To avoid that important information is taken by an illegal user during transmission, data hiding has paid more and more attention [2, 3, 4, 5, 6, 10, 12, 13, 15, 16, 17, 18, 20, 21]. The main idea of data hiding is to embed the secret data into cover image and generate quality stego-image with PSNR higher than 40dB. Since the stego-image is imperceptible when PSNR is higher than 40dB [13], the illegal user can not recognize whether the stego-image is embedded the secret data or not. Only the specific user can extract the secret data from the stego-image.
In data hiding methods, there are two important issues: the capacity of secret data and the quality of stego-image. Because pixel values in the cover image are shifted to embed the secret data, the data hiding method with higher capacity usually generates stego-image with lower quality. How to embed more secret data without reducing the quality of stego-image has became an important object for researchers.[4, 9, 10, 13, 15, 16, 21].
An effective data hiding method with high quality was proposed in 2006 by Ni et al. [13]. Assume that the sender wants to send the secret data to the receiver. The sender at first embeds secret data into cover image using Ni et al.’s method and generates stego-image with PSNR higher than 48dB. The sender outputs all the numbers of pixel values in histogram. Then the sender finds the top two highest numbers as peak points and their corresponding zero points, the numbers are zero and closest to peak points.
After shifting the pixel values between peak points and zero points, the spaces next to peak points are generated. The sender embeds the secret data “1” by shifting the pixel values from peak points to their nearby spaces and secret data “0” by remaining the pixel values. In the end, the sender transports the stego-image, peak points, zero points
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and length of secret data to the receiver. Using acquired information, the receiver can extract secret data and discover the original cover image. Ni et al.’s method can keep high quality of stego-image since each difference between original and shifted pixel value is at most one. But this method has little capacity because it depends on top two highest numbers of pixel values.
To gain more capacity, Lin et al. use the histogram of differences to embed the secret data in 2008[12]. In Lin et al.’s method, the sender computes all the absolute differences of pixel values which are adjacent to each other. Lin et al. call the differences as predictive errors. The sender outputs the numbers of predictive errors in histogram and finds a peak point and a zero point. Predictive errors between peak point and zero point are shifted to generate the space nearby peak point. The sender embeds the secret data “1” by shifting the predictive errors from peak point to its nearby space and secret data “0” by remaining the predictive errors. When all the predictive errors are scanned, the sender reverses predictive errors into pixel values and generates stego-image. Having similar values, the differences between nearing pixels are closed to zero so that the numbers of peak points are much more than Ni et al.’s. Since the capacity of data hiding depends on the sum of the number of peak points, Lin et al.’s method has more capacity than Ni et al.’s. Lin et al.’s method has higher capacity using histogram of predictive errors, but their method is not effective for complex images since some pixel values of complex images are salient.
Yang et al. proposed a data hiding method to improve the algorithm of computing predictive errors in 2009[21]. In Yang et al.’s method, the sender divides the cover image into white and black segments, like a chessboard. The sender computes the predictive errors of white segment by subtracting the average of their circumferential pixel values in floor function. The statistics of predictive errors are compiled and
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outputted in histogram. Through the histogram, the sender gets two peak points and their corresponding zero points. After shifting the pixel values between peak points and zero points, the spaces next to peak points are generated. The sender embeds the secret data “1” by shifting the pixel values from peak points to their nearby spaces and secret data “0” by remaining the pixel values. After all the predictive errors are scanned, the sender reverses predictive errors into pixel values and gets the stego-image. If there are remained secret data, the sender computes the predictive errors of black segment by subtracting the average of their circumferential pixel values in floor function. The sender compiles the embedded algorithm until all the secret data are embedded into cover image. After executing algorithm twice, the sender gets the stego-image. This method avoids the interference from salient pixel value. The capacity of Yang et al.’s method is higher than that of the presented data hiding methods.
Although many studies are proposed to improve data hiding methods over binary computers, the studies seldom focus on data hiding methods over non-binary computers. Non-binary computers are used for special purpose nowadays like quantum computer [14]. The famous non-binary computer is the ternary computer [7]. Over the ternary computer, the balanced ternary numbering system [8] is described by Knuth as
“the prettiest number system of all” [11] for its elegant arithmetic properties. The ternary concept will be found in optical computer [22] or quantum computer [14]. The main notation in the ternary computer is represented by {0, 1 ,1 }. Having the same concept, Non-Adjacent Form (NAF) is the ideal method to transform binary secret data into ternary format. The secret data in NAF format have three characteristics [8, 22]: the data are represented by {0, 1 ,1 }, 1 and 1 are never adjacent, and the probability of appearing 0 is about 66%. Based on the characteristics in NAF format, we propose a data hiding method over ternary computer with high quality of
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In our method, the sender embeds the secret data of NAF format into cover image.
The sender divides the cover image into white and black segments. The sender computes the predictive errors of white segment by subtracting the average of their circumferential pixel values in floor function. The numbers of predictive errors are outputted in histogram. Through the histogram, the sender gets a peak point and its two corresponding zero points. Predictive errors between zero points are shifted except the peak point to generate the spaces nearby the peak point. The sender embed secret data
“ 1 ” by shifting the predictive errors of peak point to their left space, secret data “1” by shifting the predictive errors of peak point to their right space and secret data “0” by remaining the pixel value. After all the predictive errors are scanned, the sender reverses predictive errors into pixel values and generates quality stego-image. If there are remained secret data, the sender computes the predictive errors of black segment by subtracting the average of their circumferential pixel values in floor function. The sender repeats the embedded algorithm until all the secret data are embedded into cover image. After executing algorithm twice, the sender gets the stego-image. In the end, the sender transports the stego-image, peak points, zero points and length of secret data to the receiver. Using acquired information, the receiver can extract secret data from the stego-image and discover cover image.
From the past researches [2, 3, 5, 6, 9, 17], the average number of peak points should be shifted is 50% in binary format [1, 2, 3, 9, 17, 19] and 33% in NAF format [7, 8, 11]. We give some experiments by Yang et al.’s method and ours. According to experiment results, our method can keep higher PSNR when the number of first peak point is three times than the number of second peak point. Further more, we prove that our method can gain 1.76 PSNR more than Yang et al.’s method in best case.
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Outline of this thesis is as follows. In Chapter 2, we introduce Ni et al.’s method, Lin et al.’s method, Yang et al.’s method and the format of NAF. Improved method is given in Chapter 3. The experiment results are shown in Chapter 4. In Chapter 5, we compare Yang et al.’s method and ours and compute the added PSNR in our method.
Finally, we make a conclusion in Chapter 6.
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