The framework of P systems applied to solve optimal watermarking problem

Membrane computing (known as P systems) is a novel class of distributed parallel computing models inspired by the structure and functioning of living cells and organs, and its application to the real-world problems has become a hot topic in recent years. This paper discusses an interesting open problem in digital watermarking domain, optimal watermarking problem, and proposes a new optimal image watermarking method under the framework of P systems. A special membrane structure is designed and its cells as parallel computing units are used to find the optimal watermarking parameters for image blocks. Some cells use the position-velocity model to evolve watermarking parameters of image blocks, while another cell evaluates the objects in the system. In addition to the evolution rules, communication rules are used to exchange and share information between the cells. Simulation experiments on large image set compare the proposed framework with other existing watermarking methods and demonstrate its superiority. HighlightsWe develop a novel framework of the P systems to solve optimal watermarking problem.We present an optimal image watermarking method based on the framework of the P systems.We present an image watermarking algorithm in ridgelet domain.