Chapter 1 Introduction
1.5 Dissertation Organization
The remainder of this dissertation is organized as follows. In Chapter 2, the proposed large-volume data hiding technique for secure image transmission is described. In Chapter 3, the proposed new data hiding technique on encrypted images based on the techniques of double image encryption and spatial correlation comparison is described. The proposed new data hiding technique via creations of fake collaboratively-written documents on collaborative writing platforms is presented in Chapter 4. In Chapter 5, the proposed new data hiding technique via message-rich character images is described, while the proposed new data hiding technique via message-rich code images is described in Chapter 6. Finally, conclusions of this study and some suggestions for future researches are included in the last chapter.
Chapter 2
A New Data Hiding Technique via
Secret-fragment-visible Mosaic Images by Nearly-reversible Color Transformation
2.1 Introduction
Data hiding is useful for applications like covert communication, copyright protection, document authentication, secret keeping, etc. Many methods for data hiding via images have been proposed [6]-[16]. In order to reduce the distortion of the resulting image, an upper bound for the distortion value is usually set on the payload of the cover image. A discussion on this rate-distortion issue can be found in [41].
Thus, a main issue of the methods for hiding data in images is the difficulty to embed a large amount of message data into a single image.
Specifically, if one wants to hide a secret image into a cover image with the same size, the secret image must be highly compressed in advance. For example, for a data hiding method with an embedding rate of 0.5 bits per pixel, a secret image with 8 bits per pixel must be compressed at a rate of at least 93.75% beforehand in order to be hidden into a cover image. But, for many applications, such as keeping or transmitting medical pictures, military images, legal documents, etc., that are valuable with no allowance of serious distortions, such data compression operations are usually impractical. Moreover, most image compression methods, such as JPEG compression, are not suitable for line drawings and textual graphics, where sharp contrasts between adjacent pixels are often destructed to become noticeable artifacts after being compressed [42].
Therefore, most existing methods can hide only text messages or images with small data volumes into cover images. However, in a recently published paper by Lai and Tsai [39], a new type of computer art image was presented, called secret-fragment-visible mosaic image, which is the result of rearrangement of the fragments of a secret image in disguise of another image called target image pre-selected from a database. The above-mentioned difficulty of hiding a huge volume of image data behind a cover image is solved automatically by the use of this
type of mosaic image, where a secret image of the same size is hidden in the mosaic image without any compression.
In more detail, as illustrated by Figure 2.1, a given secret image is first
“chopped” into tiny rectangular fragments, and a target image with a similar color distribution is selected from a database. Then, the fragments are arranged by using a fast greedy algorithm to fit into the blocks of the target image, yielding an image with a mosaic appearance looking like the target image. The mosaic image preserves all the secret image fragments in appearance, but no one can figure out what the original secret image looks like due to the tiny sizes and the randomness of the re-arranged fragments. The method may be adopted as a new way for secure keeping of secret images.
Figure 2.1. Illustration of creation of secret-fragment-visible mosaic image proposed in [39].
However, using their method, the user is not allowed to select freely his/her favorite image for use as the target image. It is therefore desired in this study to remove this weakness of the method while keeping its merit, that is, it is aimed to design a new method to transform a secret image into a secret-fragment-visible mosaic image of the same size that has the visual appearance of any freely-selected target image without the need of a database.
Specifically, after a target image is selected arbitrarily, the given secret image is first divided into rectangular fragments called tile images, which then are fit into
similar blocks in the target image, called target blocks, according to a similarity criterion based on color variations. Next, the color characteristic of each tile image is transformed to become that of the corresponding target block in the target image, resulting in a mosaic image which looks like the target image. Relevant schemes are also proposed to conduct nearly lossless recovery of the original secret image from the resulting mosaic image. The proposed method is new in the fact that it can transform a secret image into a disguising mosaic image without compression, while other data hiding methods must hide a highly compressed version of the secret image into a cover image when the secret image and the cover image have the same data volume.
2.2 Idea of Proposed Method
The proposed method includes two main phases as shown by the flow diagram of Figure 2.2: 1) mosaic image creation; and 2) secret image recovery.
