Chapter 1 Introduction
1.5 Thesis Organization
This thesis is organized as follows. In Chapter2, we review the related works of this study. In Chapter 3, the proposed method for creation of secret-fragment-visible mosaic images is described. In Chapter 4, the proposed method for covert communication via full-color secret-fragment-visible mosaic images by embedding a source-image recovery sequence and switching the orders of target blocks is described.
Then the proposed method for image steganography though grayscale secret-fragment-visible mosaic images is presented in Chapter 5. In Chapter 6, the proposed method for secret sharing through the use of multiple secret-fragment-visible mosaic images will be introduced. The conclusions of our study and suggestions for future works are included in Chapter 7.
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Chapter 2
Review of Related Works
2.1 Previous Studies on Creation and Application of Mosaic Images
Mosaic is an art of creation artworks composed of small pieces of materials which essentially can be of any form or shape. It utilizes a property of human beings’
vision that people only can see the average color of a block which is far away from them. Because of this feature, each element in a mosaic image is put at a place which has a similar color to the original image. It is in this way that the mosaic image looks like the original image when seen from a distance. Previously, mosaic images are used to decorate the walls or ceilings of Catholic churches (see Fig. 2.1 for an example).
Nowadays, mosaics have become popular and widely used for various purposes of decorations in people’s daily life.
Figure 2.1 Mosaic decorations on the walls of a church. [3]
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Many researches on automatic mosaic image creation have been conducted in recent years. How to combine art image creation and the computer technology is a new research topic.
In 1990, Haeberli [4] proposed a method for mosaic image creation. The method uses voronoi diagrams, placing the sites of blocks randomly and filling colors into the blocks based on the content of the original image. It can generate a high-resolution mosaic image from a given image, like Figure 2.2(a). Hausner [5] presented a method to create tile mosaic images by using centroidal voronoi diagrams. He made good use of it because the covered space is fair. Two example images are shown in Figures 2.2(b) and 2.3(a). Extending Haeberli’s idea, Dobashi et al. [6] improved voronoi diagrams to create tile mosaic images, like Figure 2.3(b). The method of Dobashi consists of two processes. One is to generate voronoi diagrams and optimize them by reducing the matching error value between a source image and a resulting image. The other process allows a user to add various effects to the mosaic image, such as simulation of stained glasses.
Figure 2.2 Munch’s ―The Scream‖. (a) Using Haeberli’s [4] method. (b) Using Hausner’s [5] method.
A third type of mosaic image is composed of tile images which have arbitrary
(a) (b)
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shapes. As shown by Figures 2.4(a) and 2.4(b), the final image is filled with small elements of different shapes. Kim and Pellacini [7] proposed a creation process for generating this type of mosaic image, called jigsaw image mosaic. It is composed of many arbitrary shapes of tiles which are selected from a database. However, the tiles may be distorted in the proposed algorithm. Extending the concept of Kim’s method, Blasi et al. [8] presented a new mosaic image called puzzle image mosaic which is similar to Kim’s results. The creation times of puzzle image mosaics are less than those of jigsaw image mosaics, and better effects with no distortion of tile images were obtained.
Figure 2.3 Mosaic Images. (a) Using Hausner’s [5] method. (b) Using Dobashi’s [6] method.
Figure 2.4 Mosaic images. (a) Jigsaw image mosaic [7]. (b) Puzzle image mosaic [8].
(a) (b)
(a) (b)
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2.2 Previous Studies on Information Hiding Techniques
Information hiding is a technique which changes the insensitive parts of a file format in order to embed some extra messages in it without consciousness of other people. The most well-known method is least significant bit (LSB) modification.
Many studies extended this idea of LSB modification method and utilized it in many applications. Some of them embed secret images into cover images in order to implement covert communication and invisible watermarking. For example, Wu and Tsai [9] presented a data hiding method according to a human vision model. They hid secret data in the sharp image area based on the characteristics of human vision. This method can embed secret images losslessly and create stego-images with low degradation. However, cover images with traditional LSB modifications may be changed and cannot be reversed to the original ones. Based on this drawback, many researches were conducted to implement reversible LSB modification techniques.
