compression techniques and water marking of digital image using wavelet transform and spiht coding

8/7/2019 Compression Techniques and Water Marking of Digital Image using Wavelet Transform and SPIHT Coding

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(IJCSIS) International Journal of Computer Science and Information Security,(Vol. 9 No. 3), 2011.

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COMPRESSION TECHNIQUES AND WATER MARKING

OF DIGITAL IMAGE USING

WAVELET TRANSFORM AND SPIHT CODING

G.Prasanna LakshmiComputer Science,IBSAR

Karjat,India

[email protected]

Dr. D.A.Chandulal

Professor and HOD, IBSAR

Computer Science

[email protected]

Dr.KTV Reddy)

Professor & Principal

Electronics & Telecommunications Dept.

Computer ScienceIndia

[email protected]

I. INTRODUCTION

Advances that facilitate electronic publishing and

Commerce also heighten threats of intellectual property theft

and unlawful tampering. One approach to address this probleminvolves embedding an invisible structure into a host signal to

mark its ownership. These structures are called digital

watermarks and the associated embedding process is called

digital watermarking. One major driving force for research in

this area is the need for effective copyright protection

scenarios for digital imagery. In such an application a serialnumber or a message is embedded into the image to protect

and to identify the copyright holder. So the objective of

watermarking is authenticity check. In this project the discretewavelet transform of an image is used which transforms the

image into two parts: an approximation part and a detail part.

So, using this transformation the details of an image can be

extracted. The control of the details of an image permits to

identify the invisible ones hence watermark can be inserted bychanging only the less important details of an image. The

watermark should survive the image processing techniques

like compression etc. This project compresses the image byusing two different techniques called HUFFMAN and SPIHT

Coding techniques. SPIHT (set partitioning in hierarchical

trees) is a new and a very fast Encoding techniqueSPIHTalgorithm is based on 3 concepts, they are

Ordered bit plane progressive transmission.

b) Set partitioning sorting algorithm.c) Spatial orientation trees.

Also in this project each coding technique i.e.

Huffman and SPIHT are performed by using two eliminationtechniques of wavelet transform, HH (LL and LH bands) and

H* elimination (only LL band) and then we compared the two

techniques w.r.t the objective fidelity criteria . The objective

fidelity criteria are:

a) MSE (mean square error) : if MSE is less, the compressed

image is more close to the original image

b) PSNR (peak signal to noise ratio): if PSNR is more thecompressed image is more close to the original image.

The amount of compression is measured using CR (compression ratio) for each elimination technique. If

compression ratio is more the compression is more. Further

the two coding techniques were compared w.r.t Encoding and

Decoding time.

The proposed block diagram for the compression and

decompression (at transmitter and receiver)is:

Fig: 1.1 ENCODER

Fig: 1.2 DECODER

II. DISCRETE WAVELET TRANSFORM

In DWT, we pass the time-domain signal from

various high Pass and low pass filters, which filters out either

high frequency or low frequency portions of the signal. This

procedure is repeated, and every time some portion of the

signal corresponding to some frequencies is removed from thesignal. There are two types of data elimination methods used

in wavelet transform. They are HH elimination and H*

elimination and in this project we use both elimination

techniques.The proposed architecture for HH and H* Elimination

techniques is as shown below

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Fig: 1.3 H* ELIMINATION TECHNIQUE

Fig: 1.4 HH ELIMINATION TECHNIQUE

III. DIGITAL WATERMARKING OF STILL IMAGES

One of the most used multimedia signals category is

that of images. For example 80% of the data transmitted using

the internet are images. This is the reason why it is very

important to study the digital watermarking methods of images.

In this thesis a novel watermarking approach which

embeds a watermark in the discrete wavelet domain of the

image is presented. This novel approach provides informationon specific frequencies of the image that have been modified.

IV. WATERMARKING USING WAVELETS

The discrete wavelet transform of an image transforms the

image into two parts: an approximation part and a detail part.So, using this transformation the details of an image can be

extracted. The control of the details of an image permits to

identify the invisible ones. This is very important becausechanging only the less important details of an image is easy to

insert a watermark in this image, keeping the insertionprocedure invisible. This can be a very simple and fast

procedure. Transforming these details, a new image, very

similar with the original one, can be obtained. This new image

can be regarded like the watermarked image associated to theoriginal one. Their difference can be considered the watermark

embedded in the original image. So the discrete wavelet

transform can be used to embed a watermark into an image.

This is the connection between the wavelets theory and the

digital watermarking of images representing the title of this

thesis.

V. THE WATERMARK INSERTION SYSTEM

Various insertion techniques like amplitude modulation of

frequencies etc are used for inserting the message into the

image .The watermark insertion system used in this thesis is

by using the ASCII codes of each alphabet of the message tobe inserted i.e. Watermarking is obtained by applying wavelettransform and then altering the chosen frequencies of the

original image according to the ASCII code of the alphabets in

the message. The 8 bits code of each alphabet is embedded

into the LSB’S of pixels starting from some chosen location.

VI COMPRESSION

After watermarking the next thing we present for

proper transmission of the image is to compress the image to

reduce the bandwidth required for transmission and the

memory needed to store the image. Compression refers to the

process of reducing the amount of data required to represent agiven quantity of information i.e. the reduction process is the

removal of redundant data, the data which contains no relevantinformation is called data redundancies given by

Rd = 1-1/Cr

Where Cr is the compression ratio given by

Cr = n1/n2

And n1 and n2 are the number of information carrying units of input and output image.

Compression refers to removing the redundancies so that

the image takes less memory and less bandwidth for transmission. In digital image four basic redundancies are

present

• Inter pixel redundancies• Psycho visual redundancies

• Coding redundancies

VII. INTERPIXEL REDUNDANCIES

This represents the Inter co-relation between the pixels

within an image. These are eliminated by applying image

transform which involves mapping the original image data intoanother mathematical space where it is easier to compress the

data by representing it into fewer numbers of bits than the

original image. In this project, the Wavelet Transform which

is used for watermarking to remove the interpixel dundancies.

VIII. PSYCHOVISUAL REDUNDANCIES

This is the information which has less relative importance

than other information in normal visual processing. Theseredundancies are removed by using quantization. Quantization

means mapping of a broad range of input values to a limited

number of output values. Quantization is applied on the output

obtained after applying DWT. Quantization is an irreversible

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process, hence information lost cannot be regained duringdecompression.

IX. CODING REDUNDANCIES

Coding Involves mapping the discrete data from the

quantizer onto a code in an optimal manner i.e. construction

of codes such that the number of bits used to represent the

data is reduced i.e. by assigning fewer bits to the more

probable gray levels than to the less probable ones whichachieves compression. In this project we applied two coding

techniques called Huffman coding and SPIHT Coding (Set

Partitioning in Hieraricial Trees).

X. HUFFMAN CODING

Huffman coding technique is the most popular technique

for removing coding redundancies. Huffman coding yields the

smallest possible number of code symbol per source symbol.

In terms of the noiseless coding theorem, the resulting code is

optimal for a fixed value of n, subject to the constraint that the

source symbols be coded one at a time.The Huffman algorithmcan be described in five steps.

1. Find the gray level probabilities for the image by

finding the histogram2. Order the input probabilities from smallest to largest

3. Combine the smallest two by addition

4. GOTO step 2, until only two probabilities are left

5. By working backward along the tree, generate code

by alternating assignment of 0 and 1

XI. SPIHT CODING (Set partitioning in hierarchicaltrees)

SPIHT Coding offers a new, fast and different

implementation based on set partitioning in hierarcial trees,which provides better performance than other coding

techniques. It has become the benchmark state-of-the-artalgorithm for image compression.

SPIHT algorithm is based on 3 concepts

a) Ordered bit plane progressive transmission.

b) Set partitioning sorting algorithm.c) Spatial orientation trees.

SPIHT has the following advantages:

a) Optimized for progressive image transmissionb) Produces a fully embedded coded file

c) Simple quantization algorithmd) Fast coding and decoding

e) Wide applicationf) Good image quality, high PSNR

g) Can code to exact bit rate or distortion

h) Efficient combination with error protection

XII. FIDELITY CRITERIA

A repeatable or reproducible means of quantifyingthe nature and extent of information loss is highly desirable.

Two general classes of criteria for digital images are 1)

Objective Fidelity Criteria and 2) Subjective Fidelity Criteria

In this paper we present Objective Fidelity Criteria like

1) MSE (Mean Square Error): As MSE decreases the

clarity of the image increases i.e. the compressedimage is more close to the original image.

2) PSNR (Peak Signal to Noise Ratio): As PSNR

increases the clarity of image increases i.e. thecompressed image is more close to original image.

3) CR (Compression Ratio): As CR increases we

achieve more compression.

2. LITERATURE REVIEW

2.1 TRANSFORMS

WHAT IS A TRANSFORM?

WHY DO WE NEED TRANSFORMS?

