Abstract:
Embodiments of the invention are directed toward reversible/invertible and lossless, image data hiding that can imperceptibly hide data into digital images and can reconstruct the original image without any distortion after the hidden data have been extracted in various digital image formats including, but not limited to Joint Photographic Experts Group (JPEG). In particular, embodiments of the invention provide a lossless data hiding technique for JPEG images based on histogram pairs. that embeds data into the JPEG quantized 8×8 block DCT coefficients and achieves good performance in terms of peak signal-to-noise ratio (PSNR) versus payload through manipulating histogram pairs with optimum threshold and optimum region of the JPEG DCT coefficients. Furthermore, the invented technology is expected to be able to apply to the I-frame of Motion Picture Experts Group (MPEG) video for various applications including annotation, authentication, and forensics.

Description:
DESCRIPTION OF BACKGROUND ART 
       [0001]    Reversible, also called invertible or lossless, image data hiding can imperceptibly hide data in digital images and can reconstruct the original image without any distortion after the hidden data has been extracted out. Among the various digital image formats, Joint Photographic Experts Group (JPEG) formats are by far used the most often nowadays. Hence, how to reversibly hide data in a JPEG image file is important and useful for many applications including authentication, secure data systems, and covert communications. For example, linking a group of data for some purpose to a cover image in a reversible way is particularly critical for medical images, high accuracy images, images used for legal purpose and other environments in which the original image is of great importance. Furthermore, the invented technology is expected to be able to apply to the I-frame of Motion Picture Experts Group (MPEG) video for various applications mentioned above. 
         [0002]    Reversible data hiding by using the histogram shifting techniques has been reported in the literature. Reversible data hiding was first applied to the histogram of an image in the spatial domain in Z. Ni, Y. Q. Shi, N. Ansari, W. Su, “Reversible data hiding,” IEEE International Symposium on Circuits and Systems (ISCAS03), Bangkok, Thailand, May 2003; and A. van Leest, M. van der Veen, and F. Bruekers, “Reversible image watermarking,” Proceedings of IEEE International Conference on Image Processing (ICIP), II-731-4 vol. 3, September 2003. In addition, the technique was applied to the histogram of DCT domain and integer wavelet transform domain. In general, the histogram shifting technique has achieved dramatically improved performance in terms of embedding capacity versus visual quality of stego image measured by peak signal noise ratio (PSNR). However, none of the above-discussed lossless data hiding methods apply to JPEG images. 
         [0003]    In fact, there are not many reversible data hiding techniques that have been developed for JPEG images to date. Some background art techniques are reported in J. Fridrich, M. Goljan and R. Du, “Invertible authentication watermarking for JPEG images,” Proceedings of IEEE Information Technology and Computing Conference (ITCC), pp. 223-227, Las Vegas, Nev., USA, April 2001; J. Fridrich, M. Goljan, and R. Du, “Lossless data hiding for all image formats,”  Proc. of SPIE, Electronic Imaging  2002,  Security and Watermarking of Multimedia Contents IV , vol. 4675, San Jose, Calif., pp. 572-583, 2002; and J. Fridrich, M. Goljan, Q. Chen, and V. Pathak, “Lossless data embedding with file size preservation,”  Proc. SPIE Electronic Imaging  2004,  Security and Watermarking of Multimedia Contents , San Jose, Calif., January 2004. 
         [0004]    In the first two background art references cited above, the least significant bit plane of some selected JPEG mode coefficients is losslessly compressed, thus leaving space for reversible data embedding. Consequently the payload is rather limited. In the third background art reference cited above, the run-length encoded alternating current (AC) coefficients are modified to losslessly embed data into JPEG images, aiming at keeping the size of JPEG file after lossless data hiding remaining unchanged. However, the payload is still rather limited (i.e., the highest payload in various experimental results reported in the third paper is 0.0176 bits per pixel (bpp)). 
       SUMMARY 
       [0005]    Embodiments of the invention are directed at overcoming the foregoing and other difficulties encountered by the background arts. In particular, embodiments of the invention provide novel technique based on histogram pairs applied to some mid- and lower-frequency JPEG quantized 8×8 block discrete cosine transform (DCT) coefficients (hereinafter referred to as JPEG coefficients). 
         [0006]    Embodiments of the invention provide methods using histogram pair techniques that are applied to the mid- and lower-frequency coefficients of 8×8 blocks DCT. Experimental results are presented below that demonstrate effectiveness of these methods. The data embedding capacity ranges from 0.0004, to 0.001, 0.1, up to 0.5 bits per pixel (bpp) for one-time data embedding, while the visual quality of images with hidden data measured by both subjective and objective PSNR remains high. The increase of size of image files due to data hiding is not noticeable, and the shape of histogram of the mid- and lower-frequency coefficients of DCT remains similar. It works for various JPEG Q-factors. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1A  is an exemplary high-level flow diagram of: (a) a method for lossless data embedding and (b) a method for data extraction from JPEG images. 
           [0008]      FIG. 1B  is an exemplary flow diagram of: (a) a method for lossless data embedding in JPEG images and (b) a method for data extraction from JPEG images. 
           [0009]      FIG. 1C  is an exemplary detailed block diagram of methods for lossless data embedding and data extraction from JPEG image files. 
           [0010]      FIG. 2A  is an exemplary spatial representation of image data and a histogram of the image data, with a threshold T=2. 
           [0011]      FIG. 2B  is an exemplary spatial representation of image data and a histogram of the image data after histogram shifting to form a histogram pair. 
           [0012]      FIG. 2C  is an exemplary spatial representation of image data and a histogram of the image data after embedding bit sequence D=[0,1,1]. 
           [0013]      FIG. 2D  is an exemplary bit sequence D=[0,1,0,0,1,0,1,1,0] embedded in two loops. 
           [0014]      FIG. 2E  is a 5×5 image data embedding example (to be embedded bit sequence is D=[1 10 001]. 
           [0015]      FIG. 2F  is histograms associated with  FIG. 2E . 
           [0016]      FIG. 3A  is another exemplary spatial representation of image data and its histogram of the image data, with a threshold T=2 and S=−2. 
           [0017]      FIG. 3B  is the image and histogram after histogram shifting to form two histogram pairs. 
           [0018]      FIG. 3C  is the image and histogram after the bit sequence D=[0 1 10] has been embedded. 
           [0019]      FIG. 4A  is an exemplary set of selected JPEG coefficients for data embedding {16, 36}. 
           [0020]      FIG. 4B  is another exemplary set of selected JPEG coefficients for data embedding {4, 36}. 
           [0021]      FIG. 4C  is yet another exemplary set of selected JPEG coefficients for data embedding {16, 49}. 
           [0022]      FIG. 5  is an exemplary plot of selected JPEG coefficients in a zigzag scan from 16 to 36: {16, 36} for various images. 
           [0023]      FIG. 6  is an exemplary plot of selected JPEG coefficients in a zigzag scan from 4 to 36: {4, 36} for various images. 
           [0024]      FIG. 7  is an exemplary plot of JPEG coefficients in a zigzag scan from 16 to 49: {16, 49} for various images. 
           [0025]      FIG. 8  is an exemplary plot of PSNR versus achieved by the lossless data hiding method of embodiments of the invention with three commonly used JPEG images in regular form. 
           [0026]      FIG. 9  is an exemplary plot of PSNR versus payload achieved by the lossless data hiding method of embodiments of the invention with three commonly used JPEG images in log (log (x)) form. 
           [0027]      FIG. 10  is an exemplary plot of PSNR versus payload achieved by the lossless data hiding method of embodiments of the invention with three commonly used JPEG images (with small payload). 
           [0028]      FIG. 11  is an exemplary plot of PSNR versus payload achieved by the lossless data hiding method of embodiments of the invention with three commonly used JPEG images (with large payload). 
           [0029]      FIG. 12  is an original 512×512 “Lena” JPEG image with Q-factor 80. 
           [0030]      FIG. 13  is the “Lena” JPEG image after embedding 100 bits (0.0004 bits per pixel (bpp)). 
           [0031]      FIG. 14  is the “Lena” JPEG image after embedding 5000 bits (0.0191 bpp). 
           [0032]      FIG. 15  is the “Lena” JPEG image after embedding 26,214 bits (0.1 bpp). 
           [0033]      FIG. 16  is the “Lena” JPEG image after embedding 131,072 bits (0.5 bpp). 
           [0034]      FIG. 17  is an original 512×512 “Baboon” JPEG image with Q-factor 80. 
           [0035]      FIG. 18  is the “Baboon” JPEG image after embedding 100 bits (0.0004 bpp). 
           [0036]      FIG. 19  is the “Baboon” JPEG image after embedding 5000 bits (0.00191 bpp). 
           [0037]      FIG. 20  is the “Baboon” JPEG image after embedding 26,214 bits (0.1 bpp). 
           [0038]      FIG. 21  is the “Baboon” JPEG image after embedding 131,072 bits (0.5 bpp). 
           [0039]      FIG. 22  is an original 512×512 “Barbara” JPEG image with Q-factor 80. 
           [0040]      FIG. 23  is the “Barbara” JPEG image after embedding 100 bits (0.0004 bpp). 
           [0041]      FIG. 24  is the “Barbara” JPEG image after embedding 5000 bits (0.00191 bpp). 
           [0042]      FIG. 25  is the “Barbara” JPEG image after embedding 26,214 bits (0.1 bpp). 
           [0043]      FIG. 26  is the “Barbara” JPEG image after embedding 131,072 bits (0.5 bpp). 
           [0044]      FIG. 27 . PSNR with hidden data versus Q-factors with 1000 bits embedded into 512×512 Lena image with various Q-factors (JPEG coefficient region {4, 36}). 
       
