中文摘要：

对于鲁棒矢量空间数据水印技术而言,几何变换攻击是难以对付的一种攻击。现有的抗几何变换攻击算法难以抵抗顶点攻击,因此,借用数据归一化的思想,本文提出了一种归一化的矢量空间数据盲水印算法。该算法在嵌入水印前将空间数据的坐标值进行归一化处理,以实现对平移和缩放的不变性,并通过修改顶点坐标数据的归一化值来嵌入水印。水印被多次嵌入,实现了水印的盲提取。实验结果表明,该方法对平移、缩放、増删点、裁剪、压缩、要素排序、数据格式转换等攻击具有较好的鲁棒性,同时能控制水印嵌入引起空间数据误差的大小。

英文摘要：

In vector data watermarking technology, the geometric transform attack is commonly difficult to cope with. The existing algorithms that can resist the attacks of geometric transformation, however always cannot re- sist vertexes attacks. Therefore, a blind watermarking algorithm for vector data is proposed based on the idea of data normalization to solve this problem. In this algorithm, the coordinate values of spatial data were normalized before embedding the watermarks, in order to keep invariant with respect to translation and zooming. Water- marks were embedded in the normalized values of the vertex coordinate data for several times. There are no orig- inal data needed in the procedure of watermark detecting. The experiments show that the algorithm is robust against a series of different attacks, such as translation or scaling transformations, vertex insertion and removal, cropping, compression, reordering and data format conversion. In addition, it can control and limit the relevant errors of the watermarked spatial data that produced during the watermark embedding.