國立交通大學
資訊科學與工程研究所
碩士論文
「可視秘密碎片」馬賽克畫—一種新的藝術與其在資
訊隱藏上的應用
Secret-fragment-visible Mosaic—a New Art and Its
Applications to Information Hiding
研 究 生：賴怡臻
指導教授：蔡文祥 教授
「可視秘密碎片」馬賽克畫—一種新的藝術 與其在資訊隱藏上的應用
Secret-fragment-visible Mosaic—a New Art and Its
Applications to Information Hiding
研 究 生：賴怡臻
Student: I-Jen Lai
指導教授：蔡文祥
Advisor: Prof. Wen-Hsiang Tsai
國 立 交 通 大 學
資 訊 科 學 與 工 程 研 究 所 碩 士 論 文
A Thesis
Submitted to Institute of Computer Science and Engineering College of Computer Science
National Chiao Tung University In partial Fulfillment of the Requirements
For the Degree of Master
In
Computer Science June 2010
Hsinchu, Taiwan, Republic of China
i
「可視秘密碎片」馬賽克畫—一種新的藝術與其在資
訊隱藏上的應用
研究生: 賴怡臻
指導教授: 蔡文祥 博士
國立交通大學資訊科學與工程研究所
摘要
在本論文中，我們提出了一個新的藝術畫 - 「可視秘密碎片馬賽克畫」，並 應用在這種藝術畫，發展出三種不同的資訊隱藏技術 - 秘密傳輸、影像隱匿術 及秘密分享。這種藝術畫是將一張「秘密影像」切割成許多正方形碎片，並用這 些碎片當成元件，組成起來的新型式馬賽克畫。首先，我們針對人類視覺對顏色 的敏感度，提出了一表示影像色彩分佈的公式，並用它從資料庫中篩選出與秘密 影像最相像的候選圖片，來當作製作馬賽克畫的「目標影像」。有了秘密影像以及 目標影像之後，我們利用本研究所提出的一個貪婪演算法，將秘密影像的碎片逐一嵌合 到目標影像上。另外，當資料庫中的圖片數量不足時，選出的目標影像的色彩分佈會與 秘密影像不同，導致製成的馬賽克畫和目標影像相差過遠。為此我們也提出了一個彌補 這種情況的方法。 在秘密傳輸方面，我們是在製作可視秘密碎片馬賽克畫的時候，根據「在同一長方 圖容器中(histogram bin)的秘密影像碎片會擁有相似的顏色」的這項特性，交換秘密影 像碎片所對應到的目標影像區塊的標籤，來達到藏入秘密訊息的效果。在影像隱匿術方 面，我們是將秘密文件轉換成灰階影像，並用它來製成一新的馬賽克畫，藉此達到隱藏 秘密文件的效果，並根據灰階值提出另一個特徵值的計算方法，用以提高馬賽克畫製作 的速度。最後，在秘密分享方面，我們是將一張秘密影像分成多張可視秘密碎片馬賽克 畫，並將秘密影像的碎片平均分散在各個目標影像裡。 除了上述的方法外，我們還提出了幾個增加安全性的方法，確保藏入的秘密資訊不 被駭客發現並攻擊。以上的方法皆有實驗結果證明它們在視覺方面的良好成效，以及在 資訊隱藏技術上的可行性。ii
Secret-fragment-visible Mosaic—a New Art and Its
Applications to Information Hiding
Student: I-Jen Lai
Advisor: Wen-Hsiang Tsai
Institute of Computer Science and Engineering
National Chiao Tung University
ABSTRACT
In this study, a new type of art image is created, which is called secret-fragment-visible mosaic image. And this kind of new mosaic image is used for three applications of data hiding, namely, covert communication, steganography, and secret sharing.
First, the newly-proposed secret-fragment-visible mosaic image is created to be composed of rectangular-shaped fragments which come from division of a secret image. A new 1-D h-colorscale is proposed to represent the color distribution of an image based on the color feeling of human vision. To create a secret-fragment-visible mosaic image, a new image similarity measure based on the h-colorscale is proposed, and the most similar candidate image from an image database is selected accordingly as a target image. Then, a greedy algorithm is adopted to fit every tile image in the secret image into an appropriate block in the target image. Furthermore, to solve the problem of using an insufficiently-large database, a remedy method by enlarging the size of a target image is also proposed. Secondly, for covert communication, based on the fact that tile images which are in an identical histogram bin have similar colors, the tile images in an identical histogram bin are reordered, or equivalently, the relative positions of the tile images are switched, to embed secret message bits imperceptibly. Third, for image steganography, a grayscale secret-fragment-visible mosaic image is
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created from a grayscale image of a secret document, yielding a steganographic effect of hiding the secret document into the mosaic image, though visibly. The selection of the most similar target image from a database is based on a newly-proposed k-feature of the grayscale value, which speeds up the image creation process. Finally, for secret sharing, a secret image is shared to yield multiple secret-fragment-visible mosaic images. In order to disperse tile images evenly in selected target images, the target images take turns randomly to pick appropriate tile images.
