我們的研究主要是在無遠弗屆的網路上利用semi-fragile watermarking來確保3D models的完整性。浮水印是以3D model本身的資訊及種子數（如使用者的合法註冊號碼）產生的亂數所組成，不需使用額外的資訊。驗證浮水印時只要以原種子數利用簡單的數學運算便可以評斷models的完整性。我們所提的方法可以抵擋放大、縮小、平移等常見的3D models處理，也可以抵擋點順序重新排序等攻擊。嵌入方法對3D models外型的影響非常小，因此本方法適用於精密機具或醫學的3D models。我們的方法經過實驗證明其時間及效能都令人滿意。

In this study, a semi-fragile watermarking scheme based on vertex geometry is proposed for 3D model authentication. Watermark is generated from 3D model and random number generator by a seed number. To embed and extract watermark only needs the seed number and some simple arithmetic operations. Our method is robust to general 3-D model processes, such as uniform scaling, translation, and vertex reordering. The embedding process has little impact to the original 3D models that PSNR values can be up to eighties or nineties. Thus the proposed method is very suitable for precision instruments or medical science models. Experiments demonstrate that our method is time and performance satisfactory.

目錄 I
圖目錄 III

表目錄 IV

第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 1
1.3 論文架構 2
第二章 理論基礎與研究背景 4
2.1 3D Watermarking 4
2.2 Robust 3D watermarking 10
2.3 Fragile 3D watermarking 13
2.4 Semi-Fragile 3D watermarking 15
第三章 研究方法 19
3.1 浮水印嵌入 22
3.2 浮水印萃取 34
第四章 實驗結果與分析 43
4.1 實驗結果 43
4.2 實驗結果比較 55
4.3 實驗結果探討 57
第五章 結論與未來研究方向 59
參考文獻 60
附錄-英文論文 62

圖目錄
圖1.2.1 方法流程圖 2
圖2.2.1 利用restricted edge collapse簡化Bunny 11
圖2.2.2 方法改變平均值的分布 13
圖2.3.1 Yeo和Yeung方法trace的順序 15
圖2.4.1 Hsueh-Yi Lin提出不合法點的修改方法 16
圖3.1 3D model – Aardvark 初始座落的位置和大小 20
圖3.2 VRML架構：3D model – Aardvark 20
圖3.1.1 3D models嵌入前的重心GXY 23
圖3.1.2 區段等距分段示意圖 25
圖3.2.1 3D models嵌入後的重心GO-xy 37
圖3.2.2 示意圖 41
圖4.1.1 Bunny分290段權重0.5嵌入前後 45
圖4.1.2 Horse分172段權重0.5嵌入前後 47
圖4.1.3 Aardvark 分2段權重0.5嵌入前後 48
圖4.1.4 Dog 分11段權重0.5嵌入前後 49
圖4.1.5 Aardvark 攻擊測試 51
圖4.1.6 Aardvark 放大、縮小、平移攻擊測試圖示 52
圖4.1.7 Dog 嵌入後及攻擊頭部146個點圖示 54

表目錄
表2.1.1 Robust浮水印方法攻擊整理 5
表3.1.1 3D model – Aardvark點與重心GXY距離並排序 23
表3.1.2 18個3D models利用方法一分五段後的結果 25
表3.1.3 18個3D models利用方法二分五段後的結果 26
表3.1.4 18個3D models利用综合分五段後的結果 27
表3.1.5 3D model - Aardvark分兩段產生之亂數值 28
表3.1.6 3D model – Aardvark正規化結果 29
表3.1.7 3D model – Aardvark計算每等分浮水印的第一位 30
表3.1.8 3D model – Aardvark 浮水印嵌入 31
表3.1.9 3D model – Aardvark 取前後十分之ㄧ的點當補償 33
表3.1.10 3D model – Aardvark 反正規化 34
表3.2.1 3D model – 已嵌入Aardvark點與重心GO-XY距離並排序 38
表3.2.2 3D model-已嵌入Aardvark分兩段產生之亂數值 38
表3.2.3 3D model – 已嵌入Aardvark正規化結果 39
表3.2.4 3D model – 已嵌入Aardvark求每等分浮水印的第一位 40
表3.2.5 3D model - 已嵌入Aardvark取出浮水印 42
表4.1.1 3D models點與面的資訊 44
表4.1.2 Bunny嵌入前後每段的平均差距 46
表4.1.3 Horse嵌入前後每段的平均差距 47
表4.1.4 Aardvark嵌入前後每段的平均差距 48
表4.1.5 Dog嵌入前後每段的平均差距 50
表4.1.6 Aardvark 放大、縮小、平移攻擊測試數據 53
表4.1.7 Dog 嵌入前後及攻擊頭部146個點數據 55
表4.2.1 3D model 公式15評估變化 56
表4.2.2 3D model 利用公式16評估變化 57
表4.2.3 3D models嵌入和取出花費的時間 57

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