基於俄羅斯方塊的馬賽克畫：一種新的藝術畫與其在資訊隱藏上的應用

國

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多媒體工程研究所

碩

碩

碩

碩

士

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論

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基於俄羅斯方塊的馬賽克畫：一種新的藝術畫與

其在資訊隱藏上的應用

Tetromino-based Mosaics — A New Type of Art Image and Its

Applications in Information Hiding

研 究 生：張均培

指導教授：蔡文祥 教授

中

中

中

基於俄羅斯方塊的馬賽克畫

基於俄羅斯方塊的馬賽克畫

基於俄羅斯方塊的馬賽克畫

基於俄羅斯方塊的馬賽克畫：

：

：

：一種新的藝術畫

一種新的藝術畫

一種新的藝術畫

一種新的藝術畫

與其在資訊隱藏上的應用

與其在資訊隱藏上的應用

與其在資訊隱藏上的應用

與其在資訊隱藏上的應用

Tetromino-based Mosaics — A New Type of Art Image and Its

Applications in Information Hiding

研 究 生：張均培 Student: Chun-Pei Chang

指導教授：蔡文祥 Advisor: Prof. Wen-Hsiang Tsai

國 立 交 通 大 學

多 媒 體 工 程 研 究 所

碩 士 論 文

A Thesis

Submitted to Institute of Multimedia Engineering College of Computer Science

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master

in

Computer Science

June 2009

Hsinchu, Taiwan, Republic of China

基於俄羅斯方塊的馬賽克畫

基於俄羅斯方塊的馬賽克畫

基於俄羅斯方塊的馬賽克畫

基於俄羅斯方塊的馬賽克畫：

：

：一種新的藝術畫

：

一種新的藝術畫

一種新的藝術畫與

一種新的藝術畫

與

與

與

其在資訊隱藏上的應用

其在資訊隱藏上的應用

其在資訊隱藏上的應用

其在資訊隱藏上的應用

研究生: 張均培

指導教授: 蔡文祥 博士

國立交通大學多媒體工程研究所

摘要

摘要

摘要

摘要

在本論文中，我們以俄羅斯方塊(Tetris)為基本元件，創造了一種新的藝術 畫，稱之為俄羅斯方塊馬賽克畫(tetromino-based mosaic images)，並研究自動產 生這種影像與在其中做資訊隱藏的技術。在俄羅斯方塊馬賽克畫中，我們找到了 兩種可供隱藏資訊的特性，分別是俄羅斯方塊的排列組合和其顏色的變化。首 先，我們利用樹狀搜尋演算法來找出所有俄羅斯方塊的排列組合，藉由選擇不同 的組合，將秘密資訊或浮水印隱藏於俄羅斯方塊馬賽克畫之中。同時，利用偵測 邊界所得到的資訊，我們也提出了一種強化邊緣的方法來改善上述資訊隱藏技術 所造成的雜訊。另一方面，藉由調整鄰近俄羅斯方塊的顏色，我們可以將秘密資 訊隱藏於其中，達到秘密訊息傳輸與版權保護之目的。此外，我們也提出一種可 視浮水印技術來保護俄羅斯方塊馬賽克畫的版權，而且所嵌入的可視浮水印可以 無失真地移除之。基於這種浮水印技術，最後我們利用調色盤的對應關係，將秘 密影像隱藏於浮水印區域，來達到影像秘密傳輸之目的。透過良好的實驗結果， 我們證明了所提出方法的實用性。

Tetromino-based Mosaics — A New Type of Art Image and

Its Applications in Information Hiding

Student: Chun-Pei Chang Advisor: Prof. Wen-Hsiang Tsai, Ph. D.

Institute of Multimedia Engineering, College of Computer Science

National Chiao Tung University

ABSTRACT

A new type of art image is created in this study, namely, tetromino-based mosaic

image. Methods for automatic creation of images of this type and data hiding in them

are proposed. For the creation of tetromino-based mosaic images, we find all the

possible combinations of tetrominoes by a tree enumeration algorithm. A tetromino

database is constructed with different colors and tetromino combinations for image

creation. We also propose a border enhancement process for improving visual effects of

tetromino edges. For data hiding in tetromino-based mosaic images, we utilize two

types of features of mosaic images, tetromino combination and color, to embed data.

We can hide data by using distinct combinations of tetrominoes. An edge fitting

method is used to enhance edge effects byadjusting combinations of tetrominoes using

the information obtained by edge detection. In addition, the colors of tetrominoes are

also used to hide data by shifting color values of tetrominoes slightly. For

watermarking in tetromino-based mosaic images, we propose a removable lossless

watermarking method by replacing the colors according to a mapping between two

color palettes. Based on this invertible watermarking method, an image steganographic

method is also proposed by replacing the colors of the watermark area according to the

proposed mapping between the two color palettes. Experimental results show the

ACKNOWLEDGEMENTS

I am in hearty appreciation of the continuous guidance, discussions, support, and

encouragement received from my advisor, Dr. Wen-Hsiang Tsai, not only in the

development of this thesis, but also in every aspect of my personal growth.

Thanks are due to Mr. Tsung-Yuan Liu, Mr. Chih-Jen Wu, Mr. Che-Wei Lee,

Mr. Guo-Feng Yang, Mr. Jian-Yuan Wang, Mr. Yi-Chen Lai, Miss Mei-Fen Chen,

Miss Chin-Ting Yang, Miss Chiao-Chun Huang and Miss Shu-Hung Hung for their

valuable discussions, suggestions, and encouragement. Appreciation is also given to

the colleagues of the Computer Vision Laboratory in the Institute of Multimedia

Engineering at National Chiao Tung University for their suggestions and help during

my thesis study.

Finally, I also extend my profound thanks to my family for their lasting love,

CONTENTS

ABSTRACT (in Chinese) ... i

ABSTRACT (in English)... ii

ACKNOWLEDGEMENTS ... iii

CONTENTS... iv

LIST OF FIGURES ... vii

LIST OF TABLES... x

Chapter 1

Introduction ... 1

1.1 Motivation and Background ...1

1.1.1 Motivation of Study ...1

1.1.2 Introduction to Tetris and Tetrominoes ...2

1.1.3 Introduction to Mosaic Images ...3

1.2 Overview of Proposed Methods...4

1.2.1 Definitions of Terms ...5

1.2.2 Brief Description of Proposed Method for Creation of Tetromino-based Mosaic Images ...7

1.2.3 Brief Description of Proposed Method for Data Hiding in Tetromino-based Mosaic Images by Distinct Combinations of Tetrominoes...7

1.2.4 Brief Description of Proposed Method for Data Hiding in Tetromino-based Mosaic Images by Small Tetromino Color Shiftings ...9

1.2.5 Brief Description of Proposed Method for Removable Lossless Visible Watermarking in Tetromino-based Mosaic Images ...10