A Transform is a mathematical operation that takes a

function or sequence and maps it into another one. Transforms

are used because

a) The transform of a function may give additional /hidden

information about the original function, which may not be

available /obvious otherwiseb) The transform of an equation may be easier to solve than

the original equation (recall Laplace transforms for “Diff-

Equations”)c) The transform of a function/sequence may require less

storage, hence provide data compression reduction.d) An operation may be easier to apply on the transformed

function, rather than the original function (recall convolution).

Mathematical transformations are applied to signals

to obtain further information from that signal that is notreadily available in the raw signal. Most of the signals in

practice, are Time domain signals in their raw format, i.e.

whatever that signal is measuring, is a function of time.In other words, when we plot the signal, one of the

axes is time (independent variable), and the other (dependent

variable) is usually the amplitude. When we plot time-domain

signal we obtain a Time – Amplitude representation of the

signal. This representation is not always the best

representation of the signal for most IMAGE PROCESSINGrelated applications.

In many cases, the most distinguishedinformation is hidden in the frequency content of the signal.

The frequency spectrum of a signal is basically the frequency

components (spectral components) of that signal. The

frequency spectrum of a signal shows what frequencies exist

in the signal.


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Intuitively, we all know that the frequency is something todo with the change in rate of something. If something (a

mathematical or physical variable would be the technically

correct term) changes rapidly, we say that it is of high

frequency, where as if this variable does not change rapidly,

i.e., it changes smoothly, we say that it is of low frequency. If

this variable does not change at all, then we say it has zerofrequency, For example the publication frequency of a daily

newspaper is higher than that of a monthly magazine.

Frequency is measured in cycles/second, or with a morecommon name, in "Hertz". Now, look at the following figures.

The first one is a sine wave at 3 Hz, the second one at 10 Hz

as shown below.

Fig: 2.1.1 SINE WAVES WITH DIFFERENT

FREQUENCIES

So how do we measure frequency, or how do we find thefrequency content of a signal or an image?

The answer is FOURIER TRANSFORM (FT). If the FT

of a signal in time domain is taken, the frequency-amplitude

representation of that signal is obtained. In other words, we

now have a plot with one axis being the frequency and theother being the amplitude. This plot tells us how much of each

frequency exists in our signal or image. For example the FT of

the electric current that we use in our house, we get one spikeat 50 Hz, and nothing Elsewhere, since that signal has only

50 Hz frequency component.

The following shows the FT of the 50Hz signal:

Fig: 2.1.2 FT OF A 50 Hz SIGNAL

Although FT is probably the most popular transform

being used, there are many other transforms that are used quite

often by engineers and mathematicians. Hilbert transform,

short-time Fourier transform, Wigner distributions, the RadonTransform, and of course our featured transform, the wavelet

transform constitute only a small portion of a huge list of transforms that are available at engineer's and mathematician's

disposal. Every transformation technique has its own area of

application, with advantages and disadvantages, and the

wavelet transform (WT) is no exception.

For a better understanding of the need for the WTlet's look at the FT more closely. FT and WT both are

reversible transforms, that is, it allows going back and

forwarding between the raw and processed (transformed)signals. However, only either of them is available at any given

time. That is, no frequency information is available in the

time-domain signal, and no time information is available in the

Fourier transformed signal.

The natural question that comes to mind is that is it

necessary to have both the time and the frequency informationat the same time? Recall that the FT gives the frequency

information of the signal, which means that it tells us how

much of each frequency exists in the signal, but it does not tellus when in time these frequency components exist. This

information is not required when the signal is so-called

stationary, i.e. in stationary signals, all frequency components

that exist in the signal, exist throughout the entire duration of

the signal. There is 10 Hz at all times, there is 50 Hz at alltimes, and there is 100 Hz at all times as shown below.


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Fig: 2.1.3 Stationery signal

Fig: 2.1.4 FT OF A STATIONERY SIGNAL

Note the four spectral components corresponding to the

frequencies 10, 25, 50 and 100 Hz.Contrary to the above signal, the signal shown below is a

non-stationary signal whose frequency constantly changes in

time. This signal is known as the "chirp" signal or a non

stationary signal.

Fig: 2.1.5 NON- STATIONERY SIGNAL

The above plot shows a signal with four different frequencycomponents at four different time intervals, hence a non-

stationary signal. The interval 0 to 300 ms has a 100 Hzsinusoid, the interval 300 to 600 ms has a 50 Hz sinusoid, the

interval 600 to 800 ms has a 25 Hz sinusoid, and finally the

interval 800 to 1000 ms has a 10 Hz sinusoid. And the

following is its FT:

Fig: 2.1.6 FT OF A NON-STATIONERY SIGNAL

Do not worry about the little ripples at this time; they are due

to sudden changes from one frequency component to another.

Now, compare the Figures 1.4 and 1.6. The similarity between

these two spectrums should be apparent. Both of them show

four spectral components at exactly the same frequencies, i.e.,at 10, 25, 50, and 100 Hz. Other than the ripples, and the

difference in amplitude (which can always be normalized), the

two spectrums are almost identical, although thecorresponding time-domain signals are not even close to each

other. The signals involve the same frequency components,but the first one has these frequencies at all times, the second

one has these frequencies at different intervals. So, how come

the spectrums of two entirely different signals look very muchalike? Recall that the FT gives the spectral content of the

signal, but it gives no information regarding where in time

those spectral components appear. Therefore, FT is not asuitable technique for non-stationary signal, with one

exception; FT can be used for stationary signals, if we are only

interested in what spectral components exist in the signal, but

not interested where these occur. However, if this information

is needed, i.e., if we want to know, what spectral component

occur at what time (interval) , then Fourier transform is not the

right transform to use. When the time localization of thespectral components is needed, a transform giving the Time-

Frequency representation of the signal is needed. Hence we gofor a transform called WAVELET TRANSFORM.

2.2) THE WAVELET TRANSFORM

The Wavelet transform is a transform of this type i.e. itprovides the time-frequency representation. There are other

transforms which give this information too, such as short time

Fourier transforms, Wigner distributions.

Wavelet transform is capable of providing the time

and frequency information simultaneously, hence giving a

time-frequency representation of the signal. The WT wasdeveloped as an alternative to the STFT (Short Time Fourier transform). The advantages of Wavelet Transform is a. Overcomes the present resolution problem of the STFT by

using a variable length window

b. Analysis windows of different lengths are used for

different frequencies:

c. For analysis of high frequencies, Use narrower windowsfor better time resolution


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d. For analysis of low frequencies, Use wider windows for better frequency resolution

e. This works well, if the signal to be analyzed mainly

consists of slowly varying characteristics with occasional

short high frequency bursts.

f. Heisenberg principle still holds good

g. The function used to window the signal is called thewavelet.

Wavelet Transforms basically work on two properties a)

Scaling property and b) Translation propertyTranslation Property: It is the time shift property

f(t) f(a.t) a>0If 0<a<1 then contraction takes place i.e. low scale (high

frequency)

If a>1 then dilation takes place i.e. expansion, large scale

(lower frequency)if f(t) f(a/t) a>0

If 0<a<1 then dilation takes place i.e. large scale (lower

frequency)

If a>1 then contraction takes place, low scale (high

frequency)Scaling Property : It has a similar meaning as that of scale in

maps

A. Large scale: Overall view, long term behavior B. Small scale: Detail view, local behavior

Continuous Wavelet Transform:

The continuous wavelet transform is obtained using

the equation

Computation of CWT


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DISCRETE WAVELET TRANSFORM:we need not have to use a uniform sampling rate for

the translation parameters, since we do not need as high time

sampling rate when the scale is high (low frequency).

Let’s consider the following sampling grid:

Equations

Fig: 2.2.2 SAMPLING GRID

The equations are an exception to the prescribedspecifications of this template. You will need to determinewhether or not your equation should be typed using either theTimes New Roman or the Symbol font (please no other font).To create multileveled equations, it may be necessary to treatthe equation as a graphic and insert it into the text after your paper is styled.

Number equations consecutively. Equation numbers, withinparentheses, are to position flush right, as in (1), using a righttab stop. To make your equations more compact, you may usethe solidus ( / ), the exp function, or appropriate exponents.Italicize Roman symbols for quantities and variables, but notGreek symbols. Use a long dash rather than a hyphen for aminus sign. Punctuate equations with commas or periods whenthey are part of a sentence, as in

α + β = χ.

Consider an example as shown below for a 2D Wavelet

Transform:

Fig: 2.2.3 1D WAVELET TRANSFORMS

SCALING FUNCTION:

“

The equation for a 1D DWT is

2D WAVELET FUNCTIONS:


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let other common scientific constants, is zero with subscriptformatting, not a lowercase letter “o”.

