本論文提出一個漸進式的三維模型分享方法，用以保護重要的三維模型資料。在所提n (n >= 2)階層漸進式三維模型分享技術，會將輸入之三維模型中的資料分成n群，並編碼成n + 1個分存模型。每一個分存模型的外觀為雜亂的，且當使用者取得單份分存模型時是無法得到任何原三維模型資料；而如果使用者收集到q ( 2 <= q <= n+1 ) 份分存模型時，則可還原出一個近似的三維模型，所還原出的三維模型之品質與分存數量q成正比；當使用者拿到n+1份的分存模型時，可將原三維模型無失真重建出。本研究所提的三維模型分享技術，係針對由實數構成的三維點資料來設計，開發基於IEEE−754標準浮點數表示法的分享方法，在資料分享這個領域的研究上是一項創新的設計。所設計的n 階層漸進式三維模型分享技術，將原三維模型編碼成數個較小的分存模型，使各個分存模型的傳輸與儲存更有效率外，在某些分存模型遺失或被破壞的情況下，仍可以重建回一個外觀近似的三維模型，具高度的容錯性。而所設計的點資料分群方法，可將三維模型中的點資料依空間關係平均分配至各群中，不會因為三維模型中點資料的儲存排列順序而異，讓還原出的三維模型之品質與分存模型數量q成正比，達到外觀漸進式的還原視覺效果。

This thesis presents a progressive sharing method for protecting secret 3D Models. The proposed n-level (n >= 2) progressive 3D model sharing method divides the points of a 3D model in n groups, and encodes them in n+1 shadow models. Each shadow model has noisy appearance, and knowledge of a single shadow model gets nothing about the secret 3D model. A mimicked 3D model can be revealed when q ( 2 &lt;= q &lt;= n+1 ) shadow models are available, in which the quality of the revealed model is proportional to the number of shadow models engaged in the decoding process. The original 3D secret model can be revealed without any loss when all of the n+1 shadow models are obtained. The proposed sharing method manipulates 3D points represented in real numbers. We design the sharing function to work directly on real numbers represented in IEEE−754 standard floating point representation, which is novel in the field of sharing technology. In the proposed n-level progressive 3D model sharing method, a secret 3D model is encoded in n?1 shadow models. Each shadow model occupies smaller space and can be stored in separated storage. The small-size of each shadow model benefits the further processing such as transmission or storage. Besides, a mimicked model can be reconstructed even when some of the shadow models were crashed or lost, that increases the robustness to the secret 3D model. The point grouping algorithm designed in this study classifies the points of the secret 3D model evenly in spatial distribution, which enables the ability of progressive revealing to the secret model without depending on the order about the points stored in the original secret 3D model.

摘要 i
Abstract ii
第一章 簡介 1
1.1 研究背景與動機 1
1.2 相關研究 3
1.3 研究目的 4
第二章 相關技術 6
2.1 Polygon File Format簡介 6
2.2 IEEE−754標準浮點數格式 6
2.3二的次方之Galois Field GF(2n) 9
2.4 Shamir’s (t, n)門檻式機密分享方法 14
第三章 漸進式三維模型分享技術 16
3.1 方法流程 16
3.2 三維點資料分層 18
3.2.1 簡單交錯分層法(Simple Interlacing Grouping Method, SIGM) 18
3.2.2 空間點均化分層法(Spatial Equalization Grouping Method, SEGM) 19
3.3 點資訊分享階段 20
3.4 分存模型建立 22
3.5 分存模型還原階段 23
第四章 實驗結果 25
4.1 以2層漸進式三維模型機制做分享實驗 25
4.2 以3層漸進式三維模型機制做分享實驗 29
第五章 結論與未來展望 35
參考文獻 36

