We propose a simple yet efficient steganalytic algorithm for watermarks embedded by two state-of-the-art 3D watermarking algorithms by Cho et al. The main observation is that while in a clean model the means/variances of Cho et al.’s normalized histogram bins are expected to follow a Gaussian distribution, in a marked model their distribution will be bimodal. The proposed algorithm estimates the number of bins through an exhaustive search and then the presence of a watermark is decided by a tailor made normality test or a $t$ -test. We also propose a modification of Cho et al.’s watermarking algorithms with the watermark embedded by changing the histogram of the radial coordinates of the vertices. Rather than targeting a continuous statistics such as the mean or variance of the values in a bin, the proposed watermarking modifies a discrete statistic, which here is the height of the histogram bin, to achieve watermark embedding. Experimental results demonstrate that the modified algorithm offers not only better resistance against the steganalytic attack we developed, but also an improved robustness/capacity trade-off.

We study the use of neural network algorithms in sur- face reconstruction from an unorganized point cloud, and meshing of an implicit surface. We found that for such ap- plications, the most suitable type of neural networks is a modified version of the Growing Cell Structure we propose here. The algorithm works by sampling randomly a target space, usually a point cloud or an implicit surface, and ad- justing accordingly the neural network. The adjustment in- cludes the connectivity of the network. Doing several exper- iments we found that the algorithm gives satisfactory results in some challenging situations involving sharp features and concavities. Another attractive feature of the algorithm is that its speed is virtually independent from the size of the input data, making it particularly suitable for the recon- struction of a surface from a very large point set.

We propose a steganalytic algorithm for triangle meshes, based on the supervised training of a classifier by discriminative feature vectors. After a normalization step, the triangle mesh is calibrated by one step of Laplacian smoothing and then a feature vector is computed, encoding geometric information corresponding to vertices, edges and faces. For a given steganographic or watermarking algorithm, we create a training set containing unmarked meshes and meshes marked by that algorithm, and train a classifier using Quadratic Discriminant Analysis. The performance of the proposed method was evaluated on six well-known watermarking/steganographic schemes with satisfactory accuracy rates.

We study the relationship between the noise in the vertex coordinates of a triangle mesh and normal noise. First, we compute in closed form the expectation for the angle θ between the new and the old normal when uniform noise is added to a single vertex of a triangle. Next, we propose and experimentally validate an approximation and lower and upper bounds for θ when uniform noise is added to all three vertices of the triangle. In all cases, for small amounts of spatial noise that do not severely distort the mesh, there is a linear correlation between θ and simple functions of the heights of the triangles and thus, θ can be computed efficiently. The addition of uniform spatial noise to a mesh can be seen as a dithered quantization of its vertices. We use the obtained linear correlations between spatial and normal noise to compute the level of dithered quantization of the mesh vertices when a tolerance for the average normal distortion is given.