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Efficient and High-Capacity Steganographic Algorithms for Three-Dimensional Models
|關鍵字:||three-dimensional models;三維模型;steganography;spatial subdivision;parametric functions;information hiding;資訊偽裝;空間切割;參數函數;資訊隱藏||出版社:||資訊科學系所||引用:||[Asho2004] M. Ashourian, R. Enteshari, and J. Jeon, “Digital Watermarking of Three-Dimensional Polygonal Models in the Spherical Coordinate System,” Proceedings of Computer Graphics International, pp. 590-593, 2004. [Aspe2002] N. Aspert, E. Drelie, Y. Maret, and T. Ebrahimi, “Steganography for Three-Dimensional Polygonal Meshes,” Proceedings of SPIE 47th Annual Meeting, pp. 705-708, 2002. [Bend1996] W. Bender, D. Gruhl, N. Morimoto, and A. Lu, “Techniques for Data Hiding,” IBM System Journal, Vol. 35, No. 3&4, pp. 313-336, 1996. [Bene1999a] O. Benedens, “Geometry-Based Watermarking of 3D Models,” IEEE Computer Graphics and Applications, Vol. 19, No. 1, pp. 46-55, 1999. [Bene1999b] O. 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現今的資訊隱藏技術(information hiding techniques)已逐漸採用三維模型(three-dimensional models)來當作掩護媒體(cover media)，但相關的文獻與技術上方面皆有改進的空間。首先，在文獻部分，現今大多數的內容還是以探討浮水印演算法(watermarking algorithms)為主，只有若干篇的研究著重在秘密通訊(covert communication)的資訊偽裝演算法(steganographic algorithms)上。其次，在效率方面，目前的資訊偽裝演算法，在嵌入或擷取過程中，使用了一些複雜的運算或是資料結構，皆使得執行時間變長。另外，低資訊隱藏量仍是目前資訊偽裝演算法之瓶頸，亦是技術上有待突破的部分。
在本篇論文中，我們提出了兩個資訊偽裝演算法來解決上述的缺失。其一，為利用空間切割(spatial subdivision)的概念來達到資訊偽裝的目的。我們將它實作在三維模型與彩色影像上，此方法係利用二元空間分割樹(binary space partitioning tree)，先將掩護媒體細分成許多的小子空間，稱之為「立體像素」(voxels)。在嵌入過程中，先在樹狀結構中尋找葉結點(leaf nodes)，然後藉由改變節點中頂點的位置來藏入秘密訊息。此方法既簡單、有效率，又能在低失真程度(imperceptible distortion)下達到高隱藏量。
其二，我們利用秘密訊息以及私密金鑰來控制參數函數(parametric functions)中變數(variables)的分佈情況。我們將此方法稱為「機密取樣」(embedding sampling)。這個方法有四個優點：首先，以往演算法的隱藏容量，與掩護模型的複雜度有關，而此方法的隱藏容量，則主要跟使用者欲取樣的數目成正比關係，使用我們的方法，能讓隱藏容量大為提升。其次，承載資料的模型非常有彈性，可以是一條線、一片三角形，或是一個參數曲面(parametric surfaces)。再者，執行時間非常的快，若以一個三角片的參數函數為例，只需兩秒鐘即可產生出藏有兩百萬位元秘密資訊的偽裝模型。最後，我們的方法能夠產生出平滑表面的偽裝模型，優於以往演算法都會產生出帶有粗糙表面(rough surfaces)的模型。
Nowadays, the use of three-dimensional models in information hiding techniques is gradually attracting more and more attention. Watermarking algorithms, which mainly protect copyright ownership, are still in the majority. For steganographic algorithms, which are mainly techniques of covert communication, only a few papers have been presented, and there is still much room for development. In terms of efficiency, current steganographic algorithms use complicated operations or data structures during the embedding and extracting algorithms. This may greatly increase processing time. Besides, smaller capacity for 3D models remains bottlenecked.
In this thesis, we propose two steganographic algorithms to overcome the above drawbacks. The first algorithm employs the concept of spatial subdivision to achieve the purpose of steganography. This technique applied to both 3D models and color images. Specifically, we decompose the bounding volume of the cover media into voxels based on a Binary Space Partitioning (BSP) tree data structure. In the embedding process, the tree data structure is traversed in search of leaf nodes, where a payload can be embedded by changing the positions of points. This scheme is simple and efficient, and it can achieve high data capacity with imperceptible distortion.
For the second steganographic algorithm, we use a secret payload and secret keys to control the distribution of variables in the parametric functions. We call this technique “embedding sampling.” This scheme has four advantages. First, the data capacity is proportional to the number of sample points, while previous algorithms have been dependent on input model complexity. Secondly, the input model is flexible. Third, it is very fast. For a triangle, for example, it takes less than two seconds to embed a payload of two million bits. The final advantage is shape preservation; the generated sample points are located on the surface of the three-dimensional geometry.
Experimental results show that both of these schemes are efficient and have high capacity and imperceptible distortion. They also demonstrate that our proposed algorithms meet the requirements of a good steganographic system.
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