Moment invariants based zero watermarking algorithm for trajectory data

Zero watermarking is a lossless copyright protection technology that satisfies the need for copyright protection without compromising the accuracy of trajectory data. However, existing zero watermarking algorithms for trajectory data are unable to resist random deletion point attack. Therefore, a trajectory data zero watermarking algorithm based on moment invariants was proposed to address the problem. Firstly, two compression algorithms are utilized to extract feature points from the trajectory data. Then, a coordinate system is constructed using the minimum area bounding rectangle (MABR) of the feature points. Next, based on the constructed coordinate system, the feature points are divided into subtrajectories, and the linear moment invariants generated by the subtrajectories are calculated. Finally, the zero watermark information is constructed based on the linear moment invariants, and the watermark copyright information is generated by exclusive-ORing (XOR) it with the copyright image. Experimental results demonstrate that the zero watermark information constructed by the proposed algorithm has good uniqueness and strong robustness against random deletion, compression, and other common attacks. Furthermore, the proposed algorithm has good algorithm efficiency and is applicable to vector data with plane coordinates. The study makes a positive contribution to copyright protection for trajectory data and provides useful references for research on lossless watermarking of vector geographic data.