A Blind, Semi-Fragile 3D mesh Watermarking Algorithm Using Minimum Distortion Angle Quantization Index Modulation (3D-MDAQIM)

This work proposes a semi-fragile, blind watermarking scheme in spatial domain to substantiate the authenticity of 3D models. The 3D mesh is first traversed with a topology-oriented strategy which also decides the verification units. Every verification unit comprises of a set of embedding eligible vertices and one verification code embeddable vertex. Watermark embedding is carried out by first applying dither modulation to the spherical angular values theta \((\theta )\) and phi \((\phi )\) of the embedding eligible vertices. During the process of dithering, the angular values are quantized with 3D-MDAQIM using quantization step sizes \(\varDelta _\theta \) and \(\varDelta _\phi \) that incurs minimum distortion. A theoretical analysis is conducted to present the imperceptibility assessment. In order to verify the integrity of the 3D model, verification bits are computed from the local geometry of the mesh and embedded to the respective embeddable vertices using message digit substitution scheme. Further more, experimental results show that the proposed method yields minimal distortion with regional attack localization capability. This work performs better than the state-of-the-art semi-fragile mesh watermarking algorithms in terms of embedding capacity, robustness toward content-preserving attacks and distortion control.