1.2.6 Brief Description of Proposed Method for Image Steganography by Watermarking in Tetromino-based Mosaic Images ...12

1.3 Contributions...12

1.4 Thesis Organization ...13

Chapter 2

Review of Related Works... 14

2.1 Previous Studies on Mosaic Images ...14

2.2 Previous Studies on Information Hiding Techniques ...17

2.3 Previous Studies on Information Hiding Techniques in Art Images...18

2.4 Previous Studies on Image Steganography ...21

3.1 Idea of Proposed Method ...24

3.2 Review of Traditional Mosaic Image Creation Process...25

3.2.1 Mosaic Image Creation Process...25

3.2.2 Tile Image Mosaic Database Construction ...27

3.2.3 Similarity Measure Computation...28

3.3 Proposed Tetromino-based Mosaic Image Creation Process ...29

3.3.1 Scheme of Creation Process...29

3.3.2 Tetromino Database Construction...30

3.3.3 Visual Effect Improvement by Border Enhancement ...33

3.4 Experimental Results ...34

3.5 Discussions and Summary ...34

Chapter 4

Data Hiding in Tetromino-based Mosaic Images by

Distinct Combinations of Tetrominoes... 42

4.1 Idea of Proposed Method ...42

4.2 Proposed Data Hiding Method by Distinct Combinations of Tetrominoes42 4.2.1 Scheme of Propose Method ...42

4.2.2 Data Embedding Process ...44

4.2.3 Data Extraction Process ...45

4.2.4 Experimental Results ...47

4.3 Proposed Edge Fitting Method by Adjusting Combinations of Tetrominoes Using Information Obtained by Edge Detection...49

4.3.1 Scheme of Propose Method ...49

4.3.2 Detailed Algorithms of Edge Fitting Method ...49

4.3.3 Experimental Results ...55

4.4 Discussions and Summary ...55

Chapter 5

Data Hiding in Tetromino-based Mosaic Images by Small

Tetromino Color Shiftings ... 58

5.1 Idea of Proposed Method ...58

5.2 Proposed Data Hiding by Small Tetromino Color Shifting ...58

5.2.1 Scheme of Propose Method ...59

5.2.2 Data Embedding Process ...59

5.2.3 Data Extraction Process ...62

5.3 Experimental Results ...64

5.4 Discussions and Summary ...65

Chapter 6

Removable Lossless Visible Watermarking in

Tetromino-based Mosaic Images ... 70

6.1 Idea of Proposed Method ...70 6.2 Review of A Removable Lossless Visible Watermarking Technique for

Palette images ...71

6.3 Proposed Method for Removable Lossless Visible Watermarking in Tetromino-based Mosaic Images ...77

6.3.1 Visible Watermark Embedding Process ...77

6.3.2 Lossless Recovery Process of Original Images by Removing Visible Watermark...78

6.4 Experimental Results ...80

6.5 Discussions and Summary ...88

Chapter 7

Image Steganography in Tetromino-based Mosaic Images

by Watermarking ... 90

7.1 Idea of Proposed Method ...90

7.2 Proposed Method for Image Steganography in Tetromino-based Mosaic Images by Watermarking ...91

7.2.1 Image Embedding Process...91

7.2.2 Image Extraction Process...94

7.3 Experimental Results ...95

7.4 Discussions and Summary ...96

Chapter 8

Conclusions and Suggestions for Future Works ... 101

8.1 Conclusions...101

8.2 Suggestions for Future Works...102

LIST OF FIGURES

Figure 1.1 Five basic tetrominoes...2

Figure 1.2 Close’s paintings. (a) “Keith III, State I,” 1975. (b) “Self-Portrait,” 1977...5

Figure 1.3 (a) “Lincoln Portrait” by Harmon. (b) “Lincoln in Dalivision” by Dali... .5

Figure 1.4 Creation process of tetromino-based mosaic images.... ...8

Figure 1.5 Embedding process of data hiding by distinct combinations of tetrominoes.... ...9

Figure 1.6 Embedding process of data hiding by small color shiftings... 11

Figure 1.7 Removable lossless watermarking process in tetromino-based mosaic images.... ... 11

Figure 2.1 Ancient mosaic images. (a) Detail from the mosaic floor signed Gnosis in the “House of the Abduction of Helen” at Pella, Greek, late 4th century BC, Pella, Archaeological Museum. (b) Roman mosaic of Ulysses at Carthage, Bardo Museum, Tunisia.... ...14

Figure 2.2 Mosaic images created by a number of authors. (a) By Haeberli. (b) By Hausner. (c) By Dobashi et al. (d) By Faustino and Figueiredo. (e) By Di Blasi and Gallo. (f) By Elber and Wolberg...16

Figure 2.3 Jigsaw image mosaic (JIM) created by Kim and Pellacini...17

Figure 2.4 Colored paper mosaic created by Gi et al...17

Figure 2.5 Image mosaics created by Lin and Tsai [21]. (a) A mosaic image of Lena. (b) A mosaic image of Albert Einstein...19

Figure 2.6 Art images created by Hung et al. [22]. (a) A tile mosaic image. (b) A stained glass image.... ...19

Figure 2.7 Art images created by Hsu and Tsai [23]. (a) A digital puzzle image. (b) A digital pointillistic image. (c) A digital circular-dotted image...20

Figure 2.8 Art images created by Wang and Tsai [24]. (a) An irregular hexagonal-tiled images. (b) A tile-overlapping mosaic images. (c) A variable-sized mosaic images.... ...22

Figure 3.1 The system architecture of an image mosaic creation system...26

Figure 3.2 An experimental result of image mosaic creation by Lin and Tsai [21]...27

Figure 3.3 Nineteen types of oriented tetrominoes.... ...31

Figure 3.4 Some illustrations of inputs in Algorithm 3.5. (a) A plane of 4×4 grids. (b) A tetromino combination in a plane of 4×4 grids.... ...31