Fridrich et al. [10] proposed a lossless LSB modification method with flipping functions and pixel grouping. They divided the pixels into three groups and applied flipping functions to each group. Celik et al. [11] presented a method, called lossless
generalized LSB data embedding. The proposed algorithm modifies the lowest levels,
instead of bit planes, of raw pixel values, and used the results as features. The recovery of the original image is achieved by compressing, transmitting, and recovering these features. Tian [12] proposed a reversible data embedding method by using a difference expansion scheme. The method uses some simple equations to modify the values of two pixels. Because the new values are generated from the difference between two manipulated pixels, the original pixel values can be recovered easily. Alattar [13] proposed a lossless data hiding method using the difference19
expansion of a generalized integer transform. This method extends Tian’s algorithm utilizing difference expansion of vectors, instead of pairs, to increase the hiding ability of the method.
The above-mentioned methods all have the drawback of yielding low data embedding capacities. Coltuc and Chassery [14] presented a high-capacity data embedding scheme without appealing to any additional data compression stage. This scheme is based on a reversible contrast mapping, which is a simple integer transform defined on pairs of pixels. They marked pairs of pixels as three groups, and applied different operations on them. In this study, we utilize this scheme to hide a source-image recovery sequence into a secret-fragment-visible mosaic image. In order to embed other secret messages into the mosaic image generated in this study, the method designed for hiding the recovery sequence must be reversible and has a high data embedding capacity.
2.3 Previous Studies on Information Hiding Techniques in Art Images
The combination of art image creation and information hiding techniques is a new concept of computer technology. This technique utilizes the characteristics of the art image creation process to embed extra information in the generated images. With this disguise, hackers will tend to get unaware of the data embedded in such images, and secret data can so be kept or transmitted safely and covertly.
Lin and Tsai [15] proposed methods for embedding secret data in image mosaics by adjusting regions of boundaries and altering pixel values of the hue component in the HIS color model. A result generated by the method is shown in Figure 2.5(a).
Wang and Tsai [16] also presented a data hiding method for image mosaics. By
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utilizing the overlapping space of component images, the scheme can embed secret messages in image mosaics without arousing notice from an observer. An example of the resulting images is shown in Figure 2.5(b).
Figure 2.5 Image mosaics. (a) An image mosaic created with Lin and Tsai’s method [15]. (b) An image mosaic created with Wang and Tsai’s method [16].
In addition to generating image mosaics, several studies of combining art image creation and information hiding have been conducted, yielding other types of art images. Hung and Tsai [1] proposed information hiding methods through the use of stained glass images and tile mosaic images. By modifying the tree structure used in the creation process, secret data can be hidden in computer-generated stained glass images. Moreover, they utilized the rotation angles of the tiles in tile mosaic images to design data hiding techniques. Hsu and Tsai [17] presented three new types of art images and used the characteristics of their creation processes to hide secret messages in the generated art images. First, in the digital puzzle image generated by them, the angles of puzzles are used for data hiding. Second, they proposed a method for generating a kind of so-called circular-dotted image, as shown in Figure 2.6(a). By changing the order of circular-dot overlappings, a method of information hiding was
(a) (b)
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implemented. And the last data hiding method proposed by them is the use of the pallet colors in pointillistic images for data hiding. An image yielded by their method is shown in Figure 2.6(b). Chang and Tsai [18] proposed a new type of art image, called tetromino-based mosaic, which is composed of tetrominoes appearing in a video game. By geometric shape composition, tetrominoes can be combined to one another to form blocks which in turn can be used to fill a plane with a limited shape (rectangles mostly). This is the reason why tetrominoes can be used to create mosaic images. Data hiding is made possible by distinct combinations and color shifting of the tetromino elements. Examples of the resulting images are shown in Figures 2.7(a) and 2.7(b).
Figure 2.6 Art images created by Hsu and Tsai [17]. (a) A circular-dotted image. (b) A pointillistic image.
In this study, we also propose new methods which combine art image creation and information hiding techniques to implement covert communication, image steganography, and secret sharing. By using the characteristics of the secret-fragment-visible mosaic image creation process, the images can be transmitted
(a) (b)
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with the embedded data arousing no notice from observers.
Figure 2.7 Tetromino-based mosaic images [18]. (a) Lena. (b) Peppers.
