Angle QIM: On document to watermark ratio analysis

Max Costa original results on dirty paper codes have given the foundation for Quantizatin Index Modulation (QIM) based for digital image watermarking. However, the standard QIM methods can be greatly degraded by simple amplitude scaling attacks. 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 present a theoretical analysis of the watermark distortion introduced by AQIM during the embedding process based on the angle quantization step parameter, Delta(theta). Such theoretical analysis is validated by comparison with experimental results, which are also included in this paper.