###### Abstract  
Three-dimensional models have been extensively used in several applications including computer-aided design (CAD), video games, medical imaging due to the processing capability improvement of computers, and the development of network bandwidth. Therefore, the necessity of implementing 3D mesh watermarking schemes aiming to protect copyright has increased considerably. In this paper, a blind robust 3D mesh watermarking method based on mesh saliency and wavelet transform for copyright protection is proposed. The watermark is inserted by quantifying the wavelet coefficients using quantization index modulation (QIM) according to the mesh saliency of the 3D semiregular mesh. The synchronizing primitive is the distance between the mesh center and salient points in the descending order. The experimental results show the high imperceptibility of the proposed scheme while ensuring a good robustness against a wide range of attacks including smoothing, additive noise, element reordering, similarity transformations, etc. 3D mesh watermarking; mesh saliency; wavelet transform; quantization index modulation +
Footnote †: journal: Information  
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the number of its component's edges, while the number of incidents edges of a vertex represents its valence. The majority of digital watermarking approaches have focused on image, video, and audio, while few works have been proposed for 3D meshes. This situation is mainly due to the difficulties encountered while manipulating the complex topology and irregular representation of 3D meshes, as well as the severity of the existing attacks. Unlike 2D images in which pixels have an intrinsic order to synchronize the watermark bits, 3D meshes have no obvious robust intrinsic ordering. Indeed, the intuitive order such as the order of vertices in the Cartesian coordinate system can be modified easily [3]. Each 3D watermarking technique should ensure a tradeoff between three main constraints [4]: imperceptibility, capacity, and robustness. Imperceptibility is the similarity between the original model and the stego model, while capacity refers to the maximum of bits that can be embedded in the 3D model. Robustness means the ability to extract the watermark bits from the stego mesh even after applying some manipulations called attacks. These latter can be divided into two main kinds. Geometric attacks such as local deformation operations, similarity transformations (translation, rotation, and uniform scaling), and signal processing manipulations that include noise addition, smoothing, and compression. Connectivity attacks include subdivision, cropping, remeshing, and simplification. Three-dimensional mesh watermarking techniques have different applications such as authentication, content enhancement, and copyright protection, among others. It is worth noticing that the proposed method focuses on copyright protection. There are several classification criteria for 3D watermarking methods. According to the embedding domain, the existing methods can be divided into spatial [5] and transform techniques [6]. In the spatial domain, the watermark is embedded by modifying the geometry or the connectivity of the 3D mesh, while in the transform domain the watermark is inserted by altering the coefficients obtained after a certain transformation such as wavelet transform. Based on resistance to attacks, the watermarking algorithms can be classified into robust, semi-fragile, and fragile. Each kind is used in a specific application. It is well known that the robust methods are used with the aim of protecting copyright. These methods should ensure high robustness against common attacks such as signal processing attacks as well as geometric manipulations, while maintaining good imperceptibility. The proposed method is based on wavelet transform using the subdivision of [PERSON] et al. [7]. We note that such a transformation can be applied only for semi-regular meshes [3]. Several methods using wavelet transformation have been proposed [3; 8; 9].