Optimal Histogram-Pair and Prediction-Error Based Image Reversible Data Hiding

Abstract

Abstract. This proposed scheme reversibly embeds data into image predictionerrors by using histogram-pair method with the following four thresholds for optimal performance: embedding threshold, fluctuation threshold, left-and right-histogram shrinking thresholds. The embedding threshold is used to select only those prediction-errors, whose magnitude does not exceed this threshold, for possible reversible data hiding. The fluctuation threshold is used to select only those prediction-errors, whose associated neighbor fluctuation does not exceed this threshold, for possible reversible data hiding. The left-and righthistogram shrinking thresholds are used to possibly shrink histogram from the left and right, respectively, by a certain amount for reversible data hiding. Only when all of four thresholds are satisfied the reversible data hiding is carried out. Different from our previous work, the image gray level histogram shrinking towards the center is not only for avoiding underflow and/or overflow but also for optimum performance. The required bookkeeping data are embedded together with pure payload for original image recovery. The experimental results on four popularly utilized test images (Lena, Barbara, Baboon, Airplane) and one of the JPEG2000 test image (Woman, whose histogram does not have zero points in the whole range of gray levels, and has peaks at its both ends) have demonstrated that the proposed scheme outperforms recently published reversible image data hiding schemes in terms of the highest PSNR of marked image verses original image at given pure payloads.

Reversible data hiding: Advances in the past two decades

“…Later on, in [81], Xuan et al proposed an improved method of [66]. Instead of IWT coefficients used in [66], the prediction-errors derived from the cover image are exploited for data embedding in [81]. Specifically, their method is based on HS-PEE with the following three strategies: adaptive embedding, optimal expansion-bins-selection, and histogram shrinking.…”

“…Then, for a given payload, the adaptive embedding threshold, expansion bins, and shrinking thresholds are determined such that the corresponding embedding distortion is minimized, and then the reversible embedding is carried out with the optimized parameters. With HS-PEE and optimized parameters, stateof-the-art embedding performance is achieved by [81]. For example, for the standard 512 × 512 sized Lena image at an embedding rate of 0.1 bpp, the derived PSNR is 55.44 dB.…”

“…This mechanism is first proposed in Xuan et al's work [66] and it is proved efficient for the performance enhancement of RDH. Later on, in [81], Xuan et al proposed an improved method of [66]. Instead of IWT coefficients used in [66], the prediction-errors derived from the cover image are exploited for data embedding in [81].…”

“…• Adaptive embedding strategies considering local image properties such as sorting [40], [53] or embeddinglocation-selection [54], [55], [81] are very helpful for improving the reversible embedding performance. Generally speaking, adaptive embedding can be incorporated into most RDH schemes to achieve better performance.…”

“…Specifically, their method is based on HS-PEE with the following three strategies: adaptive embedding, optimal expansion-bins-selection, and histogram shrinking. By adaptive embedding, a threshold (named fluctuation threshold in [81]) is used to select smooth local area of pixels in which only those prediction-errors whose associated neighbor fluctuation does not exceed this threshold are selected for data embedding. Moreover, the expansion bins are iteratively selected according to (9).…”