In addition, various security enhancement measures were proposed to make the embedded data more random to prevent hackers’ attacks. Experimental results show the feasibility of the proposed methods for image creation and data hiding applications.
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ACKNOWLEDGEMENTS
The author is in hearty appreciation of the continuous guidance, discussions, and support from her advisor, Dr. Wen-Hsiang Tsai, not only in the development of this thesis, but also in every aspect of her personal growth.
Appreciation is also given to the colleagues of the Computer Vision Laboratory in the Institute of Computer Science and Engineering at National Chiao Tung University for their suggestions and help during her thesis study.
Finally, the author also extends her profound thanks to her dear mom and dad for their lasting love, care, and encouragement.
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CONTENTS
ABSTRACT (in Chinese)………..i
ABSTRACT (in English)……….ii
ACKNOWLEDGEMMENTS………iv
CONTENTS………..v
LIST OF FIGURES………...viii
LIST OF TABLES………...xi
Chapter 1
Introduction ... 1
1.1 Motivation and Background ... 1
1.1.1 Research Motivation ... 1
1.1.2 Introduction to Mosaic Images ... 2
1.2 Introduction to a New Type of Mosaic Image Proposed in This Study — Secret-fragment-visible Mosaic Images ... 3
1.2.1 New Idea of Secret-fragment-visible Mosaic Image ... 4
1.2.2 Examples of Secret-fragment-visible Mosaic Images Created in This Study ... 6
1.3 Overview of Proposed Methods ... 7
1.3.1 Definitions of Terms ... 7
1.3.2 Brief Description of Proposed Method for Creation of Secret-fragment-visible Mosaic Images ... 8
1.3.3 Brief Description of Proposed Method for Covert Communication via Secret-fragment-visible Mosaic Images ... 9
1.3.4 Brief Description of Proposed Method for Image Steganography via Secret-fragment-visible Mosaic Images ... 11
1.3.5 Brief Description of Proposed Method for Secret Sharing via Secret-fragment-visible Mosaic Images ... 12
1.4 Contributions ... 13
1.5 Thesis Organization ... 14
Chapter 2
Review of Related Works ... 15
2.1 Previous Studies on Creation and Application of Mosaic Images ... 15
2.2 Previous Studies on Information Hiding Techniques ... 18
2.3 Previous Studies on Information Hiding Techniques in Art Images .... 19
Chapter 3
Creation of Secret-fragment-visible Mosaic Images ... 23
3.1 Idea of Proposed Method ... 23
vi
3.2.1 Database construction ... 24
3.2.2 Similarity measure computation and target image selection ... 27
3.2.3 Algorithm for secret-fragment –visible mosaic image creation . 29 3.3 Experimental Results ... 36
3.4 Summary ... 41
Chapter 4
Covert Communication via Secret-fragment-visible
Mosaic Images ... 42
4.1 Idea of Proposed Method ... 42
4.2 Proposed Secret Message Hiding Method via Secret-fragment-visible Mosaic images ... 43
4.2.1 Modified secret-fragment-visible mosaic image creation process for secret message embedding ... 43
4.2.2 Secret message extraction process ... 49
4.3 Security Consideration ... 53
4.3.1 Issues of security of proposed method ... 53
4.3.2 Proposed security enhancement measures ... 54
4.4 Experimental Results ... 55
4.5 Summary ... 56
Chapter 5
Image Steganography via Secret-fragment-visible Mosaic
Images ... 61
5.1 Idea of Proposed Method ... 61
5.2 Proposed Method for Image Steganography via Secret-fragment-visible Mosaic Images ... 62
5.2.1 Grayscale Secret-fragment-visible Mosaic Image Creation Process ... 62
5.2.2 Secret image recovery process ... 68
5.3 Security Consideration ... 69
5.4 Experimental Results ... 69
5.5 Summary ... 76
Chapter 6
Secret Sharing via Secret-fragment-visible Mosaic
Images ... 77
6.1 Idea of Proposed Method ... 77
6.2 Proposed Secret Sharing Method ... 78
6.2.1 Algorithm for secret sharing ... 78
6.2.2 Algorithm of proposed secret recovery process ... 85
6.3 Security Consideration ... 87
6.4 Experimental Results ... 88
vii
Chapter 7
Conclusions and Suggestions for Future Works ... 95
7.1 Conclusions ... 95 7.2 Suggestions for Future Works ... 96
viii
LIST OF FIGURES
Figure 1.1 The Mona Lisa. (a) The original image. (b) A tile mosaic image [1]. (c) A
photographic mosaic image [2]. ... 3