Figure 3.5 An original image... ...35 Figure 3.6 Some of experimental results of the proposed tetromino-based mosaic

created from Figure 3.5. (b) A partial image of the red region in (a)... ...36 Figure 3.7 Some of experimental results of the proposed tetromino-based mosaic

creation. (a) A tetromino-based mosaic image with dark border effects created from Figure 3.5. (b) A partial image of the red region in (a)... ...37 Figure 3.8 Some of experimental results of the proposed tetromino-based mosaic

creation. (a) A tetromino-based mosaic image with lightening and

shading border effects created from Figure 3.5. (b) A partial image of the red region in (a)... ...38 Figure 3.9 Some of experimental results of the proposed tetromino-based mosaic

creation. (a) An image of Eiffel Tower. (b) A tetromino-based mosaic image created from (a)...39 Figure 3.10 Some of experimental results of the proposed tetromino-based mosaic

creation. (a) An self-portrait of van Gogh. (b) A tetromino-based mosaic image created from (a)... ...40 Figure 3.11 Some of experimental results of the proposed tetromino-based mosaic

creation. (a) An image of Jolin, a singer. (b) A tetromino-based mosaic image created from (a).... ...41 Figure 4.1 Fourteen edge types in a grid of 4×4 grids.. ...46 Figure 4.2 Some illustrations of tetromino combination recognition. (a) A tetromino

combination of 4×4 grids. (b) A corresponding edge type array of (a)... ...46 Figure 4.3 An experimental result. (a) A stego-tetromino-based mosaic image with

embedded data. (b) The message extracted from (a)... ...48 Figure 4.4 A comparison between two tetromino-based mosaic images. The blue and

green regions show the differences caused by noise. (a) An original image. (b) An image created from (a) by a mosaic creation in Chapter 3. (c) An image created from (a) by our data hiding method in Section 4.2... ... 52 Figure 4.5 A Gaussian filter matrix...54 Figure 4.6 3×3 Sobel masks...55 Figure 4.7 Some illustrations of tile images for different edge directions. (a) Vertical

direction. (b) Horizontal direction. (c) Two diagonal directions.... ...55 Figure 4.8 Some experimental results. The green regions show the noise

improvement achieved by an edge fitting method. (a) A

stego-tetromino-based mosaic image created from 4.4(a) with embedded data. (b) A stego-tetromino-based mosaic image created from 4.4(a) with embedded data by the proposed edge fitting method.... ...56 Figure 5.1 A comparison of four close colors in a block. (1) Color values of RGB

channel = (255, 0, 0). (2) Color values of RGB channel = (255, 2, 0). (3) Color values of RGB channel = (253, 0, 2). (4) Color values of RGB

channel = (253, 2, 2)... ...60 Figure 5.2 An illustration of nineteen tetromino types and their pivot grids. The

black spot of each tetromino depicts its pivot grid... ...60 Figure 5.3 An experimental result. (a) A tetromino-based mosaic image. (b) A

stego-tetromino-based mosaic image created from (a) with the watermark shown in (c) embedded. (c) The watermark. (d) A watermark extracted from (b) with a correct key. (e) A watermark extracted from (b) with a wrong key...66 Figure 5.4 Another experimental result. (a) A tetromino-based mosaic image. (b) A

stego-tetromino-based mosaic image created from (a) with the watermark shown in (c) embedded. (c) The watermark. (d) A watermark extracted from (b) with a correct key. (e) A watermark extracted from (b) with a wrong key...68 Figure 6.1 An experimental result of Chen and Tsai’s method [32]. (a) A binary

watermark image. (b) A color palette image. (c) A watermarked image created by embedding the visible watermark (a) into (b). (d) A lossless recovered image created by removing the visible watermark (a) from (c)... ...76 Figure 6.2 A binary watermark image of size 256×256...81 Figure 6.3 An experimental result. (a) A tetromino-based mosaic image. (b) A

watermarked image created from (a) with the watermark shown in Figure 6.2 embedded. (c) A recovered image created with a right key. (d) A

recovered image created with a wrong key...81 Figure 6.4 An experimental result. (a) A tetromino-based mosaic image. (b) A

watermarked image created from (a) with the watermark shown in Figure 6.2 embedded. (c) A recovered image created with a right key. (d) A

recovered image created with a wrong key...85 Figure 7.1 Input images for the proposed method. (a) A binary watermark. (b) A

secret image. (c) A secret image... ...96 Figure 7.2 An experimental result. (a) A tetromino-based mosaic image. (b) A

watermarked stego-image created from (a) with a secret image shown in Figure 7.1(b) embedded. (c) The secret image extracted with a right key. (d) The secret image extracted with a wrong key... ...97 Figure 7.3 Another experimental result. (a) A tetromino-based mosaic image. (b) A

watermarked stego-image created from (a) with a secret image shown in Figure 7.1(c) embedded. (c) The secret image extracted with a right key. (d) The secret image extracted with a wrong key... ...99

LIST OF TABLES

Chapter 1

Introduction

1.1

Motivation and Background

1.1.1

Motivation of Study

With the progress of computer networks, interpersonal communication is more

and more popular than before. Exchanges of digital files have become convenient and

fast through the Internet. For example, many people have the experience of sharing

their photographs of traveling with families and friends on instant messaging services

such as MSN Messenger and Skype. However, this trend brings many drawbacks in

communication security. For example, hackers on the Internet can easily duplicate or

tamper with the contents of digital files, causing many legal problems of privacy and

copyright. In addition, important information, such as bank account passwords or

intelligence data, is extremely secret and should be protected carefully. This demand

has generated wide interests in enhancing the security involved in digital file

transmission. Therefore, the study of covert communication and copyright protection

becomes an important issue.

Different from the traditional information hiding techniques, this study tries to

combine approaches to information hiding and art image creation. Using art images as

camouflages of secret data brings some benefits. Someone who intends to steal the

data may consider that these art images are only artistic productions and ignore them

can also be applied to enhance copyright protection and authentication for the art

image which we create. These properties assure that approaches to information hiding

in art images are safer than traditional ones.

Due to geometric characters, Tetris and tetrominoes, which will be introduced in

detail in the following section, are chosen as materials to create mosaic images for use

as the art image mentioned above. Tetrominoes can be used to fill a plane in certain

arrangement without overlapping. This property makes tetrominoes become good

components of a new type of mosaic image, called tetromino-based mosaic image in

this study. It is desired to propose a method for creation of tetromino-based mosaic

images and design new information hiding techniques for covert communication and

copyright protection applications by taking advantages of the characteristics of this

new type of mosaic image.

1.1.2

Introduction to Tetris and Tetrominoes

Tetris is a popular computer game invented by a Russian mathematician, named

Alexey Pajitnov, in 1985. He derived the game’s name from the Greek numerical

prefix "tetra-" and tennis, his favorite sport. "Tetra-" means that all of the game's

pieces, called tetrominoes, contain four segments. A tetromino is a geometric shape

composed of four squares, connected orthogonally. There are five basic tetrominoes

(shown in Figure 1.1), and nineteen oriented tetrominoes obtained by rotating and

reflecting the basic tetrominoes.

The game rule of Tetris is as follows: An initial game board, a rectangular grid

with all empty cells, is given. A random sequence of tetrominoes is generated, and the

player is allowed to rotate and horizontally move the falling piece before it lands on

filled cells. If an entire row of the game board is filled with tetrominoes, all cells of

this row are cleared and the game score is increased gradually. A player loses when a

new piece is blocked by filled cells and cannot enter the game board anymore.

Breukelaar et al. [1] showed that the problem of deciding whether a given Tetris

configuration can be cleared using a given sequence of pieces is NP-hard.

