Blind, Secured and Robust Watermarking for 3-D Polygon Mesh using Vertex Curvature

Abstract

In this paper a blind, imperceptible, robust and secure watermarking scheme for 3-D mesh models is presented.Here, the watermark is embedded in deeper surface vertices to minimize the perceivable distortion. Deeper surface vertices are selected on the basis of their mean curvature (lesser than zero) and converted to spherical coordinates. Out of the three spherical coordinates, radial distance represents approximate mesh and is invariant to distortionless attack. Therefore, watermark bits are embedded by modifying the distribution of radial distance to make the proposed scheme robust against such attacks. Radial distances are divided into bins and normalized to range in [0,1]. Each bin accommodates one watermark bit. Watermark is embedded repeatedly in the 3-D mesh to resist cropping and simplification attack. To ensure higher security, a 128-bit unique watermark is generated by hashing (MD5 algorithm) the mean of histogram map obtained from a grayscale watermark image. Watermark bits are extracted from bins by comparing mean of each bin with a reference value. Since original mesh is not required at the time of extraction, the proposed scheme is blind. Through experimental results, it is demonstrate that the proposed scheme has good visual masking and higher robustness against various attacks. It shows improved performance as compared to some of the prominent schemes.