Search results for "Geometry"
showing 10 items of 4487 documents
Symmetry in Computer Vision
2002
Symmetry properties establish the invariance of a system to a given set of transformations. Physicists assign special meaning whenever symmetry is broken in nature; for example, groups of symmetry have been used to explain and predict the spatial organization of atoms in a crystal. Psychologists consider relevant the property of symmetry in the perception of visual signals. The paper will briefly describe different approaches, introduced in computer vision, to measure symmetry. A review of some applications at the Computer Vision Group (Department of Mathematics and Applications of Palermo University) is presented. They regard attentive visual processing, the analysis of faces, the recognit…
Numerical Analysis of Word Frequencies in Artificial and Natural Language Texts
1997
We perform a numerical study of the statistical properties of natural texts written in English and of two types of artificial texts. As statistical tools we use the conventional Zipf analysis of the distribution of words and the inverse Zipf analysis of the distribution of frequencies of words, the analysis of vocabulary growth, the Shannon entropy and a quantity which is a nonlinear function of frequencies of words, the frequency "entropy". Our numerical results, obtained by investigation of eight complete books and sixteen related artificial texts, suggest that, among these analyses, the analysis of vocabulary growth shows the most striking difference between natural and artificial texts…
Off-axis focal shift for rotationally nonsymmetric screens
2009
We report on an analytical formulation for evaluating the amplitude distribution along any line directed toward the geometrical focus of a spherical wave front that passes through a rotationally nonsymmetric diffracting screen. Our formula consists of two factors. The first factor involves the one-dimensional Fourier transform of the projection of the screen function onto the off-axis line. The second factor depends on the inverse distance to the screen and permits us to recognize the existence of focal shift along off-axis lines.
Resonant Beam Steering and Carpet Cloaking Using an Acoustic Transformational Metascreen
2018
International audience; We invoke the Huygens principle to derive dispersion characteristics of acoustic transformational meta-surfaces that can deflect parallel wavefronts in a desired direction. We also propose a dual-Lorentz resonator whose aperture fields can be tuned by geometrical changes to implement a particular phase with unity reflection coefficient. The proposed metascreen is designed by our arranging slightly detuned Lorentz cavities that generate the necessary interference to compensate for the incident wavefronts. Since a complete 0-2 pi range of the reflection phase is achieved, the metascreen can steer a beam across the full horizon. Moreover, since the proposed dual resonat…
Efficient analysis of in-line waveguide filters and frequency-selective surfaces with stepped holes
2003
This paper presents a novel method for the analysis of large classes of microwave and mm-wave passive components, including in-line waveguide filters, single- and multi-layer frequency selective surfaces, and open-ended waveguide array antennas. This method is based on the segmentation technique, which permits us to reduce complex components to cascaded waveguide step discontinuities, which are separately characterized through their generalized impedance matrices, as calculated by the integral equation (IE) technique and the boundary integral-resonant mode expansion (BI-RME) method. Some examples demonstrate the flexibility and efficiency of the IE/BI-RME method, and its utility in investig…
Performance analysis and comparison of symmetrical and asymmetrical configurations of evanescent mode ridge waveguide filters
2009
[1] In this paper, the trade-offs between out-of-band performance, filter length, power-handling capability, and insertion loss of both symmetrical and asymmetrical evanescent mode ridge rectangular waveguide filters are investigated. As a result, clear design methodologies for optimizing such performances are proposed. The developed methodologies are then applied to design several evanescent mode filters, and a complete performance analysis of the symmetrical and asymmetrical structures is performed. From the performance analysis results, the designer can choose the more appropriate filter topology and design strategy to satisfy the prescribed specifications.
Multicomponent line profile restoring by means of ill-posed inverse task solution
2017
The investigation of the criteria of usage of the Tikhonov regularization method for multicomponent overlapping line profiles restoring was done by means of model task solution. The influence of the width and kind of the instrumental function, number of the components of the profile and distance between components are discussed.
Irreducible components of Hurwitz spaces of coverings with two special fibers
2013
In this paper we prove new results of irreducibility for Hurwitz spaces of coverings whose monodromy group is a Weyl group of type B_d and whose local monodromies are all reflections except two.
Vacuum type I spacetimes and aligned Papapetrou fields: symmetries
2003
We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.
Ricci Tensors on Some Infinite Dimensional Lie Algebras
1999
Abstract The Ricci tensor has been computed in several infinite dimensional situations. In this work, we shall be interested in the case of the central extension of loop groups and in the asymptotic behaviour of the Ricci tensor on free loop groups as the Riemannian metric varies.