We present a method to extract polyhedral structures from a three-dimensional set of points, even if these structures are embedded in a perturbed background. The method is based on a family of affine diagrams which is an extension of the Voronoi diagram. These diagrams, namely anisotropic diagrams, are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The paramete...

We present a method to extract polyhedral structures from a three-dimensional set of points, even if these structures are embedded in a perturbed background. The method is based on a family of affine diagrams which is an extension of the Voronoi diagram. These diagrams, namely anisotropic diagrams, are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The paramete...

One of the most important properties of Complex Systems is the forming of patterns: a band of fish in the sea, a flight of birds in the sky, the dunes in the desert are only few examples, [2, 3]. These patterns are not shapes fixed in time but they evolve with the dynamics of the Complex Systems and vary according to their level of selforganization. The aim of this paper is modeling statistical...

Gaussian filter is widely used for image smoothing but it is well known that this type of filters blur the image features (e.g., edges). Two extensions of Gaussian filters will be discussed in this survey. One is the anisotropic filtering (bilateral filtering or PDE-based anisotropic diffusion) for feature-preserving smoothing and the other is the recursive implementation of various filters tha...

Aims. We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in reds...

An overview will be presented of the military challenge we are currently facing along with our investment strategy for developing advanced weapons systems. The major role of improved reliability in reducing both the operation and maintenance costs as well as increasing our military combat capability will be examined along with the key role of R&D programs in meeting future reliability requireme...

We determine the automorphism group for a large class of affine quadrics over a field, viewed as affine algebraic varieties. The proof uses a fundamental theorem of Karpenko’s in the theory of quadratic forms [13], along with some useful arguments of birational geometry. In particular, we find that the automorphism group of the n-sphere {x0 + · · · + x 2 n = 1} over the real numbers is just the...

Patchy particles are a popular paradigm for the design and synthesis of nanoparticles and colloids for self-assembly. In "traditional" patchy particles, anisotropic interactions arising from patterned coatings, functionalized molecules, DNA, and other enthalpic means create the possibility for directional binding of particles into higher-ordered structures. Although the anisotropic geometry of ...

The dynamic manipulation of colloidal particle shape offers a novel design mechanism for the creation of advanced responsive materials. To this end, we introduce a versatile new strategy for shape control of anisotropic polymeric colloidal particles. The concept utilizes temperature-sensitive absorption of a suitable solvent from a binary mixture. Specifically, increasing the temperature in the...