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Copyright Protection

Authentication of multimedia data

Robust Data Hiding and Security issues

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There are three different applications that use digital watermarking in images.

1- The detection of the presence of the embedded signal 2- The concealment of the bit stream in the image and the extraction of this information. 3- The ability to reveal whether some sort of changes was done to the image.

In the last application one of the characteristics of the hidden data should be low robustness, while in the first two high robustness of the embedded data is one of the most important requirements for successful data hiding. The first applications is implemented in the Method 1and the second one is implemented in the Method 2 of this project

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Digital watermarking is a technique for data hiding in digital multimedia

WM in images should meet the next set of requirements :

* Invisibility to a Human Visual System

* Robustness to various kinds of distortions

* Simplicity of detection and extraction to the owner

* High information capacity

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Watermarking techniques divided into two basic classes :

* Spatial Domain WM- pixels values are affected

* Frequency Domain WM- transform coefficients are affected

In this project the second technique is investigated

The advantages are high robustness and exploiting the Human Visual System features

The watermark is embedded using two transforms

* DCT based watermark

* DFT based watermark

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DCT transform algorithm is given by

The advantages of DCT are

* Real coefficients and relatively small calculation time

* Small manipulations on coefficients don’t affect the

image visual properties

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DFT transform algorithm is given by

The advantages of DFT are

* Most of the image information is contained in phase that allows great flexibility on magnitudes manipulations

* Fast FFT algorithm decreases computation time

B k l A m nk M

l NMNj

mk

M

nl

Nm

M

n

N

( , ) ( , ) exp ,

FHG

IKJ

RSTUVW

12

0

1

0

1 0 1

0 1

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The project scheme contains the following blocks :

* Encoder - embeds the WM into the image

* Channel - corrupts the watermarked image

* Decoder - detects the WM sequence from corrupted watermarked image

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The following diagram demonstrates the above :

ENCODER DECODERCH AN NELImage

X p seu d or a n d o m

seq u en ces

One W atermark s equenc e

Image+W M

Nois e

Corrupted Image + W M Detec ted W M

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The encoding schemes uses following characteristics :

* Choice of WM amplitude has an important impact on the visibility of the WM

* Selection of effected coefficients in the transformed image has to preserve the tradeoff between the robustness to corruption and the invisibility of the WM

* WM embedded sequence is a set of normally distributed numbers chosen among X pseudo-random sequences

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The following diagram demonstrates encoder block diagram

The affected coefficients are chosen according to the transform and the parameters specified above

ImageTrasformDCT/DFT

W atermarkEmbedder

InverseTrasformDCT/DFT

Im ageTransform

Coeffic ients

W M sequence

EffectedCoeffic ients

W aterm arkedIm age

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The following diagram demonstrates channel block diagram

High PassFilter

Low PassFilter

Quantizer

AW GN

JPEGCompr

Image

CorruptedImage

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The following diagram demonstrates decoder block diagram

TRANSFORM CORRELATOREXTRACTORIm ageTransform type

X pseudo randomsequences

transform edim age

extractedcoeff. r

THRESHOLDCALC

extracted coeff. >

Sz

detectedsequence

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WM embedder performs zig-zag scan on the DCT coefficients - an approximation of radial frequency

M diagonals starting from L-th are selected to vector T

New vector T’ is created by the following rule:

.

.

.

DC

High Frequences

T i T i T i wm i

wm

' ( ) ( ) | ( )| ( )

is one of X's sequences

is WM strength

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New vector T’ is reinserted in the appropriate indices

Inverse DCT is performed to create watermarked image

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The following images present the embedding of the WM in

Lena .

Original Image Image with WM

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The WM bellow was created with following parameters :

*WM amplitude: = 0.2

* width of WM: M = 50 diagonals

* first diagonal : L = 165 diagonal

The detection occurred on uncorrupted image

0 200 400 600 800 10000

0.5

1

1.5

2Detection

watermarks

res

po

ns

ecorrelationthreshold

Embbeded coefficents

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Two types of corruption are presented - AWGN and JPEG

AWGN Corrupted Watermarked Image

0 200 400 600 800 10000

0.5

1

1.5

2Detection

watermarks

resp

on

se

correlationthreshold

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Corrupted Watermarked Image-JPEG comp.

