Separable Reversible Data Hiding Based on Integer Mapping and MSB Prediction for Encrypted 3D Mesh Models

Abstract

Reversible data hiding in encrypted domain (RDH-ED) has received tremendous attention from the research community because data can be embedded into cover media without exposing it to the third party data hider and the cover media can be losslessly recovered after the extraction of the embedded data. Although, in recent years, extensive studies have been carried out about images based RDH-ED, little attention is paid to RDH-ED in 3D mesh models due to its complex data structure and irregular geometry. We propose a separable RDH-ED method for 3D mesh models based on MSB (most significant bit) prediction. Firstly, we divide all the vertices of the mesh into the "embedded" set and "reference" set according to topological information between vertices, and calculate the MSB prediction errors for the vertices of the "embedded" set. Then, bit-stream encryption is used to encrypt the mesh. Finally, data is embedded by replacing the MSB of the encrypted vertex coordinates of the "embedded" set by the additional data bits. Recipient with data hiding key can correctly extract the additional data from the marked encrypted mesh. Recipient with encryption key can recover the mesh perfectly by using MSB prediction. Experimental results show that the proposed method has higher embedding capacity and higher quality of the recovered meshes compared to the existing RDH-ED method for 3D meshes based on symmetric encryption.

High Capacity Reversible Data Hiding for Encrypted 3D Mesh Models Based on Topology

“…However, this method has the problem of bit error during extracting data. Xu et al [14] used the MSB prediction and proposed a new method based on RRBE, which increased the embedding capacity. Vertices were divided into embedding set and reference set by traversing the face data.…”

“…After division and MSB prediction, the additional data was embedded in the MSB plane of the embedding set. Based on [14], Yin et al [17] implemented higher embedding capacity by utilizing multi-MSB to hide data. However, this method does not adaptively assign payload to the vertices of the embedding set.…”

“…Vertices Division We propose a new division method and increase the number of the embedding vertices reasonably. In [4,14,16], the vertices were divided according to the face data. Each face was traversed in numbering order, and at most 1 vertex in each face was added to the embedding set.…”

“…is the Euclidean distance, and u denotes the number of elements in each set. [5,14,17] have demonstrated that as the value of p increases, although the distortion added into the models becomes smaller, the embedding capacity is lower. Under the trade-off of embedding capacity and the requirements of practical applications, the value of p is to be 5.…”

“…However, If the parameters are not chosen properly, errors may occur during extraction. Xu et al [14] proposed the most significant bit(MSB) prediction, which implemented extraction and recovery separably. In [17], the embeddable room is extended to multi-MSB.…”