Reversible data hiding for 3D mesh models with three-dimensional prediction-error histogram modification

Abstract

This study proposes a reversible data hiding (RDH) algorithm for 3D mesh models based on the optimal three-dimensional prediction-error histogram (PEH) modification with recursive construction coding (RCC). Firstly, we design a double-layered prediction scheme to divide all the vertices of 3D mesh model into the “embedded” set and the “referenced” set, according to the odd-even property of indices into the vertex list. Thanks to the geometrical similarity among neighboring vertices, we obtain the prediction errors (PEs) with a sharp histogram. Then we combine every three adjacent PEs into one prediction-error triplet (PET) and construct the three-dimensional PEH with smaller entropy than one-dimensional PEH by utilizing the correlation among PEs. Next we project the three-dimensional PEH into one-dimensional space for scalar PET sequence which is suitable for using RCC. And also, we define the distortion metrics for 3D mesh models, by which we can estimate the optimal probability transition matrix (OTPM) indicating the optimal PEH modification manner. After that, we modify the PET sequence and embed data by RCC according to OTPM. The experimental results show that our method is superior to two state-of-the-art spatial-domain RDH algorithms for 3D mesh models a lot.