A public mesh watermarking algorithm based on addition property of Fourier transform

Author name used in this publication: David ZhangCenter for Multimedia Signal Processing and Department of ComputingVersion of RecordPublishe

Steganography for Three-Dimensional Polygonal Meshes

This paper proposes a method to embed information into a 3D model represented by a polygonal mesh. The approach used consists in slightly changing the position of the vertices, in uencing the length of approximation of the normals to the surface. This technique exhibits relatively low complexity, and o ers robustness to simple geometric tranformations. In addition, it does not introduce any visible distortion to the original model

Fragile Watermarking of 3D Models in Transformed Domain

This paper presents an algorithm aimed at the integrity protection of 3D models represented as a set of vertices and polygons. The proposed method defines a procedure to perform a fragile watermarking of the vertices’ data, namely 3D coordinates and polygons, introducing a very small error in the vertices’ coordinates. The watermark bit string is embedded into a secret vector space defined by the Karhunen–Loève transform derived from a key image. Experimental results show the good performance of the method and its security

An interactive analysis of harmonic and diffusion equations on discrete 3D shapes

AbstractRecent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes

Robust watermarking of point-sampled geometry

We present a new scheme for digital watermarking of point-sampled geometry based on spectral analysis. By extending existing algorithms designed for polygonal data to unstructured point clouds, our method is particularly suited for scanned models, where the watermark can be directly embedded in the raw data obtained from the 3D acquisition device. To handle large data sets efficiently, we apply a fast hierarchical clustering algorithm that partitions the model into a set of patches. Each patch is mapped into the space of eigenfunctions of an approximate Laplacian operator to obtain a decomposition of the patch surface into discrete frequency bands. The watermark is then embedded into the low frequency components to minimize visual artifacts in the model geometry. During extraction, the target model is resampled at optimal resolution using an MLS projection. After extracting a watermark from this model, the corresponding bit stream is analyzed using statistical methods based on correlation. We have applied our method to a number of point-sampled models of different geometric and topological complexity. These experiments show that our watermarking scheme is robust against numerous attacks, including low-pass filtering, resampling, affine transformations, cropping, additive random noise, and combinations of the above

Watermarked 3D Object Quality Assessment

This work concerns the developing of new perceptual metrics for 3D watermarking quality assessment. Any water- marking algorithm, to be effective, requires that the distortions is inevitably introduces into the watermarked media is imperceptible. This requirements is particularly severe for watermarking of 3D objects where the visual quality of the original model has to be preserved, i.e. the visual aspect of the watermarked object have to be the same of the original one. Several methods based on the knowledge of Human Visual System (HVS) have been developed to achieve this goal for still images and video watermarking. Since now, no similar techniques for watermarking of 3D objects exist. Here, we propose a novel experimental methodology for subjective evaluations of 3D objects and two perceptual metrics for quality assessment of watermarked 3D objects. Such metrics have been developed combining roughness estimation of model surface with psychophysical data collected by subjective experiments based on the proposed methodology. The performances of the proposed metrics are deeply analyzed

Steganalytic Methods for 3D Objects

This PhD thesis provides new research results in the area of using 3D features for steganalysis. The research study presented in the thesis proposes new sets of 3D features, greatly extending the previously proposed features. The proposed steganlytic feature set includes features representing the vertex normal, curvature ratio, Gaussian curvature, the edge and vertex position of the 3D objects in the spherical coordinate system. Through a second contribution, this thesis presents a 3D wavelet multiresolution analysis-based steganalytic method. The proposed method extracts the 3D steganalytic features from meshes of different resolutions. The third contribution proposes a robustness and relevance-based feature selection method for solving the cover-source mismatch problem in 3D steganalysis. This method selects those 3D features that are robust to the variation of the cover source, while preserving the relevance of such features to the class label. All the proposed methods are applied for identifying stego-meshes produced by several steganographic algorithms