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Detection

watermarks

res

po

ns

e

correlationthreshold

JPEG compression (quality of 50) is a strong noise but the WM signal can still be detected

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Likely to DCT , DFT WM embedder selects square rings around DC after shift of FFT transform coefficients to the center

M squares starting from L-th are selected to vector T

New vector T’ is created by the following rule:

abs T i abs T i wm i

T i T i

wm

( ' ( )) ( ( )) ( ( ))

( ' ( )) ( ( ))

1

is one of X's sequences

is WM strength

DC

High Frequences

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As mentioned above , only magnitude of coefficients are modified in the way that preserves the symmetry of the real image DFT

New vector T’ is reinserted in the appropriate indices

Inverse DFT is performed to create watermarked image

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The following images present the embedding of the WM in

Lena .

Original Image Image with WM

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The WM bellow was created with following parameters :

* WM amplitude: = 0.17

* WM width : M =20 rings

* first square: L = 45 ring

The detection occurred on uncorrupted image Embbeded coefficents

0 100 200 300 400 500 600 700 800 900 10000

50

100

150 Detection

watermarks

resp

on

se

correlationthreshold

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Two types of corruption are presented - AWGN and JPEG

0 100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

60

70

80

90

100 Detection

watermarks

resp

on

se

correlationthreshold

AWGN Corrupted Watermarked Image

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JPEG compression (quality of 50) is a strong noise

but the WM signal can still be detected

JPEG-Corrupted Watermarked Image

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400Detection

watermarks

resp

onse

correlationthreshold

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Both of the presented transforms perform robust ,

invisible and easy to extract WM technique.

Choice of suitable parameters must be taken into

consideration , when these two transforms are compared

Tradeoff must be achieved between the invisibility and robustness when M , L and parameters are chosen

On the whole , no significant advantage was found

to recommend on DFT or DCT.

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Exploiting of characteristics of Human Visual System:

Visual masking - every pixel is changed according to its

local weighting factor

Image partition to blocks in order to enable efficient implementation

and real time processing

Choice of different set of the parameters for different images

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This method exploits WM application , in which , bit stream is the hidden signal

Unlike first technique , encoding and detection is based on FFT signaling scheme , similar to communication channel , where narrow band signal is hidden in wide band environment

This method is a relatively new in the field and has a lot of unexplored features

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Similar to Method 1 the main hierarchy includes encoder , channel and decoder.

The difference is in the way that spectral components are computed and affected

The image is divided to blocks and selected transform is applied on each block

The size of the block is a parameter of the encoding scheme

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Encoder performs the following algorithm

Blockwise spectral transform - DFT/DCT

Selection of coefficients with unique magnitude in case of DFT - only half of the coefficients are selected

Alignment of each block to one column vector

KLT transform is performed on each vector

All vectors are combined to Mc matrix

Mapping of the binary stream to the signature

Insertion of the signature

Inverse process to obtain the encoded image

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The image coefficients are highly correlated and this fact can damage the WM invisibility

An efficient way to reduce this correlation is to apply KLT on each vector of block coefficients

KLT matrix is calculated once from 15 different pictures - • For each image, Mc matrix is calculated by applying blockwise DCT/DFT • Mc matrices are merged to one matrix X. • Matrix X is multiplied by its transpose matrix X’.• The result is normalized by number of columns in X to obtain a square matrix Rx.• The Eigen vectors of Rx are calculated and combined to KLT matrix T.

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The following figure demonstrates the creation of KLT matrix

im age 1 im age 2 im age 3 im age MN

M c 1 M c 2 M c 3 M c M

Blockw ise D FT/D C T

1 M

X

2 3

X

* = R x

E igen V ectors

T

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Blockw isetransformDFT/DCT

Selectionof uniquecoefficien

ts

KLTIm age

embeddersegmentpartition

bit stream

mappingto

signature

InverseKLT

Phaseattachme

nt

Inverseblockw isetransform

Encoded Im age

The following figure demonstrates the structure of the encoder

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The insertion of the binary stream should be done with the highest efficiency and without damaging the image

The binary stream should be mapped to the signature that has high self correlation

In addition, the signature has to be low correlated with the original image in order to achieve high detection ability

The binary stream is divided to p-length segments

p is a parameter that is set in the initialization of the encoder

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In order to create high correlated sequence to map p-length segment the following algorithm should be performed

Create a random binary (±1) sequence bk of length 2p-1. Calculate Bk - DFT of bk .

Calculate Sk from Bk such that | Sk | = 1 and Sk = Bk

Take IDFT of Sk to obtain sk that is real, cyclic all pas function . All cyclic shifts of sk and their negative are orthogonal. Create a table of all cyclic shifts and their negative (MSS table) to map binary sequence length p.

