Multi-objective Particle Swarm Optimization Based Image Watermarking Scheme

A novel image watermarking scheme based on the statistics of the blocked DCT coefficients. The watermark is embedded into the middle frequency of those DCT coefficients by modulating the number of those positive and negative coefficients. In order to achieve better robustness and imperceptibility, multi-objective particle swarm optimization (MPSO) has been used in the watermark embedding and extracting procedure. The particle swarm optimization is applied to obtain optimum multiple scaling factors and the embedding strength. The experimental results show that the proposed scheme has significant improvement in term of imperceptibility and robustness under various general attacks.


Introductions
Computer and networks have been a significant way to exchange information in this era.Various digital multimedia products are spread on the Internet.Nowadays, people can copy, alter, and transmit multimedia properties easily, including texts, images, audios, videos, and so on.Modern information technology brings not only convenient and cheap digital transmission services, but also various challenges.One of the most important is how to protect the properties of the legal owner [1].In this case, digital watermarking is proposed, which means hiding information or anticounterfeit mark into the host image to protect copyright.It will be flourishing in the next decades with the urgent market demand.It is the digital watermarking technology that may be utilized as a supplement for cryptography encryption and scrambling technology [2].
During the last decade, many robust image watermarking algorithms have been proposed, which can be divided into three categories according to the domain what the watermark can be embedded: spatial domain watermarking, transform domain and hybrid domain watermarking.The spatial domain watermarking algorithms [3,4]mainly embed the watermark by modulating the image pixels or altering its gray values directly, such as the least significant bit (LSB) and so on.These algorithms are fragile to manipulations, but they have little computation work and can be easily implemented.The transform domain watermarking schemes are mainly concentrated on some signal transforms such as DCT(Discrete Cosine Transform) [5,6], DFT(Discrete Fourier Transform) [7] and DWT(Discrete Wavelet Transform) [8][9][10], etc.The watermark is embedded into the host by modifying some or all frequency domain coefficients, especially middle frequency coefficients.These methods have better robustness and can resist common attacks [11][12][13].The hybrid domain can employ the advantages in two or more domain.The typical scheme is based on two transform domains.The first transform may have some good characteristics to some common attacks, and the second transform can be robust to geometric attacks.The hybrid domain algorithms can achieve good performance, but they are complex in implementation.It may be a future development direction because computer performance is strengthening on calculation.Now, most of the proposed watermarking schemes are based on the transformation domain.In this paper, the proposed algorithm can effectively resist some geometrical attacks.
The paper is organized as follows.In section II, the particle swarm optimization is reviewed.Section Ⅲ describes the proposed watermarking scheme in detail.The experimental results are shown in section Ⅵ.And section Ⅶ conclude the paper.

The particle swarm optimization
The particle swarm optimization is a meta-heuristic swarm based algorithm widely used in parameter optimization, which is proposed by Kennedy and Eberhart [14].The particle swarm optimization mimics the simplified social models such as fish schooling and bird flocking.A swarm is defined as a set of mobile agents that collectively carry out problem solving in a distributed manner.Each agent is called one particle.In a swarm, each particle keeps track of their own attributes.
Where those parameters can be depicted as follows: (i,j): index of the position in the particle; k=1,2,…P , is the iteration number; 3) Calculate the global best, G best for the swarm.4) Update each particle's velocity and position using Eq.1.5) If termination condition is not met, goto step 2).

Proposed watermark embedding and extracting scheme
The block DCT coefficients can be divided into DC coefficient and AC coefficients.The DC coefficients of mth block can be expressed F m (0,0) and the rest may be divided into low, middle and high frequency coefficients.Since tiny modification of the DC or low frequency coefficients may degrade image subjective quality, embedding watermark into the DC or low frequency coefficients should not be adopted.The watermark information embedded into high frequency coefficients can be easily removed during the general image processing.So the middle frequency coefficients may be a better choice according to the necessity of compromise between robustness and invisibility.In this paper, the watermark is embedded into the middle frequency coefficients.Watermark embedding and extracting block diagrams are shown in Fig. 1 and Fig. 2 respectively: Firstly, the host image is divided into disjoint blocks and then transformed to frequency domain by block-DCT.And mid-frequency DCT coefficients are selected for watermark embedding.The Zigzag scanning of 8 8  coefficients and embedding positions can be shown in Fig. 3: Since slight modification of the 1 st , 2 nd and 3 rd coefficients may affect the image quality serious, middle frequency coefficients are selected for watermark embedding.The proposed watermark embedding and extraction procedure can be depicted as following steps: 1) Watermark embedding procedure   In a word, every watermark bit can be embedded in each block.The total watermark capacity may be 1024 bits.
After analyzing the characteristics of middle frequency coefficients, it can be found that the absolute values are very close, so we introduce an embedding strength factor, which can not only adjust the compromise between robustness and invisibility, but also eliminate rounding error from the function uint8.This error may affect the watermark extraction.

