Geometrically Robust Image Watermarking on a Circular Domain

In image watermarking, the watermark’s vulnerability to geometric transformations has long been a difficult problem. Using invariant image features to carry the watermark is an effective approach to addressing this problem. In this paper, a multibit geometrically robust image watermarking algorithm using Zernike moments (ZMs) and pseudo-Zernike moments (PZMs) is proposed. Unlike its counterparts in literature, this algorithm is based on our finding that not all the ZMs/PZMs are suitable for invariant watermarking. We distinguish the ’good’ ZMs/PZMs from the ’bad’ ones. By avoiding embedding watermarks onto the ’bad’ ZMs/PZMs, we have achieved impressively good watermarking results. For some selected ’good’ ZMs/PZMs of an image, dither modulation is employed to quantize their magnitudes in order to embed an array of bits. The watermarked image is obtained via reconstruction from the modified moments and those left intact. In watermark extraction, the embedded bits are estimated from the invariant magnitudes of the ZMs/PZMs using a minimum distance decoder. Simulation results show that the embedded information can be decoded at low error rates, robust against image rotation, scaling, flipping, and as well, a variety of other processes such as additive noise and lossy compression.