In the first phase, a mosaic image is yielded, which consists of the fragments of an input secret image with color corrections according to a similarity criterion based on color variations. The phase includes four stages as described in the following.
Stage 1-1 – fit the tile images of the secret image into the target blocks of a pre-selected target image.
Stage 1-2 – transform the color characteristic of each tile image in the secret image to become that of the corresponding target block in the target image.
Stage 1-3 – rotate each tile image into a direction with the minimum RMSE value with respect to its corresponding target block.
Stage 1-4 – embed relevant information into the created mosaic image for future recovery of the secret image.
And in the second phase, the embedded information is extracted to recover nearly losslessly the secret image from the generated mosaic image. The phase includes two stages as described in the following.
Stage 2-1 – extract the embedded information for secret image recovery from the mosaic image.
Stage 2-2 – recover the secret image using the extracted information.
Figure 2.2. Flow diagram of the proposed method.
2.3 Problems and Proposed Solutions for Mosaic Image Creation
Problems encountered in generating mosaic images are discussed in this section with solutions to them proposed.
A. Color Transformations between Blocks
In the first phase of the proposed method, each tile image T in the given secret image is fit into a target block B in a pre-selected target image. Since the color characteristics of T and B are different from each other, how to change their color distributions to make them look alike is the main issue here. Reinhard et al. [43]
proposed a color transfer scheme in this aspect, which converts the color characteristic of an image to be that of another in the l color space. This idea is an answer to the issue and is adopted in this study, except that the RGB color space instead of the l
one is used to reduce the volume of the required information for recovery of the original secret image.
More specifically, let T and B be described as two pixel sets {p1, p2, …, pn} and {p1′, p2′, …, pn′}, respectively. Let the color of each pi be denoted by (ri, gi, bi) and that of each pi′ by (ri′, gi′, bi′). At first, we compute the means and standard deviations of T and B, respectively, in each of the three color channels R, G, and B by the following formulas:
1 1 verified easily that the new color mean and variance of the resulting tile image T′ are equal to those of B, respectively. To compute the original color values (ri, gi, bi) of pi formula are all real numbers, and it is impractical to embed real numbers, each with many digits, in the generated mosaic image. Therefore, we limit the numbers of bits used to represent relevant parameter values in (3) and (4). Specifically, for each color channel we allow each of the means of T and B to have 8 bits with its value in the range of 0 to 255, and the standard deviation quotient qc in (3) to have 7 bits with its value in the range of 0.1 to 12.8. That is, each mean is changed to the closest value in the range of 0 to 255, and each qc is changed to the closest value in the range of 0.1 to 12.8. We do not allow qc to be 0 because otherwise the original pixel value cannot be recovered back by (4) for the reason that 1/qc in (4) is not defined when qc = 0.
B. Choosing Appropriate Target Blocks and Rotating Blocks to Fit Better with Smaller RMSE Value
In transforming the color characteristic of a tile image T to be that of a corresponding target block B as described above, how to choose an appropriate B for each T is an issue. For this, as shown in Figure 2.3, we use the standard deviation of the colors in the block as a measure to select the most similar B for each T. Specially, we sort all the tile images to form a sequence, Stile, and all the target blocks to form another, Starget, according to the average values of the standard deviations of the three color channels. Then, we fit the first in Stile into the first in Starget, fit the second in Stile
into the second in Starget, and so on.
Figure 2.3. Illustration of fitting tile images into target blocks.
Additionally, after a target block B is chosen to fit a tile image T and after the color characteristic of T is transformed, we conduct a further improvement on the color similarity between the resulting tile image T′ and the target block B by rotating T′ into one of the four directions, 0o, 90o, 180o, and 270o, which yields a rotated
version of T′ with the minimum root mean square error (RMSE) value with respect to B among the four directions for final use to fit T into B. Furthermore, the color similariy between the resulting tile image T′ and the target block B is measured in the luminance channel only, instead of in the RGB three color channels, to reduce the execution time of the proposed method. Figure 2.4 shows a result of applying this block rotation scheme to the secret image and the target image shown in Figures 2.4(a) and 2.4(b), respectively, where Figure 2.4(c) is the mosaic image created without applying this scheme and Figure 2.4(d) is the one created instead. It can be seen that Figure 2.4(d) has a better fitting result with a smaller RMSE value than Figure 2.4(c).
