1 Watermarking using wavelets Wavelets seminar Presented by: Maya Maimon.

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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 copiesNo quality lossWide 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 trans-form (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 un-watermarked 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

A signal is split into two parts of high frequencies and low frequencies.

The part with the high frequencies is basically the edge components of the signal.

The part with the low frequencies is split again into two parts of high 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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Encoding-

4. 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

Watermarked Image

Original Image

DWT

DWT

HL1

LH1HH1

HL1

LH1HH1

-cross correlation with the watermark

HH1

HH1

is there a peak?

YES

STOP

NO

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First method –Decoding

Watermarked Image

Original Image

DWT

DWT

HL1

LH1HH1

HL1

LH1HH1

-cross correlation with the watermark

is there a peak?

YES

STOP

NO

HL1

HH1

HL1

HH1

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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 non-overlapping 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 sensitivitycontrast 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))= 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).

u,v

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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)

k,l =

max (m,n) S(fik,l(m,n)) Where is 10% to 20% of the mean

value of the host image.

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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:

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…

Code word

Water-mark

(32 bit)

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Inserting the mark

We alter the lower bits of the block borders to code '0' in order to assist the decoding process.

DWT of the Color components

Partition to 10 x10

non-overlapping blocks.

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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 reliabilityRobustness- 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. Wiederholdhttp://wwwdb.stanford.edu/~wangz/project/wavemark/MARK98/

Multiresolution Watermark for Digital Image", X.Xia, C.G. Boncelet and G.r. Arcehttp://clip.informatik.uni-leipzig.de/~toelke/Watermark/ip970436.pdf

A Robust Digital Image Watermarking Method Using Wavelet-Based Fusion,D. Kundur and D. Hatzinakoshttp://ee.tamu.edu/~deepa/pdf/icip97a.pdf