cosine Transform or Singular Value

Decomposition or Discrete Wavelet Transform to embed the watermark into the

cover image.

6.3.1 ALGORITHM 6 : Hiding watermark in high frequency bands of DCT of

cover image

Embedding:

Input: cover image, watermark.

Output: watermarked image.

1. Read cover image and watermark.

2. Take DCT of cover image as well as watermark.

3. Flip the DCT matrix of the watermark and insert it in the high frequency

region of DCT of cover image.

4. Take IDCT of this DCT matrix.

80

Recovery:

Input: watermarked image, watermark.

Output: retrieved watermark.

1. Read watermarked image and original watermark.

2. Find DCT of the watermarked image.

3. Extract the coefficients from the high frequency region according to the

size of the original watermark.

4. Find Inverse DCT of this coefficient matrix. This is the retrieved

watermark.

Results of algorithm 6:

(a) (b) (c)

(d) (e) (f)

Figure 6.8: (a) -(c) Watermarked images with watermarks of sizes 512 X 512, 206 X 206, 20 X 50

respectively. (d) – (f) Recovered watermarks for images (a) - (c).

Figure 6.8 shows the watermarked images with the corresponding retrieved

watermarks. The technique used is to embed the DCT of watermark into the high

81

frequency region of the DCT matrix of the cover image. The time elapsed to obtain

watermarked images, as shown in figure 6.8 (a) – (c) is 1.5625, 1.1563 and 1.1094

respectively with PSNR of 4.1855, 7.4709 and 274.7236 respectively. As clearly

visible the technique does not yield fruitful results for watermarks comparable in size

with the cover image. The recovery time for the three varied sized watermarks is

3.6094, 2.1563 and 0.4063 respectively with BCR of 40.8043%, 88.8556% and

100% respectively. For watermarks of the size same as the cover image, the

technique is unacceptable as the image is highly corrupted after embedding the

watermark and the recovered watermark too has an unacceptable BCR, as shown in

figure 6.8 (a) and figure 6.8 (d) respectively. Even the watermark of size half the size

of the cover image has very low PSNR, the watermarked image is shown in figure

6.8 (b) and the recovered watermark is shown in figure 6.8 (e). There are only a few

DCT coefficients in which the watermark can be embedded. If we want to increase

the payload of the watermark, then these coefficients may need to be modified

significantly that will affect the quality of the image.

Figure 6.9(a)-(d) shows the watermarks retrieved from the image watermarked in the

mid frequency band, exposed to histogram equalization, Gaussian noise, median

filtering and cropping respectively. The technique is resistant to histogram

equalization and Gaussian noise, as is clear from the figure 6.9 (a) and (b) where the

watermarks are recovered with a BCR of 98.4 and 100% respectively. Median

filtering and cropping tamper the watermark highly, such that it is recovered with a

BCR of 74.8 and 49.4% respectively.

(a) (b) (c) (d)

Figure 6.9: (a) Recovered watermark from watermarked image attacked by histogram

equalization. (b) Recovered watermark from watermarked image attacked by Gaussian noise.

(c) Recovered watermark from watermarked image attacked by median filter (3X3). (d)

Recovered watermark from cropped watermarked image.

11.3.2 ALGORITHM 7: Block DCT based watermarking using comparison

between mid-band frequency component

82

Embedding:

Input: cover image, watermark.

Output: watermarked image.

1. Read the cover image and the watermark.

2. Set the block size and minimum coefficient difference, k.

3. Reshape the watermark into a vector and pad it to maximum size with ones.

4. Divide the entire cover image into blocks of size 8 X 8.

5. For each block,

a. Find DCT.

b. If (watermark bit = 1)

If (DCT(5,2) < DCT(4,3)

Swap DCT(5,2) and DCT(4,3).

Else

if (watermark bit = 0)

If DCT(5,2) ≥ DCT(4,3)

Swap DCT(5,2) and DCT(4,3).

c. Adjust the two values to a minimum difference of k such that,

If DCT(5,2) >DCT(4,3)

If (DCT(5,2) – DCT(4,3) < k)

DCT(5,2)= DCT(5,2) + k/2.