Figure 1.2 A sliding puzzle. (a) Randomly-placed block pieces of the puzzle. (b) Rearranged block pieces which show the original picture, a self-portrait of Van Gogh. ... 5
Figure 1.3 An example. (a) A secret image. (b) A secret-fragment-visible mosaic image created with (a) as the source image. ... 6
Figure 1.4 Another example. (a) A secret image. (b) A secret-fragment-visible mosaic image created with (a) as the source image. ... 6
Figure 1.5 Creation process of secret-fragment-visible mosaic image. ... 9
Figure 1.6 Embedding process of data hiding by switching the orders of tiles. ... 10
Figure 1.7 Image steganography process by creating grayscale secret-fragment-visible mosaics. ... 11
Figure 1.8 Process of secret sharing through secret-fragment-visible mosaic images.12 Figure 2.1 Mosaic decorations on the walls of a church. [3] ... 15
Figure 2.2 Munch’s ―The Scream‖. (a) Using Haeberli’s [4] method. (b) Using Hausner’s [5] method ... 16
Figure 2.3 Mosaic Images. (a) Using Hausner’s [5] method. (b) Using Dobashi’s [6] method. ... 17
Figure 2.4 Mosaic images. (a) Jigsaw image mosaic [7]. (b) Puzzle image mosaic [8]. ... 17
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]. ... 20
Figure 2.6 Art images created by Hsu and Tsai [17]. (a) A circular-dotted image. (b) A pointillistic image. ... 21
Figure 2.7 Tetromino-based mosaic images [18]. (a) Lena. (b) Peppers. ... 22
Figure 3.1 A tree structure of fitting tile images to target blocks... 30
Figure 3.2 Input images. (a) A secret image. (b) A target image. ... 32
Figure 3.3 Created mosaic images generated by a greedy algorithm. (a) Image created using Euclidean distance used to define a selection function for a greedy algorithm. (b) Image created using the h-feature to define the select function for a greedy algorithm. ... 32
Figure 3.4 Example images. (a) A secret image. (b) A target image. ... 35 Figure 3.5 Resulting mosaic images created with Figures 3.4(a) as secret image and
ix
method. (b) Mosaic image created with the proposed remedy method. ... 36 Figure 3.6 Experimental images. (a) A secret image. (b) A target image. (c) A
secret-fragment-visible mosaic image created with (a) as a source image. 37 Figure 3.7 Experimental images. (a) A secret image. (b) A target image. (c) A
secret-fragment-visible mosaic image created with (a) as a source image. 38 Figure 3.8 Experimental images. (a) A secret image. (b) A target image. (c) A
secret-fragment-visible mosaic image created with (a) as a source image. 39 Figure 3.9 Experimental images. (a) A secret image. (b) A target image. (c) A
secret-fragment-visible mosaic image created with (a) as a source image. 40 Figure 4.1 Different colors of tile images which have the same h-feature value. ... 43 Figure 4.2 Exchange of the corresponding target blocks of tile images. (a) The
original corresponding target blocks of tile images. (b) After switching the corresponding target blocks of tile images. ... 44 Figure 4.3 An illustration of generation of a recovery sequence LR. ... 45
Figure 4.4 An illustration of the regaining of the h-sorted label sequence L2. ... 50
Figure 4.5 A flowchart of applying exclusive or operation on a secret message
segment by a secret key. ... 55 Figure 4.6 An example of secret-fragment-visible mosaic images. (a) A secret image.
(b) A target image. (c) A secret-fragment-visible mosaic image without secret message embedding ... 57 Figure 4.7 Embedding the secret message ―Meet me at 20:00. Good luck.‖ with the
secret key ―test‖. ... 58 Figure 4.8 A secret-fragment-visible mosaic image into which a secret message is
hidden. ... 58 Figure 4.9 Extracting the secret message with the right secret key ―test‖. ... 59 Figure 4.10 The resulting image and the extracted secret messages of Figure 4.8,
which is recovered by the right key. ... 59 Figure 4.11 Extracting the secret message with the wrong secret key ―test123‖. ... 60 Figure 4.12 The resulting image and the extracted secret messages of Figure 4.10,
which is recovered by a wrong key. ... 60 Figure 5.1 A flowchart of the proposed image steganography method through the use
of grayscale secret-fragment-visible mosaic images. ... 62 Figure 5.2 Input images. (a) A secret image which is converted from a document. (b)
A target image... 70 Figure 5.3 Resulting secret-fragment-visible mosaic image created with Figure 5.2(a).
