Abstract In this paper, we present an experiment on stereoscopic direct volume rendering, aiming at understanding the relationship between the choice of reconstruction filter and participant performance on tasks requiring spatial understanding such as 3D path‐searching. The focus of our study is on the impact on task performance of the post‐aliasing and smoothing produced by the reconstruction filters. We evaluated five reconstruction filters, each under two different transfer functions and two different displays with a wide range of behaviours in terms of post‐aliasing and smoothing. We found that path‐searching tasks commonly found in the literature, and as the one we employed here, elicit bias in the responses which should be taken into account when analysing the results. Our analysis, which employed both standard statistical tests and techniques from signal detection theory, indicates that the choice of reconstruction filter affects some aspects of the spatial understanding of the scene.

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.

In direct volume rendering (DVR), the choice of reconstruction filter can have a significant effect on the visual appearance of the images produced and thus, on the perceived quality of a DVR rendered scene. This paper presents the results of a subjective experiment where participants stereoscopically viewed DVR rendered scenes and rated their subjective quality. The statistical analysis of the results focuses on the relationship between the quality of the stereoscopic scene and properties of the filters such as post-aliasing and smoothing, as well as the relationship between the quality of the stereoscopic scene and properties of the rendered images such as shape compactness. The experiment evaluated five reconstruction filters on four different volumetric datasets. Participants rated the stereoscopic scenes on four quality measures: depth quality, depth layout, lack of jaggyness, and sharpness. The results show that the correlation between the quality measures and post-aliasing and smoothing, which are properties associated with each reconstruction filter, is moderate and statistically insignificant. On the other hand, the correlation between the quality measures and compactness, which is a property specific to each rendered image, is strong and statistically significant.

We propose a steganalytic algorithm for watermarks embedded by Cho et al.'s mean-based algorithm [1]. The main observation is that while in a clean model the means 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. We also propose a modification of Cho et al.'s algorithm which is more resistant to the steganalytic attack and offers an improved robustness/capacity trade-off.

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.

Abstract We propose a watermarking algorithm for polygonal meshes based on the modification of the Laplacian coordinates. More specifically, we first compute the Laplacian coordinates (x,y,z) of the mesh vertices, then construct the histogram of the lengths of the (x,y,z) vectors, and finally, insert the watermark by altering the shape of that histogram. The watermark extraction is carried out blindly, with no reference to the host model. The proposed method is more robust than several existing high capacity watermarking algorithms. In particular, it is able to resist attacks such as translations, rotations, uniform scaling and vertex reordering, due to the invariance of the histogram of the Laplacian vector lengths under such transformations. Compared to the existing robust watermarking methods, our experiments show that the proposed method can better resist common mesh editing attacks, due to the good behaviour of the Laplacian coordinates under such operations.

This paper proposes a general framework for overfitting control in surface reconstruction from noisy point data. The problem we deal with is how to create a model that will capture as much detail as possible and simultaneously avoid reproducing the noise of the input points. The proposed framework is based on extra-sample validation. It is fully automatic and can work in conjunction with any surface reconstruction algorithm. We test the framework with a Radial Basis Function algorithm, Multi-level Partition of Unity implicits, and the Power Crust algorithm.

We propose a polygonal decomposition of the 1-ring neighborhood of a quadrilateral mesh, which is suitable for the study of the Catmull-Clark subdivision scheme. The initial configuration consists of 2n planar 2n-gons and under the Catmull-Clark subdivision they transform into 4n planar n-gons coming in pairs of coplanar polygons and quadruples of parallel polygons. We calculate the eigenvalues and eigenvectors of the transformations of these configurations showing their relation with the tangent plane and the curvature properties of the subdivision surface. Using direct computations on circulant-block matrices, we show how the same eigenvalues can be analytically deduced from the subdivision matrix.

We study the support of subdivision schemes: that is, the region of the subdivision surface that is affected by the displacement of a single control point. Our main results cover the regular case, where the mesh induces a regular Euclidean tesselation of the local parameter space. If n is the ratio of similarity between the tesselations at steps k and k − 1 of the refinement, we show that n determines the extent of this region and largely determines whether its boundary is polygonal or fractal. In particular if n = 2 (or n2 = 2 because we can always take double steps) the support is a convex polygon whose vertices can easily be determined. In other cases, whether the boundary of the support is fractal or not depends on whether there are sufficient points with non-zero coefficients in the edges of the convex hull of the mask. If there are enough points on every such edge, the support is again a convex polygon. If some edges have enough points and others do not, the boundary can consist of a fractal assembly of an unbounded number of line segments.

We present a method for the adaptive reconstruction of a surface directly from an unorganized point cloud. The algorithm is based on an incrementally expanding neural network and the statistical analysis of its learning process. In particular, we make use of the simple observation that during the learning process the normal of a vertex near a sharp edge or a high curvature area of the target space, statistically, will vary more than the normal of a vertex near a flat area. We use the information obtained from the study of these normal variations to steer the learning process in an adaptive meshing application, producing meshes with more triangles near the high curvature areas. The same information is used in a feature detection application.

We study the use of neural network algorithms in surface reconstruction from an unorganized point cloud, and meshing of an implicit surface. We found that for such applications, 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 adjusting accordingly the neural network. The adjustment includes the connectivity of the network. Doing several experiments 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 of the size of the input data, making it particularly suitable for the reconstruction of a surface from a very large point set.

We study the factorization of mesh refinement rules in terms of the polyhedra operator's duality, stellation, and truncation. Using this factorization, we show that the /spl radic/3-refinement and leapfrog transformation, known from its applications in discrete mathematical chemistry, differ by a conjugation by the duality operator. As an example of this relation we use a variational /spl radic/3-scheme to draw the mesh of the fullerene molecule C/sub 60/. We also find the relation between the simplest-scheme refinement and binary refinement of the Catmull-Clark scheme.

We propose a divide and conquer algorithm for the single resolution encoding of triangle mesh connectivity. Starting from a boundary edge we grow a zig-zag strip which divides the mesh into two submeshes which are encoded separately in a recursive process. We introduce a novel data structure for triangle mesh connectivity encoding, a binary tree with positive integer weights assigned to its nodes. The length of the initial strip is stored in the root of the binary tree, while the encoding of the left and right submesh are stored in the left and right subtree, respectively. We find a simple criterion determining which objects of this data structure correspond to triangle meshes. As the algorithm implicitly traverses the triangles of the mesh, it can be classified into the family of Edgebreaker like encoding schemes. Hence, the compression ratios, both in the form of theoretical upper bounds and practical results are similar to the Edgebreaker's, while the simplicity and flexibility of the algorithm makes it particularly suitable for applications where the connectivity encoding is only a small part of the problem at hand.

We describe a method for efficient calculation of coefficients for subdivision schemes. We work on the unit sphere and we express the z-coordinate of all the existing points as power series in the variable cos /spl theta/. Any linear combination of them is also a power series in cos /spl theta/ and, by solving a linear system, we determine the linear combination that will give the smoothest interpolation of the sphere at a particular point.