A Reversible Watermarking for 2D Engineering Graphics Based on Difference Expansion With Adaptive Interval Partitioning

To resolve the distortion resulting from the mismatch between the interval partition and the watermark distribution in the reversible watermarking based on difference expansion, an investigation is made to difference expansion with adaptive interval partitioning. It is found that the conventional floating number-based methods with uniform interval partitioning are not fully considering different watermark distributions, and the embedding distortion can be optimized. Thus, a reversible watermarking based on difference expansion with adaptive interval partitioning is put forward for 2D engineering graphics. Each interval is adaptively partitioned into
$2^{s}$
sub-intervals, and the watermark is embedded via transforming the positions of the vertices to its corresponding sub-intervals. The watermark extraction is accomplished by acquiring the indices of the sub-intervals of the watermarked vertices, and the graphics recovery is achieved by moving the watermarked vertices to the reverse direction. Moreover, a new polar coordinate system is built to be invariant to overall geometric transformation and vertices rearrangement. Experimental results and analysis indicate that it maintains good authentication ability and semi-fragility. Furthermore, its imperceptibility is significantly improved compared with the existing watermarking schemes under the same experimental conditions.