DCT(4,3)= DCT(4,3) – k/2.

Else

If (DCT(4,3) – DCT(5,2) < k)

DCT(4,3)= DCT(4,3) + k/2.

DCT(5,2) = DCT(5,2) – k/2.

6. Convert the watermarked image in DCT domain back to spatial domain.

Recovery

Input: watermarked image, watermark.

83

Output: retrieved watermark.

1. Read the watermarked image and the watermark.

2. Divide the entire watermarked image into blocks of size 8 X 8.

3. For each block,

a. Find DCT of the block.

b. If DCT(5,2) > DCT(4,3)

Set retrieved watermark bit = 0.

Else

Set retrieved watermark bit = 1.

4. Reshape the obtained retrieved watermark into size of the original

watermark.

Results for algorithm 7

(a) (b) (c)

(d) (e) (f)

84

0 5 10 151.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4x 10

4

minimum coefficient difference-->

PS

NR

-->

0 5 10 151.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4x 10

4

PS

NR

-->

0 5 10 1599

99.2

99.4

99.6

99.8

100

100.2

100.4

100.6

100.8

101

BC

R--

>

(g)

Figure 6.10 (a) Watermarked image using comparison of DCT coefficient technique. (b)

Retrieved watermark. (c) Recovered watermark from watermarked image attacked by

histogram equalization. (d) Recovered watermark from watermarked image attacked by

Gaussian noise. (e) Recovered watermark from watermarked image attacked by median filter

(3X3). (f) Recovered watermark from cropped watermarked image. (g) Variation of PSNR and

BCR with minimum coefficient difference.

Figure 6.10 (a) shows the watermarked image with minimum difference of 10. The

time elapsed is 2.2813 seconds and the PSNR is 2.1210e+004. The watermark was

successfully recovered with a BCR of 100 % in 1.2344 seconds. The results for test

for tamper resistance against histogram equalization, Gaussian noise, median

filtering, cropping and scaling are shown in figure 6.10 (c)-(f). The technique is

resistant to histogram equalization and median filtering but, Gaussian noise and

cropping defeat the watermarking. As the minimum difference is increased, PSNR

falls and a checker board effect is visible on the entire image. This is shown in figure

6.10(g) with the help of a graph between minimum difference, k and PSNR. The

recovery of the watermark is independent of any variation in minimum coefficient

difference. The graph between the minimum coefficient difference and BCR shown

in figure 6.10(g) also depicts the same. The BCR is constant throughout at 100%.

85

Table 6.5 summarizes the values obtained for BCR after the watermarked image was

attacked.

Type of attack BCR for retrieved watermark

Histogram equalization 99.0741

Median filtering 98.1481

Gaussian noise 55.5556

Cropping 82.9

Table 6.5: Effects of attacks on image watermarked with algorithm 7.

11.3.3 ALGORITHM 8: Threshold based correlation in DCT mid-band

Embedding:

Input: Cover image, Watermark, Key.

Output: Watermarked image

1. Read the cover image watermark and key.

2. Define block size = 8 and mid band for DCT.

3. Reshape the watermark into a vector and pad it with ones to maximum

size.

4. Set the MATLAB PN generator to state key.

5. Generate PN sequence for Zero of length equal to number of mid band

coefficients.

6. Divide the cover image into blocks of 8 X 8.

7. For each block,

a. Find DCT.

b. If (watermark bit = 0)

Add one bit of the PN sequence for Zero to each mid band

coefficient.

c. Convert the block back to spatial domain.

Recovery:

Input: Watermarked image, Key.

86

Output: Retrieved watermark.

1. Read the cover image watermark and key.

2. Define block size = 8 and mid band for DCT.

3. Determine the maximum watermark length based on size of cover image

and block size.

4. Set the MATLAB PN generator to state key.

5. Generate PN sequence for zero of length equal to number of mid band

coefficients.

6. Divide the cover image into blocks of 8 X 8.

7. For each block,

a. Find DCT.

b. Extract the middle band coefficients.

c. Find correlation between middle band coefficients and the PN

sequence for zero.

d. If correlation > threshold

Set recovered watermark bit = 0.

Else

Set recovered watermark bit = 1.

