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A Digital Watermarking Algorithm Based on Wavelet Packet Transform and BP

Neural Network

Qiao Baoming, Zhang Pulin, Kang Qiao

College of Science, Xian University of Science and Technology, Xian 710054

e-mail: qiaobm@xust.edu.cn

AbstractA new blind digital watermarking algorithm based

on wavelet packet transform and BP Neural Network was

proposed in this paper. The algorithm first decomposed the

host image via discrete wavelet packet transform, then

embedded water-marking into the position which was chosen

by the key in wavelet image. In the process of embedding

watermarking, eight neighborhood pixels around the

embedded point was selected as sample input of the BP neural

network, and the pixel value of the embedded point was chosen

as the ideal output, finally, trained the neural network. Usingthe trained neural network, blind watermarking extraction

was achieved.

Keywords-component; formatting; style; styling; insert

I. INTRODUCTIONDigital watermarking is an important branch of the

information hiding technology. The so-called digitalwatermarking is the digital signal which is not perceived tobe embedded in digital carrier. It can be images, text,symbols, figures, and all can be used as identificationinformation. A large number of perception redundancy partare common in multimedia data, so watermarking embed-

ding in them can achieve the purpose of hiding.The basic idea that wavelet transform apply to image

processing is decomposed the image by multi-resolution,then generate sub-image with different spaces andindependent bands, at last, process the coefficients of sub-image. The neural network has the characteristics ofapproaching non-linear mapping, and has good gener-alization ability. If a neural network was trained in thewatermark embedding process, through studying, thecorresponding relations of pixel values between before andafter embedding the watermark signal is obtained, then thewatermark can be extracted by using the trained neuralnetwork, thus the blind detection of the watermarkingalgorithm is achieved.

This paper presents a new algorithm of digital water-marking based on wavelet analysis and neural network . Thewatermark was embedded in the wavelet image which wasthe host image after discrete wavelet packet transform, sothat the watermarking could be embedded into a narrowerand finer band, and the transparency and robustness ofwatermarking could be enhanced better. This algorithmdecomposed the host image by discrete wavelet packettransform. Then watermarking was embedded into theposition which was chosen by the key in wavelet image. Inthe watermarking embedding process, eight neighborhood

pixels around the embedded point was selected as sampleinput of the BP neural network, and the pixel value of theembedded point was chosen as the ideal output, finally,trained the neural network. Using the trained neuralnetwork, blind watermarking extraction was achieved [1]-[11].

II. WATERMARKING EMBEDDING ALGORITHMA. The generation of waterarking sequences

In the paper, a simple and effective method is adoptedwhich is through the rearrangement of the binary watermarkby columns, one-dimensional watermark sequence W, thesize of K was obtained.

B. Doing wavelet packet teansform for the original imageFirstly, we did level 1 discrete wavelet transform for the

original host image I, and then can get the approximatecomponent CA, the level of detail component CH, thevertical detail component CV, and the detail of the angularcomponent CD. This four sub-images formed Fig.1(b),Secondly, we performed level 1 discrete wavelet transformfor the four components respectively. For example, After

transforming CA, we obtained the approximate componentCAA, the level of detail component CAH, the vertical detailcomponent CAV, and the detail of angular component CAD.After transforming CH, the approximate component CHA,the level of detail component CHH, the vertical detailcomponent CHV, and the detail of angular component CHDcan be get; After transforming CV, the approximatecomponent CVA, the level of detail component CVH, thevertical detail component CVV, and the detail of angularcomponent CVD obtained, and after transforming CD, wehad the approximate component CDA, the level of detailcomponent CDH, the vertical detail component CDV, andthe angular detail component CDD, The sixteen sub-imagesformed Fig.1(c), and Fig.1(a) is the original host image.

a (b) (c)

Fig.1 the flow chart of wavelet packet decomposition

2011 Seventh International Conference on Computational Intelligence and Security

978-0-7695-4584-4/11 $26.00 2011 IEEE

DOI 10.1109/CIS.2011.117

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C. The position selection of embedding watermarkThe wavelet packet transform domain was chosen to

embed watermark. The method to select a position ofembedding watermark was as following. Firstly, divided theimage of wavelet packet coefficients into 33 blocks,

Secondly calculate the standard deviation of each blocks,and arrange the standard deviation in ascending order. Then

choose the block center, which the first K standard devia-tion corresponding to, as an embedding position, where Kindicated the size of the watermark sequence. The positionof embedding watermark must be known first when extractthe watermark, so It is necessary to save the position matrixas a file by using the save command in MATLAB.

The average formula for each block is

++== =

1

1

1

1

),(9

1

m n

njmismean (1)

The formula of computing variance for each block is

++== =

1

1

1

1

2)),((

8

1

m n

meannjmisVar (2)

The formula of standard deviation for each block isvar=stadev (3)

),( mjmis ++ represent the wavelet coefficients of each

block; ),( jis represent the wavelet packet coefficients of

the center position in each block. Variable; nm, is the

variation that other coefficients relative to the centerposition.