... 70 Figure 5.4 Input images. (a) A secret image which is converted from a document. (b)
x
Figure 5.5 Resulting secret-fragment-visible mosaic image created with Figure 5.4(a). 71
Figure 5.6 Input images. (a) A secret image which is converted from a document. (b) A target image... 72 Figure 5.7 Resulting secret-fragment-visible mosaic image created with Figure 5.4(a).
72
Figure 5.8 Embedding the secret image with the secret key ―test‖. ... 73 Figure 5.9 The resulting image which is created with a secret key ―test‖. ... 73 Figure 5.10 Extracting the secret image with the right key ―test‖. ... 74 Figure 5.11 The resulting image and the extracted secret messages of Figure 5.4,
which is recovered by the right key. ... 74 Figure 5.12 Extracting the secret image with the wrong key ―tes‖. ... 75 Figure 5.13 The resulting image and the extracted secret message of Figure 5.4, which is recovered with the wrong key. ... 75 Figure 6.1 A flowchart of the secret sharing process via secret-fragment-visible
mosaic images. ... 80 Figure 6.2 An illustration of the combination of the new recovery sequence of each
sharing mosaic image. ... 85 Figure 6.3 An example of the proposed secret sharing method. (a) A secret image. (b)
A selected target image. (c) Another selected target image. (d) A shared secret-fragment-visible mosaic image. (e) Another shared
secret-fragment-visible mosaic image. ... 90 Figure 6.4 An example of the proposed secret sharing method. (a) A secret image. (b)
A selected target image. (c) A second selected target image. (d) A third selected target image. (e) A shared secret-fragment-visible mosaic image. (f) A second shared secret-fragment-visible mosaic image. (g) A third shared secret-fragment-visible mosaic image. ... 91 Figure 6.5 Sharing the secret image to 5 pieces, which is created with the secret key
―test‖. ... 92 Figure 6.6 The resulting images of Figure 6.5. ... 92 Figure 6.7 Recovery of the secret image with all the sharing participants and the right
secret key ―test‖. ... 93 Figure 6.8 The recovered images of Figure 6.7. ... 93 Figure 6.9 Using part of shares and the right key ―test‖ for recovering the secret image. ... 94 Figure 6.10 The recovered images of Figure 6.9 which are noise. ... 94
xi
LIST OF TABLES
Table 3.1 The Euclidean distance at block level between target images and created mosaic images. ... 41
1
Chapter 1
Introduction
1.1 Motivation and Background
1.1.1 Research Motivation
Over the last decade, the Internet has become more and more indispensable to people’s daily life. Many social network services have been built on the Internet in recent years. Therefore, people can communicate with friends and share their information, such as interesting videos or images, through the services. Part of the information, such as intelligence data, web bank account passwords, and so on, is private and should be protected carefully. When the owners of such messages want to deliver them to other people, hackers may easily steal or tamper with the data contents. Accordingly, information hiding becomes an important issue nowadays.
On the other hand, artworks often arouse interests of people in daily life, especially artistic pictures which attract people’s visual attention. Recently more and more visual arts are produced by computers, creating a new type of art, called
computer art. An example is mosaic image, though it is a form of art existing for
thousands of years, dating back to the days of Rome and Greece in the western world. Many information hiding techniques have been proposed in the past decade. Some of them were proposed via the use of images. The images, as carriers of information, were used just for the sole purpose of hiding information. If the images could be artworks like mosaic images, more attention of the people who receive them
2
will be attracted to appreciate their artistic contents, thus ignoring any other non-artistic function of the image like information hiding.
Therefore, unlike traditional information hiding techniques, in this study we try to combine data hiding and art image creation techniques for the purpose of information hiding. We will try in the first place to design new techniques for creating new types of computer art in image form. We will also investigate new techniques of embedding secret messages into the newly-designed computer art images during the creation process of them, yielding new ways of hiding information. With such disguise of the art image, illicit people who intend to thieve the hidden information will tend to believe that the image is only an artistic production and so ignore the information embedded in it, as mentioned previously.
Furthermore, it is desired to use the designed new artworks as carriers for use in as many kinds of information hiding technique as possible. That is, we will try to design new information hiding techniques for various purposes via the newly-created computer art images. Specifically, via the use of the new type of image we will try to propose new methods for image steganography, covert communication, and secret sharing, all being different types of information hiding. These methods should all make good use of the characteristics of the new type of image we are going to design.
1.1.2 Introduction to Mosaic Images
Mosaics are the art of creating works, each being composed of small pieces, such as stone, glass, or other materials. The history of mosaics goes back to 4000 years ago or more, with the use of terracotta cones to conduct various types of decorations. With the rise of Christianity, mosaics were used to decorate the windows or ceilings of churches. Nowadays, it has turned into a common type of decoration for use in
3
modern houses, public space, advertisements, books, and so on.