(a) (b)
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Chapter 3
Creation of Secret-fragment-visible Mosaic Images
3.1 Idea of Proposed Method
A sliding puzzle is composed of all block pieces but one of a divided image. The randomly-placed block pieces compose a meaningless picture. Players can slide the blocks in a certain way by observing the color or texture of them, and finish the game with a meaningful picture. The idea of the proposed art image creation method is inspired by this concept of puzzle piece sliding, as mentioned previously, to create the new type of mosaic image, the secret-fragment-visible mosaic image, as proposed in this study.
In the creation of a secret-fragment-visible mosaic image, a secret image is divided into fragment pieces. The pieces of the secret image are all visible in the mosaic image, but the size of them is tiny and the rearranged positions are random.
Therefore, people cannot extract the secret data from the mosaic image unless they have the knowledge to rearrange the pieces back into their original positions, using the right secret key from the owner as required by the proposed method.
The proposed mosaic image creation process is composed of two major procedures. The first is the construction of an image database which can be used later to select a sufficiently similar target image for a given secret image. The quality of a constructed secret-fragment-visible mosaic image is related to the similarity between the secret image and the target image. So we try to select a target image from a
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database based on the contents of a given secret image by computing a similarity measure; the selected target image should be as similar to the secret image as possible.
Another procedure is the creation of a secret-fragment-visible mosaic image, which uses the secret image and the selected target image as input. In this procedure, we divide a secret image into fragment pieces, i.e., tile images as mentioned before, and use these tile images to create the mosaic image. The number of tile images for use in mosaic image creation is limited by the size of the secret image and that of the tile images. Note that this is not the case in traditional mosaic image generation where available tile images to fit into the target image are unlimited in number. In order to solve this problem of fitting a limited number of tile images into a target image, we propose a greedy algorithm to find an appropriate answer.
In addition, we present a method for remedying a database which is not large enough for selecting a sufficiently similar target image. The method basically enlarges the size of the selected target image so that the tile images of the secret image can be fitted into the target image at more freely-chosen positions, resulting in a mosaic image more similar to the secret image.
The detailed algorithms of the above-mentioned processes are presented in the following sections.
3.2 Proposed Secret-fragment-visible Mosaic Image Creation Process
3.2.1 Database construction
First of all, we have to construct a database which keeps target images. The
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database plays an important role in the secret-fragment-visible mosaic image creation process. If a target image is dissimilar to a secret image, the created image will be distinct from the target one. In order to generate a good result, the database so should be as large as possible.
To search a target image from a database with the highest similarity to the secret image is a problem of content-based image retrieval. In general, the content of an image may be described by features like shape, texture, and color. Because only the color distributions of a secret image and a target image will affect the overall visual appearance of the resulting mosaic image, we may focus first on extracting color distributions from images by techniques developed for content-based image retrieval.
The simplest technique for extracting the color distribution of an image by content-based image retrieval is 1-D color histogram transformation [19]. This technique transforms three color channel values (such as R, G, and B or H, S, and V) into a single channel value. More details are described in the following.
First, each color channel (usually with a range of 0~255, i.e., with 256 levels) is re-quantized into less levels, yielding an new image I′ with a lower resolution in color, which we specify as (r, g, b). Let Nr, Ng, and Nb denote the numbers of levels for the new colors r, g, and b respectively. Then, for each pixel P′ in I′ with new color (r′, g′,
b′), we compute the following 1-D function value f:
f(r′, g′, b′) = r′ + N
r g′ + Nr Ng b′ (3.1) and so generate conceptually a 1D image I′′ with new ―1-D color‖ values specified byf above. Then, this new image then can be used for image content analysis and similar
image search and retrieval. Note that the sizes of I′ and I′′ are both the same as that of the original image I.However, according to our experimental experience using this 1-D color function
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f, it is found inappropriate for our study here which emphasizes human’s visual
feeling of image similarity. Therefore, we propose a new function h as follows:h(r′, g′, b′) = b′ + N
b r′ + Nb Nr g′ (3.2) where the numbers of levels, Nr, Ng and Nb, are all set to 8. Differently from the case in (3.1), we set in (3.2) the largest weight Nb Nr to the green channel value g′ and the smallest weight 1 to the blue channel value b′. The reason is that the eyes of human beings are the most sensitive to the green color, and the least sensitive to the blue color. In addition, with all of Nr, Ng, and Nb set to 8 in (3.2), an advantage of speeding up the later process of mosaic image creation can be obtained according to our experiments. In the sequel, we will say that the new color feature function h we propose above defines a 1-D h-colorscale.Furthermore, to measure the similarity between a tile image in the secret image and a target block in an image in a database for use in tile image fitting in generating a mosaic image, we propose a new feature, called h-feature, for each block image C (either a tile image or a target block), denoted as hC, which is computed by the
3. calculate the h-feature hC for C by Eq. (3.2) above, resulting in the following equation:
h
C(rC′, gC′, bC′) = bC′ + Nb rC′ + Nb Nr gC′. (3.3) With Nr, Ng, and Nb all equals 8, the range of the computed values of the27
h-feature f
C above may be figured out to be from 0 to 584. The proposed algorithm for constructing a database of candidate images (from which a target image is to be selected for each given secret image) for this study is described in the following.Algorithm 3.1: candidate image database construction.