D. The establishment of the BP neural network model forwatermarking

The embedded technique of transform domain was usedin this paper. And in order to improve the robustness, neuralnetwork was introduced, since it can fully approximate any

complicated non-linear relationship. Thus the neural net-work model established can well describe the relationshipbetween selected wavelet packet coefficients and theirneighborhood. Neural network model is as following.

1,Si j

1,Si j

1,Si j +

, 1Si j ,Si j , 1Si j+

1,Si j+

1,Si j+

1,Si j+ +

Figue2. 33 Coefficient blocks of wavelet packet

Figure.2 is a 33 block of wavelet packet coefficients,

the center was where the watermark is to be embedded. Weselect eight coefficients of wavelet packet around the centeras the input of BP neural network, and the coefficient ofcenter wavelet packet as the expected output, then train theneural network. Fig.3 was the structure of BP neuralnetwork.

For the multi-layer network, the number of input nodesand output nodes are determined by the problem itself.Choosing the size of network is mainly determining the size

of nodes in hidden layer. The selection of nodes in hiddenlayer is very important for network training and studying. Ifhidden nodes is too few, the network would not have thenecessary ability to learn and necessary information pr-ocessing capabilities.

Fig.3 BP neural network

Conversely, too many hidden nodes increased the

complexity of network structure greatly, and was easier fornetwork to fall into local minimum in the learning process.Meanwhile, It made the network learn very slowly. Thecommon method of selecting is the trail and error method,generally based on experience to select the hidden layer ofnodes, was very random. The empirical formula fordetermining the number of hidden nodes is

dcnnmN ++= (4)

Where Nis the hidden nodes; n is the number of input

nodes; m is the number of output nodes; dc, is the

parameters to be determined. In general, the followingposterior formula is used.

9298.06799.1 ++= nnmN (5)

In this article, 7.4,1,8 == Nmn ,taking 5=N ,The

neural network has three layers, there were 8 nodes in inputlayer,5 nodes in hidden layer, 1 node in output layer. Incoefficient image of wavelet packet S, the coefficient ofwavelet packet which was selected to embed the water-

marking was ijS , and the eight wavelet packet around it was

as the input of network. As shown above, the output of

neural nodes in output layer was ijy , the expected output of

net-work was ijS . We select the embedding positions of K

by the key, and these points and the points around themformed a learning sample space of the network. Thenetwork which is well trained is used for the blind detection

of watermarking.

E. Embed watermarkingEmbed watermarking using the formula as following

)1)(2)(2(),(),( ++= kwjisjip (6)

),( jip was the wavelet packet coefficient of embedded

watermarking, ),( jis was the k-th wavelet packet coeffici-

ents to be embedded according to the key; was the radio

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of the standard deviation of the coefficient block and themaximum standard deviation of all the coefficient blocks;

is constant, taking 02.0= ; was adaptive embedding

intensity, is fixed embedding strength; )(kw represent the

k-th position of watermarking.

F. the Image embedded watermarkingAfter embedding the watermarking, the image

embedded watermarking is obtained by taking inversewavelet transform.

III. WATERMARKING EXTRACTING ALGORITHM The algorithm firstly decomposed the image of em-

bedded watermarking by discrete wavelet packet.

Then determine the embedding position by using thekey, according to that, the input of BP network isdetermined. The simulation result of wavelet packetcoefficient is obtained by the trained BP networksimulation.

After the step in front, extracted the watermarkingusing the formula as following

>

=

)()(,0

)()(,1)('

11

11

kykT

kykTkw (7)

Where Kk 1= )(1 kT was the wavelet coe-

fficient of the k-th embedded watermarking after

discrete wavelet packet transform. )(1 ky was the

coefficient of wavelet packet before embedding intothe position where was simulated by BP neural

network; )(' kw was the value of the k-th extracted

watermark.

At the last, rearranged the extracted watermarkingsequence according to the key, binary watermarking

image was obtained.

IV. THE IMPLEMENTATION OF ALGORITHM

Fig.4 Original host image(I)

In the algorithm, the watermarking image w, the originalhost image I and the image embedded watermark wx arerespectively Figure.4, Figure.6 and Figure.8, the differencebetween the host image and the image embedded watermarkwas invisible, and It was successful for the transparency ofthe algorithm. Fig.5 was wavelet packet coefficient imageafter the decomposition of the original host image, Fig.7

was the wavelet coefficient graph after embeddingwatermark, Fig.9 was the training figure of BP neuralnetwork. The extracted watermark w2, shown in Fig.10, wasthe same visual effect as the image before embedding.

Fig.5 Coefficient image of wavelet packet (ss)

Fig.6 Original watermark image (w)

Fig.7 Coefficient image of wavelet packet embedded watermarking (p)

The experimental results indicated that there were novisual differences between host image and the image em-bedded watermark. And the watermarking had goodimperceptibility. The peak signal to noise ratio

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was 2035.37PSNR = , the extracted watermark and the

original watermarking similarity was 1NC = .

Fig.8 Image embedded watermarking (wx)

Fig.9 Training figure of watermarking image

Fig.10 Extracted watermark (w2)

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