    
    
     DETAILED DESCRIPTION 
       [0045]    Embodiments of the invention relate to data hiding. Data hiding techniques can be used for purpose such as copyright protection, authentication, annotation, and steganography. Reversible data hiding&#39;s unique/main characteristics are its reversibility or losslessness. Reversible data hiding is mainly used for medical images (for legal consideration) and military, remote sensing, and high-energy physics images (for high accuracy). There is a need in the art for lossless data hiding methods that can be applied to JPEG images, allows for a sizable payload and maintains the size of the JPEG file after lossless data hiding. 
         [0046]    The principles of histogram pair based lossless data embedding are used in embodiments of the invention. A histogram, h(x), is the number of occurrences (i.e., the frequency) of feature x within a set of samples X. In embodiments of the invention, the samples X are some selected JPEG quantized 8×8 DCT coefficients where the feature x is the JPEG coefficients&#39; value. The x is either positive, or negative integer, or zero, such as xε{−2, −1, 0, 1, 2, 3}. A histogram pair is defined as a part of the histogram, denoted by h=[m, n], where m and n are, respectively, the frequencies of two immediately neighboring feature values xε{a, b} with a&lt;b i.e., b=a+1, and one of the two frequencies (m and n) is 0. 
         [0047]    Histogram pairs can be formulated via a process called histogram expansion. For example, via expanding, the histogram pair h=[ m, 0 ] can be produced (note: the underline is used to mark the histogram pair). The feature value whose frequency (i.e., h value) is not 0 is called the feature&#39;s original position. The feature value whose h value is 0 is called the feature&#39;s expansion position. For embodiments of the invention, it is defined that when the feature value x is greater than or equal to 0, the histogram pair is of the format h=[ m, 0 ], which means h(a)=m and h(b)=0, when the feature value x is less than 0, the histogram pair is of h=[ 0, n ], which means h(a)=0 and h(b)=n. 
         [0048]    After the histogram pair is produced, lossless data embedding is possible. Data embedding rule may be as follows:
       a. If the to-be-embedded bit is 0, the feature&#39;s original position is used; and   b. if the to-be-embedded bit is 1, the feature&#39;s expansion position is used.
 
Alternative embodiments of the invention may be implemented with the elements of the above rule reversed. Examples of embodiments of the invention with the above rules are discussed in the following paragraphs. It is observed that after data embedding the histogram becomes more flat. When the histogram is completely flat, it is impossible to further embed data.
       
