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Current methods for Earth observation tasks such as semantic mapping, map alignment, and change detection rely on near-nadir images; however, often the first available images in response to dynamic world events such as natural disasters are…
Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann…
Worldwide geo-localization involves determining the exact geographic location of images captured globally, typically guided by geographic cues such as climate, landmarks, and architectural styles. Despite advancements in geo-localization…
Linear observed systems on groups encode the geometry of a variety of practical state estimation problems. In this paper, we propose an observer framework for a class of linear observed systems by restricting a bi-invariant system on a Lie…
We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on…
We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as `angles'. This…
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
Unaligned Scene Change Detection aims to detect scene changes between image pairs captured at different times without assuming viewpoint alignment. To handle viewpoint variations, current methods rely solely on 2D visual cues to establish…
The observation of the bending of light by mass, now known as gravitational lensing, was key in establishing general relativity as one of the pillars of modern physics. In the past couple of decades, there has been increasing interest in…
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…
Several recent papers have suggested that the cosmological constant Lambda directly influences the gravitational deflection of light. We place this problem in a cosmological context, deriving an expression for the linear potentials which…
We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light…
This paper is devoted to exploring how we can discover and study nearby (< 1-2 kpc) planetary and binary systems by observing their action as gravitational lenses. Lensing can extend the realm of nearby binaries and planets that can be…
We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool…
The collection of all topologies on the set of three points is studied treating the topology as quantum-like observable. It turns out to be possible under the assumption of the asymmetry between the spaces of bra- and ket-vectors. The…
This article presents a new way to classify geodesics on a cone in the Euclidean 3-space. This proof is obtained considering our main result, which establishes the necessary and sufficient conditions that a curve in space must satisfy: to…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
We demonstrate that gravitationally lensed quasars are easily recognized using image subtraction methods as time variable sources that are spatially extended. For Galactic latitudes |b|>20 deg, lensed quasars dominate the population of…