In this study, we will not only use tetrominoes as materials for creating a novel

type of mosaic image which is called tetromino-based mosaic image in this study, but

also develop information hiding techniques in tetromino-based mosaic images for

covert communication, copyright protection, and image steganography applications.

1.1.3

Introduction to Mosaic Images

Mosaic is the art of surface decorations composed of numerous small pieces of

colored glass, stone, or other materials. It is used for cultural or religious significance

in Greek and Roman times over 2000 years ago, and is still widely used today in

many ways, such as decorations of house interiors, commercials and church windows,

etc.

Creating different kinds of mosaic images by computing is a new research topic

in recent years. A traditional mosaic image is obtained by arranging a large number of

small images, called tile images, in a certain way so that each tile image presents a

small piece of the source image, named target image. The overall effect is that the

mosaic image seems like the source image when seen from a distance. This effect

only see the average color of a region even though the region is actually full of

different colors. As a result, the key point of mosaic image creation is to make the

average colors of tiles to be as similar to those of the target images as possible.

Battiato et al. [2] gave the mathematical problem definition of mosaic creation and

optimization issue as follows:

Given a rectangular region I2 in the plane R2, a tile dataset and a set of constraints, find N sites Pi(xi, yi) in I2 and place N tiles, one at each Pi , such that all tiles are disjoint, the area they cover is maximized and the

constraints are verified as much as possible.

In the 1970’s, American artist Close [3] began producing gridded paintings by

using some characteristics of the human visual system. Some of his paintings are

shown in Figure 1.2. Harmon [4]created the first result of mosaic images through the

computer and designed an automatic human-face recognition system for mosaic

creation in 1973. A resulting image of his method is revealed in Figure 1.3 (a). Dali [5]

imitated Harmon’s achievement to paint a famous portrait of Abraham Lincoln,

named “Lincoln in Dalivision” as seen in Figure 1.3 (b). He painted this masterpiece

by putting many small images together which include a picture of his wife.

In this research, we are not only inspired by Close’s and Dali’s paintings to raise

the idea of establishing a scheme for a new type of mosaic image creation, but also

paid attention to its applications in information hiding.

1.2

Overview of Proposed Methods

In this thesis study, we concentrate our attention on full-color images. First of all,

process are given. Then two data hiding techniques and applications of covert

communication and watermarking are proposed based on the above-mentioned

scheme. Furthermore, a removable lossless visual watermarking technique for

tetromino-based mosaic images is proposed. Finally, we propose an image

steganographic scheme for tetromino-based mosaic images based on the use of the

watermarking technique.

(a) (b)

Figure 1.2 Close’s paintings. (a) “Keith III, State I,” 1975. (b) “Self-Portrait,” 1977.

(a) (b)

Figure 1.3 (a) “Lincoln Portrait” by Harmon. (b) “Lincoln in Dalivision” by Dali.

Before describing the proposed methods, some definitions of terms are given to

facilitate the understanding of the remainder of this thesis.

1. Source image: A source image is an image chosen to produce a mosaic

image.

2. Tile image: A tile image is a small image, similar to a small specific block

of the source image.

3. Target image: A target image is a sub-image of the source image obtained

by dividing the source image into tiles. For each target image, there is a

corresponding tile image for substitution in the mosaic creation process.

4. Mosaic image: A mosaic image is obtained by arranging a large number

of tile images in a certain way, yielding an effect like the source image

when seen from a distance.

5. Cover image: A cover image is a medium to be embedded with a

watermark for copyright protection or some information for covert

communication.

6. Stego-image: A stego-image is produced by embedding a watermark or

some information into a cover image.

7. Creation process: A creation process generates a mosaic image from

source image.

8. Embedding process: An embedding process is a process to embed data in

an image.

9. Extraction process: An extraction process is a process to extract data

from an image.

10.Recovered image: a recovered image is an image that is produced by

removing an embedded visible watermark from a stego-image.

remove the embedded visible watermark from a stego-image and obtain

exactly the original cover image without distortion.

12.Image steganography: Image steganography is the scheme to embed

secret information into images for covert communication such that the

secret transmitted in the communication is imperceptible.

1.2.2

Brief Description of Proposed Method for

Creation of Tetromino-based Mosaic Images

The proposed creation process of tetromino-based mosaic images is depicted in

Figure 1.4. According to the flowchart, first of all, we construct a mosaic database

with tetromino combinations and colors. Then we divide a given image into many tile

images to find the best matching combination and colors of tetrominoes from the

mosaic database for each tile image. The tetromino-based mosaic image for the given

image is generated by composing all tile images in a certain arrangement. Moreover,

some related processes of such mosaic creation are proposed to improve the visual

effects of the generated tetromino-based mosaic image. The detailed creation process

will be described in Chapter 3.

1.2.3

Brief Description of Proposed Method for Data

Hiding in Tetromino-based Mosaic Images by

Distinct Combinations of Tetrominoes

Based on the scheme of above-mentioned tetromino-based mosaic image

using distinct combinations of tetrominoes. The data embedding process of such data

hiding is illustrated in Figure 1.5. At the beginning, we transform given data which

will be hidden into a bit sequence. The given data might be a watermark, a piece of

secret message, or any digital data which you want to transmit by covert

communication. A user key is used to strengthen the security of data hiding by

disarranging the bit sequence of the given data. Second, an edge fitting process is

performed by edge detection thresholding before the data embedding process. Finally,

a tetromino-based mosaic image with embedded data is created by the data

embedding process using distinct combinations of tetrominoes. The detailed algorithm

of the embedding method will be described in Section 4.3.2.

Figure 1.4 Creation process of tetromino-based mosaic images.

The data extraction process is an inverse version of the above-mentioned data

embedding process. After the tetromino shape detection process, the extraction

process is performed to obtain the embedded data by recognizing the combinations of

tetrominoes. Then the user key is utilized to recover the given data in its original order.

The description of the extraction process will be described in detail in Section 4.3.3.

Mosaic image Source

image

Divide image into tile images in fixed size

Mosaic database Construct tetromino database Construct color database Find the best matching

combination and color from database

1.2.4

Brief Description of Proposed Method for Data

Hiding in Tetromino-based Mosaic Images by

Small Tetromino Color Shiftings

A tetromino is composed by four squares with the same color. However, human

visual system cannot be aware of small changes of colors. According to this property,

colors of each tetromino can be shifted in small amounts to embed data. The

embedding process of data hiding is illustrated in Figure 1.5. At first a tetromino

shape detection process is performed on an input tetromino-based mosaic image. Then,

the data embedding process by small color shiftings in each tetromino is performed

and a user key is used to disarrange the given data for safety. Finally, a

tetromino-based mosaic image with embedded data is generated through an

imperceptible data embedding process.

Figure 1.5 Embedding process of data hiding by distinct combinations of tetrominoes.