In recent years, many researches have been conducted on the creation of different kinds of mosaic image. Traditional mosaic images are composed of a large number of small images, called tile images. To create a mosaic image, a user must choose an image first, called the source image. Then, the source image is divided into numerous rectangular pieces, each of which, called a target image, is replaced by a tile image similar in content. Consequently, while we see a mosaic image from a distance, as a whole it will look like its source image — an effect of a human vision property. An example is shown in Figure 1.1.
Figure 1.1 The Mona Lisa. (a) The original image. (b) A tile mosaic image [1]. (c) A photographic mosaic image [2].
1.2 Introduction to a New Type of
Mosaic Image Proposed in This
Study — Secret-fragment-visible
Mosaic Images
(b) (c)
4
1.2.1 New Idea of Secret-fragment-visible Mosaic
Image
A new type of art image which contains small fragments of a source image is proposed in this study. The idea was inspired by the sliding puzzle like that shown in Figure 1.2. The sliding puzzle challenges a player to slide randomly-placed block pieces of a picture (like Figure 1.2(a)) with a certain way to rebuild the original picture content (like Figure 1.2(b)). Note that the randomly-placed block pieces as a whole show a meaningless picture.
We extend in this study the idea of slide puzzle to create a new type of art image, called secret-fragment-visible mosaic image, which is composed of the fragments of a source image. Different from the sliding puzzle which, when randomized, looks meaningless as mentioned previously, the randomly-placed fragments in the created secret-fragment-visible mosaic image, as a whole, look like the target image instead. Observing such a type of mosaic image, people can see all of the fragments of the secret image, but because the fragments are so tiny in size and so random in position, people cannot figure out what the source image look like unless they have some way to rearrange the pieces back into their original positions, using a secret key from the image owner, as required by the proposed method. As such, the source image may be said to be secretly embedded in the resulting mosaic image, though the fragment pieces are all visible to an observer of the image. And this is just the reason why we name the resulting image as a secret-fragment-visible mosaic image. Examples of such images will be given later in this section.
In the proposed secret-fragment-visible mosaic image creation process, we divide a secret image into a large number of tile images and use them as a mosaic tile
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image database. Because the database is formed with secret tile images, the number of tile images is limited; also, the resulting mosaic image includes all of them. Thus, the method for fitting tile images becomes a tough problem to deal with. In this study, we not only develop an algorithm for fitting tile images successfully, but also propose information hiding methods which modify this algorithm in detail to achieve the designs of two information hiding techniques, namely, covert communication via
color mosaic images and image steganography via grayscale mosaic images.
Figure 1.2 A sliding puzzle. (a) Randomly-placed block pieces of the puzzle. (b) Rearranged block pieces which show the original picture, a self-portrait of Van Gogh.
Each secret-fragment-visible mosaic image is composed of many fragment pieces, and random arrangement of them forms a mosaic pattern, as mentioned previously. Extending this idea, we also use these pieces to compose multiple secret-fragment-visible mosaic images and so implement a secret sharing technique.
In short, in this study, in addition to designing a new type of mosaic image secret-fragment-visible mosaic image, we have proposed three applications of such images to information hiding, including image steganography, covert communication, and secret sharing. We will introduce them one by one subsequently.
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1.2.2 Examples of Secret-fragment-visible Mosaic
Images Created in This Study
Some examples of secret-fragment-visible mosaic images created in this study are shown here. Figures 1.3(a) and 1.4(a) are two secret images used respectively to generate the secret-fragment-visible mosaic images shown in Figures 1.3(b) and 1.4(b).
Figure 1.3 An example. (a) A secret image. (b) A secret-fragment-visible mosaic image created with (a) as the source image.
Figure 1.4 Another example. (a) A secret image. (b) A secret-fragment-visible mosaic image created with (a) as the source image.
Observing these images, we see that the resulting mosaic images are quite different from the secret images. Therefore, the proposed creation method may be
(a) (b)
7
regarded as a way of implementing the function of information hiding, though a technique for extracting the secret image from the created image is yet to be designed. More results will be shown in Chapter 3.
1.3 Overview of Proposed Methods
In this study, we propose two methods for creating secret-fragment-visible mosaic images. One is for use when the source image is a full-color one, and the other is for use when the source image is a grayscale one. At the beginning, a scheme for creation of full-color secret-fragment-visible mosaic images is presented. Next, a data hiding method for covert communication is proposed utilizing the characteristics of the proposed secret-fragment-visible mosaic images creation process. Then, a method of image steganography implemented in the process of creating grayscale secret-fragment-visible mosaic images is proposed with the input image transformed from a full-color secret document. Finally, we achieve the goal of secret sharing through the use of multiple secret-fragment-visible mosaic images. Brief descriptions of these methods are given as follows.
1.3.1 Definitions of Terms
Before describing the proposed methods, some definitions of terms used in this study are introduced first as follows.
