Transcript Slide 1

Watermarking using wavelets
Wavelets seminar
Presented by:
Maya Maimon.
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Outline
What is Watermark?
Usage
Previous approaches
Difficulties and problems
Algorithms to digital watermarking using
wavelets.
We’ll focus on the wavelet’s contributions
to the algorithms.
conclusions
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Electronic publishing
Inexpensive copies
No quality loss
Wide distribution but no control
Now can we protect copyright ???
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The use of digital watermarks
Can be used as an authentication tool.
As a method to discourage the
unauthorized copying and distribution of
electronic documents.
(Data Hiding )
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What is watermarking?
Copyright protection methods.
Consists of signing an image with a
signature or copyright message.
The message is secretly embedded in the
image.
There is no visible difference.
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What is watermarking?
Example
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Requirements
Invisibility - imperceptible within its host.
 discrete to prevent unauthorized removal.
 easily extracted by the owner.
 robust to incidental and intentional
distortions.
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Difficulties
 Digital watermarking algorithms usually use the
lower-order bit-planes of the original image, so
do intentional disturbance algorithms.
 Cannot be inserted to downgrade the quality of
the source image too much.
 Digital watermark readers are usually widely
available.
 There is a limited amount of data that can be
used to insert digital watermarks in a highly
compressed JPEG image;
 Noticeable artifacts of image compression
usually destroy watermarks easily.
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Existing methods
Method in the spatial domain and in the
frequency domain.
Visible watermarking systems are usually
able to sustain all possible image
alterations and even intentional
disturbances.
However, image quality is significantly
reduced.
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Existing methods
 Recent frequency domain water-marking
methods are based on the discrete cosine transform (DCT),where pseudo-random
sequences,such as M-sequences, are added to
the DCT coefficients at the middle frequencies
as signatures.
 This approach,of course,matches the current
image/video compression standards well,such
as JPEG,MPEG 1-2,etc.
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Problems with DCT
 A given image cannot be queried for
ownership without the original unwatermarked image.
 Robustness
 It is known that the wavelet image/video
coding,are included in the image/video
compression standards,such as JPEG 2000 and
MPEG4 Due to excellent performance in
compression.
 Therefore,it is important to study water-marking
methods in the wavelet transform domain.
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The DWT domain-reminder
The part with the low
frequencies is split again
into two parts of highThe part with the high
and low frequencies. frequencies is basically
the edge components of
the signal.
A signal is split into two
parts of high frequencies
and low frequencies.
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The DWT domain-reminder
Furthermore,from these DWT
coefficients,the original signal can be
reconstructed.
This process is called the inverse DWT
(IDWT).
The DWT and IDWT for two dimensional
images z[m,n]can be defined by:
DWTn [DWTm[x[m,n]]]
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DWT pyramid decomposition
 An image can be
decomposed into a
pyramid structure with
various band
information .
 such as:
HH,LH ,LL and HL
frequency bands.
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Watermarking in the DWT domain
 includes two parts:
encoding
Adding the watermark to the original image.
decoding.
Recognizing or extracting the watermark.
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Encoding and decoding scheme
1. De-compose an image into several bands with
a pyramid structure.
2. Add the watermark message.
3. Then,we take the two dimensional IDWT of the
modified DWT coefficients.
4. The decoding will be done by applying the
inverse procedure.
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What we are going to see?
 Three different methods:
 Adding Pseudo-random codes to the high an
middle frequencies-Delware U.
 Adding the mark with respect to the human
visual system -Toronto U.
 Extracting the mark without the original host
WaveMark-stanford U.
 For each will see its advantage, and
examples.
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First method - Delware U.
 Multi-resolution watermarking method for
digital images.
 Wavelet transform based watermarking.
 pseudo-random codes to the large
coefficients at the high and middle
frequency bands of the DWT of an image
 The message is secretly embedded in
the image and there is no visible
difference between the original and the
signed one.
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First method -Encoding
1. Calculating the DWT coefficients y[m,n]
2. The message is a Gaussian noise N[m,n]: with
mean 0 and variance 1.
  control the level of watermarking
 Squre2 indicates amplifications of the large
coefficients.
 We do not change the DWT coefficients at the
lowest resolution!
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First method -Encoding
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Encoding
3. we take the two dimensional IDWT of
the:
 modified DWT coefficients
 unchanged DWT coefficients at the lowest
resolution.
