An exact expression for the bit error probability in angle QIM watermarking under simultaneous amplitude scaling and AWGN attacks
The performance of watermarking methods based on lattice quantization schemes can be greatly degraded by simple amplitude scaling attacks. Scaling the amplitude of pixel values by relatively small amounts have the potential effect of moving the watermark vector away from its original quantization centroid, thus leading the decoder to incur erroneous decisions. In order to overcome this limitation, angle quantization index modulation (AQIM) schemes have been recently introduced. By quantizing the angle of the watermark vector according to a symbol dependent lattice, AQIM's construction leads to an inherent invariance against amplitude scaling distortions. In this paper, we proceed with a thorough theoretical analysis of the two-dimensional version of AQIM, leading to an exact expression for the bit error probability for simultaneous amplitude scaling and AWGN attacks. Such theoretical expressions were validated by comparison with experimental results, which are also included in this paper.