Levenberg–Marquardt deep neural watermarking for 3D mesh using nearest centroid salient point learning

Watermarking is one of the crucial techniques in the domain of information security, preventing the exploitation of 3D Mesh models in the era of Internet. In 3D Mesh watermark embedding, moderately perturbing the vertices is commonly required to retain them in certain pre-arranged relationship with their neighboring vertices. This paper proposes a novel watermarking authentication method, called Nearest Centroid Discrete Gaussian and Levenberg–Marquardt (NCDG–LV), for distortion detection and recovery using salient point detection. In this method, the salient points are selected using the Nearest Centroid and Discrete Gaussian Geometric (NC–DGG) salient point detection model. Map segmentation is applied to the 3D Mesh model to segment into distinct sub regions according to the selected salient points. Finally, the watermark is embedded by employing the Multi-function Barycenter into each spatially selected and segmented region. In the extraction process, the embedded 3D Mesh image is extracted from each re-segmented region by means of Levenberg–Marquardt Deep Neural Network Watermark Extraction. In the authentication stage, watermark bits are extracted by analyzing the geometry via Levenberg–Marquardt back-propagation. Based on a performance evaluation, the proposed method exhibits high imperceptibility and tolerance against attacks, such as smoothing, cropping, translation, and rotation. The experimental results further demonstrate that the proposed method is superior in terms of salient point detection time, distortion rate, true positive rate, peak signal to noise ratio, bit error rate, and root mean square error compared to the state-of-the-art methods.