 
         [0051]      FIG. 1A  is an exemplary high-level flow diagram for a (a) method for lossless data embedding and (b) a method of data extraction from JPEG images. In the method for data embedding, as shown in part (a) of  FIG. 1A , Step  11  is inputting an original JPEG image. Step  12  of the method involves entropy decoding the original JPEG image and determining JPEG quantized block Discrete Cosine Transform (DCT) coefficients from the entropy decoded original JPEG image. In Step  13 , a payload for embedding in the entropy decoded JPEG image, which is provided in Step  14 , is supplied; lossless data embedding of the payload in the entropy decoded original JPEG image occurs; and entropy encoding the data embedded entropy decoded original JPEG image. At Step  15 , a JPEG image with hidden data is the output of the method for data embedding. 
         [0052]    In the method for data extracting, as shown in part (b) of  FIG. 1A , Step  25  is inputting a JPEG image with hidden data. Entropy decoding the JPEG image with hidden data and determining JPEG quantized block Discrete Cosine Transform (DCT) coefficients from the entropy decoded JPEG image with hidden data are performed in Step  24 . Step  23  is data extracting a payload from the entropy decoded JPEG image with hidden data and entropy encoding the payload and an original JPEG image without hidden data. The original JPEG image without hidden data and a payload of extracted data is outputted in Step  22  and Step  21 , respectively. 
         [0053]      FIG. 1B  is an exemplary flow diagram of: (a) a method for lossless data embedding in JPEG images and (b) a method for data extraction from JPEG images. In the method for lossless data embedding of in part (a) of  FIG. 1B , assume the length of the to-be-embedded data is L. P is a value assumed by JPEG coefficients, which is used for data embedding. We can consider the selected P=T as the “starting point” for data embedding, and P=S as the stopping point. Payload can be measured either in number of bits, L, or bits per pixel (bpp). The term bpp is more general, since for the same L, if the image size is different, the bpp will be difference. For, say, a 512×512 images, 0.1 bpp means 26,214 bits (see the big tables later in the report), if consider a 256×256 image, 0.1 bpp means L=0.25×26,214 bits. For all of three commonly used 512×512 images, when we embed 0.1 bpp payload, the PSNR is 36 dB, meaning acceptable visual quality. Hence, roughly speaking, embedding 0.1 bpp up to 0.2 bpp has no problem with our proposed method. 
         [0054]    In Step  31 , a threshold (T) is set so T&gt;0 and set the P←T in order to let the number of the mid- and low-frequency JPEG coefficients within the range [−T, T] be greater than L. For Step  32 , in the JPEG coefficient histogram, move the portion of histogram with the coefficient values greater than P to the right-hand side by one unit to make the histogram at P+1 equal to zero (i.e., call P+1 as a zero-point). Also in Step  32 , according to whether the to-be-embedded bit is 0 or 1, embed data into P or P+1, respectively. Step  33  determines whether method for data embedding is finished. If the answer at Step  33  is “NO” (i.e., some of the to-be-embedded bits have not been embedded at this point) and the answer to P&gt;0 is “NO” in Step  34 , let P←(−P−1) in Step  36  and move the histogram (i.e., less than P) to the left-hand side by one unit to leave a zero-point at the value (P−1). Also in Step  36 , according to whether the to-be-embedded bit is 0 or 1, embeds data into P or (P−1), respectively. Then continue the method for embedding by returning to Step  32  and embedding the remaining to-be-embedded data. 
         [0055]    Alternatively, if the answer at Step  33  is “NO” (i.e., some of the to-be-embedded bits have not been embedded at this point) and the answer to P&gt;0 is “YES” in Step  34 , let P←(−P) in Step  35  and move the histogram (i.e., less than P) to the left-hand side by one unit to leave a zero-point at the value (P−1). Also in Step  35 , according to whether the to-be-embedded bit is 0 or 1, embeds data into P or (P−1), respectively. Then continue the method for embedding by returning to Step  32  and embedding the remaining to-be-embedded data. 
         [0056]    Alternatively, if the answer at Step  33  is “YES” (i.e., all the data has been embedded), then stop the method for embedding and record the value P as the stop value S (i.e., let S←P) in Step  37 . 
         [0057]    In the method for data extraction in part (b) of  FIG. 1B , assume the stop position S of data embedding is positive. In Step  41  of part (b) of  FIG. 1B , set P←S. In Step  42 , decode with the stopping value P and the value (P+1) and extract all the data until P+1 becomes a zero-point. In addition in Step  42 , move all the DCT coefficients histogram (greater than P+1) towards the left-hand side by one unit to eliminate the zero-point. If the amount of extracted data is less than C, set P←(−P−1). Continue to extract data until (P−1) becomes a zero-point. Then move the histogram (less than P−1) to the right-hand side by one unit to eliminate the zero-pint. 
         [0058]    Step  43  determines whether method for data extraction is finished (i.e., is the amount of extracted data less than C). If the answer at Step  43  is “NO” (i.e., some of the to-be-extracted bits have not been extracted at this point) and the answer to P&gt;0 is “YES” in Step  44 , let P←(−P−1) in Step  45  and move the histogram (i.e., less than P−1) to the right-hand side by one unit to eliminate a zero-point). Then continue the method for extracting by returning to Step  42  and extracting the remaining to-be-extracted data. 
         [0059]    Alternatively, if the answer at Step  43  is “NO” (i.e., some of the to-be-extracted bits have not been extracted at this point) and the answer to P&gt;0 is “No” in Step  44 , let P←(−P) in Step  46  and move the histogram (i.e., less than P−1) to the right-hand side by one unit to eliminate a zero-point). Then continue the method for extracting by returning to Step  42  and extracting the remaining to-be-extracted data. 
         [0060]    Alternatively, if the answer at Step  43  is “YES” (i.e., all the data has been extracted), then stop the method for extracting. Histogram shifting makes histogram more flat, thus embedding data into JPEG image file. Consider the horizontal axis of a histogram as representing the value of a set of selected mid- and lower frequency coefficients of an 8×8 block DCT that are integer-valued after JPEG quantization. 
         [0061]    Consider one selected pair of points in a histogram. Denote the length of to-be-embedded bit stream by L, a selected point in the horizontal axis by T, and its histogram value by h(T). If L≦h(T), this single T point is enough for data embedding. The whole histogram can be divided into three parts: (1) a central part; (2) a to-be-embedded part; and (3) an end part. The central part is the histogram whose value is less than T and kept intact during data embedding. The to-be-embedded part is the histogram pair whose values will change according to the to-be-embedded bits. The end part is the histogram whose value is greater than T and will be shifted outwards before data embedding. 
         [0062]      FIG. 1C  is an exemplary detailed block diagram of a method for lossless data hiding and a method for data extraction from JPEG images. In  FIG. 1C , data to be embedded  101  and a JPEG file  103  are configured to provide to a data embedding function  105  and a JPEG bits stream function  107 , respectively. The JPEG bit stream function  107  is configured to provide inputs to a first entropy decoding function  109 . The data embedding function  105  and entropy decoding function are configured to provide inputs to a JPEG coefficient function  111 . The JPEG coefficient function  111  is configured to provide inputs to an entropy coding function  113 . The entropy coding function  113  is configured to provide inputs to a JPEG bit stream with hidden data function  115 . The JPEG bit stream with hidden data function  115  is configured to provide inputs to a JPEG file with hidden data  117 , a JPEG image with hidden data  127  and a second entropy decoding function  123 . The second entropy decoding function is configured to provide inputs to a second JPEG coefficient function  121 . The second JPEG coefficient function  121  is configured to provide inputs to a data recovering function  125  and a second entropy coding function  119 . The data recovering function  125  is configured to provide extracted data  133 . The second entropy coding function is configured to provide inputs to a JPEG bit stream recovering function  129 . The JPEG bit stream recovering function  129  is configured to provide inputs to a recovered original image  131  and an original JPEG file  137 . The JPEG image with hidden data  127  and the recovered original image  131  are configured to provide inputs to a JPEG image display  135 . 
         [0063]      FIG. 1C  is an exemplary flow diagram of: (a) a method for lossless data embedding in JPEG images and (b) a method for data extraction from JPEG images. In the method for lossless data embedding of in part (a) of  FIG. 1C , assume the length of the to-be-embedded data is L. P is a value assumed by JPEG coefficients, which is used for data embedding. We can consider the selected P=T as the “starting point” for data embedding, and P=S as the stopping point. Payload can be measured either in number of bits, L, or bits per pixel (bpp). The term bpp is more general, since for the same L, if the image size is different, the bpp will be difference. For, say, a 512×512 images, 0.1 bpp means 26,214 bits (see the big tables later in the report), if consider a 256×256 image, 0.1 bpp means L=0.25×26,214 bits. For all of three commonly used 512×512 images, when we embed 0.1 bpp payload, the PSNR is 36 dB, meaning acceptable visual quality. Hence, roughly speaking, embedding 0.1 bpp up to 0.2 bpp has no problem with our proposed method. 
         [0064]    In Step  1 , a threshold (T) is set so T&gt;0 and set the P←T in order to let the number of the mid- and low-frequency JPEG coefficients within the range [−T,T] be greater than L. For Step  2 , in the JPEG coefficient histogram, move the portion of histogram with the coefficient values greater than P to the right-hand side by one unit to make the histogram at P+1 equal to zero (i.e., call P+1 as a zero-point). Also in Step  2 , according to whether the to-be-embedded bit is 0 or 1, embed data into P or P+1, respectively. Step  3  determines whether method for data embedding is finished. If the answer at Step  3  is “NO” (i.e., some of the to-be-embedded bits have not been embedded at this point) and the answer to P&gt;0 is “NO” in Step  4 , let P←(−P−1) in Step  6  and move the histogram (i.e., less than P) to the left-hand side by one unit to leave a zero-point at the value (P−1). Also in Step  6 , according to whether the to-be-embedded bit is 0 or 1, embeds data into P or (P−1), respectively. Then continue the method for embedding by returning to Step  2  and embedding the remaining to-be-embedded data. 
         [0065]    Alternatively, if the answer at Step  3  is “NO” (i.e., some of the to-be-embedded bits have not been embedded at this point) and the answer to P&gt;0 is “YES” in Step  4 , let P←(−P) in Step  5  and move the histogram (i.e., less than P) to the left-hand side by one unit to leave a zero-point at the value (P−1). Also in Step  5 , according to whether the to-be-embedded bit is 0 or 1, embeds data into P or (P−1), respectively. Then continue the method for embedding by returning to Step  2  and embedding the remaining to-be-embedded data. 
         [0066]    Alternatively, if the answer at Step  3  is “YES” (i.e., all the data has been embedded), then stop the method for embedding and record the value P as the stop value S (i.e., let S←P) in Step  7 . 