8. Reshape the recovered watermark according to the size of original

watermark.

Results for algorithm 8:

(a) (b) (c)

(d) (e) (f)

87

0 1 2 3 4 5 6 7 80

2

4x 10

9

PS

NR

-->

gain-->0 1 2 3 4 5 6 7 8

99

100

101

BC

R--

>

(g)

Figure 6.11: (a) Image watermarked using threshold based correlation of DCT mid band

coefficients (k = 10). (b) Retrieved watermark (threshold = 0.55). (c) Recovered watermark from

watermarked image attacked by histogram equalization. (d) Recovered watermark from

watermarked image attacked by Gaussian noise. (e) Recovered watermark from cropped

watermarked image. (f) Recovered watermark from watermarked image attacked by median

filter (3X3). (g) Variation in PSNR and BCR with change in gain.

Figure 6.11 shows the results obtained for the DCT domain technique using the

threshold based correlation between the mid band coefficients and the same sized PN

sequence generated using a secret key. Figure 6.11(a) shows the watermarked image

with gain = 10 and for this image figure 6.11(b) shows the recovered watermark

when threshold is set at 0.55. Histogram equalization of the watermarked image has

no significant effect on the watermark as shown in figure 6.11(c). Figure 6.11(d) and

(e) show the recovered watermarks after Gaussian noise is added to the watermarked

image and the watermarked image is cropped respectively. The watermark is

defeated. Figure 6.11(f) shows the recovered watermark after non-linear median

filtering of the watermarked image. The watermark is retrieved with 94.6%

correctness. Figure 6.11 (g) depicts the drop in PSNR of the watermarked image with

the increase in gain factor k. At gain = 10 the PSNR is observed to be 1.3847e+005

and the embedding of the watermark required 2.3438 seconds. The time elapsed for

recovery of the watermark is 3.5313 seconds and the BCR is 100 % which remains

88

constant independent of the value of gain. BCR first increases with the threshold

level and achieves maximum of 99% at threshold value of 0.55 and thereafter

decreases to 89.5% and becomes constant for threshold values greater than or equal

to 1.

11.3.4 ALGORITHM 9: Comparison based correlation in DCT mid-band using

a PN sequence for ‘1’ and other for ‘0’

Embedding:

Input: Cover image, Watermark, Key.

Output: Watermarked image.

1. Read the cover image watermark and key.

2. Define block size = 8, gain, ‘k’ and mid band for DCT.

3. Determine the maximum message size depending upon the

cover image and block size.

4. Reshape the watermark into a vector and pad it with ones

to maximum size.

5. Set the MATLAB PN generator to state key.

6. Generate two highly uncorrelated PN sequences for one

and zero respectively each of length equal to number of mid band

coefficients.

7. Divide the cover image into blocks of 8 X 8.

8. For each block,

a. Find DCT.

b. If (watermark bit = 0)

Embed PN sequence for zero into the mid band coefficients.

Else

Embed PN sequence for one into the mid band coefficients.

c. Convert the block back to spatial domain.

Recovery:

89

Input: Watermarked image, Watermark, Key.

Output: Retrieved watermark.

1. Read watermarked image, watermark and key.

2. Define block size and mid band for DCT matrix.

3. Calculate the maximum watermark size depending upon the watermarked

image and block size.

4. Set MATLAB PN generator state to key.

5. Generate two highly uncorrelated PN sequences for zero and one

respectively each of sizes equal to number of mid band coefficients.

6. Divide the image into blocks of size = block size X block size.

7. For each block

a. Find DCT.

b. Extract the mid band coefficients.

c. Find the correlation of these mid band coefficients with the PN

sequences for one and zero respectively.

d. If (correlation with PN sequence for one) > (correlation with PN

sequence for zero )

Set the retrieved watermark bit as 1.

Else

Set the retrieved watermark bit as 0.

