Related papers: Validity of Image Theorems under Spherical Geometr…
We tackle the problem of reflectance estimation from a set of multi-view images, assuming known geometry. The approach we put forward turns the input images into reflectance maps, through a robust variational method. The variational model…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane wave photons or electrons within the first-order…
The fundamental theorem of affine geometry says that a self-bijection $f$ of a finite-dimensional affine space over a possibly skew field takes left affine subspaces to left affine subspaces of the same dimension, then $f$ of the expected…
In recent years the shperical wave expansion method has been widely applied to the theory and calculation of electromagnetic fields. But the inner product exist in reference[1] is defined on the Banach space[2]. Through redefining the inner…
We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area and total spherical curvature. These results can…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
The skewer of a pair of skew lines in space is their common perpendicular. To configuration theorems of plane projective geometry involving points and lines (such as Pappus or Desargues) there correspond configuration theorems in space:…
We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric…
Traditional image detail enhancement is local filter-based or global filter-based. In both approaches, the original image is first divided into the base layer and the detail layer, and then the enhanced image is obtained by amplifying the…
A beam of light, reflected at a planar interface, does not follow perfectly the ray optics prediction. Diffractive corrections lead to beam shifts; either the reflected beam is displaced (spatial shift) and/or travels in a different…
The studies of influence of spin on a photon's motion in a Schwartzschild spacetime is continued. In the previous paper [13] the first order correction to the geodesic motion is found for the first half of the photon world line. The system…
Image similarity is a core concept in Image Analysis due to its extensive application in computer vision, image processing, and pattern recognition. The objective of our study is to evaluate Quasi-Euclidean metric as an image similarity…
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
Image feature matching plays a vital role in many computer vision tasks. Although many image feature detection and matching techniques have been proposed over the past few decades, it is still time-consuming to match feature points in two…
We examine additional symmetries of specific refraction index profiles that are used in the well-known phenomena of perfect imaging and cloaking.In the considered cases, the translation generator and the angular momentum are conserved. We…