Input: a set S of images, a pre-selected tile image size Z
t, and a pre-selected candidate image size Zc.Output: a database DB of candidate images with size Z
c and their h-colorscale histograms.Steps:
Step 1. For each input image I, perform the following steps.
1.1 Resize and crop I to yield an image D of size Zc. 1.2 Divide D into blocks of size Zt.
1.3 For each block C of D, calculate and round off the h-feature value hC
described by Eq. (3.3).
1.4 Generate a histogram H of the values of the h-features of all the blocks in
D.
1.5 Save H together with D into the desired database DB.
Step 2. If the input images are not exhausted yet, then go to Step 1; otherwise, exit.
3.2.2 Similarity measure computation and target image selection
Before we generate a mosaic image, we have to choose as the target image a similar candidate image from the database based on the given secret image content.
For this, we can use the 1-D h-colorscale histogram of each candidate image in the database to compute a similarity measure between the secret image and the candidate
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image. More specifically, by summing up the differences between the 1-D histograms of the secret image and that of the candidate image, we can get an error e (computed by Eq. (3.4) described later in the following). The smaller the value e is, the more similar the candidate image is to the secret image. After calculating the errors of all the candidate images in the database, we can select the candidate image with the smallest error as the desired target image for use in later mosaic image generation.
The detailed algorithm is given as follows.
Algorithm 3.2: selection of the most similar candidate image to be the target image.
Input: a secret image S, a database DB of candidate images, and the sizes Z
t and Zc of tile images and candidate images, respectively, mentioned in Algorithm 3.1.Output: a target image T selected from DB with the largest content similarity to S.
Steps:
Step 1. Resize S to yield an image S′ of size Zc to become of the same size as the candidate images in DB.
Step 2. Divide S′ into blocks of size Zt, and perform the following steps.
2.1 For each block C of S′ generated in Step 1, calculate and round off for it the h-feature value hC described by Eq. (3.3).
2.2 Generate a 1-D h-colorscale histogram HS′
for S′ from the values of the h-features of all the blocks in S′.
Step 3. For each candidate image D with 1-D h-colorscale histogram HD stored in DB, perform the following steps.
where m stands for the value of the h-feature mentioned above.
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3.2 Record the error e.
Step 4. If the images in DB are not exhausted, then go to Step 3; otherwise, continue.
Step 5. Select the image in DB which has the minimum error value and take it as the desired target image T.
3.2.3 Algorithm for secret-fragment-visible mosaic image creation
In this section, after discussing some problems which are encountered in the creation process of secret-fragment-visible mosaic images, we will present an algorithm to implement the process.
A. Problems of creating secret-fragment-visible mosaic images
We face two major problems in the secret-fragment-visible mosaic image creation process. One is about finding an optimal solution for fitting tile images in appropriate target blocks. Another is dealing with the situation of a database which is not large enough for selecting a sufficiently similar candidate image as a target image.
About the first problem, we can reduce it to a single-source shortest path problem. The shortest path problem is one of finding a path in a graph with the smallest sum of between-vertices edge weights. The state of fitting tile images represents the vertices of the graph. In the fitting process, we select a tile image for a target block, once a block. Therefore, the edge means the label of the tile image that we choose at the time. Then, the weight of an edge is the Euclidean distance between the selected tile image and the filled target block (defined later). Accordingly, we can build a tree structure for this problem, as shown by Figure 3.1.
In order to find an optimal solution of the single-source shortest path problem, we utilize Dijkstra's algorithm. In this algorithm, the running time of getting an
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optimal answer is