         [0067]    In the method for data extraction in part (b) of  FIG. 1C , assume the stop position S of data embedding is positive. In Step  11  of part (b) of  FIG. 1C , set P←S. In Step  12 , decode with the stopping value P and the value (P+1) and extract all the data until P+1 becomes a zero-point. In addition in Step  12 , move all the DCT coefficients histogram (greater than P+1) towards the left-hand side by one unit to eliminate the zero-point. If the amount of extracted data is less than C, set P←(−P−1). Continue to extract data until (P−1) becomes a zero-point. Then move the histogram (less than P−1) to the right-hand side by one unit to eliminate the zero-pint. 
         [0068]    Step  13  determines whether method for data extraction is finished (i.e., is the amount of extracted data less than C). If the answer at Step  13  is “NO” (i.e., some of the to-be-extracted bits have not been extracted at this point) and the answer to P&gt;0 is “YES” in Step  14 , let P←(−P−1) in Step  15  and move the histogram (i.e., less than P−1) to the right-hand side by one unit to eliminate a zero-point). Then continue the method for extracting by returning to Step  12  and extracting the remaining to-be-extracted data. 
         [0069]    Alternatively, if the answer at Step  23  is “NO” (i.e., some of the to-be-extracted bits have not been extracted at this point) and the answer to P&gt;0 is “No” in Step  14 , let P←(−P) in Step  16  and move the histogram (i.e., less than P−1) to the right-hand side by one unit to eliminate a zero-point). Then continue the method for extracting by returning to Step  12  and extracting the remaining to-be-extracted data. 
         [0070]    Alternatively, if the answer at Step  3  is “YES” (i.e., all the data has been extracted), then stop the method for extracting. Histogram shifting makes histogram more flat, thus embedding data into JPEG image file. Consider the horizontal axis of a histogram as representing the value of a set of selected mid- and lower frequency coefficients of an 8×8 block DCT that are integer-valued after JPEG quantization. 
         [0071]    Consider one selected point in a histogram with its feature, x, value (in the horizontal axis) equal to T, and its histogram value equal to h(T). Denote the length of to-be-embedded bit stream by L. If L≦h(T), this single T point is enough for data embedding. The whole histogram can be divided into three parts: (1) a central part; (2) a to-be-embedded part; and (3) an end part. The central part is the histogram whose value is less than T and kept intact during data embedding. The to-be-embedded part is the histogram pair whose values will change according to the to-be-embedded bits. The end part is the histogram whose value is greater than T and will be shifted outwards before data embedding. 
         [0072]      FIG. 2A  to  FIG. 2C  is a simple example to illustrate the histogram pair. Assume a simple image is the left part of  FIG. 2A . The right part of  FIG. 2A  is its histogram. We assume the threshold T is value 2. Then the central part is value 0, which is intact in data embedding. The end part is the value 3, which is going to shift to right side by one unit before data embedding in order to leave histogram value at x=3 empty for data embedding. After the edge histogram shifting, the new image and its corresponding histogram are shown in  FIG. 2B . Now the h(2) and h(3) becomes a histogram pair. 
         [0073]    In one histogram pair T and T+1, the rule for data embedding is: if the to-be-embedded bit is 0, the value is kept T. If the to-be-embedded bit is 1, the value becomes T+1. Now assume the to-be-embedded bits are [0,1,1], we scan the image from left to right and from top to down. Once we meet pixel value T, we check the to-be-embedded bit and change its value according to the be-be-embedded bit. In this way, after data embedding, the embedded image and its histogram are presented in  FIG. 2C . 
         [0074]    Consider the case of multiple selected pairs of points in histogram. If the length of to-be-embedded bit stream L&gt;h(T), then only one T (or one histogram pair) is not enough for data embedding. Then we need multiple T (or multiple histogram pairs) to embed data. These Ts are positive and negative in turn, such as [T,−T,T−1,−(T−1),T−2,−(T−2), . . . , S]. Same as the case of single T, the histogram is also divided into three parts: (1) a central part; (2) a to-be-embedded; and (3) an edge part. As discussed above, the central part is the histogram whose value is less than T and kept intact while data embedding. The to-be-embedded part is the histogram pair whose value will change according to the to-be-embedded bits. The end part is the histogram whose value is greater than T and will be shifted to outer end before data embedding. After histogram shifting, the histogram pairs are [&lt;h(T),h(T+1)=0&gt;, &lt;h(−T−1)=0,h(−T)&gt;, &lt;h(T−1),h(T)=0&gt;, &lt;h(−T)=0,h(−(T−1))&gt;, &lt;h(T−2),h(T−1)=0&gt;, &lt;h(−(T−1)=0,h(−(T−2))&gt;, . . . ]. When the embedding process stops, if the S is negative, then the histogram pair is &lt;h(S−1)=0,h(S)&gt;. If the S is positive, then the histogram pair is &lt;h(S),h(S+1)=0&gt;. 
         [0075]    As an example of reversible data embedding using single histogram pair, assume samples are X=[a,a,a,a], i.e., the number of samples is M=4, feature values xε{a,b} are greater than 0. There is one histogram pair h=[ 4,0 ]. Suppose that the to-be-embedded binary sequence is D=[1,0,0,1] whose length L is equal to 4, i.e., L=4. 
         [0076]    During data embedding, we scan the sequence X=[a,a,a,a] in a certain sequencing, say, from left to right. When we meet the first a, since we want to embed bit  1 , we change a to its expansion position, b. For the next two to-be-embedded bits, since they are bit  0 , we keep a in its original position, i.e., we do not change a. For the last to-be-embedded bit  1 , we change a to b. Therefore, after the four-bit embedding, we have X=[b,a,a,b], and the histogram is now h=[2,2]. Embedding capacity is C=L=4. Data extraction, or histogram pair recovery, is the reverse process of the above mentioned data embedding. After extracting the data D=[1,0,0,1], the histogram pair becomes [ 4,0 ] and we recover X=[a,a,a,a] losslessly. Note that after data embedding, histogram is changed from h=[ 4,0 ] to h=[2,2], histogram is completely flat and hence we cannot embed data any more. 
         [0077]    As another example of reversible data embedding we examine the method when using two loops. Given a 3×3 image, the feature values are xε{a,b,c,d}, where features are all greater than 0. According to the scan order, say, from left to right and from top to bottom, the samples X become X=[a,a,a,a,a,a,a,a,a], the total number of samples M=9, histogram is h=[ 9,0 ,0,0], as shown in FIG.  2 D(a). The histogram pair is h=[ 9,0 ]. The to-be-embedded bit sequence is D=[0,1,0,0,1,0,1,1,0] and L=9. 
         [0078]    In the first data embedding loop “Loop 1,” since the first to-be-embedded bit is 0, use the original feature position a (meaning no change for the first a), the second bit is 1, use the expansion position (meaning change a to b). In this way, we totally embed 9 bits, after data embedding, the samples become X=[a,b,a,a,b,a,b,b,a], refer to FIG.  2 D(b). After the first embedding loop, the histogram h=[ 9,0 ,0,0] becomes h=[5, 4,0 ,0]. The payload is C 1 =L=9 bits. 
         [0079]    For the second data embedding loop “Loop 2,” expanding the first: the histogram pair h=[ 4,0 ] is shifted towards the right-hand side by one position, thus producing the histogram with two histogram pairs h=[ 5,0 , 4,0 ] and the samples become X=[a,c,a,a,c,a,c,c,a], refer to FIG.  2 D(c). The second embedding loop will separately use the two histogram pairs in h=[5,0,4,0], xε{a,b,c,d} in order to avoid confliction. That is, it first uses the histogram pair with larger absolute feature values, then uses the histogram pair with smaller absolute feature values. In this example, we first embed data into the right histogram pair, then into the left histogram pair. The to-be-embedded bit sequence D=[0,1,0,0,1,0,1,1,0] is separated into two parts accordingly. That is, we first embed the front portion of data D 1 =[0,1,0,0] into the histogram pair at the right side h=[ 4,0 ], xε{c, d}, resulting in the corresponding samples X 1 =[c,d,c,c]. Then, we embed the remaining data D 2 =[1,0,1,1,0] into the left histogram pair h=[ 5,0 ], xε{a,b}, resulting in the corresponding samples X 2 =[b,a,b,b,a]. After Loop2, the histogram becomes h=[2,3,3,1] and the samples become X=[b,c,a,b,d,b,c,c,a],  FIG. 2(   d ). The embedding capacity in Loop 2 is C 2 =L=9 bits. 
         [0080]    The total capacity after two embedding loops is C=18 bits. After two embedding loops, histogram changes from h=[ 9,0 ,0,0] to h=[2,3,3,1]. It is observed that the histogram has changed from rather sharp ([9,0,0,0]) to relatively flat ([2,3,3,1]). 
         [0081]    The principles of thresholding are discussed in the following paragraphs. Histogram pair based lossless data hiding seeks not only higher embedding capacity but also higher visual quality of stego images measured by, say, PSNR (peak signal noise ratio). For instance, we may embed data with sufficient payload for annotation (such as caption) or for security (such as authentication) with reversibility as well as the highest possible PSNR of the stego image with respect to the cover image. 
         [0082]    In the background art, it was thought that one way to improve the PSNR is to use only a part of JPEG coefficients with small absolute values. In doing so, we need the so-called thresholding technique. The thresholding method is to first set a threshold T, then embed data into those JPEG coefficients, x, with |x|≦T. That is, it does not embed data into the JPEG coefficients with |x|&gt;T. In addition, it makes sure that the small JPEG coefficients after data embedding will not conflict (will not be confused) with the large JPEG coefficients with (|x|&gt;T). That is, for the JPEG coefficients satisfying |x|≦T, histogram pair based data embedding is applied. It requires that after data embedding, the coefficients between −T≦x≦T will be separable from the coefficients with |x|&gt;T. The simple thresholding will divide the whole histogram into two parts: 1) the data-to-be embedded region, where the JPEG coefficients absolute value is small; and 2) no data-to-be embedded region named end regions, where the JPEG coefficients&#39; absolute value is large. 
         [0083]    Our experimental works have indicated that the smallest threshold T does not necessarily lead to the highest PSNR for a given data embedding capacity. Instead, it is found that for a given data embedding capacity there is an optimum value of T. This can be justified as follows. If a smaller threshold T is selected, the number of coefficients with |x|&gt;T will be larger. This implies that more coefficients with |x|&gt;T need to be moved away from 0 in order to create histogram pair(s) to losslessly embed data. This may lead to a lower PSNR and more side information (hence smaller embedding capacity). Therefore in embodiments of the invention, optimum histogram pair lossless embedding, and the best threshold T for a given data embedding capacity is selected to achieve the highest PSNR. Discussion about the optimum parameters and experimental results are further discussed below. 
         [0084]      FIG. 3A  to  FIG. 3C  is an example for multiple histogram pairs.  FIG. 3A  is the original image and the corresponding histogram. Since the bit stream length is 4, it is not enough to rely on the histogram h(T)=3 of one single T (T=2). Hence the new T sequence is x=T, S=−T]. Now in  FIG. 3A , T=2; S=−2 produce two histogram pairs. After shifting the edge part of the histogram to the outer, the new image and the histogram is presented in  FIG. 3B . Now it produces two histogram pair &lt;h(2)=3,h(3)=0&gt; and &lt;h(−3)=0,h(−2)=1&gt;. Similar as the case of one histogram pair, after data embedding, the embedded image and its corresponding histogram are shown in  FIG. 3C . 
         [0085]    The following is a discussion of maximum data embedding capacity. When the stop point S is negative, then the capacity is: 
         [0000]    
       
