Notesale: Turn your study into money

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Chapter 1
Introduction
1
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They are also devised for variety of media viz
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1
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2
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Generally the message use to watermark is a narrow
band signal compared to the wide band of the cover image
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Furthermore, high frequencies are relevant for
the invisibility of the watermarked message but are inefficient as far as robustness is concerned,
whereas low frequencies are of interest with regards to robustness but are useless because of the

unacceptable visible impact
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Spread spectrum
techniques also offer the possibility of protecting the watermark privacy using a secret key to
control a pseudo noise generator
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2
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In this scheme, the discrete cosine transform (DCT) is performed on a whole image and then the
watermark is embedded in a predetermined range of low frequency components as shown in
Figure 2
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The embedded watermark signal consists of a sequence of real numbers that are
normally distributed and it is scaled according to the signal strength of the frequency
components
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Fig -2
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2
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2
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al
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E
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Fourier Transforms (DFT, DCT), Wavelet Transforms

Spread Spectrum: T (S w) = T(S) + T(X)

2
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2
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Detect the existence of a specific code, which is served as the copyright information
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Watermark detection needs the original source
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2
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3 Implementation
• Add a specific code on the 1000 largest or the 1000 lowest frequency DCT coefficients of the
image
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g
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2
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2
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2
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5 Spread spectrum watermark embedding and detection
Let B denotes the binary valued watermark bit string as a sequence of N bits
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; b N}; bi{1,-1};…………………………
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1

Let the symbol I denotes the image of size (Q X Q)
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[WQ] =

Q];

……………………………………………2
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[WQ] ; ………………………………………
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3
[WQ] =


...
2
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[WQ] ; ………………………………………
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5
where α is the gain factor or modulation index
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SS
watermarking schemes can be called as signal adaptive if  is a function of image coefficients
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, 1998)
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The decision variable ti is mathematically expressed as follows:

ti={Pi-m1(Pi),Iw-m1(Iw)}(0)

………2
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,N
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(2
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If the code patterns Pi’s are so chosen such that m1 (Pi)=0i, ti and
the bit bi are computed as follows:

ti=(Pi,Iw)

………………2
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Nj=1 bj
...
2
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3 Quantization Index Modulation (QIM) Techniques

1
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1 Quantization Index Modulation
Quantization index modulation (QIM) has recently become a popular form of data hiding based
on the framework of communications with side information
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Typical QIM is
accomplished by modulating a signal with the embedded information
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Quantization Index Modulation (QIM) data embedding
methods are a class of methods that display attractive properties from both a practical perspective
and a more theoretical perspective
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On the other hand, according to the theoretical
perspective, these systems possess a host signal interference rejection property that is an essential
characteristic of good data embedding systems
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1
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2 Dither Quantization
Chen presented dithered quantization as a special case of quantization index modulation (QIM)
for self noise suppression
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The shift is given by a dither vector d
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The output of the subtractive quantization operation is denoted by

s i = Q(xi + di) – di, 0 ≤ i < L

…………2
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………
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10

1
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3 Comparison between SS and QIM
In this section, we compare various features of spread spectrum and quantization based
watermarks
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In spread spectrum watermarking, the PN sequence is shaped by a musk computed
from the cover image, making the watermark image adaptive
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In case of SS, the embedder simply adds the watermark to the cover image, so it
acts as interference at the receiver
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Comparing the robustness of the both, in case of SS image adaptive watermarks
can resist compressions and in case of quantization, the non-image adaptive watermarks are less
robust to image adaptive attacks such as compression
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On the other hand, in quantization the
cover image as it is the quantization error of the quantiser in the embedder
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The capacity is usually limited by the interference from the host in SS
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In case of embedding multiple watermarks, in SS multiple watermarks can be
embedded by using orthogonal PN sequences
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1
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The circuit below illustrates a simple convolutional coder suitable for incorporating forward
error correction into a transmitted message
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It is now necessary to examine the
incoming bits and to extract the original data
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1
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1
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Assume the circuit starts at 00, and the following
short symbol stream is received
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While the
original symbols defined a continuous path through the trellis, the presence of errors means that
now there is no obvious continuous path through the trellis
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It is expected that the path found will exactly match
the original despite the errors which have occurred
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The "best fit" path
will be the one which best matches the above data, deviating only as required to establish
continuity
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Perhaps the symbols
leading up to the "obvious" break in the path are themselves incorrect
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In practice, a systematic approach to
identifying the best path through the trellis can be employed to correct errors automatically as
they occur
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5 Viterbi Decoding
The most commonly used decoding algorithm for convolutional codes is the Viterbi Algorithm,
which is a maximum likelihood sequence estimator (MLSE)
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The Viterbi algorithm finds the closet coded sequence v to the received sequence r by
processing the sequences on an information bit-by-bit (branches of the trellis) basis
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The likelihood of a received sequence r after transmission over a noisy channel, given that
a coded sequence