• In American English, commas, semi-/colons, periods,question and exclamation marks are located withinquotation marks only when a complete thought or

Fig: 2.2.4 IMPLEMENTATION OF 2D WAVELET

TRANSFORM

In DWT, we pass the time-domain signal from various highpass and low pass filters, which filters out either high

frequency or low frequency portions of the signal. This

procedure is repeated, and every time some portion of thesignal corresponding to some frequencies being removed from

the signal. This is the technique used for compression of an

image using Wavelet Transform.

Here is how this works: The WT can be performed by

using two elimination methods, they are 1) H-Eliminationmethod and 2) H* Elimination method. The elimination

methods are chosen based on the required compression.

Now suppose we have a signal which has frequencies upto 1000 Hz. In the first stage we split up the signal into two

parts by passing the signal from a high pass and a low pass

filter (filters should satisfy some certain conditions, so-called

admissibility condition) which results in two different versions

of the same signal: portion of the signal corresponding to 0-500 Hz (low pass portion), and 500-1000 Hz (high pass

portion). Then, we take either portion (usually low passportion) or both, and do the same thing again. This operation

is called decomposition. The figure below shows the singlestage and multi stage decomposition in Wavelet Transform.

Fig: 2.2.5 SINGLE STAGE DECOMPOSITION

Fig: 2.2.6 MULTI STAGE DECOMPOSITION

Assuming that we have taken the low pass portion, we now

have 3 sets of data, each corresponding to the same signal atfrequencies 0-250 Hz, 250-500 Hz, 500-

1000 Hz. Then we take the low pass portion again and pass it

through low and high pass filters; we now have 4 sets of signals corresponding to 0-125 Hz, 125-250 Hz, 250-500 Hz,

and 500-1000 Hz. We continue like this until we have

decomposed the signal to a pre-defined certain level. Then we

have a bunch of signals, which actually represent the same

signal, but all corresponding to different frequency bands. Weknow which signal corresponds to which frequency band, and

then based on the required compression ratio some frequencies

are computed and some frequencies are skipped as shownbelow

The results of applying Discrete Wavelet Transform onthe image in single stage and multiple stage is as shown below


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Fig: 2.2.7 ORIGINAL IMAGE

Fig: 2.2.8 FIRST STAGE DISCRETE WAVELET

TRANSFORM

name is cited, such as a title or full quotation. Whenquotation marks are used, instead of a bold or italictypeface, to highlight a word or phrase, punctuation

should appear outside of the quotation marks. Aparenthetical phrase or statement at the end of asentence is punctuated outside of the closingparenthesis (like this). (A parenthetical sentence ispunctuated within the parentheses.)

In wavelet analysis the signal is multiplied with a function, i.e.

a wavelet, similar to the window and the transform is

computed separately for different segments of the time-

domain signal. The width of the window is changed as the

transform is computed for every single spectral component,

which is probably the most significant characteristic of thewavelet transform. The term Wavelet means small wave. The

smallness refers to the condition that this (window) function isof finite length (compactly supported). The wave refers to the

condition that this function is oscillatory.

In terms of frequency, low frequencies (high scales)

correspond to a global information of a signal (that usually

spans the entire signal), whereas high frequencies (low scales)

correspond to a detailed information of a hidden pattern in the

signal (that usually lasts a relatively short time). Fortunately inpractical applications, low scales (high frequencies) do not last

for the entire duration of the signal, unlike those shown in thefigure, but they usually appear from time to time as short

bursts, or spikes.

The discrete wavelet transform (DWT), on the other

hand, provides sufficient information both for analysis and

synthesis of the original signal, with a significant reduction inthe computation time. The DWT is considerably easier to

implement when compared to the CWT. In the discrete case,

filters of different cutoff frequencies are used to analyze the

signal at different scales. The signal is passed through a seriesof high pass filters to analyze the high frequencies, and it is

passed through a series of low pass filters to analyze the lowfrequencies.

The resolution of the signal, which is a measure of the amount of detail information in the signal, is changed by

the filtering operations, and the scale is changed by up

sampling and down sampling (sub sampling) operations.

Sub sampling a signal corresponds to reducing the samplingrate, or removing some of the samples of the signal. For

example, sub sampling by two refers to dropping every other

sample of the signal. Sub-sampling by a factor n reduces the

number of samples in the signal n times. Up sampling a signalcorresponds to increasing the sampling rate of a signal by

adding new samples to the signal. For example, up sampling

by two refers to adding a new sample, usually a zero or aninterpolated Value, between every two samples of the signal.

Up sampling a signal by a factor of n increases the number of samples in the signal by a factor of n. The procedure starts

with passing this signal (sequence) through a half band digital

low pass filter with impulse response h[n]. Filtering a signalcorresponds to the mathematical operation of convolution of

the signal with the impulse response of the filter.

The convolution operation in discrete time is defined as

follows:


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The unit of frequency is of particular importance at this

time. In discrete signals, frequency is expressed in terms of

radians. Accordingly, the sampling frequency of the signal isequal to 2p radians in terms of radial frequency. Therefore, the

highest frequency component that exists in a signal will be p

radians, if the signal is sampled at Nyquist’s rate (which is

twice the maximum frequency that exists in the signal); that is,the Nyquist’s rate corresponds to p rad in the discrete

frequency domain. Therefore using Hz is not appropriate for

discrete signals.

After passing the signal through a half band low passfilter, half of the samples can be eliminated according to the

Nyquist’s rule, since the signal now has a highest frequency of

p/2 radians instead of p radians. Simply discarding every other

sample will sub sample the signal by two, and the signal willthen have half the number of points. The scale of the signal is

now doubled. Note that the low pass filtering removes the high

frequency information, but leaves the scale unchanged. Only

the sub sampling process changes the scale.

Resolution, on the other hand, is related to the amount of information in the signal, and therefore, it is affected by the

filtering operations. Half band low pass filtering removes half

of the frequencies, which can be interpreted as losing half of the information. Therefore, the resolution is halved after the

filtering operation. Note, however, the sub sampling operation

after filtering does not affect the resolution, since removing

half of the spectral components from the signal makes half thenumber of samples redundant anyway. Half the samples can

be discarded without any loss of information. In summary, the

low pass filtering halves the resolution, but leaves the scale

unchanged. The signal is then sub sampled by 2 since half of

the number of samples are redundant. This doubles the scale.

This procedure can mathematically be expressed as

Having said that, we now look how the DWT is actually computed: The DWT analyzes the

signal at different frequency bands with different resolutions

by decomposing the signal into a coarse approximation and

detail information. DWT employs two sets of functions, called

scaling functions and wavelet functions, which are associated

with low pass and high pass filters, respectively.The decomposition of the signal into different

frequency bands is simply obtained by successive high passand low pass filtering of the time domain signal. The original

signal x[n] is first passed through a half band high pass filter

g[n] and a low pass filter h[n]. After the filtering, half of thesamples can be eliminated according to the Nyquist’s rule,

since the signal now has a highest frequency of p /2 radians

instead of p. The signal can therefore be sub sampled by 2,simply by discarding every other sample. This constitutes one

level of decomposition and can mathematically be expressed

as follows:

Where yhigh[k] and ylow[k] are the outputs of the high

pass and low pass filters, respectively, after sub sampling by 2.

This decomposition halves the time resolution since only half

the number of samples now characterizes the entire signal.

However, this operation doubles the frequency resolution,since the frequency band of the signal now spans only half the

previous frequency band, effectively reducing the uncertaintyin the frequency by half. The above procedure, which is also

known as the sub band coding, can be repeated for further

decomposition. At every level, the filtering and sub sampling

will result in half the number of samples (and hence half the

time resolution) and half the frequency band spanned (andhence doubles the frequency resolution). Figure 4.1 illustrates

this procedure, where x[n] is the original signal to be

decomposed, and h[n] and g[n] is low pass and high pass

filters, respectively. The bandwidth of the signal at every levelis marked on the figure as "f".

Fig: 2.2.10 DWT COEFFICIENTS

The Sub band Coding Algorithm As an example, suppose thatthe original signal x[n] has 512 sample points, spanning a

frequency band of zero to p rad/s. At the first decomposition

level, the signal is passed through the high pass and low passfilters, followed by sub sampling by 2. The output of the high

pass filter has 256 points (hence half the time resolution), but

it only spans the frequencies p/2 to p rad/s (hence double the

frequency resolution). These 256 samples constitute the first

level of DWT coefficients. The output of the low pass filter

also has 256 samples, but it spans the other half of the


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frequency band, frequencies from 0 to p/2 rad/s. This signal isthen passed through the same low pass and high pass filters for

further decomposition. The output of the second low pass filter

followed by sub sampling has 128 samples spanning a

frequency band of 0 to p/4 rad/s, and the output of the second

high pass filter followed by sub sampling has 128 samples

spanning a frequency band of p/4 to p/2 rad/s. The second highpass filtered signal constitutes the second level of DWT

coefficients. This signal has half the time resolution, but twice

the frequency resolution of the first level signal. In other words, time resolution has decreased by a factor of 4, and

frequency resolution has increased by a factor of 4 compared

to the original signal. The low pass filter output is then filtered

once again for further decomposition. This process continues

until two samples are left. For this specific example there

would be 8 levels of decomposition, each having half thenumber of samples of the previous level. The DWT of the

original signal is then obtained by concatenating all

coefficients starting from the last level of decomposition(remaining two samples, in this case). The DWT will then

have the same number of coefficients as the original signal.