8. Reshape the retrieved watermark according to the original watermark.

Results for algorithm 9

(a) (b) (c)

90

(d) (e) (f)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

1

2x 10

8P

SN

R--

>

gain-->0 0.2 0.4 0.6 0.8 1 1.2 1.4

99

100

101

BC

R--

>

(g)

Figure 6.12: (a) watermarked image with comparison based correlation of DCT mid band

coefficients (gain =10). (b) Retrieved watermark. (c) Recovered watermark from watermarked

image attacked by histogram equalization. (d) Recovered watermark from watermarked image

attacked by Gaussian noise. (e) Recovered watermark from watermarked image attacked by

median filter (3X3). (f) Recovered watermark from cropped watermarked image. (g) Variation

in PSNR and BCR with change in gain.

The results of using comparison based correlation technique of the DCT mid band

coefficient on the cover image to embed a watermark of size 20 X 50 is shown in

figure 6.12(a) and the corresponding retrieved watermark is shown in figure 6.12(b).

The time elapsed for embedding the watermark is 2.3125 seconds and the PSNR is

4.3508e+003 for the gain factor of 10. The watermark was retrieved in 5.4375

seconds with a BCR of 99.1 %. Effects of histogram equalization, Gaussian noise,

median filtering and cropping are clearly visible in Figures 6.12(c)-(f). It can be

inferred from these results that the technique is resistant to histogram equalization

and median filtering. But, it is defeated by attacks like Gaussian noise and cropping.

Figure 6.12(g) shows the variation in PSNR with increasing gain. It is quite clear that

PSNR falls sharply as the gain increases.

91

Type of attack BCR for retrieved watermark

Histogram equalization 98.6

Median filtering 97.1

Gaussian noise 81.3

Cropping 82.9

Table 6.6: Effects of attacks on image watermarked with algorithm 9.

11.3.5 ALGORITHM 10: Watermarking using U matrix of SVD

Embedding:

Input: cover image, watermark.

Output: watermarked image.

1. Read the cover image and the watermark.

2. Reshape the watermark into vector and pad it with all ones to the

maximum allowable watermark size.

3. Set the value of constant = 0.2 and block size = 8.

4. Divide the cover image into blocks.

5. For each block

a. Find SVD.

b. Obtain the U matrix and find the absolute difference,

Difference = U(1,1) – U(2,1).

c. If (((watermark bit = 1) and (difference > constant)) or((watermark

bit = 0) and (difference < constant))

U(2,1) = -(abs(U(2,1) - (constant- difference)/2).

U(1,1) = -(abs(U(1,1) + (constant- difference)/2)

d. If (((watermark bit = 1) and (difference < constant)) or((watermark

bit = 0) and (difference > constant))

U(2,1) = -(abs(U(2,1) + (constant- difference)/2).

U(1,1) = -(abs(U(1,1) - (constant- difference)/2)

e. Take inverse SVD.

92

Recovery:

Input: watermarked image.

Output: retrieved watermark.

1. Read the watermarked image.

2. Define block size.

3. Divide the watermarked image into blocks.

4. For each block

a. Find its SVD.

b. Obtain the U matrix.

c. If (U(1,1) > U(2,1))

Set retrieved watermark bit = 1.

Else

Set retrieved watermark bit = 0.

Results for algorithm 10:

(a) (b) (c)

(d) (e) (f)

93

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

10x 10

4

PS

NR

-->

Threshold difference-->0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

50

100

BC

R--

>

(c)

Figure 6.13: (a) cover image watermarked using U matrix of the SVD of the cover image. (b)

Retrieved watermark. (c) Recovered watermark from watermarked image attacked by

histogram equalization. (d) Recovered watermark from watermarked image attacked by

Gaussian noise. (e) Recovered watermark from watermarked image attacked by median filter

(3X3). (f) Recovered watermark from cropped watermarked image. (g) Variation of PSNR with

change in threshold value.

The technique used is to modify two components of the U matrix based on their

difference compared with a threshold. The size of the watermark is always required

to be same as the number of blocks in which the image is divided, so the watermark

copyright_large is cropped to obtain a suitable watermark. The time elapsed to

embed this watermark into the cover image is 0.7969 seconds with a PSNR of

2.2390e+004. The watermark is recovered as shown in figure 6.13 (b) in 0.5 seconds

with an accuracy of 88.916%. Though transform domain is used for embedding but,

the technique is very fragile and can not tolerate any of the attack studied i.e.

histogram equalization, Gaussian noise, median filtering and cropping. The retrieved

watermarks after the watermarked image is attacked are shown in figure 6.13 (c)-(f)

respectively. With the change in the threshold value used for comparing the

difference with, the PSNR value of the watermarked image changes as shown in

94

figure 6.13 (c). Though the graph shows the maximum peak at threshold of 0.006 but

the recovery at this threshold is with only 71% of correctness.