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Binary sequence divided to p-length fragments

For each segment decimal representation Dk is calculated and entry in MSS table that is appropriate to Dk is selected

All selected sequences combined into one row vector to generate the signature

The value of p has an influence on the BPP (Bit Per Pixel) rate and on the robustness of the encoded signal

The larger p is the lower the BPP goes but the robustness of the signal increases

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The BPP is given by the following formula12

BPP p

p

0 2 4 6 8 10 12 1410

-3

10-2

10-1

100

Bit Per Pixel Rate for WM algorithm

p parameter

log

(BP

P)

It is possible to adjust the BPP in more precise way by using different coding schemes , like checksum and Reed Solomon

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The detection is made without resorting to the original image, therefore the components of the original image are an additive noise for the embedded signal

Some pre-processing is required to improve the detection efficiency - self noise suppression

The main idea is to estimate the original picture and to subtract this prediction from the received image

Error = D(Irec) = Irec - Iest

The buried information can be extracted more efficiently from Error rather then from received image itself

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The estimation too similar to received image will produce zero and this will make it impossible to detect the hidden signal

On the other hand very coarse prediction will make the detection very difficult because of large amount of noise

Some sort of quantization of the received image may by used as the estimated image

The step of the quantizer used will depend on the level of noise

QuantizationSubstraction

Decoder

Estim atedim age

Recievedwaterm arked

im age

Predictionerror w ith

hidden signal

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Not any modification of the image coefficients allowed

The error introduced should maintain the following condition

e = |C^ – C | = | s – D(C) |

where C^ is the encoded image and C is an original one

The algorithm for embedding the signature sequence s in c is if (|s(k) – D(c(k)| < v(k)) then e(k) = s(k) – D(c(k)) else e(k) = v(k)sign(s(k) – p(k)) if ( rem(abs(c(k) > /2) then e(k) = -e(k) else e(k) = e(k)

if ( c(k) 0) then C^(k) = c(k) + e(k)

else C^(k) = c(k) – e(k)

v(k) is the visual threshold calculated for each block and determines the activity a particular block

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The detected signature sdec is extracted from the spectrum coefficients of received image after KLT transform by applying Self-Noise suppression scheme

If the encoded image was not corrupted the sdec is equal to an original signature s

After the extraction the signature sdec is divided into 2p-1 - length fragment when each one is representing p-length binary segment

There are 2p possible sequences for each fragment

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Each fragment represents p-bit number

For each fragment the correlation is calculated with every entry in MSS table

The index of the entry that produced maximum correlation is the decimal representation of p-length segment

Self N oiseSuppression

rece ivedim age

2^(p-1)

M SSTable

2^p

2^p-1

x =

2^p

argm ax

p

fo r each fragm ent

fragm ent

segm ent

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The following figure summarizes the decoder

Blockw isetransformDFT/DCT

Selection ofunique

coefficientsKLTIm age correlator detected bit stream

M SS table

Signatureextractor

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The following images demonstrates the encoding scheme results when the applied transform is DFT ,p = 9 and delta = 140

Encoded with DFT , delta = 140 Original image

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The following images demonstrates the encoding scheme results when the applied transform is DCT ,p = 8 and delta = 20

original Encoded with DCT , delta = 20

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The system was checked with 5 256x256 standard images

The following table summarizes the results of the projectTransform Block

SizeSegmentLength1

Delta Number ofaffected coeff.

Number ofbits inserted

DCT 8 8 25 65536 4096DCT 16 8 25 65536 4096DFT 8 9 140 34816 1224DFT 16 8 140 33536 2096

The following table summarizes the BER of the project when the images were compressed with JPEG ( Quality = 75)

DCT DFTSegmentLength BS = 8 BS = 16 BS = 8 BS = 16

6 0.03367 0.02845 0.03714 0.031027 0.01517 0.0104 0.01713 0.01178 0 0 0.01207 09 0 0 0 0

10 0 0 0 0

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The article results report on achieved capacity of 1100 bits per image for ‘Lena’ , which matches achieved capacity in this project

DCT and DFT results show a very similar robustness and visual properties of the watermarked image

DFT has less coefficients, therefore the amount of the embedded data is smaller

Larger block size enables better detection

On the whole, results of both articles investigated, were achieved and confirmed

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Selection and manipulation on the part of the coefficients will improve the robustness

Different error insertion for each spectral component will enhance the invisibility of the watermark

Interleaving of the coefficients before the encoding and de-interleaving before the decoding will prevent from some kinds of “spike” noise like JPEG to destroy the signature

Different encoding schemes like Reed Solomon , Checksum will reduce the bit rate but will reduce the number of errors as well

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