Related papers: Observed Angles and Geodesic Light-Cone Coordinate…
Centimeter level globally accurate and consistent maps for autonomous vehicles navigation has long been achieved by on board real-time kinematic(RTK)-GPS in open areas. However when dealing with urban environments, GPS will experience…
We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting…
Strong gravitational lensing enables a wide range of science: probing cosmography; testing dark matter models; understanding galaxy evolution; and magnifying the faint, small and distant Universe. However to date exploiting strong lensing…
We revisit a weak gravitational lensing problem by constructing a setup which describes the actual system as accurately as possible and solving the null geodesic equations. Details are given for the case of a Universe driven only by a…
Monitoring edge-geodetic sets in a graph are subsets of vertices such that every edge of the graph must lie on all the shortest paths between two vertices of the monitoring set. These objects were introduced in a work by Foucaud, Krishna…
Cosmological observables are used to construct cosmological models. Since cosmological observations are limited to the light cone, a fixed number of observables (even measured to arbitrary accuracy) may not uniquely determine a cosmological…
It is well-known that lens maps are convex mappings defined in the unit disc to itself. In this brief note, we show that these mappings are convex of order $\alpha>0$, and starlike of order $\beta>0$, and establish the precise orders in…
In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere…
We describe a Bayesian sampling model for linking and constraining orbit models from angular observations of "streaks" in optical telescope images. Our algorithm is particularly suited to situations where the observation times are small…
For optical systems, states inside the light cone could be detected by far-field measurement, while those below the light cone are not detectable by far-field measurement. A new method for far-field detection has been developed for…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
The gravitational microlensing as a unique astrophysical tool can be used for studying the atmosphere of stars thousands of parsec far from us. This capability results from the bending of light rays in the gravitational field of a lens…
Localization in already mapped environments is a critical component in many robotics and automotive applications, where previously acquired information can be exploited along with sensor fusion to provide robust and accurate localization…
An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted…
Image-to-point cloud registration methods typically follow a coarse-to-fine pipeline, extracting patch-level correspondences and refining them into dense pixel-to-point matches. However, in scenes with repetitive patterns, images often lack…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
The angular correlation is a method for measuring the distribution of structure in the Universe, through the statistical properties of the angular distribution of galaxies on the sky. We measure the angular correlation of galaxies from the…
An explicit form for the geodesic equations that would describe diffracted light rays is obtained and the Levi-Civita connection that enters into it is shown to be a sum of contributions from the metric of the ambient space, the index of…
Current mainstream SAR image object detection methods still lack robustness when dealing with unknown objects in open environments. Open-set detection aims to enable detectors trained on a closed set to detect all known objects and identify…