Zero watermarking for vector geographic point data based on convex layers

Abstract

Zero watermarking plays a critical role in the copyright protection of vector geographic data in geographic information industries, as it does not distort the data. However, how to extract stable features from vector geographic point data is still a challenging problem. A zero watermarking method based on convex layers is proposed to address the issue. First, the vector geographic point data is simplified as a point set. Next, construct convex layers from the point set through convex hull peeling or onion peeling. Then, calculate the density of vertices wrapped within each convex hull of the convex layers to obtain an integer number sequence. Finally, the sequence of vertex density is binarized to the watermark by comparing each value with its adjacent counterparts. Experiments substantiate the theoretical achievements of the proposed method. Its normalized correlation coefficient always keeps at 1.00 when suffering rotation, uniform scaling, non-uniform scaling, translation attacks, and map projection transformation attacks, demonstrating superior robustness compared to the existing methodologies. The watermark uniqueness has also been verified through the analysis of a set of 100 randomly generated point datasets.