A zero-watermarking algorithm for vector geographic data based on feature invariants

Previous studies on zero-watermarking algorithms for vector geographic data focus on improving the robustness against geometrical attacks, compression attacks and object attacks. However, there are limited zero-watermarking algorithms against projection transformation. In this study, we proposed a zero-watermarking algorithm for vector geographic data based on feature invariants. After any projection transformation of vector geographic data, the number of vertices and relative storage order of objects keep consistent. Therefore, the number of vertices and relative storage order of objects can be considered as the feature invariants. The proposed algorithm consists of three steps. Firstly, according to the relative storage order of objects, the watermark bit is determined by comparing the number of vertices between any two objects. Secondly, the watermark index is calculated by the number of vertices of two objects. Then, a feature matrix is constructed by combining the watermark bit and the watermark index. Finally, the XOR operation is performed between the feature matrix and the scrambled watermark image to generate the zero-watermark image. The experimental results show that the watermark information with NC of 1.0 can be detected from the vector geographic data after any projection transformation, which shows that the algorithm can resist any projection transformation. At the same time, the useful watermark information with minimum NC values of 1.0, 0.911, 0.84, and 1.0 can be detected from the vector geographic data after the geometrical attack, object addition attack, object deletion attack and precision reduction attack. Therefore, the proposed algorithm can effectively against geometrical attacks, object addition attacks, object deletion attacks and precision reduction attacks, showing superior performance compared with previous algorithms.