         
           
             
               
                 
                   ∑ 
                   
                     - 
                     T 
                   
                 
                 S 
               
                
               
                 h 
                  
                 
                   ( 
                   x 
                   ) 
                 
               
             
             + 
             
               
                 
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                
               
                 
                   h 
                    
                   
                     ( 
                     x 
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    It produces 2(T−|S|+1) histogram pairs. When the stop point S is positive, the capacity is 
         [0000]    
       
         
           
             
               
                 
                   ∑ 
                   
                     - 
                     T 
                   
                 
                 
                   
                     - 
                     S 
                   
                   - 
                   1 
                 
               
                
               
                 h 
                  
                 
                   ( 
                   x 
                   ) 
                 
               
             
             + 
             
               
                 
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                 T 
               
                
               
                 
                   h 
                    
                   
                     ( 
                     x 
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    It produces 2(T−|S|+1)−1 histogram pairs. 
         [0086]    In addition, when the stop point S is 0, the capacity is: 
         [0000]    
       
         
           
             
               
                 
                   
                     ∑ 
                     
                       - 
                       T 
                     
                   
                   
                     - 
                     1 
                   
                 
                  
                 
                   h 
                    
                   
                     ( 
                     x 
                     ) 
                   
                 
               
               + 
               
                 
                   
                     ∑ 
                     0 
                   
                   T 
                 
                  
                 
                   h 
                    
                   
                     ( 
                     x 
                     ) 
                   
                 
               
             
             = 
             
               
                 
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                 T 
               
                
               
