Histogram shifting based reversible data hiding with multiple expansion bin pairs

As the most popular reversible data hiding (RDH) technique, histogram shifting (HS) is widely investigated due to its efficient capacity-distortion trade-off. With a given histogram, the performance of HS-based RDH mainly depends on the selection of expansion bins. However, the determination of expansion bins, especially for the case of multiple pairs of expansion bins, usually involves massive solution space and is computationally expensive. To efficiently optimize the embedding performance, in this paper, the HS-based RDH with multiple expansion bin pairs (EBPs) is theoretically investigated, and some general results about the optimal EBPs are firstly derived. Based on the theoretical results, we conclude that a part of optimal EBPs can be directly determined without any computation burden for adaptive embedding. Then, inspired by the derived results, a simple yet efficient method to find the nearly optimal EBPs is proposed with a fairly low computational cost. Finally, the proposed method is further extended to multiple histograms based embedding for better capacity-distortion behavior. Experimental results show that the proposed method achieves better performance than some state-of-the-art works, especially in terms of computational cost.