The frequencies that are most prominent in the original signal

will appear as high amplitudes in that region of the DWTsignal that includes those particular frequencies. Thedifference of this transform from the Fourier transform is that

the time localization of these frequencies will not be lost.

However, the time localization will have a resolution thatdepends on which level they appear. If the main information

of the signal lies in the high frequencies, as happens most

often, the time localization of these frequencies will be more

precise, since they are characterized by more number of

samples. If the main information lies only at very lowfrequencies, the time localization will not be very precise,

since few samples are used to express signal at these

frequencies. This procedure in effect offers a good time

resolution at high frequencies, and good frequency resolutionat low frequencies.

Suppose we have a 256-sample long signal sampled at 10

MHZ and we wish to obtain its DWT coefficients.Since the

signal is sampled at 10 MHz, the highest frequency componentthat exists in the signal is 5 MHz. At the first level, the signal

is passed through the low pass filter h[n], and the high pass

filter g[n], the outputs of which are sub sampled by two. The

high pass filter output is the first level DWT coefficients.There are 128 of them, and they represent the signal in the [2.5

5] MHz range. These 128 samples are the last 128 samples

plotted. The low pass filter output, which also has 128

samples, but spanning the frequency band of [0 2.5] MHz, arefurther decomposed by passing them through the same h[n]

and g[n]. The output of the second high pass filter is the level

2 DWT coefficients and these 64 samples precede the 128

level 1 coefficients in the plot. The output of the second low

pass filter is further decomposed, once again by passing itthrough the filters h[n] and g[n]. The output of the third high

pass filter is the level 3 DWT coefficients. These 32 samples

precede the level 2 DWT coefficients in the plot.Theprocedure continues until only 1 DWT coefficient can be

computed at level 9. This one coefficient is the first to be

plotted in the DWT plot. This is followed by 2 level 8

coefficients, 4 level 7 coefficients, 8 level 6 coefficients, 16

level 5 coefficients, 32 level 4 coefficients, 64 level 3

coefficients, 128 level 2 coefficients and finally 256 level 1coefficients. Note that less and less number of samples is used

at lower frequencies, therefore, the time resolution decreases

as frequency decreases, but since the frequency interval alsodecreases at low frequencies, the frequency resolution

increases. Obviously, the first few coefficients would not carry

a whole lot of information, simply due to greatly reduced timeresolution. One area that has benefited the most from this

particular property of the wavelet transforms is imageprocessing.

DWT can be used to reduce the image size without

losing much of the resolution.

Here is how:For a given image, you can compute the

DWT of, say each row, and discard all values in the DWT that

are less then a certain threshold. We then save only those

DWT coefficients that are above the threshold for each row,and when we need to reconstruct the original image, we

simply pad each row with as many zeros as the number of

discarded coefficients, and use the inverse DWT to reconstructeach row of the original image.

We can also analyze the image at different frequency

bands, and reconstruct the original image by using only the

coefficients that are of a particular band.

2.3) WATERMARKING

Digital watermarking is an adaptation of the commonly used

and well-known paper watermarks to the digital world. Digitalwatermarking describes methods and technologies that allow

hiding of information, for example a number or text, in digital

media, such as images, video and audio. The embedding takes

place by manipulating the content of the digital data thatmeans the information is not embedded in the frame around

the data. There are two types of watermarks. They are

1) VISIBLE WATERMARKS: These are visible to the

viewers as in a bond paper to mark the paper type

2) INVISIBLE WATERMARKS: These are invisible to theviewer and are useful for identifying the authorizedowner.


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Fig: 2.3.2 INVISIBLE WATERMARKING

First applications of watermarking that came to mindwere related to copyright protection of digital media. Inthe past duplicating artwork was quite complicated andrequired a great expertise for that the counterfeitlooked like the original. However, in the digital worldthis is not true. For everyone it is extremely easy toduplicate digital data and this even without any loss of

quality

Fig: 2.3.3 Classification of information hiding technique

2.3.1) REQUIREMENTS OF DIGITAL

WATERMARKINGDigital watermarking has to meet the following requirements:

1. Perceptual transparency: The algorithm must embed data

without affecting the perceptual quality of underlying host

signal.

2. Security: A secure data embedding procedure can not bebroken unless the unauthorized user access to a secret key that

controls the insertion of data in host signal.

3. Robustness: Watermarking must survive attacks by lossydata compression and image manipulation like cut and paste,

filtering etc

4. Unambiguous: Retrieval of watermark should

unambiguously identify the owner

5. Universal: Same watermark algorithm should be applicable

to all multimedia under consideration

6. Imperceptibility : The watermark should not be visible by

human visual system (HVS) and should not degrade the image

quality

7. Reliability: To ensure that the project application returnsthe watermark each time.

2.3.2) DOMAINS USED IN WATERMARKING

Spatial domain: This is one of the simplest techniques

Simple Technique obtained by LSB Substitution i.e.Obtain the bit planes of the Host Image and Replace

the zero bit plane of host image with watermark image

Advantages:

a) A simple technique

b) Requires no watermark image to retrieve it from

watermarked imc) No blocking artifacts

d) Maximum Capacity

Disadvantages: a) Prone to tampering and attacks like

Compression

Rotation

ScalingTranslation

Cropping etc.

Transform domain: Host image is transformed into

another domain using DCT, Hartley, and Wavelet etc. Watermark image is embedded in the frequency

coefficients of the transformed host image

Watermark is extracted from the watermarked image

by taking inverse transform and identifying thecoefficients

Advantages:

a) Robustnessb) Resistant to rotation, scaling and translation and

Compression

c) Perceptibility

Disadvantages:

a) Less Capacityb) Computationally Complex

c) Blocking artifacts due to block processing

Hybrid domain: This is intermediate between spatial and

transform domain, it is a combination of both spatialand frequency domain.

Advantages:

a) To increase the capacity of the watermark.

b) To make use of the benefit of transform domains.

c) To maximize the immunity of the watermark against various distortion attacks.

2.3.3) APPLICATIONS OF WATERMARKING

Watermarking has wide range of application .they

can be used for


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1. Data Hiding -- Providing private secret messages2. Copyright Protection -- To prove ownership

3. Copy Control -- To trace illegal copies and License

Agreement

4. Data Authenticatio -- Check if content is modified

5.Broadcasting Monitor -- For commercial Advertisement

6. Copy Protection -- To protect illegal copying of theinformation

2.3.4) WATERMARKING COMPONENTS

VISIBILITY

CAPACITY ROBUSTNESS ROBUSTNESS

CAPACITY: It refers to the amount of information we are

able to insert into the host image.

Capacity = Bytes of hidden data

Bytes of Cover image

ROBUSTNESS:

It refers to ability of inserted information to withstand imagemodifications.

At present, digital watermarking research primarily involves

the identification of effective signal processing strategies to

discreetly, robustly, and unambiguously hide the watermark

information into multimedia signals. The general process

involves the use of a key which must be used to successfullyembed and extract the hidden information. The embedding

mechanism entails imposing imperceptible changes to the hostsignal to generate a watermarked signal containing the

watermark information, while the extraction routine attempts

to reliably recover the hidden watermark from a possible

tampered watermarked signal.

The objective of this project is the security of image andsecurity has the following objectives:

- The transmitted information confidentiality-

- The transmitted information integrity,- The transmitted information authenticity,

- The transmitted information non-repudiation,

- The disposability of the required information and of therequired services,

The authenticity of the image can be verified by another

person or system connected in the same network. This kind of authenticity check is very important and was intensively

developed in the last years. The author of the message sends a

transformed form of another message, related with the firstone, to a third entity. Processing this transformed form of the

messages the third entity can establish the author. Today,

digital signatures or digital envelopes (the transformed forms

of a message) are used by specialized systems or organizationsto check the authenticity of a message.

The embedding mechanism entails imposing

imperceptible changes to the host signal to generate awatermarked signal containing the watermark information,

while the extraction routine attempts to reliably recover the

hidden watermark from a possible tampered watermarked

signal.

One of the most used multimedia signals category is that

of images. For example 80% of the data transmitted using theinternet are images. This is the reason why it is very important

to study the digital watermarking of images.

2.3.5) TYPES OF WATERMARK IN

TERMS OF FIDELITY There are three types of watermarks in terms of Fidelity.