1. Secret image: a secret image is one which is chosen as the source image to
produce a secret-fragment-visible mosaic image.
2. Target image: a target image is an image selected from a database according
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the secret image.
3. Target image database: a target image database is a database which store a
large number of target images.
4. Tile image: a tile image is one of the square pieces resulting from crumbling
a secret image.
5. Target block: a target block is the place that a tile image of the same size
should be fitted into.
6. Secret-fragment-visible mosaic image: a secret-fragment-visible mosaic
image is obtained by rearranging the fragments of a secret image in a certain way, yielding a visual effect like the target image.
7. Creation process: a creation process produces a secret-fragment-visible
mosaic image from a secret image.
8. Recovery process: a recovery process reconstructs the secret source image
from a secret-fragment-visible mosaic image.
9. Recovery sequence: a recovery sequence is a sequence which records the
corresponding labels of the tile images and the target blocks, based on which the recovery process can be conducted to retrieve the secret image. 10. Image steganography: image steganography is a scheme to embed data into
images for covert communication, which, though obvious, transmits the secret imperceptibly.
11. Embedding process: an embedding process hides secret data into an image. 12. Extraction process: an extraction process retrieves secret data from an
image.
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Creation of Secret-fragment-visible Mosaic
Images
The main steps of the proposed creation process of secret-fragment-visible mosaic images are described in Figure 1.5. First, we construct a target image database which records the color histogram of the stored images. Second, based on a given secret image, a similarity measure proposed in this study is computed and used to choose a target image from the database. Then, the secret image is divided into tile images, which then are rearranged to fit a target image to create a secret-fragment-visible mosaic image. The detailed creation process will be introduced in Chapter 3.
Figure 1.5 Creation process of secret-fragment-visible mosaic image.
1.3.3 Brief Description of Proposed Method for
Covert Communication via
Secret-fragment-visible Mosaic Images
Based on the method of the above-mentioned creation process, we propose a
Secret image
Construct target image database
Search the best matching target image
from DB
Divide secret image into tile images Target
database DB
Create secret-fragment-visible mosaic image with tile images
Mosaic image
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covert communication scheme via full-color secret-fragment-visible mosaic images by embedding a source-image recovery sequence and switching the orders of target blocks. A modified version of the secret-fragment-visible mosaic image creation process for use as the secret message embedding process for cover communication is shown in Figure 1.6. First of all, we calculate the 1-dimensional color histograms of a given secret image and a selected target image. Second, the secret messages which are transmitted by users are transformed into a bit string. With the histogram values of a secret image and a target image, we switch the corresponding target blocks of the tile images which are in the same histogram according to each bit to be embedded. After these steps, a secret-fragment-visible mosaic image into which the secret messages are hidden is created by the use of the modified fitting target blocks and a secret key. Finally, a source-image recovery sequence is embedded into the resulting image by a scheme of lossless least significant bit (LSB) modification. With the recovery sequence, the secret image can be retrieved quickly and easily. The detailed algorithm is presented in Chapter 4.
Figure 1.6 Embedding process of data hiding by switching the orders of tiles. Secret image Target image Compute 1-D histogram Compute 1-D histogram Secret data
Data embedding process by switching the orders of tiles
Secret key Creation process of secret-fragment-visible mosaics Mosaic image Secret histogram Target histogram
Transform into a bit string
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1.3.4 Brief Description of Proposed Method for
Image Steganography via Secret-fragment-visible
Mosaic Images
The proposed method for image steganography is achieved in the process of creating grayscale secret-fragment-visible mosaic images. Grayscale images are still being used frequently in modern days. People can utilize software packages (many available on the Internet) to transform secret documents, such as e-mail, PDF and Microsoft WORD, into grayscale images. We use this type of image to create a secret-fragment-visible mosaic image in order to disguise the transformed secret image as a grayscale art image. With this technique, while we deliver the document disguised as a grayscale mosaic image to other people, hackers will hardly notice that the file is carrying a secret image. And because the transformed image keeps the readability of the original documents by image fragments, a receiver can understand what the document content is after he/she regains the secret image from a secret image recovery process. The detailed algorithms will be given in Chapter 5.
Figure 1.7 Image steganography process by creating grayscale secret-fragment-visible mosaics. Secret
document S
Use software to transform S into grayscale image
Secret-fragment-visible mosaic creation Recovery Process of secret-fragment-visible mosaic Secret image Mosaic image
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1.3.5 Brief Description of Proposed Method for
Secret Sharing via Secret-fragment-visible
Mosaic Images
A method for secret sharing is proposed in this study. It is based on partitioning secret tile images into a number, say n, of sections and using them separately to create secret-fragment-visible mosaic images. As shown in the process illustrated by Figure 1.8, first, we select n target images from a database based on a secret image, and then divide the secret image into tile images of appropriate sizes. After that, we use a key to decide which target image can select tile images first, and then fit the selected tile image to the corresponding target block. The target images will take turns in this way of picking appropriate tile images.
