Watermarking Digital Images in the Frequency Domain: Performance and Attack Issues

Abstract

Abstract. In this work we propose an efficient model 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 selfinverting permutation, can be represented in a two dimensional (2D) object and thus, since images are 2D structures, we propose a watermarking algorithm that embeds marks on them using the 2D representation of w in the frequency domain. In particular, we propose a watermarking technique that 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, Gaussian noise addition, and geometric transformations. The experimental results show an improvement in comparison to the previously obtained results and they also depict the validity of our proposed codec algorithms.

Algorithmic techniques for encoding permutations and permutation graphs for watermarking software, image, audio, and text

“…We next describe the embedding algorithm of our proposed technique which encodes a selfinverting permutation * into a digital image I [16,18,22]. Recall that, the permutation * is obtained over the set N n * , where n * = 2n + 1 and n is the length of the binary representation of an integer w which actually is the image's watermark [28].…”