They are

a) Robust Watermark : This watermark has the ability to

withstand various image attacks thus providingauthentication.

b) Fragile Watermark : This watermark is mainly used for

detecting modification of data. This watermark getsdegraded even for a slight modification of data in theimage.

c) Semi Fragile Watermark : It is an intermediate between

fragile and robust watermarks. It is not robust against all

possible image attacks.

2.3.6) WATERMARK INSERTION SYSTEMThe watermarks can be inserted by using various techniques

like

a) Flip the lowest order bit of chosen pixelsb) Superimpose a symbol over the area of an image

c) By using color separation, i.e. the watermark appears

in only one color band

d) By applying transforms and then altering the chosen

frequencies from the original

2.4) COMPRESSIONCompression refers to the process of reducing the amount of data required to represent a given quantity information. The

compression system model consists of two parts:

1. The Compressor 2. The Decompressor

Image compression model

Fig: 2.4.1 SOURCE ENCODER


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Fig: 2.4.2 SOURCE DECODER

The data which contains no relevant information is called data

redundancies given byRd = 1-1/Cr

Where Cr is the compression ratio given by

Cr = n1/n2

And n1 and n2 are the number of information carrying units of

input and output image. In digital image three basicredundancies are present which can be eliminated for

compression

1) Interpixel redundancies2) Coding redundancies

3) Psycho visual redundancies

2.4.1) INTERPIXEL REDUNDANCIES

The correlations which exist between the pixels due to

structural or geometric relationships between the objects of theimage .some redundancies arise due to this Inter correlation

between the pixels within an image. A variety of names like

spatial redundancies, Geometric Redundancies, and Interframe

redundancies .these are eliminated in an image , the 2D pixelarray normally used for human viewing and interpretation

must be transformed into a more efficient format i.e. the

difference between adjacent is used to represent an image .

This is usually done by applying transforms. This process isalso known as mapping. In this project interpixel redundancies

are removed by using Wavelet Transforms.

2.4.2) PSYCHOVISUAL REDUNDANCIESHuman eye does not respond with equal sensitivity to all

visual information. Certain information simply has less

relative importance than other information in normal visual

processing. This information is said to be psycho visually

redundant which can be removed without significantly

impairing the quality of image perception because theinformation itself is not essential for normal visual processing.

Since the elimination of psycho visual redundant data

results in a loss of quantitative information, it is commonlyreferred to as Quantization. Quantization is mapping of a

broad range of input values to a limited number of output

values. Quantization is an irreversible process and results in

lossy compression.

2.4.3) CODING REDUNDANCIES

In the process of removing coding redundancies the shortest

code word is assigned to the grey levels that occur most

frequently in an image i.e. fewer bits are assigned to the mostprobable grey levels than to the less probable ones and this

achieves data compression. This process is referred to as

variable length coding. Coding redundancies are removed byusing the process of encoding. There are various encoding

process like variable length coding

1) Huffman coding

2) Arithmetic coding

3) LZW Coding4) Bit plane coding

5) SPIHT Coding

In this project we have used two different encoding

techniques i.e. Huffman coding and SPIHT coding using both

HH and H* Elimination techniques.

2.4.4) HUFFMAN CODINGThe Huffman code, developed by D. Huffman in 1952, is a

minimum length code which is the most popular technique for

removing coding redundancies. Huffman coding yields thesmallest possible number of code symbol per source symbol.

In terms of the noiseless coding theorem, the resulting code is

optimal for a fixed value of n, subject to the constraint that thesource symbols be coded one at a time.

Huffman coding gives a statistical distribution of the gray

levels (the histogram), the Huffman algorithm will generate a

code that is as close as possible to the minimum bound. For

complex images, Huffman coding alone will typically reduce

the file by 10% to 50% but this ratio can be improved to 2:1 or 3:1 by preprocessing for irrelevant information removal.

The Huffman algorithm can be described in five steps

1. Find the gray level probabilities for the image byfinding the histogram

2. Order the input probabilities from smallest to largest

3. Combine the smallest two by addition

4. GOTO step 2, until only two probabilities are left5. By working backward along the tree, generate code

by alternating assignment of 0 and 1.

An example of how the Huffman coding algorithm works is asshown below:

1) The first step in Huffman’s approach is to create a series

of source reductions by ordering the probabilities of thesymbols under considerations and combining the lowest

probability symbols into a single symbol that replaces them in

the next source reduction as shown in the tabular columnbelow

The second step in Huffman’s procedure is to code each

reduced source, starting with the smallest source and working

back to the original source and the minimal length binary code

for a two symbol source, is the symbols 0 and 1.


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The final code appears at the far left in the abovetable which shows that fewer bits are allotted to the most

probable symbols. Huffman encoded symbols can be decoded

by examining the individual symbols of the string in a left toright manner.

2.4.5) SPIHT CODING

SPIHT Coding offers a new, fast and different

implementation based on set partitioning in hierarchial trees,which provides better performance than other coding

techniques. It has become the benchmark state-of-the-art

algorithm for image compression.

SPIHT has the following advantages:1) good image quality , high PSNR, especially for

color images

2) it is optimized for progressive image

transmission

3) produces a fully embedded coded file4) simple quantization algorithm

5) fast coding/decoding time

6) has wide application, completely adaptive

7) can be used for lossless compression8) can code to exact bit rate or distortion

9) efficient combination with error protection

Image quality:

SPIHT yields very good quality visual images byexploiting the properties of wavelet transform images.

Progressive image transmission:

I some systems with progressive image transmission

(like WWW browsers) the quality of the displayed imagesfollows the sequence: (a) weird abstract art; (b) you begin to

believe that it is an image of something; (c) CGA-like quality;

(d) lossless recovery. With very fast links the transition from

(a) to (d) can be so fast that you will never notice. With slow

links (how "slow" depends on the image size, colors, etc.) thetime from one stage to the next grows exponentially, and it

may take hours to download a large image. Considering that it

may be possible to recover an excellent-quality image using10-20 times less bits, it is easy to see the inefficiency.

Furthermore, the mentioned systems are not efficient even for lossless transmission.

The problem is that such widely used schemes employ a very

primitive progressive image transmission method. On theother extreme, SPIHT is a state-of-the-art method that was

designed for optimal progressive transmission (and still beats

most non-progressive methods!). It does so by producing afully embedded coded file in a manner that at any moment the

quality of the displayed image is the best available for the

number of bits received up to that moment.

So, SPIHT can be very useful for applications where theuser can quickly inspect the image and decide if it should be

really downloaded, or is good enough to be saved, or need

refinement.

A. Optimized Embedded Coding:

Suppose you need to compress an image for three remote

users. Each one have different needs of image reproduction

quality, and you find that those qualities can be obtained withthe image compressed to at least 8 Kb, 30 Kb, and 80 Kb,

respectively. If you use a non-embedded encoder (like JPEG)to save in transmission costs (or time) you must prepare one

file for each user. On the other hand, if you use an embedded

encoder (like SPIHT) then you can compress the image to a

single 80 Kb file, and then send the first 8 Kb of the file to the

first user, the first 30 Kb to the second user, and the whole fileto the third user.

Surprisingly, with SPIHT all three users would get (for

the same file size) an image quality comparable or superior to

the most sophisticated non-embedded encoders available

today. SPIHT achieves this feat by optimizing the embedded

coding process and always coding the most important

information first.

B. Compression Algorithm:

SPIHT represents a small "revolution" in image

compression because it broke the trend to more complex (inboth the theoretical and the computational senses)

compression schemes. While researchers had been trying to

improve previous schemes for image coding using very

sophisticated vector quantization, SPIHT achieved superior

results using the simplest method: uniform scalar quantization.Thus, it is much easier to design fast SPIHT codes.

C. Encoding/Decoding Speed:

The SPIHT process represents a very effective form of entropy-coding. When compared to SPIHT coding to other

coding techniques the difference in compression is small,

showing that it is not necessary to use slow methods. A

straightforward consequence of the compression simplicity isthe greater coding/decoding speed. The SPIHT algorithm is

nearly symmetric, i.e., the time to encode is nearly equal to the

time to decode. (Complex compression algorithms tend to

have encoding times much larger than the decoding times.)

D. Applications:

SPIHT exploits properties that are present in a wide

variety of images. It had been successfully tested in natural(portraits, landscape, weddings, etc.) and medical (X-ray, CT,

etc) images. Furthermore, its embedded coding process proved

to be effective in a broad range of reconstruction qualities. For

instance, it can code fair-quality portraits and high-quality

medical images equally well (as compared with other methods

in the same conditions).


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E. Lossless Compression:

SPIHT codes the individual bits of the image wavelet

transform coefficients following a bit-plane sequence. Thus, it

is capable of recovering the image perfectly (every single bit

of it) by coding all bits of the transform. In other words, theproperty that SPIHT yields progressive transmission with

practically no penalty in compression efficiency applies to

lossless compression too.