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First method -Encoding
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Encoding4. For the resultant image to fit within the 0
to 255 integer values:
5. This is resultant watermark image.
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First method -Encoding
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First method –Decoding
DWT
HL1
Watermarked Image
LH1 HH1
HH1
DWT
Original Image
cross
correlation
with the
watermark
HL1
is there a
peak?
LH1 HH1
HH1
YES
STOP
NO
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First method –Decoding
DWT
HL1
LH1 HH1
cross
correlation
with the
watermark
Watermarked Image
DWT
HL1
is there a
peak?
LH1 HH1
Original Image
YES
STOP
NO
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First method -Decoding
6. Otherwise,we consider the signature
added in the HLI,LH1,and HHI
bands,we continue to decompose the
original and the received signals in the
LL1 band into four additional subbands
LL2,LH2,HL2 and HH2 and so on until a
peak appears in the cross correlations.
7. Otherwise,the signature can not be
detected.
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First method - Advantages
 The method is hierarchical.The computation
load needed to detect the watermark depends
on the noise level in an image.
 Adding watermarks on these large coefficients
is difficult for the human eyes to perceive.
 Matches the emerging image/video
compression standards. Robust to wavelet
transform based image compressions (e.g.
EZW) image compression scheme, and as well
as to other common image distortions,such as
additive noise,and halftoning.
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Example
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Robustness to compression
DWT
DCT
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Robustness to high additive noise
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Second method
 Stage I: The host image and the
watermark are transformed into the
wavelet domain.
 Only the 1st level discrete wavelet
decomposition of the watermark is
performed.
 We perform the Lth level discrete wavelet
decomposition of the host image.
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Second method
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Second method
 Size of the watermark: Nwx X Nwy
 Stage II: The detail images of the host at each
resolution level are segmented into nonoverlapping Nwx X Nwy rectangles.
 The watermark is embedded by a simple
scaled addition of the watermark to the
particular Nwx X Nwy.
 The scaling of the watermark is a function of
the salience of the region. The greater the
salience S, the stronger the presence of the
watermark.
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Second method
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Second method
 Stage III: The corresponding Lth level
inverse wavelet reconstruction of the
fused image components is performed to
form the watermarked image.
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Second method
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The merging process – stage ||
 we discuss the details of the watermark
merging process which is performed in
the second stage of the proposed
method.
 Mathematically,contrast sensitivity is
defined as the reciprocal of the contrast
necessary for a given spatial frequency
to be perceived.
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The merging process – stage ||
 The resulting contrast sensitivity for a
particular pair of spatial frequencies is
given by:
C(u,v)=5.05e-0.178(u+v) (e-0.1(u+v) -1)
 C(u, v) is the contrast sensitivity matrix and u
and v are the spatial frequencies given in units
of cycles per visual angle (in degrees).
 A conversion to radians per pixel must
be made prior to the use of C.
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The merging process – stage ||
 Saliency- mathematical quantity to
measure the importance of an image
component.
 S(fik,l(m,n))=u,v C(u,v) |Fik,l(m,n)|2
 C(u,v) - is the contrast sensitivity matrix,
 Fik,l(u,v) - is the discrete Fourier
transform of the image component
f i k,l(m,n).
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The merging process – stage ||
 The watermark is embedded:
 gik,l(m,n) = fik,l(m,n)+
k,l  S(fik,l(m,n)) Wk,l(m,n)

max (m,n)  S(fik,l(m,n))
 Where  is 10% to 20% of the mean
value of the host image.
 k,l =
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Second method- decoding
 The watermark is extracted, using the
host image, by applying the inverse
procedure at each resolution level to
obtain an estimate of the watermark.
 The estimates for each resolution level
are averaged to produce an overall
estimate of the watermark.
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The Human Visual System
 Multi-resolution wavelet decomposition of both
the host image and the watermark.
 When an image undergoes a wavelet
decomposition, its components are separated
into bands of approximately equal bandwidth
on a logarithmic scale much as the retina of
the eye splits an image into several
components.
 It is, therefore, expected that use of the DWT
will allow the independent processing of the
resulting components much like the human
eye.
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Second method advantages
1. Provides a simultaneous spatial localization
and frequency spread of the watermark within
the host image.
