Minimal surface distortion function for optimizing 3D watermarking

Abstract

A blind 3D watermarking method based on optimizing the placement of displaced vertices on the surface of the 3D object is proposed in this paper. A new mesh distortion function is used as a cost function for the Levenberg-Marquardt optimization algorithm in order to ensure a minimal distortion to the 3D object surface after watermarking. The surface distortion function consists of the sums of Euclidean distances from the displaced vertex to the original surface, to the new surface and to the original vertex location. Experimental results assess the level of distortion produced to 3D surfaces by watermarking as well as the robustness to various attacks.