Rate or Distortion Specification:

Almost all image compression methods developed so far do

not have precise rate control. For some methods you specify a

target rate, and the program tries to give something that is nottoo far from what you wanted. For others you specify a

"quality factor" and wait to see if the size of the file fits your

needs. (If not, just keep trying...). The embedded codingproperty of SPIHT allows exact bit rate control, without any

penalty in performance (no bits wasted with padding or

whatever).

The same property also allows exact mean squared-

error (MSE) distortion control. Even though the MSE is notthe best measure of image quality, it is far superior to other

criteria used for quality specification.

Error Protection

F. Errors in the compressed file cause havoc for

practically all important image compression methods.

This is not exactly related to variable length entropy-

coding, but to the necessity of using context generation

for efficient compression. For instance, Huffman codes

have the ability to quickly recover after an error.

However, if it is used to code run-lengths, then that

property is useless because all runs after an error would be shifted.

SPIHT is not an exception for this rule. Onedifference, however, is that due to SPIHT embedded coding

property, it is much easier to design efficient error-resilientschemes. This happens because with embedded coding the

information is sorted according to its importance, and the

requirement for powerful error correction codes decreases

from the beginning to the end of the compressed file. If an

error is detected, but not corrected, the decoder can discard thedata after that point and still display the image obtained with

the bits received before the error. Also, with bit-plane coding

the error effects are limited to below the previously coded

planes. Another reason is that SPIHT generates two types of data. The first is sorting information, which needs error

protection as explained above. The second consists of

uncompressed sign and refinement bits, which do not need

special protection because they affect only one pixel.

While SPIHT can yield gains like 3 dB PSNR over

methods like JPEG, its use in noisy channels, combined with

error protection as explained above, leads to much larger gains, like 6-12 dB.

G. Use with Graphics

SPIHT uses wavelets designed for natural images. It wasnot developed for artificially generated graphical images that

have very wide areas of the same color. Even though there are

methods that try to compress efficiently both graphic and

natural images, the best results for graphics have been

obtained with methods like the Lempel-Ziv algorithm.

Actually, graphics can be much more effectively compressed

using the rules that generated them.

There is still no "universal compression" scheme, in

the future documents we will use more extensively what is

already being used by WWW browsers: one decoder for text,

another for sound, another for natural images (how about

SPIHT?), another for video etc.

2.4.6) SPIHT ALGORITHM

SPIHT algorithm is based on 3 concepts:

1) Ordered Bit Plane Progressive Transmission

2) Set Partitioning Sorting Algorithm3) Spatial Orientation Trees

Ordered Bit Plane Progressive Transmission:

A major objective in a progressive transmission scheme isto select the most important information- which yields thelargest distortion reduction- to be transmitted first.

It incorporates two concepts:

Ordering the coefficients by magnitude

Transmitting the most significant bits (MSB’S) first.Set Partitioning Sorting Algorithm:

The sorting algorithm divides the set of pixels into

partitioning subsets Tm and performs the significance test by

using the function

Sn (T) = 1, max {(I, j) € T[C i, j] > 2n

= o, otherwise where n is the

number of pass

Spatial Orientation Trees:

Fig : 2.4.3 SPATIAL ORIENTATION TREES

• O (i, j): set of coordinates of all offspring of node (i, j);

children only

• D (i, j): set of coordinates of all descendants of node (i, j);

children, grandchildren, great-grand, etc.

• H (i, j): set of all tree roots (nodes in the highest pyramidlevel); parents

• L (i, j): D (i, j) – O (i, j) (all descendents except theoffspring); grandchildren, great-grand, etc.

For practical applications the following sets are used to

store ordered lists LSP: List of significant pixels


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LIP: List of insignificant pixelsLIS: List of insignificant sets

To illustrate how the SPIHT Coding works lets look at the

following example

INITIALIZATION

The first step in SPIHT coding is the initialization of the sets

LSP, LIS, LIP which is done as shown below

Fig 2.4.5 INITIALIZATION

Then the pixels are sorted according to a threshold which is

given below i.e.

After First Sorting Pass

Threshold To= 2n=2

4=16

• Process LIP• S(0,0)=26>To, we transmit 1, since 26 is +ve ,we

transmit 0; then move (0,0) to LSPT (Temporary),

then

• S(0,1)=6, S(1,0)= -7, S(1,1)=7 are all <To hence they

are insignificant , therefore

transmit three 0,

Process LIS

• DS(0,0)=13, DS(0,1)=10, DS(1,0)=4 ,DS(1,1) are all

less than To hence we transmit 0 for the complete set

S(0,1) similarly the sets S(1,0) and S(1,1) areinsignificant hence

transmit two 0’s

We need not process LSP since it is null

• Update LSPT to LSP

• The transmitted bit stream is 10000000(8 bits)

• LIP={(0,1),(1,0),(1,1)}

• LIS={D(0,1),D(1,0),D(1,1)}

• LSP={ (0,0)}

Fig: 2.4.6 BLOCK DIAGRAM AFTER FIRST SORTING PASS

After Second Sorting Pass

n=4-1=3, Threshold T1= 2n=23=8

Process LIP

S(0,1)=6, S(1,0)=-7, S(1,1),=7, are insignificant ,hence

we transmit 3 0’S,

Process LIS DS (0, 0) =13, DS (0, 1) =10, these two are > T1 hence

we transmit 1 for the set then we transmit 10 for 1 and

again we transmit 10 for 10, then move (0, 2) and (0, 3) to

LSPT

DS(1,0)=6 and DS(1,1)=4 < T1 we transmit two O’S ,thenmove (1,2) and(1,3) to LIP

The sets D (1, 0) and D (1, 1) are insignificant hence we

transmit two 0’S

Process LSP

C (0, 0) =26= (11010)2 ---- TRANSMIT NTH MSB =1

• Update LSPT to LSP

• The transmitted bit stream is 0001101000001(13 bits)

• LIP={(0,1),(1,0),(1,1),(1,2),(1,3)}• LIS={D(1,0),D(1,1)}

• LSP={ (0,0),(0,2),(0,3) }

Fig: 2.4.7 BLOCK DIAGRAM AFTER SECOND SORTING

PASS

ITIALIZATION

LIP

(0, 0) = 26

(0, 1) = 6

(1, 0) = -7

1 1 = 7

LSP

EMPTY

LIS

(0, 1)= {13, 10, 6, 4}(1, 0)= {4,-4, 2,- 2}(1, 1)= {4,-3,-2, 0}

n = log2 (MAX COEFF)n=log2(26) =4


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DECODER

An example of decoding the above transmitted bit is as shownbelow

First ReceiveGet n=4, To=2n = 16

LIP = {(0, 0), (0, 1), (1, 0), (1, 1)}

LIS ={ D(0,0),D(0,1),D(1,0),D(1,1)}

LSP = { }The transmitted bit stream is 10000000(8 bits)

Process LIPGet 1=S(0,0) is significant, next is zero hence +ve value;

move S(0,0) to LSP, Then construct

C(0,0)=(3/2)TO=(3/2)16 =24

Get three 0 = S (0, 1), S (1, 0), S (1, 1) are insignificant

Process LIS

Get three 0 = DS (0, 1), DS (1, 0), DS (1, 1) areinsignificant

LIP = {(0, 1), (1, 0), (1, 1)}

LIS ={ D(0,1),D(1,0),D(1,1)}

LSP = {(0, 0)}

Fig: 2.4.8 PIXELS AFTER FIRST RECIEVE

Second receive

Get n=4-1=3, T1=2n = 8

LIP = {(0, 1), (1, 0), (1, 1)}LIS ={ D(0,1),D(1,0),D(1,1)}

LSP = {(0, 0)}

The transmitted bit stream is 0001101000001(13 bits)

Process LIP Get 000 =S (0, 1), S (1, 0), S (1, 1) are insignificant

Process LIS

Get 1 = DS (0, 1) is significant

Get 10 = C (0, 2) is a positive significance

Move (0, 2) to LSP, then reconstruct C (0, 2) = +(3/2) T1 = (3/2)8 = 12

Get 10 = C (0, 3) is a positive significance

Move (0, 3) to LSP then reconstruct C (0, 3) = + (3/2) T1

= (3/2)8 =12

Get 00 = C (1, 2), C (1, 3) are insignificant move to LIP

Get 00 = DS (1, 0), DS (1, 1) are insignificant

Process LSP

Get 1, then add 2 n-1 to C (0, 0) = 24+2 n-1=24+2 2 =24+4 =28

Fig: 2.4.9 PIXELS AFTER SECOND RECIEVE

2.5) DECOMPRESSION

The decompression process is exactly the reverse of the

compression process. Decompression is involved with

decoding. The decoding process consists of Huffman decodingor SPIHT decoding. The reconstruction is done by using

Inverse Wavelet Transform. The watermark can be retrieved by

changing the frequency of the LSB’S of the output image.

