Related papers: Beyond the ABCDs: A better matrix method for geome…
With its three independent parameters, the $ABCD$ matrix serves as the beam transfer matrix in optics. If it is transformed to an equi-diagonal form, the matrix has only two independent parameters determined by optical devices. It is shown…
In the paraxial regime of Newtonian optics, propagation of an ensemble of rays is represented by a symplectic ABCD transfer matrix defined on a reduced phase space. Here, we present its analogue for general relativity. Starting from…
3D Gaussian Splatting (3DGS) is a process that enables the direct creation of 3D objects from 2D images. This representation offers numerous advantages, including rapid training and rendering. However, a significant limitation of 3DGS is…
Transfer matrix method is a well-known and extensively used tool to compute the reflection and transmission coefficients of electromagnetic waves when interacting with a system of layers parallel to each other. We present here a modified…
Computing on graphics processing units (GPUs) has become standard in scientific computing, allowing for incredible performance gains over classical CPUs for many computational methods. As GPUs were originally designed for 3D rendering, they…
Capturing the 3D geometry of transparent objects is a challenging task, ill-suited for general-purpose scanning and reconstruction techniques, since these cannot handle specular light transport phenomena. Existing state-of-the-art methods,…
In order to avoid collisions with space debris, the near Earth orbit must be continuously scanned by either ground- or spaced-based facilities. For the low Earth orbit, radar telescopes are the workhorse for this task, especially due to…
3D motion tracking is a critical task in many computer vision applications. Unsupervised markerless 3D motion tracking systems determine the most relevant object in the screen and then track it by continuously estimating its projection…
Optics related to non-Euclidean geometry has been attracting growing interest for emerged novel phenomena and the analog for general relativity, while most studies are limited to the free space on rotationally-symmetric surfaces. In this…
For diffraction-limited optical systems an accurate physical optics model is necessary to properly evaluate instrument performance. Astronomical observatories outfitted with coronagraphs for direct exoplanet imaging require physical optics…
Optical trapping can be used to manipulate the three-dimensional (3-D) motion of spherical particles based on the simple prediction of optical forces and the responding motion of samples. However, controlling the 3-D behaviour of…
The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the…
A two-point ray-tracing technique for 3D smoothly heterogeneous, weakly transversely-isotropic media is based on Fermat's principle and takes advantage of global Chebyshev approximation of both the model and curved rays. This approximation…
We propose a novel method for non-rigid 3-D motion correction of orthogonally raster-scanned optical coherence tomography angiography volumes. This is the first approach that aligns predominantly axial structural features like retinal…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
Full 3D estimation of human pose from a single image remains a challenging task despite many recent advances. In this paper, we explore the hypothesis that strong prior information about scene geometry can be used to improve pose estimation…
We introduce the concept of paravectors to describe the geometry of points in a three dimensional space. After defining a suitable product of paravectors, we introduce the concepts of biparavectors and triparavectors to describe line…
Matrix imaging paves the way towards a next revolution in wave physics. Based on the response matrix recorded between a set of sensors, it enables an optimized compensation of aberration phenomena and multiple scattering events that usually…
Context. High accuracy astrometric instruments like Gaia aiming at an accuracy of 1 microarcsecond cannot be considered as point-like observers in the framework of relativistic modelling of observable quantities. Aims. Special-relativistic…
The accuracy of stellar distances inferred purely from parallaxes degrades rapidly with distance. Proper motion measurements, when combined with some idea of typical velocities, provide independent information on stellar distances. Here I…