According to the above operations, n secret-fragment-visible mosaic images are created from a secret image. Then, the recovery sequence of every mosaic image is divided into n 1 parts and hidden in the resulting share images. In this way, the secret image will be retrieved only if all of the share images are collected together. The detailed operations are described in Chapter 6.
Figure 1.8 Process of secret sharing through secret-fragment-visible mosaic images. Secret image Target database Secret key Target images Secret sharing process via
secret-fragment-visible mosaic images
Hide recovery sequences of every mosaic image
Mosaic images
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1.4 Contributions
Some major contributions of this study are listed as follows.
1. A method for creation of a new type of mosaic image, called secret-fragment-visible mosaic image, is proposed.
2. A greedy method is proposed, which fits tile images into appropriate target blocks in secret-fragment-visible mosaic images by computing the 1-dimensional color histograms of target images and secret images.
3. An algorithm is proposed, which can be used to decrease the running time of fitting tile images into appropriate target blocks.
4. A remedy method is proposed for reducing the target-block fitting error between a secret image and a selected target image while the image number of a database is not large enough for selecting a sufficiently similar target image.
5. A method is proposed to embed secret messages in secret-fragment-visible mosaic images by switching the corresponding target blocks of tile images. 6. A method for enhancing the security of the embedded secret message is
proposed.
7. An algorithm for creating grayscale secret-fragment-visible mosaic images for the aim of image steganography is proposed.
8. An algorithm for modification of the grayscale histogram to decrease the running time of the secret image hiding process for image steganography is proposed.
9. A method for enhancing the security of the secret image hiding process in the proposed method is proposed.
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secret-fragment-visible mosaic images is proposed.
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.
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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
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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)
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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 difference
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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
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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
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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.
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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
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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′ + Nr g′ + Nr Ng b′ (3.1)
and so generate conceptually a 1D image I′′ with new ―1-D color‖ values specified by
f 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.
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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′ + Nb 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
following steps:
1. compute the average of the color values (R, G, B) of all the pixels in C as (RC, GC, BC);
2. re-quantize (RC, GC, BC) into (rC′, gC′, bC′) using the new Nr, Ng, and Nb color
levels; and
3. calculate the h-feature hC for C by Eq. (3.2) above, resulting in the following
equation:
hC(rC′, gC′, bC′) = bC′ + Nb rC′ + Nb Nr gC′. (3.3)
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h-feature fC 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 Zt, and a pre-selected candidate
image size Zc.
Output: a database DB of candidate images with size Zc 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 Zt 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.
3.1 Compute an error e as the similarity measure between HS' and HD by the
following equation:
584 0 D m s' e H m H m
; (3.4)29
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
V2 , where V stands for the number of vertices. According to Figure 3.1, the number of vertices in this problem is as follows:
1 1 1 ! ! N n N n
,where N is the number of target blocks which is larger than 40,000 for the images used in this study. Obviously, the computation cost for getting an optimal solution for such a large N is too high. In this case, we have to find other possible solutions for fitting tile images in order to create a secret-fragment-visible mosaic image.
Figure 3.1 A tree structure of fitting tile images to target blocks.
The second problem is about how to select a sufficiently similar target image from a database which is not large enough. While we use such a database in the secret-fragment-visible mosaic creation process, the process will very likely to choose a dissimilar target image. As a result, the resulting image will look unlike the target one. In this case, we have to design a remedy method to deal with such a problem of use of a small-sized database.
B. Possible solutions for fitting tile images
…… …… S Depth 1 2 3 N Vertices 1 N-1 (N-1)×(N-2) (N-1)×(N-2)×…×1
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One possible solution for fitting tile images is the greedy algorithm. We try to calculate the Euclidean distance between a tile image and a target block as a selection function for a greedy algorithm. However, as shown by Figure 3.3(a), the resulting image of using such a greedy algorithm for fitting tile images is incomplete with its lower part being filled with fragment pieces with inappropriate colors. This phenomenon comes from the reason that the number of tile images obtained from the secret image, Figure 3.2(a), is limited by its own size, so that the available tile images for choice to fit the target blocks in Figure 3.2(b) become less and less near the end of the fitting process. As a result, the differences in terms of the Euclidean distance between the later-fitted tile images and the target blocks become bigger and bigger than the earlier-fitted ones, resulting in the poorly-fitted bottom part of Figure 3.3(a).