2.6) FIDELITY CRITERIA

During the removal of redundancies i.e. compression

some information of interest may be lost, a repeatable or reproducible means of quantifying the nature and extent of

information loss is highly desirable. There are two types of

criteria used to make such an assessment. They are 1)Objective Fidelity Criteria 2) Subjective Fidelity

Criteria.Subjective Fidelity Criteria: Most decompressedimages are ultimately evaluated by human observer therefore

measuring image quality by subjective evaluation of human

observer is done in subjective criteria which is done byshowing a decompressed image to a cross section of viewers

and averaging their evaluations. The evaluations may be made

using an absolute rating scale or by side by side comparison of

original and decompressed image.Objective Fidelity Criteria:

This offers a very simple and convenient mechanism for

evaluating information loss.Here the level of information loss is expressed as a

function of the original image and the decompressed image.For objective fidelity we use MSE (mean square error), PSNR

(peak signal to noise ratio) and CR (compression ratio).

Let f( x , y ) and f '( x ,y ) represent an input and a

compressed image then for any value of x, y the error e( x, y)

is defined as e( x, y) = f '(x , y)- f (x , y) then the total error

between two images of size MX N isM-1 N-1

Σ Σ [f '(x, y) – f (x, y)]

x=0 y=0

24 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

28 0 12 12

0 0 0 0

0 0 0 0

0 0 0 0


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The root mean square error is the square root of the squarederror averaged over the MXN array given by

M-1 N-1

MSE = [Σ Σ [f '(x, y) – f (x, y)] 2]1/2

x=0 y=0

If f(x, y) is considered as a combination of original image f(x,y) and noise signal e(x, y) then the mean square signal to noise

ratio is given as

M-1 N-1

Σ Σ [f '(x, y)] 2

x=0 y=0PSNR = ----------------------------------------------------

M-1 N-1

Σ Σ [f '(x, y) – f (x, y)] 2

x=0 y=0

No. of input pixels

The compression ratio is given by CR = -----------------------

No. of output pixels

In this project we use the above Objective Fidelity Criteria for the assessment of the quality of image and a comparison is

made between Huffman and SPIHT w.r.t MSE, PSNR and

CR.

2.7) INTRODUCTION TO MATLAB 7.0

Fig 2.7.1 MATLAB

The software used in this project is MATLAB 7.0. MATLAB

stands for Matrix Laboratory. The very first version of MATLAB, written at the University of New Mexico and

Stanford University in the late 1970s was intended for use in

Matrix theory, Linear algebra and Numerical analysis. Later

on with the addition of several toolboxes the capabilities of

Matlab were expanded and today it is a very powerful tool at

the hands of an engineer. It offers a powerful programminglanguage, excellent graphics, and a wide range of expert

Knowledge. MATLAB is published by and a trademark of The

Math Works, Inc.The focus in MATLAB is on computation, not

mathematics: Symbolic expressions and manipulations are not

possible (except through the optional Symbolic Toolbox, a

clever interface to Maple). All results are not only numericalbut inexact, thanks to the rounding errors inherent in computer

arithmetic.

The limitation to numerical computation can be seen

as a drawback, but it is a source of strength too: MATLAB is

much preferred to Maple, Mathematical, and the like when it

comes to numeric. On the other hand, compared to other numerically oriented languages like C++ and FORTRAN,

MATLAB is much easier to use and comes with a huge

standard library. The unfavorable comparison here is a gap in

execution speed. This gap is not always dramatic, and it can

often be narrowed or closed with good MATLABprogramming. Moreover, one can link other codes into

MATLAB, or vice versa, and MATLAB now optionally

supports parallel computing. Still, MATLAB is usually not thetool of choice for maximum-performance computing.

Typical uses include:

a) Math and Computation

b) Algorithm

development

c) Modeling, simulationand prototyping

d) Data analysis,exploration and visualization

e) Scientific andengineering graphics

f) A p p l i c a t i o n

development which includes graphical user interface

building.MATLAB is an interactive system whose basic data

element is an array. Perhaps the easiest way to visualize

MATLAB is to think it as a full-featured calculator. Like abasic calculator, it does simple Math like addition, subtraction,

multiplication and division. Like a scientific calculator it

handles Square roots, complex numbers, logarithms and

trigonometric operations such as sine, cosine and tangent. Like

a programmable calculator, it can be used to store and retrieve

data; you can create, execute and save sequence of commands,also you can make comparisons and control the order in which

the commands are executed. And finally as a powerful

calculator it allows you to perform matrix algebra, tomanipulate polynomials and to plot data. When you start

Matlab the following window will appear:


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Fig: 2.7.2 Main screen of MATLAB

When you start MATLAB, you get a multipaneled desktop.

The layout and behavior of the desktop and its components are

highly customizable (and may in fact already be customized

for your site). The component that is the heart of MATLAB is

called the Command Window, located on the right by default.Here you can give MATLAB commands typed at the prompt,

>>. Unlike FORTRAN and other compiled computer

languages, MATLAB is an interpreted environment—you give

a command, and MATLAB tries to execute it right awaybefore asking for another. At the top left you can see the

Current Directory. In general MATLAB is aware only of files

in the current directory (folder) and on its path, which can be

customized. For simple problems, entering the commands atthe MATLAB prompt is fast and efficient.

However as the number of commands increases, or

when you wish to change the value of a variable and then re-

valuate all the other variables, typing at the command promptis tedious. Matlab provides for this a logical solution: I.e.

place all your commands in a text file and then tell Matlab to

evaluate those commands. These files are called script files or

simple M-files. To create an M-file, chose from the File menuthe option NEW and then chose M-file. Or click at the

appropriate icon at the command window.

Then you will see this window:

Fig: 2.7.3 M- File Screen

Then to run it go at the command prompt and simple type its

name or in the M-file window press F5.MATLAB is huge. Nobody can tell you everything

that you personally will need to know, nor could you

remember it all anyway. It is essential that you becomefamiliar with the online help. There are two levels of help:

• If you need quick help on the syntax of a command, use

help. For example, help plot shows right in the CommandWindow all the ways in which you can use the plot command.

Typing help by itself gives you a list of categories that

themselves yield lists of commands.• Typing doc followed by a command name brings up more

extensive help in a separate window. For example, doc plot is

better formatted and more informative than help plot.In the left panel one sees a hierarchical, brows able

display of all the online documentation. Typing doc alone or

selecting Help from the menu brings up the window at a

“root” page. The heart and soul of MATLAB is linear algebra.In fact, MATLAB was originally a contraction of “Matrix

laboratory.” More so than any other language, MATLAB

encourages and expects you to make heavy use of arrays,

vectors, and matrices.

MATLAB is oriented towards minimizingdevelopment and interaction time, not computational time. In

some cases even the best MATLAB code may not keep upwith good C code, but the gap is not always wide. In fact, on

core linear algebra routines such as matrix multiplication and

linear system solution, there is very little practical differencein performance. MATLAB’s language has features that can

make certain operations, most commonly those involving

loops in C or FORTRAN.

After you type your commands save the file with an

appropriate name in the directory “work”. Functions are the

main way to extend the capabilities of MATLAB. Compared

to scripts, they are much better at compartmentalizing tasks.

Each function starts with a line such as Function [out1, out2] =myfun (in1, in2, in3)

The variables in1, etc. are input arguments, and out1 etc. are

output arguments. You can have as many as you like of eachtype (including zero) and call them whatever you want. The

name myfun should match the name of the disk file.

3) METHODOLOGY

Flow diagram showing the methodology of work

for ENCODER

Fig: 3.1 ENCODER FLOW DIAGRAM

The flow diagram showing the methodology of

work done for DECODER


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Fig: 3.2 DECODER FLOW DIAGRAM

4) RESULTS

Input image:

The first block is an input image, In this project we used apart of the satellite image as input which is shown below.

Fig: 4.1 ORIGINAL IMAGE

WAVELET TRANSFORM

Discrete Wavelet transform was applied on this input

image in two stages. In the first stage only L and H bands were

formed as shown below

Fig: 4.2 First Stage Discrete Wavelet Analysis

Further a second stage wavelet transform was applied on this

to create LL, LH, HL and HH bands as shown below

Fig: 4.5 Image after embedding the message using Huffman

coding and LL band (H* Elimination)

Fig: 4.3 Second Stage Discrete Wavelet Transform

Then the embedding process was done by using HH and H*

Elimination method. The message which was embedded in the

project was “SIT DEPT” any other message can also be

embedded, there is a provision to embed any message in thisproject.

