Grayscale-Invariant Reversible Data Hiding Based on Multiple Histograms Modification

Grayscale-invariant reversible data hiding (GI-RDH) in color images is a data embedding framework in which the grayscales of a marked color image must be identical to those of the host color image. Recently, some state-of-the-art GI-RDH schemes were proposed. However, their performance in embedding distortion is unsatisfactory. In order to obtain better image quality, a well-known histogram-shifting-based RDH method called multiple histograms modification (MHM) is considered. In this paper, we propose an MHM-based GI-RDH scheme. First, we modified our previous GI-RDH scheme using a multiple-histogram-shifting approach instead of a difference expansion approach. Next, we designed a procedure to select expansion–bin pairs for generated histograms to achieve low embedding distortion through further data embedding. Specifically, we analyzed the expected embedding distortion of our MHM-based GI-RDH scheme given any set of expansion–bin pairs. We then formulated an optimization problem called the GI-MHM minimization problem to identify the optimal expansion–bin pairs for further embedding tasks. Finally, we generated an approximated solution for the GI-MHM minimization problem and conducted the embedding task with these selected expansion–bin pairs. The experimental results revealed that the proposed GI-RDH scheme outperformed previous methods when the embedding capacity was small.