To get a possible solution to this problem, we try to vary the select function for use in the greedy algorithm. After many trials, we find that the effect on the created mosaic images becomes better if the previously-proposed h-feature, instead of the Euclidean distance, is used for defining the selection function for the greedy algorithm. This feature takes the global color distribution of an image into consideration. That makes the content of a created mosaic image using the proposed creation process resemble a target image, as shown by Figure 3.3(b)
C. Remedy method for creation process
By using the greedy algorithm with the selection function defined in terms of the
h-feature, we can generate a secret-fragment-visible mosaic image successfully. Yet
we still have the small-sized database problem to deal with. While a database is not large enough, the mosaic image creation process will select from the database a candidate image dissimilar to the secret image. As shown by Figure 3.5(a) which is a created mosaic image, which is created with Figures 3.4(a) and 3.4(b) as the secret
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and the selected target image, the major color of the created mosaic image is quite different from the selected target one.
Figure 3.2 Input images. (a) A secret image. (b) A target image.
Figure 3.3 Created mosaic images generated by a greedy algorithm. (a) Image created using Euclidean distance used to define a selection function for a greedy algorithm. (b) Image created using the
h-feature to define the select function for a greedy algorithm.
To solve this problem, during the candidate image selection process, after we
(b) (a)
(b) (a)
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compute an error between a secret image and a candidate image to measure the similarity, if the error is large, the selected target image is inappropriate for the creation process. In this case, we propose to enlarge the size of the target image. The reason is that if the size of a target image is larger than that of the secret image, the number of target blocks, or equivalently, the number of positions to fit the tile image, may be more freely chosen.
Furthermore, to deal with the surplus target blocks coming from enlargement of the target image, we fill each of them with the most similar tile image in the sense of the h-feature or with the average color of itself. More specifically, if the difference between the h-feature of the most similar tile image and that of the target block is larger than a certain threshold, then the target block is filled in the average color instead of the selected tile image. In this way, the resulting mosaic image is better than before, as shown by Figure 3.5(b).
D. Algorithm for secret-fragment-visible mosaic image creation
According to above-mentioned related processes, an algorithm for the proposed secret-fragment-visible mosaic image creation is described in the following. Basically, in the process of tile image fitting, we try to sort the h-feature values of tile images and target blocks, and then get two block-label sequences from the sorted feature values of them. By one-by-one mapping these two block-label sequences, each tile image can be fit into a most similar target block achieving the greedy search goal and decreasing the running time to
nlogn
. The detailed algorithm is given as follows.Algorithm 3.3: secret-fragment-visible mosaic image creation.
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Output: A secret-fragment-visible mosaic image R. Steps:
Stage 1 --- embedding secret image fragments into a selected target image.
Step 1. Crop S to yield an image S′ which is divisible by size Zt.
Step 2. Perform following steps to select a target image T. 2.1 Select a candidate image by Algorithm 3.2 as T.
2.2 If the error e computed in Step 3.1 of Algorithm 3.2 is larger than a pre-selected threshold Th, then enlarge the size of T e Th times.
Step 3. Perform the following steps to obtain a block-label sequence of each of S′ and
T.
3.1 Divide S′ into a sequence QS′ of blocks S1′, S2′, …, Sn′ as tile images based
on size Zt, where each block Si′ is said to have the label i.
3.2 Divide T into a sequence QT of blocks T1, T2, …, Tn as target blocks based
on size Zt, where the label of Ti is similarly defined.
3.3 For each tile image of S′ and each target block of T, calculate the h-feature values of them based on Eq. (3.3).
3.4 Sort the h-feature values of all Si′ and all Ti, and re-order accordingly the
blocks in QS′ and QT, respectively, to get two re-ordered block sequences
QS′′ and QT′.
3.5 Get the new label sequences L1 and L2 from the re-ordered block
sequences QS′′ and QT′, and call them h-sorted label sequences of the
resized secret image S′ and the selected target image T.
Step 4. Fit the tile images to the target blocks based on the one-to-one mappings from the ordered labels of L1 to those of L2, thus completing the embedding of all
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Stage 2 --- dealing with unfilled target blocks.
Step 5. Perform the following steps to fill each of the remaining unfilled target blocks, B, if there is any.
12.1 Compute the difference e′ between the h-feature hB of B and the h-feature hA
of each of the tile images, A, by the following equation:
e′ = |hB hA|. (3.5)
12.2 Pick out the tile image Ao with the smallest error e′ and compare e′ with
another pre-selected threshold Th′ in the following way:
A. if e′ < Th′, then fill the tile image Ao into the target block B;
B. if e′ Th′, fill the average R, G, and B values of all the pixels in B into
B.
Stage 3 --- generating the desired mosaic image.
Step 6. Generate the desired output image R by composing all the tile images fitted at their respective positions as an image.
Figure 3.4 Example images. (a) A secret image. (b) A target image. (b)