Source image Mosaic image Tetromino-based mosaics creation process Data embedding process

by distinct combinations Edge enhancement by edge detection thresholding Given data Transform into a bit sequence User key

The data extraction process is a reversed procedure of the data embedding

process. After the execution of a tetromino shape detection process, the extraction

process by tetromino color detection is performed to obtain the embedded data. The

detailed algorithm of the data embedding and extraction processes will be stated in

Section 5.2.2 and 5.2.3, respectively.

1.2.5

Brief Description of Proposed Method for

Removable Lossless Visible Watermarking in

Tetromino-based Mosaic Images

Tetromino-based mosaic images are composed by limited colors which integrally

are similar to a palette in concept. As a result, we can employ this characteristic to

apply some palette-like watermarking technique to tetromino-based mosaic images.

The proposed process of removable lossless watermarking in tetromino-based mosaic

images is illustrated in Figure 1.7. In the first place, two palettes called source palette

and secret palette are created by counting the colors of the source image and the

secret image respectively. Second, a corresponding table of these two palettes for

watermarking is constructed by the use of a measure of Euclidean distance. At last,

the colors of the source image in the watermarked area are replaced with the

corresponding colors in the table to form a watermarked stego-image. The watermark

removing process is an inverse process of the watermark embedding process. The

Figure 1.6 Embedding process of data hiding by small color shiftings

Figure 1.7 Removable lossless watermarking process in tetromino-based mosaic images.

Source image Secret image

Count the occurrence of colors Sort color palette by occurrence of colors Count the color palette

of secret image

Count the color palette of source image Source palette Secret palette Construct the corresponding table of two palettes Watermarked Stego-image Use the table to replace the colors of source image

in watermarked area Watermark User key Mosaic image Mosaic image Tetromino-based mosaic

image creation process Data embedding process

by small color shiftings Given data Transform into a

bit sequence User key

Tetrominoes shape detection process

1.2.6

Brief Description of Proposed Method for

Image Steganography by Watermarking in

Tetromino-based Mosaic Images

The proposed method for image steganography is achieved by the concept of the

removable watermarking technique. A watermarked tetromino-based mosaic image is

created as a cover image to embed a secret image by the palette-like watermarking

technique. In other words, the watermarked area is used to embed a secret image for

image steganography. The detailed algorithm will be described in Chapter 7.

1.3

Contributions

Some major contributions of this study are listed as follows.

1. A method to find all arrangements of tetrominoes to fill a plane and

construct a tetromino database for mosaic creation.

2. A method to create a new type of mosaic images composed of

tetrominoes is proposed.

3. A method to recognize the tetromino combinations in tetromino-based

mosaic images is proposed.

4. A method for data hiding in tetromino-based mosaic images by distinct

combinations of tetrominoes is proposed.

5. A method for data hiding in tetromino-based mosaic images by small

tetromino color shiftings is proposed.

6. A method to enhance the visual effects of edges by a border enhancement

images.

7. A method for removable lossless watermarking technique for

tetromino-based mosaic images is proposed.

8. A method for image steganography by watermarking in tetromino-based

mosaic images is proposed.

1.4

Thesis Organization

The remainder of this thesis is organized as follows. In Chapter 2, we review the

related works of this study. In Chapter 3, the proposed method for creation of

tetromino-based mosaic images is described. In Chapters 4, the data hiding method by

distinct combinations of tetrominoes in tetromino-based mosaic images is presented.

The edge fitting method by edge detection thresholding is also described. Then, the

proposed data hiding method by small tetromino color shiftings is described in

Chapter 5. We present the proposed removable lossless watermarking method for

tetromino-based mosaic images in Chapter 6. In Chapter 7, the proposed method for

image steganography by watermarking in tetromino-based mosaic images will be

presented. Conclusions of our works and discussions on future works are included in

Chapter 2

Review of Related Works

2.1

Previous Studies on Mosaic Images

Mosaic image is a common type of decorations composed of numerous small tiles

arranged in a certain way. Tile mosaics appeared in Greek and Roman times over 2000 years

ago. Two examples are shown in Figure 2.1. They are still widely used today. Creation of

mosaic images is a new research topic in recent years.

(a) (b)

Figure 2.1 Ancient mosaic images. (a) Detail from the mosaic floor signed Gnosis in the “House of the Abduction of Helen” at Pella, Greek, late 4th century BC, Pella, Archaeological Museum. (b) Roman mosaic of Ulysses at Carthage, Bardo Museum, Tunisia.

Haeberli [6] used Voronoi diagramsto place the Voronoi sites at random and fill

each tile with a color which is sampled from the image. However, Haeberli’s method

does not attempt to follow the edge features of the image and the tiles all have

utilizing centroidal Voronoi diagrams. In Hausner’s method, the method proposed by

Hoff [8] was extended to draw a Voronoi diagram efficiently, and Lloyd’s algorithm

[9] was utilized to produce centroidal Voronoi diagrams by moving each seed to the

centroid of its Voronoi region.

Extending the original idea of Haeberli’s method, Dobashi et al. [10] optimized

Voronoi diagrams by using the sites and edges of the Voronoi diagrams to reduce the

error between the original image and the resulting image. Faustino and Figueiredo [11]

presented a technique similar to Dobashi’s method. The main difference is that

Faustino and Figueiredo created tiles whose sizes are adapted to the edge features of

the image. This method is achieved by using a centroidal Voronoi diagram with a

density function that emphasizes edge features. Di Blasi and Gallo [12] created

another type of mosaic images by emphasizing boundaries by placing tiles along edge

directions. Elber and Wolberg [13] proposed an advanced approach to rendering

traditional mosaic images by recovering free-form feature curves from the image and

laying rows of tiles along edge curves. Figure 2.2 shows some examples of the results

of the above-mentioned methods.

Photomosaics created by Silvers and Hawley [14] is a different kind of mosaic

where a collection of small images is arranged in a rectangular grid. When viewing

the mosaic composed by small images from a distance, the small images combine to

yield an impressive integrated painting. Kim and Pellacini [15] introduced a new kind

of mosaic, called jigsaw image mosaic (JIM), as shown in Figure 2.3, where image

tiles of arbitrary shape are used to compose the final picture. Gi et al. [16] proposed a

technique of generating and arranging fragmentary piece of colored tiles to simulate

(a) (b)

(c) (d)

(e) (f)

Figure 2.2 Mosaic images created by a number of authors. (a) By Haeberli. (b) By Hausner. (c) By Dobashi et al. (d) By Faustino and Figueiredo. (e) By Di Blasi and Gallo. (f) By Elber and Wolberg.

Figure 2.3 Jigsaw image mosaic (JIM) created by Kim and Pellacini.

Figure 2.4 Colored paper mosaic created by Gi et al..

2.2

Previous Studies on Information

Hiding Techniques

Many information hiding techniques have been proposed to embed data into

given media for various purposes, such as covert communication or copyright

the human visual system, for example, by changing the least significant bits of the

pixels of a cover image to embed information [17]. The information embedded in an

image can be used to protect the copyright of the image, verify the authenticity of the

image, convey a secret message, and so on.

