Reversible data hiding for 3D mesh models based on spatial polygon prediction and dual sorting

Reversible data hiding (RDH) is a crucial information hiding technique for copyright protection and integrity verification of digital media, as it ensures the original content can be perfectly restored. However, current research on RDH remains predominantly focused on images, and relatively little attention has been paid to three-dimensional (3D) models. To address this gap, this paper proposes a RDH method for 3D mesh models based on spatial polygon prediction and dual sorting. First, a three-layer vertex division mechanism is introduced to enable a two-round embedding process, thereby expanding the number of embeddable vertices and increasing embedding capacity. Then, a spatial polygon prediction scheme is designed to balance the dual objectives of enhancing prediction accuracy and preserving embedding capacity. Furthermore, a dual sorting strategy that jointly considers angular smoothness and edge-length regularity is proposed to prioritize the smoother embedding units for data embedding, leveraging their smaller prediction errors to reduce geometric distortion. Finally, secret data is reversibly embedded into 3D mesh models using a prediction error expansion (PEE) technique guided by the dual sorting. The experimental results demonstrate that the proposed method achieves a better balance between high embedding capacity and low geometric distortion compared with other state-of-the-art spatial-domain RDH methods.