A novel reversible data hiding method in encrypted images using efficient parametric binary tree labeling

Reversible data hiding in encrypted images (RDHEI) is a challenging task since it requires the complex processing of encrypted images and the lossless recovery after the data extraction. Several RDHEI methods have been proposed to balance the privacy and security of images in cloud environments. However, they can only embed less identifier information. Recently, a novel encoding technology called parametric binary tree labeling (PBTL) has gained popularity. However, existing PBTL-based schemes either inefficiently encode nonembeddable pixels or leave them unprocessed. In light of this issue, we propose an efficient parametric binary tree labeling method for RDHEI (EPBTL-RDHEI). In the pixel division, we design a novel EPBTL encoding rule to encode all pixels except reference pixels into three groups including non-embeddable pixels, embeddable pixels, and self-recording pixels. In this way, the length of auxiliary information is reduced. Furthermore, we derive theoretical conditions for the improved embedding performance with the introduction of self-recording pixels. Experiments demonstrate that the payload capacity of our presented EPBTL encoding surpasses that of the state-of-the-art RDHEI schemes. The average embedding rates on public datasets such as BOSSbase, BOWS-2, and UCID reach up to 2.667, 2.637, and 2.370 bpp (bit per pixel) with a full reversibility, and the improvement percentages are up to 175.24%, 232.80%, and 1,842.29% compared to the two comparative PBTL-based methods.