Information hiding in images is a popular research topic in recent years.

Researches on this topic can be classified into three approaches, namely, the

spatial-domain approach, the frequency-domain approach, and the combination of

them [18]. Ni, et al. [19] presented a novel reversible data hiding algorithm in the

spatial domain by utilizing the zero or the minimum point of the histogram and

slightly modifying the pixel values to embed data. Cheng and Tsai [20] proposed a

DCT-based method for embedding an invisible watermark by adjusting the magnitude

relation of certain DCT coefficient pairs in the frequency domain. No matter what

domains they belong to, most of these researches are based on pixel-wise or

block-wise operations. Generally speaking, information hiding in the frequency

domain is more robust than that in the spatial domain, but produces more distortion

sometimes.

2.3

Previous Studies on Information

Hiding in Art Images

Lin and Tsai [21] proposed two methods to hide information in image mosaics.

One is to manipulate the four borders of tile images. The other is to modify the

histogram of tile images. Hung et al. [22] proposed two methods to hide information

in art images. One is to embed data in the tile mosaic image by modifying the

orientations, sizes, and textures of tile mosaic images. The other is to embed data in

Lin and Tsai [21] are shown in Figure 2.5. Two images generated by Hung et al. [22]

are shown in Figure 2.6.

(a) (b)

Figure 2.5 Image mosaics created by Lin and Tsai [21]. (a) A mosaic image of Lena. (b) A mosaic image of Albert Einstein.

(a) (b)

Figure 2.6 Art images created by Hung et al. [22]. (a) A tile mosaic image. (b) A stained glass image.

Hsu and Tsai [23] proposed three methods to hide information in art images. One

is to embed data in digital puzzle images by modifying the orientations, sizes, and

varying the RGB values of each color dot of the pointillistic image. The other is to

embed data in the circular-dotted image by modifying the drawing order of the

circular dots of the circular-dotted image. Some examples of the art images created by

Hsu and Tsai [23] are shown in Figure 2.7.

(a) (b) (c)

Figure 2.7 Art images created by Hsu and Tsai [23]. (a) A digital puzzle image. (b) A digital pointillistic image. (c) A digital circular-dotted image.

Wang and Tsai [24] proposed the creations of three types of art images and their

applications for information hiding. First, information is hidden in irregular

hexagonal-tiled images by adjusting the locations of the two specific vertices and

modifying the inner colors of hexagons. For tile-overlapping mosaic images, the

information hiding work was implemented by changing the overlapping degrees of

adjacent tile images. Last, an information hiding method in variable-sized mosaic

images was proposed by changing the sizes of them without creating holes and

overlapping areas in the resulting stego-image. Some examples of the art images

created by Wang and Tsai [24] are shown in Figure 2.8.

the combinations of mosaic image creation and information hiding techniques will be

proposed. We will focus on tetromino-based mosaic images, a novel type of mosaic

image. A method for automatic creation of tetromino-based mosaic images and two

data hiding methods for such images are proposed. Furthermore, we propose a

technique of removable lossless visible watermarking in tetromino-based mosaic

image. Using this watermarking technique, an image steganography method for

tetromino-based mosaic images is also proposed in this study.

2.4

Previous Studies on Image

Steganography

Steganography, which means “covered writing” in Greek, is the science of

communicating a message by embedding it into data files of certain forms. This

technique differs from cryptography in that communication is evident but the content

of the communication is camouflaged. Unlike data hiding and digital watermarking,

the main goal of steganography is to create complete imperceptibility. Many different

file formats can be used as cover media for data hiding, but digital image are the most

popular file type because they are used everywhere on the Internet.

Least significant bit (LSB) insertion is the most common approach to embedding

information in a cover image [17]. In this approach, the least significant bit of each

byte inside an image is changed to hide at least a bit of the secret message. Lee and

Chen [25] proposed an image steganographic model based on variable-sized LSB

insertion to maximize the embedding capacity while maintaining image fidelity.

images by using the compression properties of the frequency domain. Fridrich and Du

[27] presented a steganographic technique for palette images by hiding message bits

into the parity bits of colors which are close to one another.

Marvel et al. [28] presented a new type of digital image steganography, called

spread spectrum image steganography (SSIS). The SSIS system proposed by them

combines spread spectrum communication, error control coding, and image

processing to hide information in images. Fridrich and Goljan [29] presented a new

steganographic method for digital images in raster formats. Message bits are

embedded in the cover image by adding a weak noise signal with a specified but

arbitrary probabilistic distribution. A steganographic technique for embedding secret

messages into a gray-valued cover image was proposed by Wu and Tsai [30].

Information is embedded into a cover image by replacing the difference values of the

two-pixel blocks of the cover image with similar ones in which bits of embedded data

are included.

(a)

Figure 2.8 Art images created by Wang and Tsai [24]. (a) An irregular hexagonal-tiled images. (b) A tile-overlapping mosaic images. (c) A variable-sized mosaic images.

(b)

(c)

Figure 2.8 Art images created by Wang and Tsai [24]. (a) An irregular hexagonal-tiled images. (b) A tile-overlapping mosaic images. (c) A variable-sized mosaic images (continued).

Chapter 3

Creation of Tetromino-based Mosaic

Images

3.1

Idea of Proposed Method

Lin and Tsai [21] proposed a method to create an image mosaic by arranging a

large number of small tile images with each tile image resembling a similar-sized

block of a given image. The image mosaic composed of all the tile images looks

integrally like the source image when seen from a distance. The idea of the proposed

art image creation method in this study was inspired by Lin and Tsai’s method to

create a new type of mosaic images, called tetromino-based mosaic image, as

mentioned previously. The idea of tetromino-based mosaic image creation was

developed by two main concepts. The first is an integration of art and computer

technology. Users can create their own images which look more artistically with

special visual effects for decorations. The second concept is that a mosaic image can

be used as a fine medium for covert communication. As a result, the proposed method

also deals with the problem of copyright protection.

In geometry, tetrominoes can be repeated to fill a plane and combined closely to

one another to form a square lock. This is the reason why tetrominoes are also good

units for mosaic image creation as proposed in this study. However, tiling a plane

with tetrominoes is more difficult than traditional mosaic creation because

kinds of tetrominoes to create a variety of distinct mosaic image is a critical issue. In

addition, using tetrominoes as components to generate mosaic images can provide a

new style of visual effects for viewers. The tetromino-based mosaic image creation

and other related processes are stated in the following sections.