Type of attack BCR for retrieved watermark

Histogram equalization 71.2408

Median filtering 50.6592

Gaussian noise 55.2734

Cropping 77.7344

Table 6.7: Effects of attacks on image watermarked with algorithm 10.

11.3.6 ALGORITHM 11: Watermarking using D matrix of SVD

Embedding:

Input: cover image, watermark.

Output: watermarked image.

1. Read the cover image and the watermark.

2. Reshape the watermark into vector and pad it with all ones to the

maximum allowable watermark size.

3. Set the value of constant = 0.2 and block size = 8.

4. Divide the cover image into blocks.

5. For each block

i. Find SVD.

ii. Obtain the D matrix.

iii. Find the maximum value of D matrix and store in max_D.

6. Find the minimum and maximum value in max_D.

7. Define n, number of steps with size = (max(max_D)-min(max_D))/n.

8. Determine number of bins.

9. For each value of max_D, determine the corresponding bin such that the

value lies within the minimum and maximum value of the bin.

10. For each bin determine the mid level as the quantizer level.

95

11. for each watermark bit(i)

a. If (watermark bit = 0)

Corresponding value in max_D is modified as

max_D(i) =( low(k)+mid(k))/2, where low(k) and mid(k) are

the minimum and the mid value of the corresponding bin, k.

Else

Corresponding value in max_D is modified as

Max_D(i) = (high(k)+mid(k))/2, where high(k) and mid(k) are

the maximum and the mid value of the corresponding bin, k.

12. For each block of the cover image

a. Find SVD.

b. Obtain D matrix.

c. Replace the maximum value in this D matrix with the modified value

from step 11.

d. Take inverse SVD.

Recovery:

Input: watermarked image.

Output: retrieved watermark.

1. Read watermarked image.

2. Determine the maximum allowable watermark size.

3. Define the block size same as that used for embedding.

4. Divide the watermarked image into bllocks.

5. For each block

a. Find SVD.

b. Obtain the D matrix.

c. Find the maximum value of D matrix and store in max_D.

6. Find the minimum and maximum value in max_D.

7. Define n, number of steps with size = (max(max_D)-min(max_D))/n. the

value of n should be same as that used for embedding.

8. Determine number of bins.

96

9. For each value of max_D, determine the corresponding bin such that the

value lies within the minimum and maximum value of the bin.

10. For each bin determine the mid level as the quantizer level.

11. for each value in max_D

if ((max_D(i) ≥ low(k)) and (D(i) < mid(k)))

Set the retrieved watermark bit, i = 0.

else

Set the retrieved watermark bit, i = 1.

Results for algorithm 11

(a) (b) (c)

(d) (e) (f)

5 10 15 20 25 30 35 40 45 50100

200

300

400

PS

NR

-->

Number of bins-->5 10 15 20 25 30 35 40 45 50

40

60

80

100

BC

R--

>

(g)

Figure 6.14: (a) cover image watermarked using D matrix of the SVD of the cover image. (b)

Retrieved watermark. (c) Recovered watermark from watermarked image attacked by

histogram equalization. (d) Recovered watermark from watermarked image attacked by

97

Gaussian noise. (e) Recovered watermark from watermarked image attacked by median filter

(3X3). (f) Recovered watermark from cropped watermarked image. (g) Variation of PSNR and

BCR with change number of bins.

