A General Region Nesting-Based Semi-Fragile Reversible Watermarking for Authenticating 3D Mesh Models

Abstract

Aiming to reduce the distortion in the existing reversible watermarking for 3D mesh models, this paper generalizes two-dimensional (2D) region nesting to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -dimensional space, and proposes a general region nesting based semi-fragile reversible watermarking for authenticating 3D mesh models by combing watermark generation based on vertex projection and mesh topology. For any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -dimensional space, each hypercube space is partitioned into several nested watermark sub-spaces, and the watermark is embedded by placing the original vertex and the mapped vertex on a straight line. The watermark is extracted by acquiring the position of the vertices, and its original coordinates can be restored by inverse mapping. Furthermore, a new coordinate system is built for 3D mesh models based on reference vertices to achieve semi-fragility, and the watermarks generated by vertex projection and mesh topology is utilized for integrity authentication. Experimental results and analysis show that the proposed scheme can significantly reduce the distortion, achieve semi-fragility in RST (Rotation, Scaling and Translation) and vertex reordering, identify the tampering type, and accomplish tampering location at vertex level. It has great potential to be applied for content authentication of 3D mesh models.