4.1) HUFFMAN RESULTS:

Fig: 4.4 Image before embedding the message using Huffman

coding and LL band (H* Elimination)


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Fig: 4.11

Image after reconstruction using Huffman

decoding and HH Elimination

Fig: 4.12

Final output image using Huffman coding and

H* Elimination

Fig: 4.13

Final output image using Huffman coding and

HH Elimination

4.2) SPIHT CODING AND DECODING RESULTS:

Fig: 4.14

Image before embedding using SPIHT coding

and H* Elimination

Fig: 4.15


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Image after embedding using SPIHT coding and

H* Elimination

Fig: 4.16

Image before embedding using SPIHT

coding and HH Elimination

Fig: 4.17

Image after embedding using SPIHT coding and

HH Elimination

Fig: 4.18

Image after decoding using SPIHT and H*

Elimination

Fig: 4.19


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Image after reconstruction (IDWT) using SPIHT

and H* Elimination

Fig: 4.20

Image after decoding using SPIHT and HH Elimination

Fig: 4.21

Image after reconstruction (IDWT) using SPIHT

and HH Elimination

Fig: 4.22

Final output image using SPIHT coding and H*

Elimination

Fig: 4.23

Final output image using SPIHT coding and HH

Elimination


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4.3) COMPARISON OF RESULTSFinally the results were compared for Huffman coding

between H* and HH Elimination with respect to MSE, PSNR

and CR and the results obtained were

Fig: 4.24 Result of compression using Huffman coding and

H* Elimination method

The results of Huffman coding and H* Elimination method

wereMSE: 4.167

PSNR: 41.94

CR: 5.91

Fig: 4.25 Result of compression using Huffman coding and

HH Elimination method

MSE: 0.42PSNR: 51.89CR : 2.75

Fig: 4.26 Result of SPIHT coding using H* Elimination

Results were

MSE: 4.18PSNR: 41.94

CR : 2.13

Fig: 4.27 Results of SPIHT coding using HH Elimination

MSE: 0.42PSNR: 51.69

CR : 1.68Finally a comparison was made between the two coding

techniques i.e. Huffman coding and SPIHT coding withrespect to coding and decoding time and the results obtained

were


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Fig: 4.28 RESULT OF COMPARISON BETWEEN ENCODING

AND DECODING TIME

Huffman Coding Time: 4.146 sec Huffman Decoding Time: 1.807 secSPIHT Coding Time: 1.723 sec SPIHT Decoding Time: 0.511 sec

5) A GLANCE THROUGH THE GUI’S OF

THE PROJECTThis is the main screen of the software. Choose the encoding

technique from the above screen

Fig: 5.1 Main Screen

Choose the band i.e. LL or LL and LH and import the inputimage by clicking on the browse button.

Fig: 5.2 Screen after importing the original image

This is the screen after importing the input image. click on the

message button and write the message which is to be

embedded in the input image and then click on the embedbutton to embed the message and compress the image then the

decoding operation is applied by pressing the retrieve buttonand the reconstructed image obtained as shown below.

Fig: 5.3 Screen after reconstructing the image using

Huffman coding and H* Elimination

Then the values of MSE, PSNR and CR is obtained by

pressing the validate button


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Fig: 5.4 Screen showing the results of MSE, PSNR and CR

using Huffman coding and H* Elimination

Then these results are cleared by pressing the clear button and

the above process is repeated by choosing both LL and LHbands as shown below

Fig: 5.5 Screen after importing and embedding the

message using HH Elimination

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

Fig: 5.6 Screen after reconstructing the image using both

LL and LH bands and Huffman coding

Fig: 5.7 Screen showing the values of MSE, PSNR and CR

using Huffman coding and HH Elimination

SPIHT CODING


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Fig: 5.8 Screen after importing the image using LL SPIHT

Coding and H* Elimination

Fig: 5.9 Screen after reconstructed image using SPIHT

coding H* Elimination

Fig: 5.10 Screen showing the values of MSE, PSNR andCR of SPIHT coding and H* Elimination

Fig: 5.11 Screen after importing the input image

using SPIHT coding and HH Elimination


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Fig: 5.12 Screen after reconstructed image using SPIHT

coding and HH Elimination

Fig: 5.13 Screen showing the values of MSE, PSNR and

CR using SPIHT coding and HH Elimination

Finally the two techniques i.e. Huffman and SPIHT codingtechniques were compared by clicking the validate button on

the main screen as shown below

Fig: 5.14 Screen showing the encoding and

decoding time for Huffman and SPIHT coding

6) CONCLUSION

The results obtained are put in a tabular column for easy

comparison


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When the above results are analyzed we come to a conclusion

that

a) In both Huffman Coding and SPIHT Coding when a

comparison is made between H* and HH EliminationTechniques, we see that MSE which was 4.1 is reduced to 0.4

when two bands were used indicating that the signal error decreases with increase in number of bands.

b) Similarly in both Huffman and SPIHT Coding, the PSNR

has increased when two bands (HH Elimination) are used

indicating that the signal is more compared to noise withincrease in number of bands.

c) When a comparison is made between the CR, in both the

techniques there is a decrease in compression with increasein number of bands.

d) If a comparison is made between the two techniques i.e.

Huffman and SPIHT we see that MSE and PSNR are

almost same for both the techniques whereas there is a

decrease in the value of CR (compression ratio) i.e.

SPIHT gives 50 % less compression compared toHuffman coding whether single LL band ( H*

Elimination) is used or both LL and LH bands (HHElimination) is used.

e) If a comparison is made between the two techniques i.e.

Huffman and SPIHT in terms of encoding and decoding

time we see that SPIHT encoding is FOUR times faster

than Huffman encoding and in terms of decoding timeSPIHT decoding is very fast compared to Huffman

decoding i.e. it is around 12 times faster than Huffman

decoding.

Finally we come to a conclusion that when ever there is aneed for large compression we go for only LL band(H*

Elimination) but a compromise should be made with respect toerror in signal , but if we need more clarity of image we

compromise with less compression and go for both LL and LHbands ( HH Elimination).

Alsowhen

choos

ing

amon

g the

twotechn

iques

i.e.Huff

man

and

SPIH

T acompromise should be made between he speed and the amount

of compression because SPIHT is very fast but gives less

compression compared to Huffman which is slow but givesmore compression compared to SPIHT.

Therefore SPIHT is used for large images like satelliteimages which are very big where compression can be achieved

very fast but with a compromise in compression ratio.

7) FUTURE DEVELOPMENT

Though this project has been tested

for attacks on watermark due to compression, this

project can further be tested for various other

attacks on watermark like noise filtering and

other digital image processes. This project can

also be further extended by embedding an image in

an image.

Future work on this project would be the Visual

Cryptography where n images are encoded in a way

that only the human visual system can decrypt the

hidden message without any Cryptographic

computations when all shares are stacked together.

It is basically hiding a colored Image into

multiple colored cover images. This scheme

achieves lossless recovery and reduces the noise

in the cover images without adding any

computational complexity.

8) LIST OF FIGURES

Fig: 1.1 Encoder

Fig: 1.2 Decoder

Fig: 1.3 H* Elimination Technique

Fig: 1.4 HH Elimination Technique

Fig: 2.1.1 Sine Waves With Different Frequencies

LL

BAND

LL AND

LH BANDS

MSE PSNR CR MSE PSNR CR

HUFFMAN

CODING 4.167 41.94 5.91 0.42 51.89 2.75

SPIHT

CODING 4.18 41.94 2.13 0.42 51.69 1.68

ENCODING

TIME

DECODIN

TIME

HUFFMAN

CODING

4.146

SEC 11.807 SE

SPIHT

CODING

1.723

SEC 0.511 SEC


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6) Crash Course in Matlab by Trobin A. Driscell.7) Digital Watermarking Of Images and Wavelets –

Alexandru, ISAR , Electronics and Telecommunications

Faculty, "Politehnica" University, Timiúoara.

8) Introduction to Graphical User Interface (GUI) MATLAB

6.5 by: Refaat Yousef Al Ashi,

Ahmed Al Ameri and Prof. Abdulla Ismail A.9) Digital Watermarking Technology by Dr. Martin Kutter and

Dr. Frédéric Jordan.

10) SPIHT Image Compression by SPIHT description .htm.11) Watermarking Applications and Their Properties by

Ingemar J. Cox, Matt L. Miller and Jeffrey A. Bloom NEC

Research Institute.

12) Watermarking of Digital Images by Dr. Azizah A. Manaf

& Akram M. M. Zeki Zeki University Technology Malaysia.

13) Digital image processing by A.K. Jain.14) Digital Image Processing, a Remote Sensing Perspective

by John. R. Jensen.

15) Lillesand, R. M and R.W.Kiefer, 1994,’Remote Sensingand Image Interpretation’, New York, 1996.

16) Wavelet Transforms: Introduction to Theory and

Applications by Bopardikar, Addison Wesley, 1998.

17) Wavelets and Filter Banks, Gilbert Strang and TruongNguyen, Wellesley-Cambridge press, 1997.18) Introduction to Wavelets and Wavelet Transforms: A

Primer, Burrens, Gopinath and Guo.

19) Digital Image Processing by Milan soni.20) Digital Image Processing: a Remote sensing Perspective

by John .R. Jensen, 2ND Edition.

compression techniques and water marking of digital image using wavelet transform and spiht coding

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