Strengthen Geography Transformation and Forgery Resistance of Fragile Watermarking with 3D Model by Combining Error-Correcting Code and Cryptography

數位資訊的呈現包括文字、語音、二維與三維影像、二維與三維影片、三維模型等多媒體形式。由於電腦科技的普及，從網路上盜用別人的作品稍做修改後當作是自己作品的例子比比皆是。強調創新與創造的社會裡，著作權的保護議題被日益重視，如何設計一個既實用又高效率、低成本、電腦運算速度快的演算法成為被研究的重要主題之一。 本研究專注於設計不可視的盲型易碎形浮水印，利用錯誤修正編碼與密碼學編碼加強三維模型被偽造之抵抗能力，主要目的是保護模型的著作權所有權。這裡所謂的三維模型，是指在計算機中以虛擬三維空間由點、線、面、三角、曲線、曲面等幾何圖形和色彩設計組合後產生的虛擬立體三維多邊型造型。本研究主要是對多媒體嵌入浮水印資訊後，要能夠在沒有原始多媒體資訊的情況下偵測出被惡意修改的部分並標記出來，為了滿足此目標，浮水印必須分散在多媒體的各個角落。另一方面，浮水印的嵌入，多少都會造成多媒體資訊有些微的改變，但只要是在人體感官無法察覺的前提下，是可以被接受的，因此，在實驗結果會以失真率來評比多媒體失真的幅度。 本研究可以分為三個部分，針對電腦上的模型做所有權保護，實驗結果都具體顯示實用效益以及可靠性。 從模型本體萃取重要資訊，使用錯誤更正碼對該資訊做編碼後將輸出視為浮水印，藏在模型上。本演算法比過去相關文獻的研究擁有更高的浮水印藏量、更高效率的驗證效果，而且要大幅降低多媒體的失真度與電腦的運算成本。 利用密碼學Feedback Mode對模型做加密，加密資料 (plaintext) 來自於模型本身，加密後的資料 (cyphertext) 取代原始模型頂點小數六位以下的數值二進制最後三個位元，優點是藏在LSB能控制失真度。能讓模型不只能有高浮水印藏量、高效率的驗證、低失真度，重要的是能有更高的安全性。 三維模型有三個軸向座標 (X,Y,Z) ，在轉換成球座標系統 (r,φ,θ) 後，模型的資訊從單純的頂點變成了點、距離、角度的單位，三者相互拉鋸、影響，能夠增加演算法的韌性，讓使用者可以用非惡意的方式適度修改模型外觀，如：放大、縮小、位移，亦指在幾何空間，一個向量空間進行一次線性變換並接上一個平移，變換為另一個向量空間。如同前面所撰，模型於計算機中是由虛擬點線面所組成，記憶體內的記憶方式為笛卡爾座標系統，本階段會先將模型從笛卡爾座標系統轉換為球座標系統，再以第一、二個部分的演算法分別作編碼，實驗結果中可明顯發現加上球標系統的特性，能夠使模型有效抵抗仿射轉換，且不影響高驗證性。Multimedia is text, audio, two-dimensional and three-dimensional image, two-dimensional and three-dimensional video, and three-dimensional mesh collectively. Since the technology of computer has grown, there are more and more examples that people take an existed multimedia from Internet and claim it is their work after making a little alteration. Innovation and creativity are important for products. Therefore, copyright is an issue that has become importance and needs to be protected. There are some literature on the subject. The algorithms were designed on blind fragile watermarking in this thesis. Utilize error correcting code and cryptography to enhance the attack verification ability. The objective is to protect the copyright of three-dimensional models. In this research, the meshes were used from a public database. These meshes refer to the virtual three-dimensional space in a computer by the point, line, surface, triangle, curve, and other geometric graphics and color design combination of virtual three-dimensional polygon modeling. The watermark can be used for detecting malicious modification and marking out the area from an attacked stego media. Therefore, the watermark should be embedded into all over the cover media as much as possible. However, embedding information will make some alterations on the media. It is tolerable if it cannot be noticed under human senses. The distortion ratio of each model is shown in experimental results. This research can be divided into three parts. All of them are designed for protecting the polygonal meshes on computer. Experimental results show that they are efficient in reality applications. (a)Extract data bits from a cover model and encrypted by error correcting code. Considered the output of the coding procedure is a watermark, which is embedded into the cover model itself. The advantage is that it can achieve lower time complexity than previous literature, control distortion ratio bellow 10-6, contain100% embedding capacity, and get efficient verification. (b)Use cryptography, Feedback Mode, to encrypt a cover model. Extract a vertex as a plaintext, and consider the cyphertext as a watermark, which is embedded in the last significant bit (LSB) under decimal six or less after convert into binary. The advantage is that replace the LSBs can control the distortion rate. In the experiment results show that this algorithm can have high watermark embedding rate, high detect efficiency, low distortion rate and even more, higher security. (c)A three-dimensional model has three coordinates (X,Y,Z). A spherical coordinate system (r,φ,θ) combine information with vertex, distance, and angle unit. Interaction between this three information can increase the tenacity of the algorithm. So that users can use a non-malicious way to moderately modify the appearance of a model, such as, scanning, zooming, and shifting, which is called affine transformation or geographic transformation. A geographic transformation is a mathematical operation that converts the coordinates of a point in one geographic coordinate system to the coordinates of the same point in another geographic coordinate system. A three-dimensional model is referred to virtual three-dimensional space in a computer by point, line, and surface. In a computer, a model is recorded by Cartesian coordinate system. Convert an input model from Cartesian coordinate system into spherical coordinate system in the very beginning. Then apply the first part and the second part encoding algorithm respectively by using a referenced vertex. The experiment results show that spherical coordinate system can resist affine attack efficient and still achieve high malicious attack detection rate.Contents Acknowledgement i 摘要 ii Abstract iv List of Figures viii List of Tables ix Chapter 1 Introduction 1 1.1 Motivation 2 1.2 Background 3 Chapter 2 Related Works 5 2.1 Related works of the hamming code 7 2.2 Related works of cryptography – Output feedback model 10 2.3 Related works of spherical coordinate system 11 Chapter 3 Error Correcting Code for 3D Model 14 3.1 Watermark embedding process 14 3.2 Extraction and verification process 16 Chapter 4 An OFB-Based Fragile Watermarking Scheme for 3D Polygonal Meshes 19 4.1 Watermark embedding process 19 4.2 Extraction and verification process 22 Chapter 5 Geography-Transformation-Resistant Watermarking for 3D Model 24 5.1 The embedding process 24 5.2 The extraction process 26 Chapter 6 Results Analysis 28 6.1 Distortion ratio measuring 29 6.2 Comparison with previous methods 31 6.3 Geography-transformation-resistant watermarking 32 Chapter 7 Conclusions 34 7.1 Error correcting code for 3d model 34 7.2 An OFB-based fragile watermarking scheme 34 7.3 Geography-transformation-resistant watermarking 34 Bibliography 3