                 
                   h 
                    
                   
                     ( 
                     x 
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    It produces 2T histogram pairs. When T includes all the histogram value, in that case, the capacity is largest. It equals the integral of the histogram. 
         [0087]    The maximum PSNR is discussed in the following paragraphs. When threshold T is small, the capacity is also small. Experimental results demonstrate that when the threshold T is large, it will increase the PSNR. Hence, if the length of to-be-embedded bit stream is fixed, we can get the highest PSNR and its corresponding threshold T through experiments. 
         [0088]    An example of a histogram pair based lossless data embedding is discussed in the following paragraphs. In this example, the to-be-embedded bit sequence D=[1 10 001] has six bits and will be embedded into an image by using the proposed histogram pair scheme with threshold T=3, and stop value S=2. The dimensionality of the image is 5×5, as shown in FIG.  2 E(a). The image has 12 distinct feature (grayscale) values, i.e., xε{−5,−4,−3,−2,−1,0,1,2,3,4,5,6}. The grayscale values of this image have the histogram h 0 =[0,1,2,3,4,6,3,3,1,2,0,0] (as shown in 1 st  row of  FIG. 2F ). As said before, for x≧0, the histogram pair is of form h=[ m,0 ], for x&lt;0, the histogram pair is h=[ 0,n ]. The second row of  FIG. 2F  is expanded image histogram: h 1  (expanded), it has three histogram pairs. The first histogram pair is in the far-right-hand side h=[ 1,0 ]; the second histogram pair is in the left-hand side h=[ 0,2 ]; the third histogram pair is in the right-hand side near the center h=[ 3,0 ]. The third row of  FIG. 2F  is the image histogram after data embedding; h 2  (bits embedded). 
         [0089]      FIG. 2F  and Table 1 use red line square to mark the third histogram pair. The first histogram pair [ 1,0 ] is used to embed the 1 st  bit  1 , the second histogram pair[ 0,2 ] is used to embed the next two bits  1 , 0 , and the third histogram pair [ 3,0 ] is used to embed three bits:  0 , 0 , 1 . During expanding, we 1 st  making h(4)=0, then making h(−4)=0, finally making h(3)=0. During each zero-point creation the histogram shifting towards one of two (left and right) ends is carried out, the resultant histogram becomes h 1 =[1, 0,2 ,3,4,6,3, 3,0 , 1,0 .2] (refer to FIG.  2 E(c) and 2 nd  row of  FIG. 2F ). There histogram pairs are thus produced: in the right-most h=[ 1,0 ], in the left h=[ 0,2 ] and in the right (near center) h=[ 3,0 ]. 
         [0090]    After data embedding with bit sequence D=[1 10 001] with the selected scanning order (from right to left and from top to bottom), the histogram becomes h 2 =[1,1,1,2,4,6,3,2,1,0,1,2] (refer to FIG.  2 E(c) and 3 rd  row of  FIG. 2F ). The three histogram pairs changed: in the right most from h=[ 1,0 ] to h=[0,1], in the left from h=[ 0,2 ] to h=[1,1], and in the right (near center) from h=[ 3,0 ] to h=[2,1] 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1.0 
               
               
                   
               
               
                 Example of histogram pair based data embedding with T = 3, S = 2, D = [1 10 001] 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 X 
                 −5 
                 −4 
                 −3 
                 −2 
                 −1 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                 2 
                 h 0   
                 0 
                 1 
                 2 
                 3 
                 4 
                 6 
                 3 
                 3 
                 1 
                 2 
                 0 
                 0 
               
               
                   
                 (original) 
               
               
                 3 
                 h 1   
                 1 
                 0 
                 2 
                 3 
                 4 
                 6 
                 3 
                 3 
                 0 
                 1 
                 0 
                 2 
               
               
                   
                 (expanded) 
               
               
                 4 
                 h 2  (bits 
                 1 
                 1 
                 1 
                 2 
                 4 
                 6 
                 3 
                 2 
                 1 
                 0 
                 1 
                 2 
               
               
                   
                 embedded) 
               
             
          
           
               
                 5 
                 embedded 
                 no 
                 [1 0] 
                 no 
                 [001] 
                 [1] 
                 no 
               
               
                   
                 (ordering) 
                 embedding 
                 embedded 
                 embedding 
                 embedded 
                 embedded 
                 embedding 
               
               
                   
                   
                   
                 (second) 
                   
                 (third) 
                 (first) 
               
               
                   
               
             
          
         
       
     
         [0091]    After data embedding, not only the image pixel values but also three histogram pairs have been changed. For example, embedding the last three bits  0 , 0 , 1  causes the histogram pair at the right-hand side (near center) to change from h=[ 3,0 ] to h=[2,1], and three image pixel values marked with small rectangles (in red) to change from [2,2,2] to [2,2,3] (refer to FIG.  2 E(c) and 3 rd  row of  FIG. 2F ). Through this example, it becomes clear that the threshold can also be viewed as the starting point to implement histogram pair lossless data hiding. 
         [0092]    Formulae of lossless data hiding based on histogram pairs are discussed in the following paragraphs. The proposed method divides the whole histogram into three parts: (1) the part where data to be embedded; (2) central part—no data embedded and the absolute value of coefficients is small; (3) end part—no data embedded and the absolute value of coefficients is large. The whole embedding and extraction procedure can be expressed by the formulae in Table 2 below. 
         [0093]    In Table 2, T is selected threshold, i.e., start position, S is stop position, x is feature (JPEG coefficient) values before embedding, x′ is feature values after embedding, u(S) is unit step function (when S≧0; u(S)=1, when S&lt;0; u(S)=0), └x┘ rounds x to the largest integer not larger than x. 
         [0000]                                                        TABLE 2                   Formulae of lossless data hiding based on histogram pairs                Embedding   Recovering                after       after           parts of histogram   embedding   condition   recovering   condition               Data to be   x′ = 2x + b − |S|   |S| ≦ x ≦ T   x = └(x′ + |S|)/2┘, b = x′ + |S| − 2x   |S| ≦ x′ ≦ 2T − 1 − |S|       embedded region       (right side)       (positive or zero)       Data to be   x′ = 2x − b + |S| + u(S)   −T ≦ x ≦ − |S| − u(S)   x = └(x′ − |S| − u(S) + 1)/2┘   −2T − 1 + |S| + u(S) ≦ x′ ≦ −|S| − u(S)       embedded region           b = x′ − |S| − u(S) − 2x       (left side)       (negative)       Central part   x′ = x   −|S| − u(S) &lt; x &lt; |S|   x = x′   −|S| − u(S) &lt; x′ &lt; |S|       (small absolute       value)       Right edge part   x′ = x + T + 1 − |S|   x &gt; T   x = x′ − T − 1 + |S|   x′ &gt; 2T + 1 − |S|       (positive)       Left edge part   x′ = x − T − 1 + |S| + u(S)   x &lt; − T   x = x′ + T + 1 − |S| − u(S)   if x′ &lt; −2T − 1 + |S| + u(S)       (negative)                    
Moreover, the formulae corresponding to the above example are listed in Table 3 below.
 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Formulae of third example (T = 3; S = +2, 6 bit data D = [1 10 001]) 
               
             
          
           
               
                   
                 Embedding 
                 Recovering 
               
             
          
           
               
                   
                 after 
                   
                 after 
                   
               
               
                   
                 embedding 
                 condition 
                 recovering 
                 condition 
               
               
                   
                   
               
             
          
           
               
                 right to- 
                 x′ = 2x + b − 2 
                 if 2 ≦ x ≦ 3 
                 x = floor((x′ + 2)/2), 
                 if 2 ≦ x′ ≦ 5 
               
               
                 be- 
                 b = 0: x′ = [2, 4] 
                 b = 0: x = [2, 3] 
                 b = x′ + 2 − 2x 
                 b = 0: x′ = [2, 4] 
               
               
                 embedded 
                 b = 1: x′ = [3, 5] 
                 b = 1: x = [2, 3] 
                 b = 0: x = [2, 3] 
                 b = 1: x′ = [3, 5] 
               
               
                   
                   
                   
                 b = 1: x = [2, 3] 
               