3.2

Review of Traditional Image Mosaic

Creation Process

3.2.1

Mosaic Image Creation Process

Two issues, mosaic database construction and similarity measure selection, play

important roles in mosaic image creation. The former is the first step of the mosaic

creation process to generate tiles images. Tile images are not only the basic

components of mosaic images but also the key components determining how mosaic

images look like. The latter issue is the design of a good measure for use in the

process of choosing the best matching tile image from a mosaic database. In Lin and

Tsai’s study [21], mosaic images were created according to the following procedures.

First, a mosaic database was constructed by selecting a set of tile images and then

extracting from their relevant features which depend on what types of tile images are

used as the input to the construction process. Next, the image mosaic creation process

starts with a source image as an input. The process divides the source image into

many small target images based on a given size. A similarity measure is then used to

search the best matching tile images of the given size from the mosaic database.

Finally, after putting the best-matching tile images together, a mosaic image is

Algorithm 3.1. Traditional mosaic creation process.

Input: a source image I, a tile image database DB, and a given tile size S. Output: a mosaic image I′.

Steps:

Step 1. Divide I into blocks of target images based on the given size S.

Step 2. Extract features from each target image.

Step 3. For each target image, search the best matching tile image from tile image

database DB according to a similarity measure.

Step 4. _{Compose all tile images to generate a mosaic image I′.}

The architecture of traditional mosaic creation is shown in Figure 3.1. The

experimental result is show in Figure 3.2.

Figure 3.1 The system architecture of an image mosaic creation system. Divide image into target images

Extract features of each tile image

Search best matching till image from DB

Compose all tiles to create mosaic image

Mosaic image Extract color features from

original tile images

DB

Generate new tile images from color features

Mosaic Creation Process Original

image Images

Mosaic Database Construction

Similarity measure computation Add tile images to database

Figure 3.2 An experimental result of image mosaic creation by Lin and Tsai [21].

3.2.2

Tile Image Mosaic Database Construction

For mosaic image creation, we have to construct a database to accelerate the

computation of searching the best matching tile image. We accomplish tile image

database construction using the following algorithm.

Algorithm 3.2. Tile image database construction. Input: a set of original tile images, M = {I1, I2, …, In}.

Output: a set of new tile images, N = {T1, T2, .., Tn} and a set of feature vectors V =

Steps:

Step 1 Calculate the average color of each original tile image Ii in each of the RGB

channels.

Step 2 Represent the average colors as a one-dimension feature vector Vi with three

elements Ri, Gi, and Bi for Ii.

Step 3 Generate a new tile image Ti by resizing and cropping each original image Ii

to a predefined tile size.

Step 4 Add all Ti and associated Vi to DB.

3.2.3

Similarity Measure Computation

In Algorithm 3.1, computation of the similarity measure between a target image

and a tile image is mentioned. An input source image is first divided into blocks of

small target images and the feature vector of each target image is obtained by

calculating three average color values of the target image in the RGB channels. The

vector extracted from a target image is taken as an input to the similarity measure

computation with another input being the feature vector extracted from a tile image in

the mosaic database. A tile image from the mosaic database is considered to be similar

to the target image if the resulting value of the similarity measure, say a Euclidean

distance between the two feature vectors, is the smallest among all the tile images in

the database. The detailed algorithm of similarity measure computation is described as

follows.

Algorithm 3.3. Similarity measure computation.

Input: a target image T, and a tile image L from the database DB. Output: a similarity measure value D between T and L.

Steps:

Step 1. Divide T and L into N parts, where N is a predefined number.

Step 2. Extract color features from each part of T to form a vector VT with

N×3

elements.

Step 3. Extract color features from each part of L to form a vector VL with N×3

elements.

Step 4. Calculate the Euclidean distance between the color vectors VT and VL

according to the following similarity measure:

2

T L

D

=

=

=

=

V

−

−

−

−

V

.

3.3

Proposed Tetromino-based Mosaic

Image Creation Process

3.3.1

Scheme of Creation Process

In this section, based on above-mentioned traditional mosaic image creation

process we show how to create a tetromino-based mosaic image as an algorithm as

follows.

Algorithm 3.4. Creation process of tetromino-based mosaic images.

Input: a source image I, a given size s of one square in a tetromino, and a tile image database DB.

Output: a tetromino-based mosaic image I′. Steps:

Step 1.Construct a tetromino database DB by generating numerous tile images with

Step 2.Divide the source image I into many target images with the given size s.

Step 3.For each target image T, perform the following operations.

3.1 Calculate the distance between T and each tile image L in the tetromino

database DB by Algorithm 3.3.

3.2 Choose the tile image Lo in DB with the smallest distance as the best

matching tile image for T.

3.3 Perform a border enhancement process to enhance the visual effect of

each tetromino in T.

Step 4.For each target image T in I, replace it with the best matching tile image to

create a tetromino-based mosaic image I′ as output.

In the above steps, a best matching tile image, which is the most similar to the

corresponding target image, is found by the similarity measure computation as stated

in Algorithm 3.3. The construction of the tetromino database DB mentioned in the

above algorithm is described in the next section.

3.3.2

Tetromino Database Construction

The tetromino database is used to find the best matching tile image for each

target image, as described in the previous algorithm. It is desired to control the

number of colors and combinations of the tetrominoes in the database. Before the

beginning of tetromino database construction, we have to design an algorithm to

enumerate all the possible tetromino combinations in a fixed-sized region. Nineteen

types of tetrominoes, as shown in Figure 3.3, are used as inputs for the tetromino

database construction algorithm. In this study, the fixed-sized region is a plane of 4×4

combinations in a 4×4 grid. The detail of the enumerating process of tetromino

combinations is described in Algorithm 3.4 below. The tetromino database is

constructed by Algorithm 3.5 below.

Figure 3.3 Nineteen types of oriented tetrominoes.

Figure 3.4 Some illustrations of inputs in Algorithm 3.5. (a) A plane of 4×4 grids. (b) A tetromino combination in a plane of 4×4 grids.

Algorithm 3.5. Process for enumerating tetromino combinations. Input: 19 types of tetrominoes E and a plane P of 4×4 grids.

Output: a set of all possible tetromino combinations T = {T1, T2, .., Tn} in P.

Steps:

Step 2.In first level, for each tetromino type X in E, perform the following operations.

2.1 For each position which can be used to place X, perform the following

operations.

2.1.1 Generate a child node Cr of root r.

2.1.2 If the filled tetromino crosses the boundary of P, delete Cr and go

back to 2.1.

2.1.3 Record the tetromino type X and the position of X in Ck

Step 3.For each node of level Li , where 2≧i≧4, perform the following operations.

3.1 For each node D in level i − 1, perform the following operations. 3.1.1 Choose one type from E and denote it by Y.

3.1.2 For each position which can be used to place Y, perform the

following operations.

3.1.2.1 Generate a child node Ck of node D.

3.1.2.2 If the filled tetromino Y crosses the boundary of P, delete

the child node Ck and go back to Step 3.1.2.