(a) (b)
(c) (d)
Figure 2.4. Illustration of effect of rotating tile images before fitting them into target blocks. (a) Secret image. (b) Target image. (c) Mosaic image created from (a) and (b) without block rotations (with RMSE = 23.261). (d) Mosaic image created from (a) and (b) with block rotations (with RMSE = 20.870).
C. Handling Overflows/Underflows in Color Transformation
After the color transformation process is conducted as described previously, some pixel values in the new tile image T′ might have overflows or underflows. To deal with this problem, we convert such values to be non-overflow or non-underflow ones and record the value differences as residuals for use in later recovery.
Specifically, we convert all the transformed pixel values in T′ not smaller than 255 to be 255, and all those not larger than 0 to be 0. Next, we compute the differences between the original pixel values and the converted ones as the residuals and record them as part of the information associated with T′. Accordingly, the pixel values which are just on the bound of 255 or 0, however, cannot be distinguished from those with overflow/underflow values during later recovery since all the pixel values with overflows/underflows are converted to be 255 or 0 now. To remedy this, we define the residuals of those pixel values which are on the bound to be “0” and record them as well.
But as can be seen from (3), the ranges of possible residual values are unknown, and this causes a problem of deciding how many bits should be used to record a residual. To solve this problem, we record the residual values in the un-transformed color space rather than in the transformed one. That is, by using the following two formulas we compute first the smallest possible color value cS (with c = r, g, or b) in T that becomes larger than 255 as well as the largest possible value cL in T that becomes smaller than 0, respectively, after the color transformation process has been residuals of ci will all lie in the range of 0 to 255 as can be verified. Consequently, we can simply record each of them with 8 bits. And finally, because the residual values are centralized around zero, we use further in this study the Huffman encoding scheme to encode the residuals in order to reduce the numbers of required bits to represent them.
D. Embedding Information for Secret Image Recovery
In order to recover the secret image from the mosaic image, we have to embed relevant recovery information into the mosaic image. For this, we adopt a technique proposed by Coltuc and Chassery [44] and apply it to the least significant bits of the pixels in the created mosaic image to conduct data embedding. Unlike the classical LSB replacement methods [6], [45], [46], which substitute LSBs with message bits directly, the reversible contrast mapping method [44] applies simple integer transformations to pairs of pixel values. Specifically, the method conducts forward and backward integer transformations as follows, respectively, where (x, y) are a pair of pixel values and (x', y') are the transformed ones:
2 , 2
The information required to recover a tile image T which is mapped to a target block B includes: 1) the index of B; 2) the optimal rotation angle of T; 3) the truncated means of T and B and the standard deviation quotients, of all color channels; and 4) the overflow/underflow residuals. These data items for recovering a tile image T are integrated as a five-component bit stream of the form
M = t1t2…tmr1r2m1m2…m48q1q2…q21d1d2…dk, represent the rotation angle of T because there are four possible rotation directions; 3) 48 bits are required to represent the means of Tand B because we use eight bits to represent a mean value in each color channel; 4) it needs 21 bits to represent the quotients of T over B in the three color channels with each channel requiring 7 bits;
and 5) the total number k of required bits for representing all the residuals depends on the number of overflows or underflows in T.
Then, the above-defined bit streams of all the tile images are concatenated in order further into a total bit stream Mt for the entire secret image. Moreover, in order to protect Mt from being attacked, we encrypt it with a secret key to obtain an encrypted bit stream Mt′, which is finally embedded into the pixel pairs in the mosaic image using the method of Coltuc and Chassery [44] described above. It may require more than one iteration in the encoding process since the length of Mt′ may be larger than the number of pixel pairs available in an iteration. A plot of the statistics of the numbers of required bits for secret image recovery is shown in Figure 2.10(b).