2) Determining multiple scaling factors: A parameter
) , ( q p  which is used to control the tradeoff between the imperceptibility and robustness, generally used as scaling factor, should be decided firstly.If the scaling factor is different in each watermark bit to be embedded,  can be a matrix, i.e. multiple scaling factors.To determine the optimal values of these multiple scaling factors can be viewed as an optimization problem.Multi-objective particle swarm optimization may be applied. The block diagram of multi-objective optimization is a closed-loop control system.The system input is multiple scaling factors and objective measure as system output.This measure is calculated from original image I, watermarked image w I , watermark W and the (T+1) extracted watermarks.
The steps for applying a multi-objective particle swarm optimization into the proposed watermarking scheme are enumerated.
3) Watermark extraction procedure： (a) Divide the suspected image into , M*N is the original host image size.

Experimental results
In order to evaluate the performance of the proposed method, some experimental results are done on MATLAB Ra2008.The experiments are carried out on several images including "Lena", "Pepper", "Plane", "Baboon", which represent different texture complexity.Due to the limitation of space, here only demonstrate the experimental results on Lena with size 256 256  Lena gray image.Fig. 5 shows the original image, watermarked image, logo watermark and the extracted watermarked.

Objective image visual quality evaluation
Image visual quality evaluation methods can mainly be divided into two categories which are subjective ones and objective ones.The subjective ones are the methods of grading subjective quality or video expert group, etc.The objective one are the methods of the mean square error (MSE), the signal-to-noise ratio (SNR), the peak signalto-noise ratio (PSNR), the structure similarity (SSIM), and other methods based on human visual characteristics.Here mainly uses the mean square error (MSE) and the peak signal-to-noise ratio (PSNR) to measure the image quality.
Suppose the host image The smaller MSE is, the distortion is less and the PSNR is larger; the larger MSE is, the distortion is more serious and the PSNR is smaller.

Extracted watermark quality evaluation
The original watermark and the extracted watermark can be denoted as Where  . is the sum on all the bit errors, and 8 / , 0 N j i   .

Experimental results
We

Conclusions
A novel block DCT based image watermarking scheme is proposed in this paper.MPSO is used to optimize the embedding scaling factors to achieve a good compromise between the invisibility and robustness.The experimental results show that the proposed method based on MPSO is robust to general attacks and resilience to some geometric attacks.
p are randomly created.Each particle represents a candidate solution to optimize problem by calculate its fitness.The fitness of each particle is evaluated by an objective function.During iteration, the best location visited by each particle is kept as the local best position new population is created based on a preceding one and the particles are updated by the following equations:

:
velocity of the particle in the swarm at the position index (i,j); position of the particle at the position index (i,j); procedure of PSO algorithm can be depicted as follows: Algorithm 1. Particle Swarm Optimization(PSO) 1) Create a population, P of random particles.2) For each particle calculate the fitness value and find the local best Pbest.

( 1 )
Divide the original image into 8Those selected coefficients are modified by changing the sign of the least coefficients in ascending order of their absolute values until the numbers of positive or negative coefficients to be Tp or Tn ,respectively.
transformed by inverse block DCT and merged into the watermarked image ' I .

8 8 
blocks and perform the DCT transform on each block.The m -th block coefficients are denoted as select those coefficients between the th k 1 and th k 2 .The positive and negative numbers of them are counted as ) Merge those extracted bitsewatermark into logo image.
. The PSNR and the BER result of watermark extraction non-using MPSO and using MPSO method are shown in Table1.