Figure 6.14 shows the results and analysis graphs for algorithm 11 which uses D

matrix of SVD to embed the watermark. Figure 6.14(a) shows the watermarked

image from which the retrieved watermark is shown in (b). The PSNR of the

watermarked image is 1.1336e+004 and the BCR of the retrieved watermark is

87.3779. The computational cost is quite low. It takes 1.2188 seconds for embedding

and 0.5938 seconds for recovery of the watermark. As for algorithm 10, which is

SVD based, this algorithm too is fragile and can be damaged due to histogram

equalization, Gaussian noise, median filtering and cropping. The recovered

watermarks after the attacks are shown in figure 6.14(c)-(f) and their accuracy is

shown as BCR in the table 6.8. The technique is thus suitable for tamper detection

applications. The above results are obtained for 30 bins. The graph in figure 6.14(h)

shows that higher PSNR can be obtained at reduced number of bins. However if the

number of bins is reduced to 12 the watermark becomes quite visible.

Type of attack BCR for retrieved watermark

Histogram equalization 53.7109

Median filtering 82.3486

Gaussian noise 48.2666

Cropping 57.0313

Table 6.8: Effects of attacks on image watermarked with algorithm 10.

ALGORITHM 12: Watermarking using CDMA using Single level DWT

Embedding:

Input: cover image, watermark and key.

Output: Watermarked image.

1. Read the cover image, watermark and key.

2. Convert the watermark into a vector.

98

3. Reset MATLAB PN generator to state key.

4. Find the first level DWT of the cover image using haar wavelet.

5. For each bit of watermark vector,

a. Generate two PN sequences for horizontal and vertical

components.

b. If watermark bit = 0

Add the PN sequences to the respective components.

6. Take the inverse DWT.

Recovery

Input: watermarked image, watermark, key.

Output: retrieved watermark.

1. Read the watermarked image, watermark and the key.

2. Reset the MATLAB PN generator to state key.

3. Initialize retrieved watermark to ones for size given by watermark.

4. For each bit

a. Generate two PN sequences for horizontal and vertical component

each.

b. Find the correlation using,

correlation_h=corr2 (cH1,pn_sequence_h).

correlation_v=corr2 (cV1,pn_sequence_v).

correlation=(correlation_h+correlation_v)/2.

c. If correlation > threshold

Set retrieved watermark bit = 0.

5. Reshape the retrieved watermark according to the size of the watermark.

Results for algorithm 12

99

(a) (b) (c)

(d) (e) (f)

Figure 6.15: (a) watermarked image. (b) Retrieved watermark. (c) Recovered watermark from

watermarked image attacked by histogram equalization. (d) Recovered watermark from

watermarked image attacked by Gaussian noise. (e) Recovered watermark from watermarked

image attacked by median filter (3X3). (f) Recovered watermark from cropped watermarked

image.

Figure 6.15 shows the results for using level 1 DWT decomposition for watermark

embedding. Figure 6.15(a) shows the watermarked image with PSNR of 575.6946.

The PSNR value is quite low. The texture of image becomes rough after embedding

the watermark. The computational cost for embedding is 25.3438 seconds which is

quite high a value. The retrieved watermark is shown in figure 6.15(b). The

watermark is retrieved in 40.1563 seconds with a BCR of 99.9%. Histogram

equalization of the watermarked image does not affect the watermark at all and the

watermark is still retrieved with 99.9% BCR as shown in figure 6.15(c). The drop in

BCR of the retrieved watermark due to Gaussian noise is negligible. Figure 6.15(d)

shows the retrieved watermark, after Gaussian noise is added to the watermarked

image. The other two intentional attacks i.e. median filtering and cropping totally

destroy the watermark with a respective BCR of 60.2 and 49.2%. The watermarks

obtained after the watermarked image is attacked are shown in figure 6.15(e) and (f).

ALGORITHM 13: WATERMARK EMBEDDING USING SECOND LEVEL

DWT DECOMPOSITION

100

Embedding

Input: cover image, watermark, key.

Output: watermarked image.

1. Read the cover image, watermark and key.

2. Decompose the cover image using DWT to obtain level 1 horizontal sub

band.

3. Decompose this horizontal sub band using DWT to obtain level 2

horizontal sub band.

4. Reset MATLAB PN generator to state key.

5. For each bit of watermark,

a. Generate a PN sequence of size same as horizontal sub band.

b. If watermark bit = 0,

Add the PN sequence to horizontal sub band.

6. Take inverse DWT twice to obtain the watermarked image.

Recovery

Input: watermarked image, watermark, key.

Output: retrieved watermark.

