Watermarking Images in the Frequency Domain by Exploiting Self-Inverting Permutations

Abstract

In this work we propose efficient codec algorithms for watermarking images that are intended for uploading on the web under intellectual property protection. Headed to this direction, we recently suggested a way in which an integer number w which being transformed into a self-inverting permutation, can be represented in a two dimensional (2D) object and thus, since images are 2D structures, we have proposed a watermarking algorithm that embeds marks on them using the 2D representation of w in the spatial domain. Based on the idea behind this technique, we now expand the usage of this concept by marking the image in the frequency domain. In particular, we propose a watermarking technique that also uses the 2D representation of self-inverting permutations and utilizes marking at specific areas thanks to partial modifications of the image’s Discrete Fourier Transform (DFT). Those modifications are made on the magnitude of specific frequency bands and they are the least possible additive information ensuring robustness and imperceptiveness. We have experimentally evaluated our algorithms using various images of different characteristics under JPEG compression. The experimental results show an improvement in comparison to the previously obtained results and they also depict the validity of our proposed codec algorithms.