2. In addition, the watermark merging process is
adaptive as it depends on the local image
characteristics at each resolution level.
3. Robust as it embeds the watermark more
strongly into more salient components of the
image.
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Example
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Results 1: JPEG compression
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Results 2: Additive noise
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Results 3: Mean filtering
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The third method-overview
 The algorithm in WaveMark uses discrete
wavelet transforms and error-correcting
coding schemes to provide robust
watermarking of digital images.
 The watermark recovery procedure does not
require a match with an uncorrupted original
image.
 The system is practical for real-world
applications, encoding or decoding images at
the speed of less than one second each on a
Pentium Pro PC.
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Using wavelet
 The use of Daubechies' advanced
wavelets makes the watermarked
images more perceptively faithful than
Haar.
 The watermark is adaptively applied to:
 Different frequency bands
 Different areas,based on the smoothness
 increases robustness within the limits of
perception.
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Encoding
 We 1st convert and store the image in a
component color space with intensity and
perceived contrasts.
 For each color component, we perform a
4-level wavelet transform using
Daubechies-4 wavelet.
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Encoding
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Encoding-Smoothness analysis.
 extract a rough smoothness region overlay for
each image.
 We use the variances of 4 x 4 blocks in the
intensity band to distinguish between 5
different smoothness classes.
 We apply watermark coding with lower
strength to regions classified as highly smooth
regions (such as sky).
 We apply watermark coding with higher
strength to regions of lower levels of
smoothness.
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Smoothness analysis.
 extract a rough smoothness region overlay
for each image.
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Encoding
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Error correction coding
A Hamming code is used to add
redundancy to the bits so that the errors
can be detected or corrected to a certain
extent.
we use a (8,4) extended Hamming code.
4 bytes are the input
8 bytes include the input +4 parity bytes.
Such a code can correct a one-bit error
and detect up to three one-bit errors.
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Error correction coding
a 64-bit watermark code:
Water-mark
(32 bit)
1
8
1
…
8
1
8
Code word
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Inserting the mark
Partition to 10 x10
non-overlapping blocks.
DWT of the
Color
components
We alter the lower bits of the block borders
to code '0' in order to assist the decoding
process.
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Inserting the mark
 With 8 X 8 matrix entries within each block, we
are able to hide a 64-bit watermark code.
 As we have shown,the Hamming encoded
watermark has 64 bits.
 We can simply encode each entry in the
transformation matrices with one bit of the
watermark code.
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Inserting the mark
We alter the lower bits of the coefficients
according to the:
 Frequency represented in the band,
 Smoothness region overlay,
 Encoded watermark code.
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Getting the final result
 After the watermark code is placed in the
transform matrices, we perform a 4-level inverse
wavelet transform for each of the three matrices
using Daubechies-4 wavelet.
 Then we use the inverse color transformation to
obtain a coded color image in the RGB color
space.
 This image is the final image coded with the
duplicated watermark codes.
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Decoding
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Results
fast speed
 high reliability
Robustness- alterations including
compression, intentional disturbances and
image processing operations.
 The algorithm is able to detect the
invisible digital watermark within each
altered image after performing Hamming
error-correcting decoding.
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Limitations
WaveMark is designed to sustain image
alterations such as compression, additive
noise and even some intentional
disturbances.
 However, like other wavelet-based
watermarking algorithms, it is not suited to
handle significant rescaling, aspect ratio
changes and rotational transformations.
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examples
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conclusions
 we have demonstrated an wavelet-based
watermarking algorithms for digital images.
 The use of DWT (Daubechies) makes the
watermarked images more perceptively faithful.
 The subject is work-in-progress.
attempting to make the algorithm more robust
 and to conduct a formal performance evaluation.
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references
 WaveMark: Digital Image Watermarking Using
Daubechies‘ Wavelets and Error Correcting Coding", J.
Z. Wang and G. Wiederhold
http://wwwdb.stanford.edu/~wangz/project/wavemark/MA
RK98/
 Multiresolution Watermark for Digital Image", X.Xia, C.G.
Boncelet and G.r. Arce
http://clip.informatik.unileipzig.de/~toelke/Watermark/ip970436.pdf
 A Robust Digital Image Watermarking Method Using
Wavelet-Based Fusion,
D. Kundur and D. Hatzinakos
http://ee.tamu.edu/~deepa/pdf/icip97a.pdf
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