1. Read the watermarked image and the key.

2. Decompose the watermarked image using DWT to obtain level 1

horizontal sub band.

3. Decompose this horizontal sub band using DWT to obtain level 2

horizontal sub band.

4. Reset MATLAB PN generator to state key.

5. Generate a retrieved watermark of all ones of size same as original

watermark.

6. For each bit of retrieved watermark,

a. Generate a PN sequence of size same as horizontal sub band.

101

b. Find correlation between the generated PN sequence and

horizontal sub-band.

c. If correlation > threshold

Set retrieved watermarked bit = 1.

7. Reshape retrieved watermarks according to the original watermark.

Results for Algorithm 13:

(a) (b) (c)

(d) (e) (f)

Figure 6.17: (a) Watermarked image. (b) Retrieved watermark. (c) Recovered watermark from

watermarked image attacked by histogram equalization. (d) Recovered watermark from

watermarked image attacked by Gaussian noise. (e) Recovered watermark from watermarked

image attacked by median filter (3X3). (f) Recovered watermark from cropped watermarked

image.

Figure 6.17(a) shows the image watermarked with level 2 DWT decomposition. The

computational cost for the embedding is 3.6875 seconds with a PSNR of

1.7791e+004, when ‘bior1.1’ wavelet is used. The watermark is recovered as shown

in figure 6.17(b) in 6.1094 seconds with a BCR of 99.9%. Similar to algorithm 12,

this technique is also resistant to histogram equalization and Gaussian noise. The

retrieved watermark after equalizing the histogram of the watermarked image and

adding the Gaussian noise to it are shown in figure 6.17(c) and (d) with 99.9% and

97.9% accuracy respectively. Unlike algorithm 12, this technique is resistant to

median filtering. The recovered watermark after median filtering is shown in figure

102

6.17(e). It has a BCR of 98.4%. However, cropping defeats the watermarking. This is

clear with the recovered watermark after watermarked image is cropped, as shown in

figure 6.17(f).

CHAPTER 7

CONCLUSION

This study has introduced a number of techniques for the watermarking of digital

images, as well as touching on the limitations and possibilities of each. Several

conclusions are drawn on the basis of results and their analysis about digital

watermarking.

LSB substitution is not a very good candidate for digital watermarking due to its lack

of even a minimal level of robustness. LSB embedded watermarks can easily be

103

removed using techniques that do not visually degrade the image to the point of

being noticeable. Furthermore if one of the more trivial embedding algorithms is

used, the encoded message can be easily recovered and even altered by a 3rd party. It

would appear that LSB will remain in the domain of steganography due to its

tremendous information capacity.

Another observation is that transform domains are typically better candidates for

watermarking then spatial, for both reasons of robustness as well as visual impact.

Embedding in the DCT domain proved to be highly resistant to JPEG compression as

well as significant amounts of random noise. By anticipating which coefficients

would be modified by the subsequent transform and quantization, we were able to

produce a watermarking technique with moderate robustness, good capacity, and low

visual impact. This holds true in general for watermarking; robustness can be

improved significantly when the subsequent degradation techniques are known. This

holds particularly true in the case of compression techniques, were the compression

algorithms are well known. 

The wavelet domain as well proved to be highly resistant to both compression and

noise, with minimal amounts of visual degradation. More sophisticated wavelet-

domain techniques will almost certainly improve on both of these, and hopefully

lower it’s computational requirements. The wavelet domain may be one of the most

promising domains for digital watermarking yet found.

A final note is that of geometric transforms. Geometric transforms are one of the

most difficult for a watermarking technique to deal with. Embedding domains may

be chosen that display both shifting or rotational invariance such as Cartesian or

Polar DCT, however these domains are typically are resistant to only a specific

geometric distortion and not the complete set. Furthermore, this greatly reduces our

flexibility, as promising domains such as the DWT may no longer be considered.

Although not discussed here, the counters proposed to these attacks typically rely on

discovering the exact rotation, or shifting used in the attack, and then transforming

the image back into its pre-attack state. Typically these techniques are

104

computationally pricey, and unpredictable. This remains one of the major problems

in the development of robust digital watermarking for digital images.

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