Moreover, we have to embed as well some related information about the mosaic image generation process into the mosaic image for use in the secret image recovery process. Such information, described as a bit stream I like M mentioned previously, includes the following data items: 1) the number of iterations conducted in the process for embedding the bit stream Mt′; 2) the total number of used pixel pairs in the last iteration for embedding Mt′; and 3) the Huffman table for encoding the residuals.
With the bit stream Mt′ embedded into the mosaic image, we can recover the secret image back as will be described later. It is noted that some loss will be incurred in the recovered secret image, or more specifically, in the color transformation process using (3) where each pixel’s color value ci is multiplied by the standard deviation quotient qc and the resulting real value ci′′ is truncated to be an integer in the range of 0 through 255. However, because each truncated part is smaller than the value of 1, the recovered value of ci using (4) is still precise enough to yield a color nearly identical to its original one. Even when overflows/underflows occur at some pixels in the color transformation process, we record their residual values as described previously and after using (4) to recover the pixel value ci, we add the residual values back to the computed pixel values ci to get the original pixel data, yielding a nearly losslessly-recovered secret image. According to the results of the experiments conducted in this study, each recovered secret image has a very small RMSE value with respect to the original secret image, as will be shown later in Section 2.5.
2.4 Algorithms of Proposed Method
Based on the above discussions, the detailed algorithms for mosaic image creation and secret image recovery may now be described as follows.
Algorithm 2.1. Mosaic image creation.
Input: a secret image S, a pre-selected target image T, and a secret key K.
Output: a secret-fragment-visible mosaic image F.
Steps:
Stage 1 － fitting the tile images into the target blocks.
Step 1. If the size of the target image T is different from that of the secret image S, change the size of T to be identical to that of S; and divide the secret image S into n tile images {T1, T2, …, Tn} as well as the target image T into n target blocks {B1, B2, …, Bn} with each Ti or Bi being of size NT.
Step 2. Compute the means and the standard deviations of each tile image Ti and each target block Bj for the three color channels according to (1) and (2); and compute accordingly the average standard deviations for Ti and Bj, respectively, where i = 1 through n and j = 1 through n.
Step 3. Sort the tile images in the set Stile = {T1, T2, …, Tn} and the target blocks in the set Starget = {B1, B2, …, Bn} according to the computed average standard deviation values of the blocks; map in order the blocks in the sorted Stile to those in the sorted Starget in a 1-to-1 manner; and reorder the mappings according to the indices of the tile images, resulting in a mapping sequence L of the form: T1 → Bj1, T2 → Bj2, …, Tn Bjn.
Step 4. Create a mosaic image F by fitting the tile images into the corresponding target blocks according to L.
Stage 2 － performing color conversions between the tile images and the target blocks.
Step 5. Create a counting table TB with 256 entries, each with an index corresponding to a residual value, and assign an initial value of zero to each entry (note that each residual value will be in the range of 0 to 255).
Step 6. For each mapping Ti → Bji in sequence L, represent the means c and c′ of Ti and Bji, respectively, by eight bits; and represent the standard deviation quotient qc appearing in (3) by seven bits, according to the scheme described in Section 2.3(A) where c = r, g, or b.
Step 7. For each pixel pi in each tile image Ti of mosaic image F with color value ci
where c = r, g, or b, transform ci into a new value ci′′ by (3); if ci′′ is not
smaller than 255 or if it is not larger than 0, then change ci′′ to be 255 or 0, respectively; compute a residual value Ri for pixel pi by the way described in Section 2.3(C); and increment by 1 the count in the entry in the counting table TB whose index is identical to Ri.
Stage 3 － rotating the tile images.
Step 8. Compute the RMSE values of each color-transformed tile image Ti in F with respect to its corresponding target block Bji after rotating Ti into each of the directions = 0o, 90o, 180o and 270o in the luminance channel; and rotate Ti
into the optimal direction o with the smallest RMSE value.
Stage 4 － embedding the secret image recovery information.
Step 9. Construct a Huffman table HT using the content of the counting table TB to
Step 9. Construct a Huffman table HT using the content of the counting table TB to