               
                 left to-be- 
                 x′ = 2x − b + 3 
                 if −3 ≦ x ≦ −3 
                 x = floor((x′ − 2)/2), 
                 if −4 ≦ x′ ≦ −3 
               
               
                   
                 b = 0: x′ = [−3] 
                 b = 0: x = [−3] 
                 b = x′ − 3 − 2x 
                 b = 0: x′ = [−3] 
               
               
                 embedded 
                 b = 1: x′ = [−4] 
                 b = 1: x = [−3] 
                 b = 0: x = [−3] 
                 b = 1: x′ = [−4] 
               
               
                   
                   
                   
                 b = 1: x = [−3] 
               
               
                 central 
                 x′ = x 
                 if −2 &lt; x &lt; 2 
                 x = x′ 
                 if −2 − u(S) &lt; x′ &lt; |S| 
               
               
                   
                 x′ = [−2, −1, 0, 1] 
                 x = [−2, −1, 0, 1] 
                 x = [−2, −1, 0, 1] 
                 x′ = [−2, −1, 0, 1] 
               
               
                 right end 
                 x′ = x + 2 
                 if x &gt; 3 
                 x = x′ − 2 x = [4] 
                 if x′ &gt; 5 x′ = [6] 
               
               
                   
                 x′ = [6] 
                 x = [4] 
               
               
                 left end 
                 x′ = x − 1 
                 if x &lt; −3 
                 x = x′ + 1 x = [−4] 
                 if x′ &lt; −4 
               
               
                   
                 x′ = [−5] 
                 x = [−4] 
                   
                 x′ = [−5] 
               
               
                   
               
             
          
         
       
     
         [0094]    The selection of JPEG coefficients (i.e., JPEG quantized 8×8 Block DCT Coefficients) used for lossless data hiding is discussed in the following paragraph. In order to make data embedding less perceivable and make hidden data more robust, we may choose lower- and mid-frequency coefficients to embed data in the implementation of our invented technology. Among all of the JPEG coefficients, we determined the part of JPEG coefficients that has the best performance. In particular, we scan all of JPEG quantized 8×8 block DCT coefficients in the zigzag way to produce the histogram and data is embedded through histogram pairs based scheme as described above. 
         [0095]      FIG. 4A  to  FIG. 4C  show three regions of selected JPEG coefficients for data embedding. Experimental results in terms of PSNR of the stego images with respect to thresholds T when embedding of 500 bits into these different parts of the JPEG coefficients are shown in  FIG. 5 ,  FIG. 6 , and  FIG. 7 , respectively. Data was embed in the region of {16, 36} in  FIG. 4A , {4,36} in  FIG. 4B  and {16,49} in  FIG. 4C  of the DCT coefficients. Since the histogram of the DCT coefficients in {16, 36} and {16,49} are more concentrated, the maximum shown threshold T value in  FIG. 4A  to  FIG. 4C  is taken as 15. On the other hand, for {4, 36} (i.e.,  FIG. 4A ), the maximum shown threshold T value is taken as 40. In general, the region of {4,36} appears to bring out better performance. 
         [0096]    The results of our analysis of Lossless Data Hiding in JPEG Image Files produced by embodiments of the invention are discussed below. Some experiments on JPEG images with Q-factor equal 80 were done to evaluate the performance of embodiments of the invention. In particular, the test images used are: Lena.jpg (512×512), Barbara.jpg (512×512) and Baboon.jpg (512×512). The data is embedded in the JPEG coefficients in the region of {4, 36}. The experimental results are presented in Table 4 below. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Lossless data hiding in three commonly used 512 × 512 JPEG Images with 
               
               
                 Q-factor 80 and the region of selected region of JPEG coefficients R = {4, 36}. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Payload 
                 0.0004 
                 0.0011 
                 0.0019 
                 0.003 
                 0.0038 
                 0.0114 
               
               
                   
                 bpp (bits) 
                 (100) 
                 (300) 
                 (500) 
                 (800) 
                 (1000) 
                 (3000) 
               
               
                   
               
               
                 Lena 
                 PSNR 
                 58.4707 
                 53.7209 
                 52.6613 
                 51.0275 
                 49.8880 
                 44.9344 
               
               
                   
                 T(begin) 
                 12 
                 9 
                 5 
                 6 
                 5 
                 2 
               
               
                   
                 S(stop) 
                 12 
                 −9 
                 5 
                 −6 
                 −5 
                 −2 
               
               
                   
                 time(sec) 
                 0.182 
                 0.373 
                 0.179 
                 0.382 
                 0.375 
                 0.342 
               
               
                   
                 JPEG(bit) 
                 37956 
                 37980 
                 38024 
                 38119 
                 38120 
                 38913 
               
               
                 Baboon 
                 PSNR 
                 58.2083 
                 53.1640 
                 51.6615 
                 49.4362 
                 48.4424 
                 43.2057 
               
               
                   
                 T(begin) 
                 19 
                 16 
                 14 
                 8 
                 10 
                 5 
               
               
                   
                 S(stop) 
                 19 
                 −16 
                 −14 
                 8 
                 −10 
                 −5 
               
               
                   
                 time(sec) 
                 0.192 
                 0.44 
                 0.363 
                 0.194 
                 0.387 
                 0.414 
               
               
                   
                 JPEG(bit) 
                 78696 
                 78675 
                 78771 
                 78735 
                 78776 
                 79387 
               
               
                 Barbara 
                 PSNR 
                 58.3384 
                 53.3831 
                 51.2756 
                 48.5166 
                 48.3079 
                 43.5953 
               
               
                   
                 T(begin) 
                 13 
                 11 
                 9 
                 7 
                 7 
                 4 
               
               
                   
                 S(stop) 
                 13 
                 −11 
                 −9 
                 −7 
                 −7 
                 −4 
               
               
                   
                 time(sec) 
                 0.18 
                 0.372 
                 0.552 
                 0.364 
                 0.404 
                 0.387 
               
               
                   
                 JPEG(bit) 
                 48361 
                 48406 
                 48406 
                 48483 
                 48555 
                 48678 
               
               
                   
               
               
                   
                 Payload 
                 0.0191 
                 0.1 
                 0.2 
                 0.3 
                 0.4 
                 0.5 
               
               
                   
                 bpp (bits) 
                 (5000) 
                 (26214) 
                 (52429) 
                 (78643) 
                 (104858) 
                 (131072) 
               
               
                   
               
               
                 Lena 
                 PSNR 
                 44.4357 
                 36.5374 
                 32.5016 
                 30.9442 
                 29.7305 
                 27.6371 
               
               
                   
                 T(begin) 
                 2 
                 2 
                 0 
                 0 
                 1 
                 6 
               
               
                   
                 S(stop) 
                 −2 
                 −1 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 time(sec) 
                 0.367 
                 0.745 
                 0.187 
                 0.204 
                 0.597 
                 2.474 
               
               
                   
                 JPEG(bit) 
                 38913 
                 42884 
                 52486 
                 57733 
                 60792 
                 65090 
               
               
                 Baboon 
                 PSNR 
                 41.5645 
                 33.2079 
                 27.8094 
                 27.1292 
                 24.6459 
                 21.8980 
               
               
                   
                 T(begin) 
                 4 
                 1 
                 1 
                 1 
                 3 
                 13 
               
               
                   
                 S(stop) 
                 −4 
                 −1 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 time(sec) 
                 0.417 
                 0.671 
                 0.623 
                 0.592 
                 1.571 
                 5.392 
               
