Rate-Distortion Model For Grayscale-Invariance Reversible Data Hiding

Reversible data hiding(RDH)is a novel technology for copyright protection and integrity authentication.After embedding the specific watermark into the host file,we can both reconstruct the original host file and the specific watermark from the marked file without loss.Since the marked image is modified,its post-processing,such as recognition and matching,will be affected.However,many algorithms for color image,such as SIFT(scale invariant feature transform),the first step is to convert the color image into the gray one,and then execute algorithms on gray image.As for these image processing algorithms,as long as keeping the gray value of the color image unchanged,the post-processing of the image will not be affected.As for grayscale-invariance RDH,the basic problem is what are the theoretical bound and the optimal modification manner.In the researching field of RDH,the rate distortion model based on position-independent modification has been established,that is,the modification of red,green and blue channels is independent from each other.However,for grayscale-invariance RDH,the modification of the three color channels is interrelated,that is,the modification distortion is joint.The main contribution of this paper is to decompose the joint modification distortion by associating the modification distortion of green channel,blue channel and red channel,so as to transform position-dependent rate distortion model into position-independent model.Secondly,the existing color image RDH algorithms are widely based on the method of difference expanding.However,the optimal coding is proved to be the optimal modification method both in theory and experiment.By converting position-dependent modification model to position-independent modification model,we can execute the optimal coding to finish grayscale-invariance RDH.Theoretical and experimental results show that the proposed model expands the application range of optimal coding and can significantly improve the rate distortion performance of grayscale-invariance RDH.In addition to expanding the rate distortion model,a linear predictor based on separable gray level is also proposed in this paper.By further mining the correlation between each color channel and gray value,a steeper host histogram is produced,which provides a better host sequence for RDH.