Geometrically invariant image watermarking using Polar Harmonic Transforms

This paper presents an invariant image watermarking scheme by introducing the Polar Harmonic Transform (PHT), which is a recently developed orthogonal moment method. Similar to Zernike moment (ZM) and pseudo-Zernike moment (PZM) approaches, PHT is defined on a circular domain. The magnitudes of PHTs are invariant to image rotation and scaling. Furthermore, the PHTs are free of numerical instability, so they are more suitable for watermarking. In this paper, the invariant properties of PHTs are investigated. During embedding, a subset of the accurate PHTs are modified according to the binary watermark sequence. Then a compensation image is formatted by reconstructing the modified PHT vector. The final watermarked image is obtained by adding the compensation image to the original image. In the decoder, the watermark can be retrieved from the magnitudes of the PHTs directly. Experimental results illustrate that the proposed scheme outperforms ZM/PZM based schemes in terms of embedding capacity and watermark robustness and is also robust to both geometric and signal processing based attacks.