               
                   
                 JPEG(bit) 
                 79387 
                 84610 
                 91659 
                 94485 
                 98173 
                 100922 
               
               
                 Barbara 
                 PSNR 
                 40.2392 
                 33.8112 
                 31.8271 
                 30.5232 
                 28.5581 
                 24.8663 
               
               
                   
                 T(begin) 
                 1 
                 0 
                 0 
                 0 
                 1 
                 7 
               
               
                   
                 S(stop) 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 time(sec) 
                 0.176 
                 0.171 
                 0.193 
                 0.204 
                 0.6120 
                 2.941 
               
               
                   
                 JPEG(bit) 
                 49903 
                 57623 
                 62525 
                 67062 
                 70639 
                 74112 
               
               
                   
               
             
          
         
       
     
         [0097]    For the 512×512 JPEG Lena images with different Q-factors (30, 40, 50, 60, 70, 80, 90, 100), the experimental results when 1000 bits are embedded into JPEG coefficients in the range of {4,36} are listed in Table 5 below. 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Experimental results with 1000 bits embedded into 512 × 512 Lena JPEG 
               
               
                 Image (0.0038 bpp) with various Q-factors (the JPEG coefficient region 
               
               
                 selected for data embedding is R = {4, 36}). 
               
             
          
           
               
                   
                 Q-factors 
               
             
          
           
               
                   
                 30 
                 40 
                 50 
                 60 
                 70 
                 80 
                 90 
                 100 
               
               
                   
                   
               
             
          
           
               
                 PSNR 
                 41.7598 
                 44.5994 
                 45.3630 
                 46.0381 
                 47.9433 
                 49.8880 
                 52.9991 
                 58.2008 
               
               
                 T 
                 2 
                 2 
                 2 
                 2 
                 4 
                 5 
                 7 
                 9 
               
               
                 S 
                 −2 
                 2 
                 2 
                 2 
                 −4 
                 −5 
                 −7 
                 9 
               
               
                 Time (sec) 
                 0.337 
                 0.179 
                 0.185 
                 0.1841 
                 0.364 
                 0.375 
                 0.392 
                 0.358 
               
               
                 Original 
                 15,159 
                 18,027 
                 20,919 
                 24,076 
                 29,294 
                 37,937 
                 59,197 
                 162,247 
               
               
                 image file 
               
               
                 size (bits) 
               
               
                 Image file 
                 15,423 
                 18,216 
                 21,142 
                 24,359 
                 29,403 
                 38,120 
                 59,419 
                 162,437 
               
               
                 size after 
               
               
                 data 
               
               
                 embedding 
               
               
                 (bits) 
               
               
                 Image file 
                 264 
                 189 
                 −777 
                 283 
                 109 
                 −817 
                 222 
                 190 
               
               
                 size 
               
               
                 increase 
               
               
                 after data 
               
               
                 embedding 
               
               
                 (bits) 
               
               
                 Image file 
                 1.7% 
                 1.0% 
                 1.1% 
                 1.2% 
                 0.4% 
                 0.5% 
                 0.4% 
                 0.1% 
               
               
                 size 
               
               
                 increase 
               
               
                 after data 
               
               
                 embedding 
               
               
                 (%) 
               
               
                   
               
             
          
         
       
     
         [0098]    In the background art reference entitled: “Lossless data embedding with file size preservation,” by Fridrich et al. discussed above, the highest payload reported in their experimental results on 50 images was 0.0176 bpp. In contrast, as the experimental results indicated Table 4 and Table 5 suggest, for all of three commonly used images, embodiments of the invention can easily embed 0.0191, 0.1, 0.2, 0.3, 0.4, and 0.5 bpp. That is, embodiments of the invention can embed much more data into JPEG images than the background art. 
         [0099]    In addition, embodiments of the invention can keep data-size increases unnoticeable (e.g., when compared with the original JPEG image (before data embedding)). Specifically, when embedding 1000 bits to three commonly used JPEG images with Q-factor ranges from 30 to 100, the image size increase after embedding ranges from 1.7% (264 bits) to 0.1% (190 bits). 
         [0100]    Further, The PSNR versus payload of these three images is shown from  FIG. 8  to  FIG. 11  and  FIG. 12  to  FIG. 26  is some images after embedding different amount of data (i.e., small payload and large payload). These figures indicate that the embodiments of invention work well with JPEG images with Q-factor equal 80. 
         [0101]    The advantages of embodiments of the invention over the background art include, but are not limited to:
       a. the histogram pair based lossless data hiding technique can be applied to JPEG quantized 8×8 block DCT coefficients, and the I-frame of MPEG videos;   b. the selection of optimum threshold and optimum JPEG coefficient region for data embedding can further improve the PSNR of stego images with a given payload;   c. the histogram pair JPEG image lossless data hiding technique does not noticeably increase the size of JPEG image file;   d. specifically, when 1000 bits are embedded into 512×512 Lena JPEG image (0.0038 bpp) with a Q-factor ranging from 30 to 100, the PSNR of the resultant stego images ranges from 41 dB to 58 dB;   e. further, before and after the data embedding, the increase of the JPEG file size ranges from 1.7% to 0.1%;   f. the amount of image-file-size increase ranges from 264 bits to 190 bits, which indicate satisfactory performance; and   g. compared to the background art, it appears that embodiments of the invention can achieve higher payload.       
 
         [0109]    Moreover,  FIG. 27  shows a plot of the curve of PSNR of images with hidden data with respect to the original images versus the varying Q-factors. In particular,  FIG. 27  indicates that embodiments of the present invention also work for different Q-factors well. 
         [0110]    It will, of course, be understood that, although particular embodiments have just been described, the claimed subject matter is not limited in scope to a particular embodiment or implementation. For example, one embodiment may be in hardware, such as implemented to operate on a device or combination of devices, for example, whereas another embodiment may be in software. Likewise, an embodiment may be implemented in firmware, or as any combination of hardware, software, and/or firmware, for example. Likewise, although claimed subject matter is not limited in scope in this respect, one embodiment may comprise one or more articles, such as a storage medium or storage media. This storage media, such as, one or more CD-ROMs and/or disks, for example, may have stored thereon instructions, that when executed by a system, such as a computer system, computing platform, or other system, for example, may result in an embodiment of a method in accordance with claimed subject matter being executed, such as one of the embodiments previously described, for example. As one potential example, a computing platform may include one or more processing units or processors, one or more input/output devices, such as a display, a keyboard and/or a mouse, and/or one or more memories, such as static random access memory, dynamic random access memory, flash memory, and/or a hard drive. For example, a display may be employed to display one or more queries, such as those that may be interrelated, and or one or more tree expressions, although, again, claimed subject matter is not limited in scope to this example. Likewise, an embodiment may be implement as a system, or as any combination of components such as computer systems, mobile and/or other types of communication systems and other well known electronic systems. 
         [0111]    In the preceding description, various aspects of claimed subject matter have been described. For purposes of explanation, specific numbers, systems and/or configurations were set forth to provide a thorough understanding of claimed subject matter. However, it should be apparent to one skilled in the art having the benefit of this disclosure that claimed subject matter may be practiced without the specific details. In other instances, well known features were omitted and/or simplified so as not to obscure the claimed subject matter. While certain features have been illustrated and/or described herein, many modifications, substitutions, changes and/or equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and/or changes as fall within the true spirit of claimed subject matter.