3次元モデルを対象とした電子透かし・検索・圧縮技術に関する研究

在上个财政年度，我们专注于研究3D模型的数字水印和形状相似性搜索。数字水印：在上一财年，我们开发了一种新的用于3D多边形网格的数字水印算法，该算法使用了网格频谱分析技术(我们在IPSJ期刊和Graphics Interface2001上发表了这一结果)。使用该方法嵌入的水印具有抗加性随机噪声、网格平滑和其他干扰的能力。同时，该方法具有高的信息有效负载(即，每顶点数目嵌入的信息比特)。然而，该方法有一对弱点，即如果网格的连通性受到干扰(例如，由于网格简化)，则水印被破坏，并且网格频谱分析的计算成本相当高，需要花费数小时来为具有几千个顶点的网格添加水印。在本财年，我们对算法进行了相当大的改进，以超越…更何况这两个弱点。即在三个方面进行了改进：(1)采用高效的特征分解算法；(2)对几何变换后的网格进行逐块对齐；(3)通过重新划分网格来恢复原始网格的连通性。我们对改进后的算法进行了实现和评估。(新算法的结果将在2002年9月的EUROGRAPHICS‘2002上公布。)另外，我们改进了用于矢量数字地图的数字水印算法，以使其具有抗裁剪能力。压缩我们在本财政年度没有研究过压缩。形状相似性搜索：我们研究了各种形状特征和比较特征的方法。形状相似性搜索算法有两个共同的困难：(1)模型对齐是进行适当的相似性比较所必需的；(2)机械地计算相似性往往会遗漏基于人的感知的结果。在本财年，我们通过结合Osada等人的形状特征，开发了一种新的形状相似性搜索方法。以及一种称为支持向量机的学习分类器。我们的初步结果表明，该方法反映了人类的感知/认知，对模型中的不规则现象，如拓扑误差和几何退化，具有很强的鲁棒性。较少

During this last fiscal year, we foctised our effort on tlie study of digital watermarking and shape similarity search of 3D models.1. Digital Watermarking : In the last fiscal year, we developed a new digital watermarking algorithm for 3D polygonal meshes that employs the mesh spectral analysis technique (We published the results in the IPSJ Journal and at the Graphics Interface 2001). Watermarks embedded by using this method are resilient -against additive random noise, mesh smoothing, and other interferences. At the same time, the method has a high information payload (i.e., information bits embedded per number of vertices). However, the method has a pair of weakness, that are, the watermarks are destroyed if connectivity of the mesh is disturbed (e.g., by mesh simplification), and that the computational cost of mesh spectral analysis is quite high, taking hours to watermark a mesh having a few thousands of vertices. In this fiscal year, we refined the algorithm quite a bit to overc … More ome these two weaknesses. Namely, we improved in three areas ; (1) by employing an efficient eigen-decomposition algorithm, and (2) by per-patch alignment of meshes after geometrical transformations, and (3) by recovering the original mesh connectivity through remeshing. We implemented and evaluated the improved algorithm. (The results of the new algorithm will be presented at EUROGRAPHICS '2002 in September 2002.)Separately, we have improved our digital watermarking algorithm for vector digital maps in order to give it a resiliency against cropping.2. Compression We have not worked on compression in this fiscal year.3. Shape Similarity Search : We studied various shape features and methods to compare the features. Shape similarity search algorithms have two common difficulties : (1) Alignment of models is necessary for proper comparison of similarity, and (2) a similarity computed mechanically often misses the result based on human perception. In this fiscal year we developed a new shape similarity search method by combining a shape feature due to Osada, et al. and a learning classifier called Support Vector Machine. Our preliminary results show that the method reflects human perception/cognition and is quite robust against irregularities in the model such as topological error and geometrical degeneracies. Less