SVD and Neural Network Based Watermarking Scheme Swanirbhar Majumder1, Tirtha Shankar Das2, Vijay H. Mankar2, and Subir K. Sarkar2 1
Department of ECE, NERIST (Deeed University), Arunachal Pradesh 791109, India
[email protected] 2 Department of ETCE, Jadavpur University, Kolkata, West Bengal, India
[email protected],
[email protected]
Abstract. Presently the WWW phenomenon has brought the world in to the personal computer. Digital media is thereby given high priority. But this has increased the frequency of security breach of intellectual properties. Therefore copyright protections and content integrity verification are highly recommended. What we need is newer data hiding techniques that must be imperceptible, robust, highly secured, etc. Digital image watermarking is one of the ways that is resilient to various attacks on the image based digital media where data authentication is done by embedding of a watermark in image characteristics. This work incorporates singular value decomposition (SVD) based image watermarking. Here unlike previous work done by researchers, error control coding (ECC) and artificial neural networks (ANN) for the authentication purposes have been used. ECC and ANN increase the robustness of the method against malicious attacks. Keywords: SVD, Error control coding, Artificial Neural Network, Watermark.
1 Introduction Till date a lot of digital watermarking techniques, for copyright protection of multimedia data, have been proposed to avoid their misuse [1] [2]. Implementation of these watermarking schemes requires main focus on robustness, trustworthiness and imperceptibility [3] [4]. In a broader sense, the embedding of watermark for any multimedia data (audio, video or image) is either in spatial or in the transform domain [5]. In the spatial domain, embedding of watermark is implemented by directly adding it to the data in terms of any particular algorithm. It is faster than the latter, due to its simpler operations and implementation, but is less robust. Therefore for noise, filtering or compression mechanisms, it is better to go for the transform domain, despite of higher computing cost to attain higher robustness of the watermark [6]. Various transforms, as well as their hybrids have been used for getting better robustness than each other comparatively. Here SVD has been used along with error control coding and back propagation neural networks to enhance the performance at the cost of algorithmic complexity. The singular value decomposition (SVD) technique is a generalization of the eigen-value decomposition, used to analyze rectangular matrices. This mathematical V.V Das et al. (Eds.): BAIP 2010, CCIS 70, pp. 1–5, 2010. © Springer-Verlag Berlin Heidelberg 2010
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technique has been used in various fields of image processing. The main idea of the SVD is to decompose a rectangular matrix into three simple matrices (two orthogonal matrices and one diagonal matrix) [5] [6]. It has been widely studied and used for watermarking by researchers for long. When SVD is undergone on an image (IMxN) matrix it produces 3 matrices (UMxM, SMxN and VNxN). The main image characteristics are in the S. U and V contain the finer details respective to the Eigen values at S. By using any rank R, the UMxM becomes UMxR and SMxN becomes SRxR and VNxN becomes VNxR. Their resultant operation is image I’MxN , where I’ is the image generated from UMxR, SRxR and VNxR. This I’ does have approximately similar features as I for optimum value of R. Here SVD is used to hide the logo for watermarking, in its Eigen values. To improve the robustness error control coding is applied, for which the convolution encoder is used with Vitrebi decoder as per a particular polynomial and code trellis has been implemented [7]. Along with the SVD and the error control coding scheme the next important technique employed is the back propagation algorithm based neural network. This is because among different learning algorithms, back-propagation algorithm is a widely used learning algorithm in Artificial Neural Networks. The Feed-Forward Neural Network architecture is capable of approximating most problems with high accuracy and generalization ability [8] [9]. This algorithm is based on the error correction learning rule. Error propagation consists of two passes through the different layers of the network, a forward pass and a backward pass. In the forward pass the input vector is applied to the sensory nodes of the network and its effect propagates through the network layer by layer. Finally a set of outputs is produced as the actual response of the network. During the forward pass the synaptic weight of the networks are all fixed. During the back pass the synaptic weights are all adjusted in accordance with an error-correction rule. The actual response of the network is subtracted from the desired response to produce an error signal. This error signal is then propagated backward through the network against the direction of synaptic conditions. The synaptic weights are adjusted to make the actual response of the network move closer to the desired response.
2 Watermark Embedding The prerequisites for image watermarking are the subjective watermark (logo image) and the host image for data concealment. After generation of the code trellis, the watermark is passed through an error control convolution encoder to obtain an encoded logo data stream. The singular value decomposition (SVD) of host image is performed to obtain the matrices U, S, and V. The S matrix consisting of the diagonal values is converted to one dimension via zig zag scan, done in order to add the logo near the most significant Eigen values. This leads to a matrix S'
S '1D = S zigzag1D + key × Logo1D
(1)
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Since the number of bits in S is greater than that of the logo, number of bits in S' is same as that of S. Moreover, to reduce the intensity of the logo, it is multiplied with a number 'key', which is less than 1. This reduces the intensity of logo in the S matrix and does not degrade the host image significantly.
Fig. 1. Watermark embedding steps
This one dimensional S' is then converted back to two dimensional (2D) form using the anti-zigzag algorithm. On having the 2D S' the SVD operation is applied on it for the second time to have S1, U1 and V1 as output of the SVD operation on S'. The S1 of second SVD operation along with the earlier extracted U and V from the first operation are incorporated to obtain the watermarked image IW from equation 2.
IW = U × S1× V T
(2)
Now using the leftover matrices U1, S and V1 we get the key image IK given by:
I K = U1× S × V1T
(3)
Further the 16x16 logo (watermark) is divided into blocks of 4x4 pixels, with eight bits in each pixel. Then a back propagation based neural network is used to train the neurons to identify the logo by weight adjustment of the synapse. This is applied on the normalized pixel bits (in range 0 to 1). Thereby with some amount of pixel alteration the network can still identify the logo (that it has been trained to recognize).
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3 Watermark Extraction The detection of the watermarked logo from the stego image is just the opposite of the embedding method. This is of non-oblivious type, as the key and Key image IK are to be available at the receiver end, where the stego image I'W (due to malicious attacks IW turns to I’W) is received instead of IW. Therefore, SVD is applied on the key image IK to obtain to obtain U1, S1 and V1 and the distorted watermarked image I'W to obtain U2, S2 and V2.
Fig. 2. Watermark extraction steps
Here S1 is replaced by S2 and the inverse SVD is performed to obtain D where:
D = U1× S2× V1T
(4)
Now, this D and the previously obtained S1 from key image are reshaped to one dimension by zigzag operation. Then at the receiver end, encoded logo code C is estimated.
C = 1/ key × (D − S1)
(5)
The difference of the two arrays is multiplied by the reciprocal of key to reinstate the lost intensity of code in the decoder. This extracted code is further decoded using a hard Viterbi decoder with the same trellis structure used during encoding. But the problem is that sometimes due to heavy duty attacks; even the presence of error control coding cannot help the recognition of the logo. In these conditions the tentative logo is checked via the back propagation based neural network (BPNN) trained during the embedding process. In case nominal logo characteristics are present in the tentative logo it is recognized, as in the figure below. Else it is considered to be a malicious logo with no characteristics of the logo that was embedded.
SVD and Neural Network Based Watermarking Scheme
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Fig. 3. BPNN pre-trained with the logo during the embedding process that detects tentative logo and rejects malicious ones
4 Conclusion In this paper a method of watermarking logo using the SVD technique has been proposed. This scheme has been enhanced with the use of error control coding as well as back propagation neural network. This method can be checked for results by Checkmark 1.2. So for these standard attacks the robustness of the watermarking method may thereby be judged.
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