P(r/ ) =

is sent, is given by the conditional probability:

(rj/γj);

………
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11

For the BSC channel, a maximum- likelihood decoder (MLD) is equivalent to choosing the code
sequence that minimizes the Hamming distance

dH r,( ) =

(rj , γj);

…………………
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12

Similarly, for the AWGN channel, it is the squared Euclidean distance:

dE r,( )

;

…………………………2
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5
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From here, only two paths
are possible
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These two values are recorded on the
trellis for the next step
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Step 2 - Four paths are defined leading to the
next stage, two from each of the incoming
states from Step 1
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Here, the
corresponding dibits are shown superimposed
on each candidate path segment, and
the cumulative error is shown for each
endpoint
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The best path so
far appears to be the lower path which still has
zero error
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The error associated with a given path
segment depends on the actual symbol '11'
received, as compared to the symbol defined
for that segment
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For example, the topmost path arrives at state
00 with a cumulative error of 5, but another
path leads to this same state with a cumulative
error of 2
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The best overall path is
uncertain at this point since there are two
states with error 1 (of course, an error in the
received data has just occurred)
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At the far end of the trellis there is one path which gives the lowest cumulative error, and which
corresponds to the correct data
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This path can then be traced back and is shown highlighted
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Note that a better path seemed to be emerging at stages 'E' and 'F' when the uppermost path had a
cumulative error of 1
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The final path cannot be traced until all possible paths have been
explored
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Note that in stage 'F' two paths arrive with weight 3 at state 11
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The same happens
at state 01
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1
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The acronym JPEG
stands for the Joint Photographic Experts Group, a standards committee that had its origins
within the International Standard Organization (ISO)
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PEG's goal was to produce a set of industry
standards for the transmission of graphics and image data over digital communications networks
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And although JPEG itself
does not define a standard image file format, several have been invented or modified to fill the
needs of JPEG data storage
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Instead, it may be thought of as a toolkit of image
compression methods that may be altered to fit the needs of the user
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Conversely, JPEG is capable of producing very high-quality
compressed images that are still far smaller than the original uncompressed data
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6
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Segmentation into Blocks - The host image data is divided into 8x8 pixel blocks (these
blocks are the Minimum Coded Unit)
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2
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Basically, the contents of

the image are converted into a mathematical representation that is essentially a sum of
wave (sinusoidal) patterns
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The sequence 1100110011 can be represented by
a wave that repeats every four pixels
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Now imagine that this mapping to wave
equations (known as the DCT basis functions) is done in both the X and Y directions
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Quantization - Given the resulting wave equations from the DCT step, they are sorted in
order of low-frequency components (changes that occur over a longer distance across the
image block) to high-frequency components
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The JPEG algorithm discards many of these high-frequency (noise-like) details and
preserves the slowly-changing image information
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Components that either had a small coefficient or a large divisor in
the quantization table will likely round to zero
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On the converse, the highest
quality setting would have quantization table values of all 1's, meaning the all of the
original DCT data is preserved
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Zigzag Scan - The resulting matrix after quantization will contain many zeros
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By re-ordering the matrix from
the top-left corner into a 64-element vector in a zig-zag pattern, the matrix is essentially
sorted from low-frequency components to high-frequency components
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This is important for the next step
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DPCM on DC component - On a block-by-block basis, the difference in the average
value (across the entire block, the DC component) is encoded as a change from the
previous block's value
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6
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As the 1x64 vector contains a lot of zeros, it is more efficient to save the
non-zero values and then count the number of zeros between these non-zero values
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More common strings / patterns use
shorter codes (encoded in only a few bits), while less frequently used strings use longer
codes
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JPEG Compression

Down
Sampling

Forward
DCT

Quantizati
on

Encoding

Raw
Image
Data

JPEG
compressed
Data

Up
Sampling

Inverse
DCT

DeQuantization

JPEG Decompression

Fig 1 - JPEG compression and decompression

Decoding

1
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It can also be used to create digital signatures
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It is also known as asymmetric cryptography because the key used to encrypt a message differs
from the key used to decrypt it
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The private key is kept secret, while the public key may be
widely distributed
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The keys are related mathematically, but the
private key cannot be practically derived from the public key
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To

use symmetric cryptography for

communication, the sender and receiver must share a key in advance
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This
is used to ensure confidentiality
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This is used to ensure authenticity
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e
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The usual approach to this problem is to
use a public-key infrastructure (PKI), in which one or more third parties, known as certificate

authorities, certify ownership of key pairs
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All known public key techniques are much more computationally intensive than their secret-key
counterparts, but can be made fast enough for a wide variety of applications
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Such combinations are called hybrid cryptosystems
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For digital signatures, the sender hashes the
message (using a cryptographic hash function) and then signs the resulting "hash value"
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The most obvious application of a public key encryption system is confidentiality; a message
which a sender encrypts using the recipient's public key can be decrypted only by the recipient's
private key

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