[1] P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Optics Letters, Vol. 20, No. 7, pp. 767–769, 1995.
[2] P.P. Dang and P.M. Chau, “Image encryption for secure Internet multimedia applications,” IEEE Transactions on Consumer Electronics, Vol. 46, No. 3, pp. 395–403, 2000.
[3] F.A.P. Petitcolas, R.J. Anderson, M.G. Kuhn, “Information hiding-a survey,” Proceedings of the IEEE, Vol. 87, no. 7, pp. 1062–1078, Jul. 1999.
[4] R.B. Wolfgang and E.J. Delp, “A watermark for digital images,” Proceedings of IEEE International Conference on Image Processing, Vol. 3, pp. 219–222, 1996.
[5] A. Shamir, “How to share a secret,” Communications of the ACM, Vol. 22, No. 11, pp. 612−613, 1979.
[6] C.C. Thien and J.C. Lin, “Secret image sharing,” Computers and Graphics, Vol. 26, No. 5, pp. 765−770, 2002.
[7] R.Z. Wang and C.H. Su, “Secret image sharing with smaller shadow images,” Pattern Recognition Letters, Vol. 27, No. 6, pp. 551−555, 2006.
[8] C. Asmuth and J. Bloom, “A modular approach to key safeguarding,” IEEE Transactions On Information Theory, Vol. IT-29, No. 2, pp, 208−210, 1983.
[9] G.R. Blakley, “Safeguarding cryptographic keys,” AFIPS Conference Proceedings, Vol. 48, pp. 313−317, 1979.
[10] A. Beimel and B. Chor, “Secret sharing with public reconstruction,” IEEE Transactions On Information Theory, Vol. 44, No. 5, pp. 1887−1896, 1998.
[11] D. Wang, L. Zhang, N. Ma, and X. Li, “Two secret sharing schemes based on Boolean operations,” Pattern Recognition, Vol. 40, No. 10, pp. 2776–2785, 2007.
[12] H. Wang and D.S. Wong, “On secret reconstruction in secret sharing scheme,” IEEE Transactions On Information Theory, Vol. 54, No. 1, pp. 6−13, 2008.
[13] R.Z. Wang and S.J. Shyu, "Scalable secret image sharing," Signal Processing: Image Communication, Vol. 22, No. 4, pp. 363−373, 2007.
[14] C.C. Lin and W.H. Tsai, “Secret image sharing with steganography and authentication,” Journal of Systems & Software, Vol. 73, No. 3, pp. 405−414, 2004.
[15] C.N. Yang, T.S. Chen, K.H. Yu, and C.C. Wang, “Improvements of image sharing with steganography and authentication,” Journal of Systems and Software, Vol. 80, No. 7, pp. 1070−1076, 2007.
[16] C.C. Chang, Y.P. Hsieh, and C.H. Lin, “Sharing secrets in stego images with authentication,” Pattern Recognition, Vol. 41, No. 10, pp. 3130−3137, 2008.
[17] P.Y. Lin, J.S. Lee, and C.C. Chang, “Distortion-free secret image sharing mechanism using modulus operator,” Pattern Recognition, Vol. 42, No. 5, pp. 886−895, 2009.
[18] P.Y. Lin and C.S. Chan, “Invertible secret image sharing with steganography,” Pattern Recognition Letters, Vol. 31, No. 13, pp. 1887−1893, Oct. 2010.
[19] D. Cotting, T. Weyrich, M. Pauly and M. Gross, “Robust Watermarking of Point-Sampled Geometry,” Proceedings International Conference on Shape Modeling and Applications, pp. 233-242, 2004.
[20] B.L Yeo and M.M Yeung, “Watermarking 3D objects for verification,” IEEE Computer Graphics and Applications, Vol.19, pp. 36−45, 1999.
[21] R. Ohbuchi, H. Masuda, and M. Aono, “Watermarking three-dimensional polygonal models,” Proceedings of the ACM International Multimedia Conference & Exhibition, pp. 261−272, 1997.
[22] O. Benedens, “Geometry-Based Watermarking of 3D Models,” IEEE Computer Graphics and Applications, Vol. 19, pp. 46−55, 1999.
[23] H.Y. Lin, H.Y. Liao, C.S. Lu, and J.C. Lin, “Fragile watermarking for authenticating 3-D polygonal meshes,” IEEE Transactions on Multimedia, Vol. 7, pp. 997−1006, 2005.
[24] C.M Chou and D.C Tseng, “A public fragile watermarking scheme for 3D model authentication,” CAD Computer Aided Design, Vol. 38, pp. 1154−1165, 2006.
[25] R. Ohbuchi, A. Mukaiyama and S. Takahashi, “Watermarking a 3D shape model defined as a point set,” International Conference on Cyberworlds, pp. 392−399, 2004.
[26] F. Cayre and B. Macq, “Data Hiding on 3-D Triangle Meshes,” IEEE Transactions on Signal Processing, Vol. 51, pp. 939−949, 2007.
[27] M.W Chao, C.H Lin, C.W Yu, and T.Y Lee, “A high capacity 3D steganography algorithm,” IEEE Transactions On Visualization and Computer Graphics, Vol. 15, pp. 274−284, 2009.
[28] C.M Wang and Y.M Cheng, “An efficient information hiding algorithm for polygon models,” Computer Graphics Forum, Vol. 24, No. 3, pp. 591−600, 2005.
[29] Y.M Cheng and C.M Wang, “A high-capacity steganographic approach for 3D polygonal meshes,” The Visual Computer, Vol. 22, No. 9, pp. 845−855, 2006.
[30] C.M Wang, Y.M Cheng, K.C Wu, C.W Tao, Y.T Tseng and Y.K Liao, “A Secret 3D Polygonal Model Sharing Algorithm with Steganography,” Journal of Engineering, National Chung Hsing University, Vol. 18, No. 1, pp. 41−53, 2007.
[31] R.Z. Wang, Y.H. Chiou, “Sharing and Hiding Secret 3D Point-Sampled Model with Natural Stego-Models,” Conference on Computer Vision, Graphics, and Image Processing 2010.
[32] Greg Turk. (1998). [Online]. Available: http://www.cc.gatech.edu/~turk/
[33] ANSI/IEEE Standard 754-1985, Standard for Binary Floating Point Arithmetic, New York:The Instiute of Electrical and Electronics Engineers, 1985.
[34] R.Z. Wang, Y.Y. Lin, “Region Incrementing Multisecret Image Sharing,” Thesis of Computer Science and Engineering, Yuan-Ze University, 2009.