ИСПОЛЬЗОВАНИЕ ПОЛЯРНЫХ ГАРМОНИЧЕСКИХ ПРЕОБРАЗОВАНИЙ ПРИ РАЗРАБОТКЕ МЕТОДОВ МАРКИРОВАНИЯ ИЗОБРАЖЕНИЙ РОБАСТНЫМ ЦИФРОВЫМ ВОДЯНЫМ ЗНАКОМ

Abstract

The need for developing a robust image watermarking method remains relevant. This is caused by the fact that existing watermarking methods are either not robust enough to various types of attacks on images, or computationally complex, or they are subject to the so-called numerical instability, i.e., accumulation of errors. This paper proposes the use of polar harmonic transformations as the basis of the method for image watermarking, including algorithms for embedding and extracting a watermark, and methods for multiple marking are proposed: multiple embedding and extracting by majority rule, multiple embedding and extracting according to the rule of greater similarity, embedding and extracting fragments of a watermark. The performance characteristics, such as robustness to various attacks, embedding and extraction time for a fixed area size, and maximum size of watermark, are measured using attacks implemented in StirMark BenchMark 4. The proposed method has been proven to be robust to many types of geometric attacks, JPEG-compression and other attacks, to have a high embedding and extraction rate, and to be numerically stable. The proposed method can be used to watermark JPEG images for copyright protection.