3.1.2.3 If the filled tetromino Y overlaps with any existing

tetromino, delete child node Ck and go back to Step 3.1.2.

3.1.2.4 If the filled tetromino combination Y already exists in the

tree, delete child node Ck and go back to Step 3.1.2.

3.1.2.5 Record the tetromino type and the position of Y in Ck.

Step 4. Through a tree traversal, search all paths from all leaves in level 4 to the

root.

Step 5. For each path Pi in the tree, form a tetromino combination Ti by extracting

data from each node of Pi.

Input: 19 types of tetrominoes, and a fixed number N of colors. Output: a tetromino database DB with all possible tile images. Steps:

Step 1. Generate a set of all possible tetromino combinations T = {T1, T2, .., Tn} in a

plane of 4×4 grids by Algorithm 3.5.

Step 2. Generate a set of N distinct colors, C = {C1, C2, .., CN}, in the RGB color

space uniformly.

Step 3. Create all possible tile images by generating all possible combinations of Ti

in T and Ci in C.

3.3.3

Visual Effect Improvement by Border

Enhancement

Through the above-proposed algorithms, a basic tetromino-based mosaic image

is created. However, a problem occurs in our creation process. If two tetrominoes

which are close to one another have the same or similar color, the edge between these

two tetrominoes may be hard for the viewers to recognize. It is desire to enhance the

boundary of tetrominoes in tetromino-based mosaic creation. Furthermore, we also

hope to make each piece of tetrominoes look more three-dimensional. As a result, two

visual effects, lightening and shading borders, are created as a post-processing step in

this study after the tetromino-based mosaic image creation process, which we call

border enhancement. An algorithm for this purpose is described as follows.

Algorithm 3.7. Border enhancement.

Input: a plane Y of 4×4 grids with a tetromino combination P. Output: Y with lightening and shading effects P′.

Steps:

Step 1. For each tetrominoes t in P, transform the color of the tetromino from the

RGB model to the HSL model

Step 2. For each tetrominoes t in P, check its edge type according to the follow

steps.

2.1 If it is a top or left edge in t, then lighten the edge by increasing the L

channel value of the color at the borders.

2.2 If it is a bottom or right edge in t, then shade the edge by decreasing

the L channel value of the color at the borders.

3.4

Experimental Results

Some tetromino-based mosaic images generated by the proposed creation

process (Algorithm 3.4) are shown in this section. All the tetromino-based mosaic

images in our experimental results were created by the use of a tetromino database

with 125 kinds of colors and 117 types of tetromino combinations constructed in this

study. Figures 3.6, 3.7 and 3.8 show the results of using different border

enhancements. Figures 3.9, 3.10 and 3.11 show some experimental results of using

different kinds of original images obtained from the proposed mosaic image creation

process.

3.5

Discussions and Summary

In this chapter, we reviewed a traditional mosaic image creation process and

proposed accordingly an idea of creating a novel type of mosaic image composed by

In addition, an algorithm has been proposed to generate a tetromino database with

different colors and tiling styles. Finally, we also proposed a border enhancement

process for improving edge effects in tetromino-based mosaic images. Some

experimental results are presented to show the effects of the proposed algorithms.

Colors and tetromino combination are the most important characteristics in

tetromino-based mosaic image creation. With these two features, we will propose two

data hiding methods in the two following chapters.

(a)

(b)

Figure 3.6 Some of experimental results of the proposed tetromino-based mosaic creation. (a) A tetromino-based mosaic image without border effects created from Figure 3.5. (b) A partial image of the red region in (a).

(a)

(b)

Figure 3.7 Some of experimental results of the proposed tetromino-based mosaic creation. (a) A tetromino-based mosaic image with dark border effects created from Figure 3.5. (b) A partial image of the red region in (a).

(a)

(b)

Figure 3.8 Some of experimental results of the proposed tetromino-based mosaic creation. (a) A tetromino-based mosaic image with lightening and shading border effects created from Figure 3.5. (b) A partial image of the red region in (a).

(a)

(b)

Figure 3.9 Some of experimental results of the proposed tetromino-based mosaic creation. (a) An image of Eiffel Tower. (b) A tetromino-based mosaic image created from (a)

(a)

(b)

Figure 3.10 Some of experimental results of the proposed tetromino-based mosaic creation. (a) An self-portrait of van Gogh. (b) A tetromino-based mosaic image created from (a).

(a)

(b)

Figure 3.11 Some of experimental results of the proposed tetromino-based mosaic creation. (a) An image of Jolin, a singer. (b) A tetromino-based mosaic image created from (a).

Chapter 4

Data Hiding in Tetromino-based

Mosaic Images by Distinct

Combinations of Tetrominoes

4.1

Idea of Proposed Method

As mentioned in Chapter 3, we create a new type of mosaic images in this study,

named tetromino-based mosaic images. This type of mosaic image is generated by the

use of distinct tetromino combinations. Combinations of tetrominoes can be encoded

to hide data. However, using this way to hide data may damage the tetromino-based

mosaic images which we create. Therefore, we propose to use edge fitting to maintain

visual qualities of tetromino-based mosaic images by sacrificing a portion of capacity

of data hiding. In this chapter, we will describe the proposed data hiding method using

distinct combinations of tetrominoes and an edge fitting technique based on edge

detection.

4.2

Proposed Data Hiding Method by

Distinct Combinations of

Tetrominoes

The main concept of the proposed method for data hiding using tetromino-based

mosaic images is to encode tetromino combinations during tetromino-based mosaic

image creation. The creation can be regarded as a two-level hierarchical operation.

The lower level of the operation is to fill four tetrominoes into a block of 4×4 grids

for tile image generation. And the upper level is to put all tile images together to

create a tetromino-based mosaic image. As a result, we can use the lower level of this

two-level hierarchical image creation to hide data. Through the tetromino database

construction described in Chapter 3, 117 kinds of tetromino combinations can be

found by an enumerating process, as mentioned previously. In theory, we can only

embed six bits in a block of 4×4 grids by fundamental binary encoding because the

largest power of 2 smaller than 117 is 26. To increase the capacity of our data hiding technique, a transformation process between a binary digit system and a decimal digit

one are proposed. At first, the given data are transformed into a binary digit sequence.

Subsequently, we transform the binary number sequence into a decimal digit sequence.

Then, we encode 100 tetromino combinations for every two digits of the decimal digit

sequence for data hiding. Because the capacity of the maximum integer data type in

C/C++ is 64 binary bits long, which equals 20 decimal digits, we can embed

64×(2/20)=6.4 bits in a block of 4×4 grids by the above-mentioned process. The detail of the process is described as algorithm below.

Algorithm 4.1. Data transformation from binary to decimal. Input: message data D and a secret key K.

Output: a randomized decimal digit sequence Sr to be used in the data hiding process.

Steps:

Step 1.Transform D into a binary digit sequence S = {S1, S2, ..., Sn}.